GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: rsterne on March 03, 2015, 01:45:00 PM
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When I first started in airguns, I believed that the BC of a pellet was a constant.... different for each pellet, but a constant number that could be applied regardless of velocity.... Once I got a Chrony, and started taking some actual measurements of velocity at the muzzle and downrange, I discovered that this was not the case, and a few years ago I published this graph, which shows very approximately what happens with the .22 cal JSB Exact series of pellets as you change the velocity....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/JSBBCs.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/JSBBCs.jpg.html)
This one is taken from only one set of data, without a lot of data points, and just represents the TRENDS that I observed, and it was met with a lot of skepticism at the time.... I have recently decided that the time has come to refine the data, and if possible, come up with a new "Drag Function" or model, that more closely represents pellets.... Before we get into this, here is an excerpt from an article you may wish to read, that summarizes what is going on.... The entire article can be viewed here.... http://www.exteriorballistics.com/ebexplained/articles/the_ballistic_coefficient.pdf (http://www.exteriorballistics.com/ebexplained/articles/the_ballistic_coefficient.pdf)
Why Ballistic Coefficients are not Constant, but Change with Bullet Velocity
It was explained above that the form factor (or shape factor) had to be used in the drag scale factor equation because the actual drag on a real bullet did not always scale as expected with bullet weight and diameter. It also was found experimentally that the form factor was not a constant, but in fact it changed value in different bullet velocity ranges (see, for example, Exterior Ballistic Charts, Wallace H. Coxe and Edgar Beuglesss, E. I. du Pont de Nemours & Company, Wilmington, DE, 1936). These authors have been measuring bullet ballistic coefficients since about 1970. We also have found that ballistic coefficients of almost all bullets change with bullet velocity. What does this mean?
It means that the standard drag on the standard bullet does not faithfully represent the actual drag on an actual bullet at all velocities. Therefore, a single ballistic coefficient value cannot produce the actual drag values at all bullet velocities. So, if scaling the standard drag idea is to be made to work, then we must either (1) allow the ballistic coefficient to change values in different velocity regions in order to have a value in each region which scales the standard drag sufficiently well for accurate trajectory computations, or (2) find a new standard bullet which is a more appropriate model for the actual bullet.
It is my desire that we come up with a new "standard bullet pellet", and in so doing, achieve a much better understanding of what happens to pellet drag, and therefore wind drift and trajectory, over the range of velocities we deal with.... I hope that this is an ongoing discussion, continually refined, as we learn more about this subject.... The latest version of ChairGun has a new drag function, called "GA", but I think it leaves a lot to be desired and can be drastically improved on.... Please, let's try and stay on topic, as this is a wide subject and it would be easy to get sidetracked....
Bob
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Benefit would be had if BC data could be generated for even multiple fixed velocities.
Say 400 , 700 and 1000 fps (MKS units if one prefers) Standard velocities if you will. (The user could connect the dots ;-)
That would give most applications 2 useful references to compare. (considering high and low power shooting) Perhaps not showing the peak values for any pellet, but there may be enough information to get one interested to obtain more thorough evaluations as they come available.
Of course more data points would be nice, but can we ask for more from the manufacturers? Thus far we get less, and still things seem to work out. ;-)
A BC at muzzle max velocity has always seemed quite pointless. The pellet spends so little time there. ;-) Still, the calculators seem to work well....
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I agree, Cal.... a few points are better than one.... but I hope for eventually more data.... I am going to start listing a Bibliography in this post, and will be adding to it, so everyone can check back, and PM me with additions.... Here are a few gems....
http://www.jbmballistics.com/ballistics/topics/bcs.shtml (http://www.jbmballistics.com/ballistics/topics/bcs.shtml)
http://www.jbmballistics.com/ballistics/topics/cdkd.shtml (http://www.jbmballistics.com/ballistics/topics/cdkd.shtml)
http://www.jbmballistics.com/ballistics/topics/dragfunctions.shtml (http://www.jbmballistics.com/ballistics/topics/dragfunctions.shtml)
http://www.frfrogspad.com/extbal.htm (http://www.frfrogspad.com/extbal.htm)
http://www.frfrogspad.com/drgshape.htm (http://www.frfrogspad.com/drgshape.htm)
http://www.geoffrey-kolbe.com/external_ballistics.htm (http://www.geoffrey-kolbe.com/external_ballistics.htm)
Bob
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I've run some of John Cripes swaged slugs through the Corbin BC program. At fist glance this program seems oversimplified but after a little poking around I found quite a few parameters that can be adjusted. Nose, base, hollow base, boattail and VELOCITY. As the velocity is lowered from the 2500 fps default the BC rises as expected. I have not had the time fully analyize the results of the program or do actual field BC tests with the chrony but the numbers generated are interesting. (higher than expected) The program calculates the 139 gn baby boattail I've been shooting at ~.15 when using 950 fps. I plugged in the .15 in Chair gun with a 60 yard zero, used the 100 yard holdover and the results were right on. After the Expo I plan do the chrony testing with this slug to see how close the program actually is.
Tom
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Here are some of the common shapes used in Ballistics Models (Drag Functions).... For most of the profiles, the caliber is 1", and the other dimensions are multiples/fractions of that.... Obviously for the Sphere (which is 9/16") that is not the case, and likely not that for the RA4 (.22LR) either.... so I don't know if that affects how they compare when plotted on one graph....
G1 (Standard Spitzer)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/g1_zps09zm9zd2.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/g1_zps09zm9zd2.jpg.html)
G7 (Long Spitzer Boattail)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/g7_zpsscbkua7h.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/g7_zpsscbkua7h.jpg.html)
GS (Sphere)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/gs_zps0tqbx76z.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/gs_zps0tqbx76z.jpg.html)
GC (Cylinder)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/gc_zpsi5mnfd2r.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/gc_zpsi5mnfd2r.jpg.html)
GL (Blunt Lead)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/gl_zpsub9acuuz.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/gl_zpsub9acuuz.jpg.html)
RA4 (.22LR)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/ra4a_zpsjpnjy3tp.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/ra4a_zpsjpnjy3tp.jpg.html)
I am searching for really good data for the Drag Coefficient for these profiles, and while there is a chart in ChairGun, it isn't great.... I have from the JBM website excellent data for the G1, G7, and GS profiles, and have downloaded them into Excel.... Here is the raw data as downloaded.... Note the huge increase in drag at Mach 1....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drag%20Coefficients_zpsmvh8fg13.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drag%20Coefficients_zpsmvh8fg13.jpg.html)
Here is the same data, omitting everything over 2000 fps, and using fps for the horizontal axis.... I used 1130 fps for Mach 1....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drag%20Coefficients%20Below%202000%20fps_zpsq9mxrmkw.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drag%20Coefficients%20Below%202000%20fps_zpsq9mxrmkw.jpg.html)
You will note the huge difference in drag between the three shapes.... If and when I can get similar, detailed Cd data for the other shapes, I will add them to this graph.... The point of this is to help you realize that what you get for a BC will depend entirely on the Ballistics Model (Drag Function) that you choose to base it on.... My ultimate goal is to come up with a good model for pellets.... Since round nosed pellets are what we use for longer ranges, where wind is more important, it makes sense to me to concentrate our efforts on those.... I also want to develop a drag model for cast bullets of 1.5-2.5 calibers in length with a 60% (or so) meplat, both for flat based bullets and for my Bob's Boattails.... but that is a parallel project.... As the data becomes available, I will keep it in this thread....
Bob
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I'm thinking that the most plausible solution to acquiring useful data across a broad range is to input those shapes into a wind tunnel simulator and varying the airflow speeds..
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Bob, I'd love to run some BBTs of known BC through the Corbin program just to see. Do you have any the BBTs BC qualified?
Tom
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I only have one data point.... Here is the quote from that post....
I finally had a chance to get out and measure the Ballistics Coefficient of the .250 cal 51 gr. BBT from the mold that Veral at LBT made.... I used my Disco Double, which has a 14" twist TJ's liner with a .250 groove and .243 bore.... The muzzle velocity was 873 fps and the velocity at 50 yards was 824 fps, so the BC works out to 0.125.... This is 30% better than the .25 ACP 53 gr. Round Nose made from the Lyman # 57902 mold, which started out at 868 fps and was going 804 fps at 50 yards, giving a BC of 0.096.... The improvement in BC will reduce the wind drift at 100 yards by over an inch.... and compared to a JSB King the drift is reduced by 70% from nearly 12" to well under 4" in a 10 mph crosswind.... In addition, the BBT retains 80% of it's energy at 100 yards compared to just 50% for the Kings.... The rebated boattail design is doing just what it was supposed to....
Here is the drawing for that BBT....
(http://i378.photobucket.com/albums/oo221/rsterne/Bullet%20Casting/250%20BBT%20as%20built_zpsnocnacth.jpg) (http://s378.photobucket.com/user/rsterne/media/Bullet%20Casting/250%20BBT%20as%20built_zpsnocnacth.jpg.html)
I ran it through the Kolbe Drag Calculator, and here is the results.... The discontinuities are a result of limitations of the program, but are just above Mach 1 anyway
(http://i378.photobucket.com/albums/oo221/rsterne/Bullet%20Casting/250%20BBT%20Drag_zps0qlzuexd.jpg) (http://s378.photobucket.com/user/rsterne/media/Bullet%20Casting/250%20BBT%20Drag_zps0qlzuexd.jpg.html)
This is the type of drag model I wish to develop, but from measured data, not derived from calculations.... The only way to do that is to shoot it at various muzzle velocities and measure the downrange velocities....
Bob
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I was not able to find the drag profiles for the GC, GL, or RA4 profiles anywhere but in ChairGun, and in one other diagram on the internet, at http://www.frfrogspad.com/extbal.htm (http://www.frfrogspad.com/extbal.htm) .... Inspecting the two sources, it appears they are in close agreement, and may in fact have come from the same datasets.... so I read the points from the graph in ChairGun, input them into my Excel spreadsheet using curve smoothing, and here they are....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drag%20Coefficients%20Including%20ChairGun_zpskfyhpxvr.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drag%20Coefficients%20Including%20ChairGun_zpskfyhpxvr.jpg.html)
You will immediately notice how poor a cylinder is.... The GL profile, which is a cylinder with a round nose, matches the G1 profile almost exactly from 300 fps to 1600 fps, which is interesting, as that means that for round-nosed bullets we should be able to use the G1 profile, which is fortunate because it is the most widely published by far.... I therefore eliminated the cylinder and combined the GL and G1 profiles, and reduced the area of interest to 300 to 1600 fps, to produce the following graph.... In fact, I may eliminate the GS (Spherical) profile to expand the vertical axis to make it even easier to read the graph in future....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drag%20Coefficients%20of%20Interest2_zpsjqnyzjal.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drag%20Coefficients%20of%20Interest2_zpsjqnyzjal.jpg.html)
You can now see the new GA (airgun) profile proposed in the latest version of ChairGun.... When you look at it in the dropdown menu, it is described as "Diabolo Airgun Pellet Candidate".... I take that to mean it is a work-in-progress.... You will note that it is virtually identical to the G1 (and GL) profiles above 1100 fps, but shows a bit less drag below that, particularly below 800 fps.... I find the close resemblance to the G1 model curious, and would agree, therefore, with the use of the word "candidate".... It is improving that model that is the primary purpose of this thread.... I have two other questions regarding the above profiles, but nobody to ask about them.... Both the RA4 (.22LR) and G7 (boattail) profiles are straight lines below 900 fps.... I'm betting the data was pretty flat below that, but would seriously doubt the lines are completely flat, particulatly all the way down to zero.... My guess is that no testing was done below 500-600 fps, maybe even higher.... They studied the transonic performance, and didn't bother with the bottom end.... Of particular interest to me, personally, is the significantly lower subsonic drag of the boattail G7 profile.... That, of course, is exactly why I came up with the idea of rebated boattail bullets for airguns....
Bob
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Bob,
How do you go about creating a realistic drag model for pellets?
Mike
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I think the way to go is to determine the BC from velocity measurements, using another model, such as the G1, and then convert that data to a Cd.... I have to get up to speed on the math for that, but I think it is proportional.... There should also be a formula somewhere for calculating the pure Cd using the pellet weight, diameter, muzzle velocity, range to 2nd Chrony, and downrange velocity, (without going through the BC), I just haven't come across it yet.... The whole idea of a drag model is that if you get it perfect, the BC is a constant value across all velocities.... In other words although the drag changes, the BC is a constant....
Once (if) we get a drag profile that matches our pellet, then we can put that into ChairGun as their custom profile.... Then whatever muzzle velocity you input, ChairGun will calculate the trajectory and wind drift based on your custom model.... I've done a preliminary attempt, using some of the data I have, and it looks do-able.... There are some simple formulas to remember, relating BC to Sectional Density.... If we look at what those mean....
BC = SD / FF .... where the FF is the Form Factor.... If your bullet (adjusted for SD) matches the drag of the G1 bullet, the FF = 1.... That is because the G1 bullet is a 1" caliber and weighs 1 lb. (7000 gr.)... and SD = W (gr.) / 7000 / Cal.^2 .... In other words, for a G1 shaped bullet, BC = SD.... Therefore, if the BC is less than the SD, the FF>1.... and if your BC is less than the SD, your FF<1.... Also, the FF = Cd (your bullet) / Cd (G1).... That means that if your BC is 10% higher than predicted for a bullet of your SD by the G1 model, then your Cd is 10% less.... To me, that means that if you calculate your G1 BC, and compare it to the SD, then you can use that same correction factor and apply it to modify the Cd curve for the G1 profile and come up with your own profile.... Interestingly, I have searched for such a method to no avail.... but it seems to follow from the known relationships, IMO.... NOTE: see your definition of "confidence" above.... *LOL*....
Bob
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Bob; have you heard of the program called "Java Foil"? It is more intended for wings,but I have tried it a time or two for pellets, and it seems to give a reasonable drag number. You do have to input a Reynolds Number. IMHO we are working with R/Ns around 50k or less, I could be way off on that though. I have it on my computer but it is down awaiting parts. :'(
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Not that particular program, but I'm familiar with airfoil programs, I used to design R/C Sailplanes and Yachts.... The Kolbe Drag Calculator is great for bullets, not so great for pellets, it has no way of allowing for the waist....
Bob
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I use Chairgun. The new GA model is better than the old model. When I used the old drag model, I was regularly trying to push the pellet velocity close to 1000fps but was not seeing the benefits that the older Chairgun was predicting. With the new GA model, the results are more true (at least for the various weights of JSB/AA .177 pellets). And the program now correctly shows that there is not much point in pushing those type of pellets past about 900fps. Many experienced airgunners were already aware of this. Now that Chairgun more accurately models the drag, I just accept it. I no longer have those discrepancies to reconcile (predicted vs actual).
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A point regarding the questions no one is asking,...
What lengths must have been taken to obtain meaningful data out to 2000fps for some of the profiles?
roundball? Blunt cylinder? 22 slug? at 2000fps? How? rifled or smoothbore? lead, patched or jacketed?
The data values for the entire curves must be suspect as having been calculated or transferred from some other source.
A testimony of how difficult (laborsome) it will be to compile a broad range of data.
limits are good!
But I have no issues with the "crack" at the Mach. The .22rf has been doing it for all the years I've been shooting, and now the AR6 Evanix sends out pellets with the same signature. That detail hasn't detracted from the enjoyment of either.
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I see the logic in that, Bob.....but I'm still at the stage where I'm wrapping my head around the whole process of how they came up with the initial drag models.....and how that relates. I have to do a lot more reading.
In more simplistic terms.....is percent retained energy a good indicator of wind drift for pellets shot at the same range?
I guess I always assumed that it was.
Mike
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Scotchmo.... I agree that the new ChairGun GA profile is an improvement on using G1 in practical terms.... However, the fact that it is labelled as a "candidate", and gives data well above Mach 1, leads me to believe that they just took the G1 profile and modified it a bit by dropping the drag in the subsonic region.... My obervations are that the drag of pellets rises MUCH more quickly in the transonic region than the G1 model suggests.... Since the G1 model is so well established and confirmed through hundreds of measurements, and is so widely available, I think we should use that for our baseline for any calculations to produce a new, hopefully improved, airgun pellet drag profile.... I think that earlier versions of ChairGun didn't use accurate drag models in their calculations, but a more simplified, linear deceleration, and I agree with you that the output data wasn't near as good as the current version....
Cal, I agree completely, I don't think any serious work has ever been done on measuring the BC of pellets past Mach 1, because of the difficulty in achieving those velocities.... I actually hope to run some of those numbers today.... That part of the process can, and in fact should, be done at very close range, because the pellet slows so quickly.... I did a small amount of testing years ago with a distance between the Chrony locations of only 5 yards, and I have more powerful PCPs available now, so I'm hoping for some good results to quickly nail down what happens in the 1000+ fps area of the drag curve....
Michael, I'm not sure if the percentage velocity or FPE retention is the best measure of resistance to wind drift when you compare different velocities, but for sure you are on the right track.... At a constant muzzle velocity, you are 100% correct, the pellet with the highest retained velocity at the target will have the least wind drift.... I think as we progress through this process, it will become clearer just how good the percent retention downrange is for comparing different velocities....
One thing I am going to change, is that for convenience I am going to start using the standard, default atmospheric conditions in ChairGun as the reference point, where the BC correction factor is 1.0000.... That is 20*C (68*F), 1013 mB (29.95" Hg), 50% humidity, and sea level, resulting in Mach 1 = 1126 fps.... This is for convenience, so that anyone taking measurements can quote those items (as close as they can) and ChairGun can make the necessary correction.... The other thing we need to agree on is when we make a velocity delta measurement over a given range, and calculate the appropriate G1 BC, what value do we assign to that BC as the velocity?.... Not all measurements will (or should) be made at the same range, so I propose that the velocity assigned to that BC, for purposes of determining the Cd, be the average of the two Chrony readings.... For longer ranges and high velocities, a numerical average will not be the correct answer, as the pellet slows more quickly initially of course.... This is a reason to keep the range increments as short as can produce reliable, repeatable results.... After all, we are trying to develop a drag curve which can then be used to predict trajectory and wind drift over long ranges, one that is made up of increments more accurately determined (hopefully) than a simple average over, say 100 yards....
I have updated the G1 graph so that Mach 1 = 1126 fps, and maximized the scales, covering the useful range from 300 to 100 fps.... In now has minor gridlines every 10 fps and down to 0.01 increments for the Cd.... I would suggest than anyone interested in this save the pic to their computer, it is a simple .jpg file, and photobucket has saved it at 1024 x 547 pixels, you should be able to view it and save it at that size by clicking on the image below....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg.html)
I have a slightly larger version I can send you by email if you PM me your addy....
Bob
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One other little thing I have been pondering before I start doing some testing.... By definition, if your bullet matches the drag function perfectly, the Ballistics Coefficient equals the Sectional Density.... BC = SD.... That means that if we are using the G1 drag function, and our pellets matched that, they would have a constant BC at all velocities, equal to the SD, as shown in the graph below....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/SD%20and%20G1%20BC%20vs%20Weight_zpsjtvs2bfj.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/SD%20and%20G1%20BC%20vs%20Weight_zpsjtvs2bfj.jpg.html)
For those of you that don't know, you can calculate the SD of your pellet from the weight and caliber, as follows:
SD = Wt (gr.) / (7000 x cal. x cal.) .... The 7000 converts the grains to lbs. and then you divide by the diameter of the pellet squared....
So if you want to think about it this way, the SD of your pellet is a "target" for the BC, if it is less than that (and using the G1 drag function it will be), then your Form Factor will be greater than 1.000 where that can be calculated from:
FF = SD / BC .... The higher the Form Factor, the "draggier" your pellet compared to the G1 standard.... If we can come up with a new drag model, then FF = 1.000
Bob
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I only have one data point.... Here is the quote from that post....
I finally had a chance to get out and measure the Ballistics Coefficient of the .250 cal 51 gr. BBT from the mold that Veral at LBT made.... I used my Disco Double, which has a 14" twist TJ's liner with a .250 groove and .243 bore.... The muzzle velocity was 873 fps and the velocity at 50 yards was 824 fps, so the BC works out to 0.125.... This is 30% better than the .25 ACP 53 gr. Round Nose made from the Lyman # 57902 mold, which started out at 868 fps and was going 804 fps at 50 yards, giving a BC of 0.096.... The improvement in BC will reduce the wind drift at 100 yards by over an inch.... and compared to a JSB King the drift is reduced by 70% from nearly 12" to well under 4" in a 10 mph crosswind.... In addition, the BBT retains 80% of it's energy at 100 yards compared to just 50% for the Kings.... The rebated boattail design is doing just what it was supposed to....
Here is the drawing for that BBT....
(http://i378.photobucket.com/albums/oo221/rsterne/Bullet%20Casting/250%20BBT%20as%20built_zpsnocnacth.jpg) (http://s378.photobucket.com/user/rsterne/media/Bullet%20Casting/250%20BBT%20as%20built_zpsnocnacth.jpg.html)
I ran it through the Kolbe Drag Calculator, and here is the results.... The discontinuities are a result of limitations of the program, but are just above Mach 1 anyway
(http://i378.photobucket.com/albums/oo221/rsterne/Bullet%20Casting/250%20BBT%20Drag_zps0qlzuexd.jpg) (http://s378.photobucket.com/user/rsterne/media/Bullet%20Casting/250%20BBT%20Drag_zps0qlzuexd.jpg.html)
This is the type of drag model I wish to develop, but from measured data, not derived from calculations.... The only way to do that is to shoot it at various muzzle velocities and measure the downrange velocities....
Bob
I ran this shape through the Corbin DC-1001 program touted as "Instant Answers "
BC at 875 = .176
Form Factor = 1.56 ? no ideas what this is
Twist Rate = 20.9
Sectional Density = .119
Tom
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Hey Bob,
Valuable information........Thanks ;)
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Well I dragged out my Disco Double today, with the .22 cal barrel on it, and tethered it at 2900 psi, cranked up the hammer strike, and started blasting pellets downrange in my shop.... I used 1 yard for the muzzle velocity and 6 yards for the downrange (carefully measured) so the difference was exactly 5 yards.... I recorded the temperature, barometric pressure and altitude, and used those in ChairGun to determine the G1 Ballistics Coefficients.... I used all of the different weights of JSB Exacts in .22 cal, and maxed out the RS were over 1300 fps, and even the 25 gr. Monsters were Supersonic.... I started with the gun maxed out, shot 5 shot groups recording the near and far velocities and the ES for each set of five for each pellet, then reduced the hammer strike and repeated the procedure three more times at progressively lower velocities.... Here is the raw data.... If you click on it you should be able to read it....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Data%205%20yards_zpsdwmxgckt.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Data%205%20yards_zpsdwmxgckt.jpg.html)
Once the muzzle velocities dropped below 1000 fps, the downrange velocity was too close to the muzzle velocity, so data below 1000 fps will have to wait until later in the year when I can work outside and out of town, with a greater distance between the Chrony positions.... However, I think I got some really good preliminary data, which certainly shows that the G1 (and GA) models are useless with pellets in the transonic and supersonic regions.... The drag is MUCH higher than those models predict, which I knew, this data confirming it solidly.... Here are three graphs showing the data in different ways.... First the raw data plotted as points, with each run being a different colour.... They represent the Cd that each data point has, rising way above the G1 baseline....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Coeff%205%20yards_zpsp5vrrmnh.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Coeff%205%20yards_zpsp5vrrmnh.jpg.html)
The second graph breaks it down by pellet.... You will notice that the RWS Hobbies, which are a wadcutter, have a MUCH higher drag, and no sign of it coming down towards the G1 baseline, even at 1000 fps.... I could probably run another couple of data points at lower velocities with that pellet inside.... Also, the JSB Monster has a rather unexpected trend as well, not fitting well in with the rest of the Exact Series.... perhaps because of its more cylindrical shape or vastly higher SD....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Coeff%20Various%201000fps_zpso8clrn7t.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Coeff%20Various%201000fps_zpso8clrn7t.jpg.html)
In the third graph, I left out the Hobbies and Monsters, and the data is organized once again by run.... I have added a dotted line representing the general trend for the Cd, which I think may be a pretty good representation of what the Drag Profile for the Exact Series does in the transonic and supersonic range....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Coeff%20Exacts%201000fps_zpsz5mxx6mo.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Coeff%20Exacts%201000fps_zpsz5mxx6mo.jpg.html)
This is only preliminary data, but I think it gives a pretty good idea of what is happening with pellets at higher velocities.... I would go so far as to suggest that creating a new Custom Profile in ChairGun, starting from the GA profile, and modifying it as per the dotted black line above, might be a pretty good place to start in the creation of a Custom Airgun Profile....
Bob
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That is some great work and stuff that I am quite interested in. Thank you for taking the time to compile this data. There is so much to learn that it can be overwhelming sometimes but I think it is worth the effort!!
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That is very interesting, Bob. I'm very, very curious to see where things go once you get down into the 750-850 range. In particular, I want to see those 25.3 monsters around 785. That is the energy cutoff (35fpe) for the open class. Not sure of anyone having much luck shooting them all that accurately.....but that may be a good project for me all by itself.
Nice work, Bob.
Mike
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My problem now is that we have new neighbours.... I used to be able to shoot in my backyard, but not any more.... Now when I want to test at anything over 20' I have to pack up and go out into the woods.... I have an excellent place to shoot, with over 100 yards available and a bench, but no power, and I really like running my Chrony with the indoor light kit, even when outside.... It is just much more stable and reliable, which of course is critical for a situation where you have to move the Chrony downrange for half the testing.... Unfortunately, it is in a forest clearing on the north side of a mountain, and the snow doesn't melt until about April, in a good year.... I may have to resort to a generator....
If anyone wants to contribute data, *ahem* Michael *ahem* then you can send it to me at.... bob at mozey-on-inn dot com.... I need the near and far velocities (with ES if you wish), the distance between, pellet type and weight, plus the temperature, barometric pressure, altitude, and the humidity if you have it (minor effect, I didn't, and will use 50% if you don't have it).... I would suggest testing at 20-25 yards to get a large enough difference in velocity for accurate calculations, 5-10% will do.... If the distances are too close (for the velocity loss) the ES will be too large a percentage, reducing the accuracy.... If the distances are too far apart, the pellet will be slowing over such a large range that we won't get enough resolution to produce a good drag profile.... Shoot 5 shots groups (or more) and record the average velocity at both distances.... If the sum of your two ES numbers is greater than the velocity loss, you need to either increase the distance between your Chrony readings, or use a different gun or setup with a smaller ES.... as the data may be unreliable.... I am particularly interested in completing the drag profile for the .22 cal JSB Exact Series of pellets, as they consistently have one of the best BCs around, so it makes sense to me to use them as the benchmark to measure other pellets against....
Bob
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One thing to note, if you guys didn't pick up on it.... Even pellets starting out at over 1300 fps fall back subsonic by the time they have travelled about 10 yards.... a bit further for a round-nose, a bit closer for a wadcutter.... It sure shows the folly of trying to shoot pellets above Mach 1....
That huge velocity loss is why I tested (and in fact could and should test) inside at only a 5 yards distance change.... Even using 10 yards would have lost half the data points....
Bob
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Bob,
The only real data I have that would be relevant is my HV data shooting the AA 16.0's
I had more data in the note section of my iPhone.....but did a stupid move and erased it. It seems there may be some way to recover it, but I haven't tried that, yet. I had the .22 RS, Express, and the 18.1's.
Temperature was 68F, elevation is 5700, pressure is 30.37in......according to the airport. The near measurement was 1yd from the muzzle, and the distance between was 23yd.
AA16.0gr Near-752 Far 709
Near-855 Far 796
If I remember, these were about 10% better (GA) BC than the JSB 15.9's.....weird, but very repeatable.
Sounds like going supersonic will be the ticket for game at 5 yards or less.......or I suppose you could use a baseball bat.... ;D
Mike
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Michael, thanks for those two data points.... I have calculated the BCs, using ChairGun and the G1 Profile, and corrected for your altitude, etc. and I get 0.0411 for the lower velocity and 0.0369 for the higher.... Your high altitude makes a huge difference.... ChairGun is not very friendly for correcting for altitude and pressure, you have a choice of one or the other.... I found a Density Altitude Calculator here.... http://wahiduddin.net/calc/calc_da_rh.htm (http://wahiduddin.net/calc/calc_da_rh.htm) .... When I input your data, I get an absolute pressure of 24.631" Hg, so that is what I used in ChairGun.... I used the same method for me here yesterday (2450', 30.07", 68*F) and got 27.504" Hg, which I used in ChairGun to calculate my data.... Anyway, here are the results of your two measurements (with the AA's) and my three (with the Exacts)....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Coeff%20JSB%20AA_zpskw1oqld1.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Coeff%20JSB%20AA_zpskw1oqld1.jpg.html)
Eventually I will fill in the data in the 900s, but the trend is becoming very clear.... The more data we collect, the better our Drag Model will be....
Bob
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Hi Bob,
I am going to CA for the weekend to shoot at the place that is hosting the Nationals this year (Open Grove). I can't wait....it should be a great time.
When I get back, I can do some BC testing with the other .22 JSB's I have and give you the data. It will be mid 700's to mid 800's. I have a bigger valve that I can put in one of my guns and probably get up to 950 or so with the 18.1's. I don't have any of the 25.3's on hand......but will see if anyone has some I can bring back from CA.
Mike
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Thanks, Mike, the more data the better.... Have fun in CA.... If you're ever up here, drop in....
Bob
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Bob, are you only interested in pellet data? I can test 357 JSB and H&N from 800 to 1200 fps.
Tom
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I would welcome your results, Tom.... No reason not to have multiple drag profiles if the answers are radically different.... If you can test even lower velocities that is also valuable for downrange, after the pellet/bullet slows.... I hope to do the Exact series down to 500 fps, maybe even lower.... If it turns out the larger calibers fit into the same profile, that is what I will do.... I suspect that they might have similar form factors, making the difference in BC due to the difference in SD.... If you notice, that is mostly what is happening in the .22 cal from 13-18 gr.... pretty much following the same profile.... I want to also develop a drag profile for flat-based bullets and another for boattails, that are suitable for airguns....
Bob
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Thanks, Mike, the more data the better.... Have fun in CA.... If you're ever up here, drop in....
Bob
I will definitely stop in if I'm in the neighborhood. Maybe even plan to be in your neighborhood....lol. My wife and I like to see new things. Never been up that way before.
Mike
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Bob, BC is still .0303 with the 18.2 grain pellets..am i getting it right? lol
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Depends on the model you are using.... Using the most common G1 model, it was 0.0321 @ 1198 fps, 0.0369 at 1079 fps, and 0.0519 at 1003 fps.... The last number may not be very accurate because the sum of the two ES's was greater than the velocity loss over 5 yards (the distance is too short to get a reliable answer).... What we can say, with confidence, is that once you go over 1000 fps the drag skyrockets, so you should avoid those velocities....
If we manage to create a new drag profile that replicates the JSB Exact Series, then whatever the BC ends up being will only be usable with that drag profile (function).... This is no different than today.... You can't use a G1 BC with the G7 drag function, or vice versa.... it's like comparing apples and oranges.... If you end up with a drag function that is a perfect match for the pellet, the BC will be a constant over the entire range of velocities, and it will equal the SD.... Getting the correct data for the trajectory and wind drift then requires that you use that drag profile in ChairGun....
Bob
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I did some more testing today, still inside.... I ran the Hobbies down to a lower velocity, and tested the Predator Polymags and H&N Baracudas as well.... Here are all the results....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Coeff%20Various%20Pellets_zpsd3e0iyu5.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Coeff%20Various%20Pellets_zpsd3e0iyu5.jpg.html)
The first thing you will notice is that even down at 700 fps, the Hobbies have nearly 3 times the drag of the G1 model.... This is typical of a wadcutter, and shows how hopeless they are at retaining velocity and energy, and the faster you push them, the worse they get.... The Predators follow a more typical drag curve, similar to the Exacts, but their drag is higher at all the velocities tested.... This is typical of a pointed pellet, they are in between a wadcutter and a round-nose in drag.... Right at the speed of sound, they actually have more drag than the Hobbies.... If you are using them, stay below 1000 fps.... The Baracudas were pretty similar in overall drag to the Exacts.... That means they will have a better BC because they are heavier.... It will be interesting to collect more data on them when we do more testing at lower velocities and longer range increments.... The data on the Baracudas isn't great at the lower velocities because the DeltaV is small.... they need testing over more distance to increase the accuracy of the results....
I think the testing I can do inside, at high velocities, is pretty much done.... All the pellets have a LOT more drag when they go over 1050 fps.... It is also pretty clear to me that using the JSB Exact Series to establish a new Drag Model for pellets is a pretty sound idea.... They are available in a lot of weights, the shapes are consistent from weight to weight and caliber to caliber, and they exhibit some of the lowest drag of any pellets I have tested, not only in these tests, but previously.... If we develop our new Drag Profile (Function) around them, then pellets having more drag will have lower BCs than the equivalent weight Exact, just as they should.... However, comparing them to the JSB Drag Profile should be a lot closer to reality than comparing them to the G1 (or GA) profiles currently in use.... It will be interesting to see how much data we can collect and how close it all fits so that a true trendline can be drawn....
Bob
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Would there be some reason to adopt a standard based on geometry rather than a "Manufacturers product"?
Round ball, blunt cylinder etc.
After all, why go to the trouble to generate a new reference only to need to qualify it as "from years 2001 through 2016" etc. , assuming the pell maker could change offerings for any reason, at any time.
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Of course, and I would suggest the pellets that have the lowest drag, in other words round-nose designs.... not domes, but those where the nose is a hemi-sphere.... That leaves us with JSB Exacts, Crosman Premiers, H&N FTTs, and possibly the H&N Baracudas (although not a true hemi-sphere).... It excludes the RWS Superdomes and similar pellets where there is a significant angle or ridge at the back of the head.... they are known to have more drag.... and also pointed pellets or wadcutters (flat or semi-domed) or hollowpoints....
All it takes is for somebody to get their tail in gear and do the work.... Of course the further the design moves away from a hemispherical nose, the more the drag will move away from the model.... There are a zillion pellet designs out there, but only one "round ball" or "blunt cylinder".... so of course the more designs you include, and the wider the variety of those designs, the more compromise you have to make in the model.... Perhaps we should just go back to the GA or G1.... or how about a constant Cd model like was used in the first versions of ChairGun, where the Cd was simply assumed to be about 0.20 at all velocities.... They work just fine.... except that the BC changes so drastically with velocity that any trajectory and wind drift predictions are pretty much useless, because as the velocity decays with distance, the drag no longer matches the model.... However, when comparing different pellets, fired from the same gun (adjusted the same), a better BC will mean a flatter trajectory and less wind drift.... so in that respect, they do the job....
The other alternative is to choose ONE pellet, caliber, weight, and design, measure it, draw it out with dimensions, and declare it to be the standard airgun projectile, just like the Krupp model, or the G1, or the G7.... If that is what you are suggesting, how do you propose we decide on what to use?.... A target shooter might well prefer a wadcutter, for example.... IMO, there is no perfect solution, because pellets vary all over the map.... To me it makes sense to come up with a model that is much closer to the best pellets (ie the least drag) available today, as it will be a lot closer to reality with all pellets than what we have now.... If you have a better solution, let's hear it....
Bob
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I was working with ChairGun last night, and had a revelation this morning as I was laying in bed about 6AM.... Last night I was looking through the built in Drag Profiles in the latest version of ChairGun, and in the widget on customizing the Gx (custom) profile were two choices that didn't make a lot of sense.... The were constant drag, with the Cd = 0.50 or Cd = 0.19.... I didn't think too much about it, but did remember seeing one of the PB Ballistics Website mention that Airgunners sometimes used a profile where the Cd was constant with Cd = 0.20.... Over the last couple of days, when I was calculating BCs at supersonic and transonic velocities, I noticed that I was getting totally different answers to what I had 3-4 years ago, and chalked it up to ChairGun using a different Model.... but when I woke up this morning, I suddenly thought that the earlier versions of ChairGun may have used a straight-line, constant Cd model.... So this morning, I loaded that into ChairGun and re-checked my data from 4 years ago, and it was very close to the BCs I calculated then.... When I adjusted the Profile to a constant Cd of 0.20, the results agreed 100% with what I did then.... So, when I drew that graph in the first post in this thread, the BCs were calculated by ChairGun using a constant drag profile, where Cd = 0.20 over all velocities.... This was a fortunate piece of luck, or I never would have noticed that the drag was changing with velocity.... Here is what is happening....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/BC%20Varies%20with%20Drag%20Profiles_zpsxk5vdnij.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/BC%20Varies%20with%20Drag%20Profiles_zpsxk5vdnij.jpg.html)
The upper graph shows the G1 drag profile and the old constant drag profile used in early versions of ChairGun.... It also shows the data collected by Michael and I for the 16 gr. AA/JSB pellets over the last couple of days.... The lower graph shows the BCs as calculated by ChairGun using the two different profiles.... You will notice that they are almost identical at the lower velocities, because the drag profiles are almost identical there.... However, at above Mach 1 the calculated values of the BC are totally different, depending on what drag model you use to make those calculations.... As I said, it was fortunate that the early version of ChairGun used the "wrong" drag model, or I would likely not have noticed that the BC was changing with velocity....
This brings up an interesting point for somebody like Michael, who is interested only in determining what velocity the very best BC occurs at, at a constant range.... He might be better using a constant drag model to calculate his BCs, because it emphacizes the difference.... On the other hand, once he determines the best RANGE of velocities where the BC peaks, he should shift over to the best available drag model (what I hope to achieve) to determine the absolute best muzzle velocity to produce the least wind drift over the 25 yard distance, to compensate for the velocity loss over that range.... Of course he already knows the range of usable velocities, so which method he uses doesn't really matter, and in fact he should probably develop his own drag model, for the specific pellets he uses, over the specific range of velocities that is useful to him....
It is interesting how things change over the years.... It hasn't been that long since ChairGun was first introduced, and yet the drag calculations it uses to predict trajectory and wind drift over a wide range of velocities are now MUCH better than when it was first introduced.... If you assumed the BC was constant over velocity 3-4 years ago (as most did) then you could justify shooting at >1000 fps and expect less wind drift.... Now that ChairGun uses better drag profiles, that is no longer the case, even if you use a constant value for the BC.... If we manage to develop an even more accurate drag profile for Diabolo pellets, then we will have an even better understanding of the optimum velocities to use to overcome wind, our greatest nemesis, at longer ranges.... It is getting more and more likely that we will stop using velocities much over 900 fps.... exactly what the benchrest guys like Timmy Mac have known for a very long time.... His latest EBR win at 75 yards was done at ~880 fps.... Michael is gradually dropping his velocities for 25 yd. benchrest down under 800 fps.... Finally.... finally.... it is becoming clear to me why....
Bob
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I added the data for some more pellets today, I tested the other two types of round-nosed pellets, Crosman Premiers and H&N FTTs, and I also tested a pointed pellet, the JSB Straton.... Here is a graph showing all the results....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Coeff%20More%20Pellets_zpsexiqg49z.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Coeff%20More%20Pellets_zpsexiqg49z.jpg.html)
The Crosman Premiers were not too far off the drag of the JSB Exact Series, a bit higher in the 950-1050 fps range, otherwise fairly close.... However, the H&N FTTs had a lot more drag, and the JSB Straton pointed pellets even more, in fact in the 900s they have more drag than the one wadcutter I tested, the RWS Hobby.... I don't know what JSB knows that the other manufacturers are missing, but their pellets have consistently less drag in the 900-1100 fps range in particular, the only other pellet that is similar is the H&N Baracuda, so far.... The rapid increase in drag in the transonic region is delayed for that group of pellets....
I have added a potential candidate for a new Drag Profile (Function) running through the drag curves for the JSB Express, Exact, Heavy, and H&N Baracuda, and the supersonic values for the Crosman Premier.... It is shown as the black dotted line above.... As a simplification, we could use a Cd of 0.20 below 700 fps, 1.00 above 1300, and an "S" shaped curve forming the transition between the two.... The exact details of the shape, particularly in the area from 700-1000 fps, needs a lot more work.... When I do more testing in that area, I am going to concentrate on the JSBs, but will include the Baracudas and Premiers, and the Predator Polymags as well.... All the other pellets have significantly more drag in that range, so IMO are a poor choice to include in the modelling process any further.... While an argument can be made that they should be included, I am beginning to view the new model I am trying to create as a MINIMUM drag for Diabolo pellets, or nearly so.... at least one that represents what is current state-of-the-art in pellet design.... I think this makes a great deal of sense, as then pellets which are more "draggy" will consistently fall above the model, and have lower BCs, just as they should.... By creating a drag profile that is representative of the best, their BCs will match their SDs, which is the way a Drag Function is supposed to work.... If anyone disagrees, they are more than welcome to create their own drag profile for their pellets of interest, of course....
Bob
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that I have seen but not investigated in detail:
We already know that BC varies with muzzle velocity.
It also seems to vary with distance, even when velocity is accounted for.
Example:
#1) When shot with a muzzle velocity of 850fps, I might get a BC of .028 average over the 1-25 yard distance.
#2) When shot with a muzzle velocity of 1000fps, I might get a BC of .024 average over the 1-25 yard distance.
#3) When shot with a muzzle velocity of 1000fps, the velocity at 25 yards is 850fps, the same as the muzzle velocity of #1. I would then say that the measured BC of #2 from 26-50 yards should be the same as #1. Instead, I get a BC of .025 over the 26-50 yard distance.
A velocity of 850fps near the muzzle gives a BC of .028 over the next 24 yards (1-25 yards).
A velocity of 850fps taken downrange gives a BC of .024 over the next 24 yards (26-50 yards).
Speculation:
When fired at 1000fps, the pellet velocity drops to 850fps at 25 yards but the rpm of the rotating pellet remains about the same as when it exited the barrel. The excessive angular momentum tends to fight the drag stabilizing tendencies of the Diabolo shape. The result would be a slightly increased "angle of attack" as the pellet arcs downward, which would increase the drag and reduce the BC.
Any thoughts?
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It's possible, I suppose.... I have never investigated the BC from 26-50 yards.... If, as you say, the BC is lower than starting from the same velocity at the muzzle, then your explanation of a nose-up attitude increasing the BC may well be valid.... It should then be less noticeable if the twist rate is lower, and more noticeable if the pellet is spinning faster than required.... Overstabilzed bullets have a tendency towards precession (spiraling), caused by a nose high attitude, which increases downrange from that very effect.... On the other hand, recent tests have also shown that the BC decreases if the SF is less than 1.5 as well, because the bullet has a very slight wobble, so that the "ideal" stability for the very best BC seems to occur in a narrow range around an SF of 1.5-2.0.... Even disregarding their "shuttlecock" stability, most pellets are overstabilized by that measure.... many have an SF > 4.0....
Bob
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By SF, I assume that you mean Spin Factor.
If the behavior that I saw is common, it gives us another reason to avoid much above 900fps. At 1000+fps, the velocity falls off fast, but you are left with an abnormally high SF. And that may hurt on the really long shots.
I saw that tendency with the 8.44gr JSB when shot at over 1000fps. Accuracy was good but velocity fell of fast. I've since switched back to 10.34gr JSB. Most of my shooting is in competition with a 20fps limit, so not much concern with shooting the 10.34gr too fast.
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SF = Stability Factor.... under 1.0 is unstable, the Military use 1.5 - 2.5, and over about 3.5 - 4.0 may be overstabilized.... All that really means is that when you spin a bullet too fast, it emphasizes any imperfections in the bullet, particularly an off-center CG, and the groups open up.... As mentioned, it can also cause a bullet to remain nose high at long ranges, which causes it to generate a lift force, which in turn causes it to yaw and/or spiral.... There was a tendency for a while for Benchrest PB shooters to push the stability down to 1.3 or even 1.2, but current thinking is that when you do under 1.5 the bullet may be stable enough to still group well, but wobbling enough to show a reduction in BC.... so my understanding is that most feel that trying to get as close to SF = 1.5 is the optimum.....
I am constantly amazed at how quickly pellets lose velocity when pushed to and above 1000 fps.... The 14.3 gr JSB Express starting out at 1294 fps is down to 1210 in 5 yards.... It then drops from 1210 to 1137 in the next 5 yards.... Therefore it has gone from ~1300 fps to under Mach 1 in just 32 feet.... which when you consider the amount of air wasted, and the amount of noise generated, trying to get it to 1300 fps is a complete and total waste....
As I work on this problem, I am beginning to realize more and more how little point there is to push pellets much past 900 fps, as you say.... If and when we can nail down the new Drag Profile, I think people will be amazed at how low the optimum velocities are for minimum wind drift.... which after all, is the toughest thing to overcome in the field....
Bob
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Is there any chance of someone using a real high speed camera to film the attitude of a pellet at different ranges? Would that help explain different BC as velocity degrades?
On a different note; I was tired of trying to "fit" the hawke pellet path model to my actual tested pellet drops so I used the empirical method and shot groups out to 125 yds with 25 yard increments beyond 45 yard zero mark. My results were basically zero drop at 45, 4.5" at 75yds, 13.5" drop at 100yds, and 28.25" drop at 125 yds. The muzzle velocity was averaged to be 907 fps using JSB Diablo Exact Heavies at 18.13 gr. I am willing to put my chrony out to different ranges since there is a 300 yard field just outside of work and the boss likes that I take care of the mice and starlings on the business property. Bob, what ranges and velocities would you like for your data model? I can oblige over the next few days to provide some for you. I can also provide the local airport altitude densities, temp, pressure, and actual altitude as well.
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I think that pellet "attitude" may be closely related to spin rate, so although interesting, would be hard to work into any model.... By keeping the distances short, it will not be an issue, IMO....
As I mentioned earlier, using long distances between the two Chrony locations, while providing good data to see what the AVERAGE Ballistics Coefficient is over that range, won't really do us much good in developing the model.... We need to break the velocity down into smaller pieces, so that we can plot the entire drag profile.... I have done the work that I can for over 1000 fps, because the velocity degrades so quickly I could do that indoors.... We now need the data from 1000 fps and slower, and for most pellets (certainly the JSBs Exacts) that can be done at 20-25 yards between the Chronys.... Wadcutters you might be able to use 10-15 yards until you get down under 700 fps, but I don't really care, because I can't see how they can be included in the model.... It looks like only round-nosed pellet can be be included, and perhaps not even all of those.... Assuming that your data has a relatively small ES (under 1% is ideal) then the DeltaV (difference between the two Chrony readings) I would like to see is 5-10%.... Under 5% the accuracy in the BC calculations will be falling off (due to the ES), and over 10% we may be looking at too large a piece of the drag profile.... We need data at velocities in about 100 fps increments from 1000 fps all the way down to under 500 (even down to 300, if anybody cares) so that we can plot the entire drag curve.... That data must include, eventually, all the JSB Exact Series pellets, in all calibers.... in other words, a lot of shooting.... Any data you can provide is most appreciated....
Bob
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I can start on gathering data Tuesday. Today and tomorrow I am away from my gun, sadly. I do have crossman premier hollow points that I can use but I just might keep with the JSB's. I will tether the gun to my scuba tank so there is more consistent pressure and record muzzle velocities at 1 yd and at 26 yds and see how far I get down the line of velocities with the available time.
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Sounds good....
Bob
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If one only has one chrony what would be the best way to gather data. My .25 is reg'ed at 1400 and shoots a good consistent fps.
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Set the Chrony up at 1 yard to the first sensor and shoot 5-shot groups with each pellet.... If you know you got an ERR, take an extra shot, so you are averaging 5 shots.... Record the average velocity and the ES for each group.... Move the Chrony to 20-25 yards (make sure you know the distance from the first sensor to the first sensor, and it's easier if it is exactly "X" yards), and shoot and record 5 shots with each pellet again.... Bring the Chrony back to the 1 yard point, adjust the velocity down about 100 fps and repeat the process for each pellet.... Record the temperature, altitude, barometric pressure, and if you can the humidity.... I only have one Chrony, and this is what I do....
You can either PM me the data, or email it to me at bob at mozey-on-inn dot com.... Please include the pellet type and weight for each set of data....
Bob
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I dragged out my Grouse Gun today, and it is quiet enough I can do some limited testing outside.... It is set up for ~ 21 FPE, and I tested several pellets.... The G1 Model BC's I got today may be of interest to you....
JSB RS 13.4 gr. - 0.027 @ 818 fps (20 FPE)
JSB Express 14.3 gr. - 0.030 @ 806 fps
Crosman Premier 14.3 gr. - 0.026 @ 806 fps
JSB Exact 15.9 gr. - 0.032 @ 778 fps
JSB Heavy 18.2 gr. - 0.035 @ 732 fps
H&N Baracuda 20.3 gr. - 0.027 @ 702 fps
JSB Monster 25.3 gr. - 0.035 @ 626 fps (22 FPE)
The pellets that had a BC that came the closest to their SD were the JSB RS, Express, Exact, and Heavy, they all had a Form Factor of about 1.5.... The other pellets were worse, with the FF of the heavier pellets pushing over 2.0 (twice the drag of the G1 model)....
Bob
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I forgot my allen wrenches so I was unable to get different velocities from where the gun is set already, but here is what I was able to get.
1 yd 26 yd
912.2 852.4
922 857.6
903.9 859.4
913.7 859.1
911 865.7
916.6 857.1
907.6 851.8
907.0 861.8
910.2 845.2
915.4 869.6
Pellet was JSB diablo exact heavy at 18.3 gr
temp was upper 48
27% dew point
44% humidity
altitude density 30.18 and falling
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What was your altitude above sea level.... I assume the 30.18 is corrected for sea level?.... I will use average velocities of 912 near and 858 far, 25 yard separation....
Bob
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I was about 4700ft above sea level.
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Your absolute pressure is 25.403" Hg, which means a conversion factor of 0.882 for the BC.... That gives a sea level BC of 0.0569 using the G1 Model.... That results in the first calculation for a Form Factor of less than 1.0, at 0.970.... At first I though that might not be a good fit, but when I plotted it with the rest of my data for the 18.1 gr. JSB Heavy, in fact it works out really well.... I am concentrating on the JSBs, with the Baracudas thrown in, as they are also a long range candidate....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Baseline1_zpslpxixjnu.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Baseline1_zpslpxixjnu.jpg.html)
You will notice that the drag of the Heavies seems to go through a minimum at right about where your data is, an average velocity of 885 fps.... This should be refined further as we add more data points, but thanks for that, it seems to fit well.... BTW, the little zig-zag in the data for the Exacts is because the bottom two data points are for AA pellets, not JSBs, and according to Michael, they have a bit less drag.... which seems to be showing up there.... Again, more data will fill in the blanks.... A possible new Drag Profile (Function) is shown as the black dotted line....
Bob
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Is the stability factor of the Greenhill formula the same as that of the Miller formula, or is a conversion factor needed to reconcile them?
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The Stability Factor is the same, but the Miller formula has additional factors not found in the Greenhill formula, which only used length and caliber, then added bullet density, and eventually velocity.... Even better is the stability calculations done by the McGyro program from Robert McCoy, and available in an online calculator by Geoff Kolbe at http://www.geoffrey-kolbe.com/barrel_twist.htm (http://www.geoffrey-kolbe.com/barrel_twist.htm)
Bob
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I shot 10 shots with the JSB Exact 18.1grain (.22)
I took the median in at 1yd, and 36yd.
1yd: 956fps
36yd: 854fps
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I would need the altitude, temperature, barometric pressure, and if possible the humidity.... to do a BC calculation consistent with our other data and include that in our database....
Bob
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1400ft (Phoenix, AZ) Temp 80F, Barometric Pressure 29.98, 15% humidity.
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Your absolute pressure is 28.495" Hg, which means the BC correction factor is 0.933.... That gives a corrected sea level BC of 0.0451 using the G1 model.... That puts that data point a bit higher in drag than what HPAJunkie found the other day over a shorter distance increment (25 yards instead of 35).... However, both sets of data are still within an acceptable zone to fit with the data I did.... We can't ever have too much data, IMO....
Bob
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Cool, I'll do some testing tomorrow, or Friday from 1yd to 25yd.
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If you have the ability to test at different velocities, yet with a stable ES, we need data from 1000 fps and slower, down to 500 fps or less.... At the moment I am concentrating on the JSB Exact series, but all data is welcome, although may not influence or be included in the eventual drag model we develop....
Bob
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I received more data from Michael today, and added it to the database.... Here is a detailed view of the high subsonic and transonic region....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Coeff%20JSB%20AA%20Details_zpsot5m8kad.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Coeff%20JSB%20AA%20Details_zpsot5m8kad.jpg.html)
The lines look a little wiggly, but when you consider they were take by three people, in three locations, with four different barrels and everyone using different batches of pellets, I think it is remarkably consistent.... I still want to fill in the data between 900-1000 fps, and below 750 fps, of course.... Note how close the data for the AA and JSB pellets sits on top of each other, 4 of the 6 AA data points lie right on the JSB curve....
Bob
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Educate us ohh, Bob the grey.
Joke aside, this show how much drag they have, so lower number is better.
I think the JSB 15.9 grains shows a lot of promise....somewhat better than the 18grains in the 800-880 area.
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Wow, a LOT of reading to catch up on.
Not sure if it was touched on since I haven't had time to really read all the responses, but it seems to me this problem (is BC a constant at various velocities) reminds me of a similar type of question in astronomy (is the expansion of the universe a constant).
if, with BC, if you assume it isn't, you want to figure out how measurements differ from the "flat" line of being constant. The velocity tests seem to be a logical way to do this since if the BC is flat, a very calculable outcome can be estimated. But getting good V1 with relationship to V0 seems to me to be the hurdle.
we are dealing with some very small variations, at least subsonic and that is fine for me since I don't plan to be shooting anything over M1 anytime soon. Getting rid of as many variables as possible is going to make data reduction a whole lot easier. I see comments about measuring muzzle velocity and down range velocity. I didn't notice, but are two chroneys being used for these tests so the V0 and V1 measurements are related to the same shot? the muzzle velocity, even out of a regulated rifle is going to change enough to throw off the dV of any test pair. So, two chroneys definitely need to be used. Then you need to normalize Temp, Humidity, and stray winds. This definitely sounds like an indoor test but trying to do measurements past 20 yards is going to be tough unless there is a 50yd firing range available.
If we could create an SOP for doing the test, then a whole lot of people could participate. but like the scientific method describes, the tests have to be repeatable. Even accuracy of chronographs need to be taken into consideration to insure the error bar isn't so big that it makes the data worthless.
I think with all the engineers out there, some data collecting methodology can be described.
do the pros publish their test methods?
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Two Chronys have the problem of making sure they are identical.... Using the average of 5 shots is not a perfect solution with using a single Chrony and moving the location, but for most of us, it is really the only solution available.... While I would agree that the data we are collecting is not perfect, it is a LOT better than what is currently available, which is base on the form of a spitzer bullet, or a simple assumption that drag is a constant, which we know is NOT the case.... Given enough data, I think we can come up with a model that may approximate the best pellets that are currently available, and that it will be a large improvement over what we have now, which drastically underestimates the drag increase in the transonic region....
Bob
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Hey Bob,
This upcoming week I should be able to obtain some data on 18.3 jsb's below 750 fps for you. I currently can push them over 800 fps, but my gun being a pumper I can really set the velocity to whatever you need below that. I will try to get data points for 500, 600, and 700 fps when possible for you.
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I agree with Bob, empirical data, granted with some level of error/variation, still proves trends that can provide a good basis for calculating a better BC for airgun pellets.
On that topic it baffles me, that the large pellet manufacturers like JSB doesn't do this themselves and release the data chart to aid in user setup.
It seems that would provide data to them as well, maybe also to the point of making better designed pellets, since such is a result of iterating based on data collected.
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The Drag Coefficient of the G1 Model is roughly 3 times as great at Mach 1 as it is at Mach 0.5, but in fact pellets have 4 to 5 times as much drag at Mach 1.... This really emphacizes how little sense it makes to try and push supersonic, and how much more wind drift you will get in the transonic range.... Even if all we accomplish is to establish a model that has a much larger increase in drag in the transonic region, it will allow a much better understanding of the futility of driving pellets supersonic or nearly so....
Bob
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JSB .25 25.4g 68° 30.25in Humidity 68% 233' elevation
1yd 26yd
755 686
753 688
758 686
755 689
755 689
755 690
755 692
758 688
751 690
754 688
1yd 26yd
722 659
725 660
723 662
725 659
721 663
721 661
717 666
721 659
720 662
719 664
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Thank you for the addition of that data on the .25 cal Kings.... It falls very close to the data for the .22 cal .18 gr. Heavies at the same velocities.... I used the averages of each 10-shot string....
Bob
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Hey Bob,
Since we know that pellets experience 4-5 times more drag when supersonic, I thought of a couple of points. Let's assume we fire two jsb pellets, one at 1200 fps and the other at 850 fps for this thought exercise. Since the supersonic pellet is undergoing a significant increase in drag, will the time of flight difference between the two pellets be much different at 50, 75, or 100 yards? Which pellet will carry more energy to the target at those distances?
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The one that starts faster will always have a shorter time of flight and greater retained velocity and energy at a given distance.... However, the slower one will have the greatest PERCENT retained velocity and energy.... The faster one will have more wind drift at all distances....
Bob
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Very fascinating. What's interesting is th greater wind drift with the faster projectile. It makes sense since the BC is lower, but at the same time it arrives at the target faster so it would seem that it is exposed to wind gusts less and should therefore move less. Weird.
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You need to read up on wind drift.... The flight time is not the governing factor, it is the DIFFERENCE in flight time between the real world and what would happen in a vacuum.... The BC, or more properly the Drag, is the governing factor....
Bob
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Interesting. I am just getting into the physics of all of this stuff so I probably should! Lol.
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So I just did some calculations on the ballistics of a jsb with .043 BC at 819 fps, and one at 1100 fps with an assumed BC of .015. This may be over simplified, but interesting:
Jsb 0.043 at 819 fps:
Muzzle fpe: 27 fpe
25 yards: 758, 23 fpe
50 yards: 704, 20 fpe
75 yards: 655, 17 fpe
100 yards: 609, 15 fpe
Average velocity: 714 fps
Time of flight: .42 seconds
Jsb 0.015 at 1100 fps:
Muzzle fpe: 49 fpe
25 yards: 813, 27 fpe
50 yards: 657, 17 fpe
75 yards: 533, 11 fpe
100 yards: 430, 7 fpe
Average velocity: 765 fps
Time of flight: .392 seconds
The energy bleeds off very rapidly at 1100 fps and really the .03 secs faster flight time has no major advantage and is carrying much less energy (assuming my calculations are correct).
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So I just did some calculations on the ballistics of a jsb with .043 BC at 819 fps, and one at 1100 fps with an assumed BC of .015. This may be over simplified, but interesting:
Jsb 0.043 at 819 fps:
Muzzle fpe: 27 fpe
25 yards: 758, 23 fpe
50 yards: 704, 20 fpe
75 yards: 655, 17 fpe
100 yards: 609, 15 fpe
Average velocity: 714 fps
Time of flight: .42 seconds
Jsb 0.015 at 1100 fps:
Muzzle fpe: 49 fpe
25 yards: 813, 27 fpe
50 yards: 657, 17 fpe
75 yards: 533, 11 fpe
100 yards: 430, 7 fpe
Average velocity: 765 fps
Time of flight: .392 seconds
The energy bleeds off very rapidly at 1100 fps and really the .03 secs faster flight time has no major advantage and is carrying much less energy (assuming my calculations are correct).
The data as shown looks like it assumes a constant BC.
The pellet with 1100fps muzzle velocity is at 813fps by 25 yards.
At that point, the BC is probably closer to 0.043 for the remainder of the flight.
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So I just did some calculations on the ballistics of a jsb with .043 BC at 819 fps, and one at 1100 fps with an assumed BC of .015. This may be over simplified, but interesting:
Jsb 0.043 at 819 fps:
Muzzle fpe: 27 fpe
25 yards: 758, 23 fpe
50 yards: 704, 20 fpe
75 yards: 655, 17 fpe
100 yards: 609, 15 fpe
Average velocity: 714 fps
Time of flight: .42 seconds
Jsb 0.015 at 1100 fps:
Muzzle fpe: 49 fpe
25 yards: 813, 27 fpe
50 yards: 657, 17 fpe
75 yards: 533, 11 fpe
100 yards: 430, 7 fpe
Average velocity: 765 fps
Time of flight: .392 seconds
The energy bleeds off very rapidly at 1100 fps and really the .03 secs faster flight time has no major advantage and is carrying much less energy (assuming my calculations are correct).
The data as shown looks like it assumes a constant BC.
The pellet with 1100fps muzzle velocity is at 813fps by 25 yards.
At that point, the BC is probably closer to 0.043 for the remainder of the flight.
That is correct. That's the main problem with the G1 model. I know the G7 model can be used as a constant and be much more accurate (even though the G7 model is not 100% constant either, it's much better. Although g7 is for boat tail spitzers only). I guess this brings up a good point about the G1, how do you accurately account for really long distances when the velocity and BC are ever changing? I believe i have read that long range shooters will use the BC to get really close and adjust from there.
Edit: assuming a BC of 0.043 at 25 yards for the 1100 fps pellet(after a starting BC of 0.015), the average velocity over 100 yards is 875 fps, 100 yard velocity is 650 fps, 100 yard energy is 17 fpe, and the time of flight is approximately 0.343 seconds. Still only about 0.077 seconds faster, but with a significant decrease in efficiency.
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I think you should go back and read the entire thread.... The changing BC as the velocity drops, and the poor fit of the G1 Model for pellets (and the G7 is much worse), is exactly the reason for this thread and all the measurements.... The BC is only a measure of how the pellet matches the model, whereas the curves I am drawing are the actual Drag Coefficients....
As far as the calculations you did, they are assuming the G1 Model (I just ran them through ChairGun to check), so they DO take into account the reduction in drag as the velocity drops, even though they are using a constant BC.... If the G1 Model was an exact match for the pellet in question, then you would be able to use the same BC for all velocities, and the drag reduction as the pellet slowed would match reality.... The testing we have done on the JSB Heavy suggests that using the G1 Model the BC is about 0.036 at 1100 fps and 0.042 at 819 fps.... Using those values, and others in between, for the appropriate parts of the flight, and the G1 Model, should give you reasonably close results.... With a better model, we should be able to use just a single BC for the entire flight of the pellet from muzzle to target....
Bob
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My apologies for the errant posts. I will do a much more thorough read of the subject. Very fascinating stuff. I also mentioned the G7 as an example of a model specifically suited for a specific type of projectile, in no way did mean or think that for pellets the G7 was better than the G1. My approximation for the bc at 1100 was simply extending the curve in the jsb graph posted a bit earlier so it was in no way an accurate estimation, just an example for my post. I will say that I have learned quite a bit just from this thread and am anxious to send you some results for the drag model.
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The very first graph posted, based on data several years old, was calculated with an early version of ChairGun that used a linear drag function with a Cd = 0.20 for all velocities.... That is why the BC varies so drastically.... That is explained in a more recent post....
Today I am beginning to investigate what we need to do to establish a new Drag Model (Profile, or Function, all terms are used).... The first thing I thought I would investigate is what the G1 Profile looks like for various values of the Form Function.... To remind readers, the FF is how the drag of a projectile matches the drag model chosen.... If the FF is 1.0, then by definition the BC = the SD exactly.... The more drag the shape has, the higher the FF.... When the FF is 2.0, then the BC is 1/2 the SD, as given by the formula:
BC = SD / FF
For this graph, I took the G1 Function and multiplied the Cd by various FF's from 1 to 2, with the following results.... The current data on the JSB Exacts are shown as well for comparision....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Models%20Change%20FF_zpsfyq8rfjz.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Models%20Change%20FF_zpsfyq8rfjz.jpg.html)
If the pellet was a perfect match for the G1 profile, the FF would be a constant, and it's drag curve would lie along one of the G1 lines that matches that FF.... As you can see, the match is very poor, the FF varies from about 1.5 down to 1.2, back up to 1.8 and then back down to 1.6.... Now it will be impossible to achieve a new drag profile that is a perfect match for even one pellet, let alone useful for many.... but at a minimum what we need to achieve is a steeper slope between the lowest FF (at around 850 fps for this pellet) and the highest FF (right around Mach 1).... What I am proposing, based on current data, and subject to change as we collect more, is to use the G1 profile up to about 700 fps, and a profile like the G1 but with a FF of around 1.5 - 1.6 above Mach 1, with a much steeper transition between those two velocities.... to more closely represent what happens with Diabolo pellets.... I will give some examples in a future post....
Bob
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The JSB Exact is the 15.9gr, correct?
Good work by the way!
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Yes, the Exact is the 15.9 gr.... Here is a graph showing some possible new Drag Function Profiles where the slope in the Transonic Region is steeper....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/New%20Drag%20Models%20Change%20Slope_zpsgxhyhlfi.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/New%20Drag%20Models%20Change%20Slope_zpsgxhyhlfi.jpg.html)
I used the G1 Profile up to Mach 0.75 (845 fps), and then three of the curves from the above graph, with Form Factors of 1.4, 1.6, and 1.8 at Mach 1 and above.... In between, the FF increased in a linear manner to blend a FF of 1.0 to the three upper curves.... IMO the curve blending into the FF = 1.6 curve above Mach 1 is the best match.... This is still subject to change as we collect more data, of course, but is one possible way to come up with a new Drag Function for Diabolo Pellets....
Bob
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I was able to shoot some more and the distance between was 20 yds this time with .22 JSB diablo 18.13gr.
Humidity- 33%
Density- 30.03 inHg
36deg dew point
elevation 4590ft
All shots were 10 shot strings and these are the averages:
0 yd 20 yd difference
855.77 801.82 53.95
808 761 47
753.82 713.97 39.85
699.63 658.34 41.29
I am not sure why the difference on the last string is higher than the difference on the second to last but I ran the numbers twice.
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It is not uncommon for the BC to decrease at lower velocities, you can see it above with the 15.9 gr. Exacts.... I have included the data, and it agrees well with what we have for the 18.1 gr. Heavies.... Oh, do you have the temperature?.... I do have one data point that should be redone to confirm it, however, and that is the one you did previously with MV = 912 and downrange at 858.... If you get a chance to check it again, that would be great....
Bob
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Yesterday the temp was 55 degrees at the time of the test. Last week when the first test was done I think the temp was in the upper 40's but I can check the upper velocity range again. I will try to get around 950 at the muzzle and also 900 at the muzzle.
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That would be great.... thanks....
Bob
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Have there been any more updates on this topic? I have not been able to add more data yet, but knowing what we do about BC of diablo pellets how do we use this to make more accurate shots? I have not used chairgun much but what are the next steps to start using the data in chairgun?
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Once we agree on a new Drag Model, I will convert it into Cd data to be used to customize the Gx profile in ChairGun.... Once the model more closely matches what our pellets do, then you would just select that model and input the BC for your pellet the way you normally would, but it would match reality close over a wider range of velocities than by using the G1 or GA models....
If you are interested in just one pellet, you can do a custom Gx profile just for that one pellet, of course, and then it should be 100% accurate over the range of velocities you have measured.... You can store as many Gx profiles as you want in ChairGun and name the files, but you can only select one to use at a time.... so you would have to remember to change profiles to the one for that pellet.... That is the "best" way, but I'm hoping to come up with a Gx that is "good enough" to use for all diabolo pellets, and much better than the G1 and GA currently in ChairGun.... To optimize it for your gun, it would still be a good idea to measure the BC for your pellet at one velocity, and use that BC and the Gx profile from there....
Bob
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OK - So we know that forward velocity affects the BC. And BC determines how much affect a side wind has on a pellet.
I'm trying to reconcile some BC data that I collected yesterday while shooting in a 4-12mph side wind. I measured the BC by taking velocity readings at 1yard and 35 yard.
I have a related question but not sure if there is a connection:
Will a side wind change the measured BC of a pellet?
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I have no idea.... I suppose it's possible because there is now a very slight sideways "angle of attack" due to the crosswind, but by vector analysis, the angle will be very small.... If the wind is 10 mph (14.7 fps) and the pellet velocity is 800 fps, the angle of attack is a whisker over 1 degree.... Pellets aren't exactly long and skinny, closer to a sphere (which should have no change in drag) than an airfoil, so I can't imagine the Cd would be much larger (or smaller) with a 1* change in the angle of flow.... Certainly the shot to shot (and pellet to pellet) variation should reduce the cross angle to just "noise", I would think....
On the other hand, the "nose up" angle of the pellet at 50 yards.... ie the difference between the boreline and the flight direction.... is also just a bit over 1 degree (strange they just happen to be about the same).... Of course that angle of attack is increasing as the pellet goes downrange (assuming the pellet stays aligned with the bore), whereas the angle of attack due to the wind is a constant (assuming the wind is the same speed from muzzle to target).... IIRC, didn't you find a measureable reduction in BC at longer ranges compared to the BC at the same velocity close to the muzzle?....
There is no question, of course, that if you have a headwind or tailwind, your downrange velocities will be affected, giving incorrect BC calculations.... In this case the actual airspeed would be the (vector sum of) sum of the groundspeed and the windspeed.... I wonder if your previous change in BC with range was seeing such an effect?....
Bob
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Interesting topic, no doubt. It would be critical to know if there is a declining BC when there is sidewind for us that chase absolute accuracy.
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Note the comment I added above about headwinds/tailwinds and the vector sum affecting BC measurement.... Yet another source of error in the measurements.... A 10 mph headwind will decrease the calculated BC by about 5% and a tailwind increase it by about 5%.... assuming you don't correct for it (which we aren't)....
To quantify BC changes, a 10% change in BC (quite large) would change the drift about 10%.... A 10% change in windspeed (from 9 mph to 10) has the same effect....
Bob
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Our range is usually windy. I'll need to get a calm day when testing to make any sense of it. This gun is shooting with a very consistent muzzle velocity and is very accurate.
Initial velocity: 785fps, ES 11fps.
Down range (34 yard spread) velocity: 653fps, ES=49fps.
Wind meter readings during test: 4-12mph (measured at eye level)
Flight is approx 1' off the ground so wind gradient would come into play.
According to ChairGun data, a 3-9mph wind could account for the amount of drift. That's probably about right after accounting for the wind gradient.
Variation from expected POI (35 yards downrange):
Vertical: +.25" to -.3"
Horizontal: +.7" to +1.8"
BC calculated average was .021, with a likely range of .026-.017 for 10 shots.
That seems like a big spread.
I did see a lower BC than expected when checking down range velocity in earlier tests. I was guessing that it was the increased angle of attack. Now I'm thinking maybe it was wind. Or maybe it's a combination. A 1 degree x 1 degree vector gives a 1.44 degree vector. That's still not much.
I don't want to steer this discussion off track, just seeing if it was a phenomenon that others experience.
Data in the wind can be useful, but the problem is that the wind varies second to second.
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Yes, with the total of the two (slightly greater than) 1* vectors being only 1.50*, when you consider how short and blunt a shape we are dealing with, my guess is that compared to all the other variables, it is insignificant.... As you say, the range of possible BC values over 10 shots is pretty large, all we can do is play the averages.... Better yet, if we can graph all the data points and then smooth out the curve, using the smoothed curve instead of the points, we are likely to get even closer....
One of the ways this can be used for those who are really fussy, is to them to take their own mass of data, over a wide range of (useful) velocities and develop their own drag model for a given pellet in their gun.... That could be extremely accurate, likely better than the pellet to pellet variation.... Imagine filling out the blue line for the 15.8 gr. JSBs in post 83 above with the missing data points, and using that line for the model, and you would get the idea....
Bob
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Yes, with the total of the two (slightly greater than) 1* vectors being only 1.50*, when you consider how short and blunt a shape we are dealing with, my guess is that compared to all the other variables, it is insignificant.... As you say, the range of possible BC values over 10 shots is pretty large, all we can do is play the averages.... Better yet, if we can graph all the data points and then smooth out the curve, using the smoothed curve instead of the points, we are likely to get even closer....
One of the ways this can be used for those who are really fussy, is to them to take their own mass of data, over a wide range of (useful) velocities and develop their own drag model for a given pellet in their gun.... That could be extremely accurate, likely better than the pellet to pellet variation.... Imagine filling out the blue line for the 15.8 gr. JSBs in post 83 above with the missing data points, and using that line for the model, and you would get the idea....
Bob
I do use the averages. But:
I would like to account for all variation that I can.
That .017-.026 BC variation would account for about 1/2 of the of the vertical dispersion that I'm getting. The rest could be me or the guns inherent inaccuracy.
If that BC variation is correct, I want to look for ways to reduce it if possible. This was 8.44gr. I need to try some 7.87gr and 10.34gr, but it will be later. I could spend all my time testing for the optimum but this is already good enough for FT pistol competition. The farthest target in pistol matches is only 35 yards, so BC is not that critical.
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IMO the only way to quantify the variation in BC is to use two Chrony's and calculate the BC for each shot.... then examine the ES for the BCs themselves....
I have mixed feelings about using two Chrony's.... On one hand, you get the BC for each shot, but on the other hand, just a 0.5% difference in how they read will give an error in the BC of ~4%.... If you use just one Chrony and move it, at least in theory the velocity readings should be consistent, but then you have to deal with the shot to shot variation, which could easily be 1% ES or more.... However, by taking the average velocity at near and far ranges, I have a gut feeling that using a single Chrony and moving it is better.... unless you have two Chrony's that read identical to each other consistently....
Bob
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To your point Bob. A larger data set from multiple sources is a good way of aggregating a reasonably accurate result.
That same process works both in macro and micro. So moving a single chrony, and doing an average over say 10-20 shots for each location, gives enough data to diminish the effect of outliers.
Infact, I would to some extent suggest anyone participating in this, to remove shots that are more than 5-10% outside the trend in a shot string in each location. Those being a result of variation in the gun delivering the expected fps, a bad pellet, hitting a mosquito on the way down range, etc.
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In fact I do this on my data.... If I am experiencing a 1% ES and I get a shot that is 1% from the average velocity and therefore well outside the dataset, I discard it and shoot another one, which is almost always within the dataset.... If that replacement shot is "just" outside the next slowest or fastest, I keep it.... I know, it's a subjective choice, but it's just the way I do it.... I agree it is often a damaged or renegade weight pellet....
Bob
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In fact I do this on my data.... If I am experiencing a 1% ES and I get a shot that is 1% from the average velocity and therefore well outside the dataset, I discard it and shoot another one, which is almost always within the dataset.... If that replacement shot is "just" outside the next slowest or fastest, I keep it.... I know, it's a subjective choice, but it's just the way I do it.... I agree it is often a damaged or renegade weight pellet....
Bob
That approach would have made my last data set look very reasonable. I should have just shot more but I thought 10 was enough. For now, I'm dropping the theory of the side wind significantly impacting the BC.
Down range velocity:
661.4
659.3
674.8
650.3
667.3
666.8
626.9
625.6
627.1
674.7
Those don't look right. I should have thrown them out.
For now, I'm going to attribute the three outliers to some unknown anomaly or just bad luck.
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Kamakaze Mosquitoes....
Bob
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I have only measured the BC of the .177 Crosman Premiere Light brown box pellets twice and came up with .0190 over 33 yards from my Challenger at 790 fps and .0230 from my Talon SS over 12 yards and 840 fps.
.
A 24 inch .177 barrel for the Talon and 2 chronies (maybe 3) would easily get a full set of data from 1,400 fps down on one tank.
.
Playing with Chairgun using the GA model and .0230 for that pellet and a 10 mph side wind shows increasing wins drifts from 5.00 inches at 900 fps to 5.34 at 1,000 fps to 5.90 at 1,100 to 6.56 at 1,200 fps. Just because of the short period of time of the flight where the BC is so much worse in the trans sonic region. Even tough the total time of flight is so much less. .163 seconds at 1,200fps vs .196 at 900.
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Don't bother shooting airgun pellets above 900 fps.
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You've got it exactly right.... and the new model, when we develop it, will show that to be the case even more, because the GA Model doesn't have a large enough difference in drag between subsonic and supersonic....
Bob
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I've got a question about BCs.
How can two pellets that have the same weight and shape have different BCs???
Two pellets that I had been playing around with.
The CPHP @ 4.3 gr.
The JSB Express Exact @ 14.35 gr
Both in .22 cal.
I can't imagine the 0.05 gr would make any difference at all. These two pellets look the same have the same shape, and are the same weight. They also produce the same muzzle velocity of 891 in one of my rifles. According to Chairgun they have very different BCs. How can this be?
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The BC's may have been measured at different velocities.... Additionally, it only takes a tiny difference in shape to change the BC.... Certainly the HP on the Crosman wouldn't help.... When I measured the Express at 923 fps and Premier (solid) at 922 fps, I got 0.023 for the JSB and 0.020 for the Crosman.... not a huge difference, but a difference, and it wasn't the velocity.... The H&N FTT, which is a similar shape, had a BC of only 0.015 at 912 fps.... It is also quite possible that the shape after firing, when the skirt has expanded, may be quite different between the three pellets....
Bob
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The more I look at the more I think it has to do with the wasp waist. Pellets of the same weight, and head size will have different BCs based on how skinny the waist section is.
I've noticed that pellets with a fat waist have a better BC than pellets with a much thinner wasp waist. Seems that pellets with almost no wasp waist have better performance than pellets with a super tiny wasp waist. Maybe that is why. Now if someone would produce a diablo wasp waist pellet that almost no wasp waist at all. That might be the best pellet for sure. Has anyone tried to produce pellets with a very low about of wasp waist?
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There is the JSB Monster and the th H&N Rabbit Mag. Both have a reputation for poor accuracy. BC is great but hitting your target is better :)
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Actually, the Monsters have a good BC only because of their weight.... Factor out the weight, and the FF isn't as good as their lighter cousins.... No idea why....
Bob
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I don't know why a boolit shaped projectile much like the old BP Minnie' ball would not be a good fit in modern rifled AGs. The velocities are about the same really. The wasp waisted pellets were a concession to smooth bore rifles of the 1800's and early 1900's. Why we kept that shape has never really made a lot of sense to me. If you can flip a pellet 'round backwards and it manages to stay in that orientation all the way to a fifteen or twenty yard target because of the rifling, the the waist serves no function. The hollow base, sure...
It would seem to me that it would be easier for vendors to form a hollow base spitzer pellet than a wasp waisted pellet anyway.....
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Yep, they work just fine, in the more powerful PCPs.... Mike (Carson Rat Sniper) is selling hollow based spitzers in .25 cal in a few weights, from 31 gr. up to about 45 gr.... Most big-bore shooters just use cast bullets, either RN or FN designs....
Bob
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I've got a question about BCs.
How can two pellets that have the same weight and shape have different BCs???
Two pellets that I had been playing around with.
The CPHP @ 14.3 gr.
The JSB Express Exact @ 14.35 gr
One is a hollow point and one is a dome. They are not even close to the same shape. What's really weird is when the same pellet has a different BC out of two different guns. And that BC drops off with increasing range. Due to an increasing nose up attack and the onset of spiraling?
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Actually, depending on the muzzle velocity, the BC often increases with range, because the velocity slows into a region where the Drag Coefficient is lower.... This is particularly true if you start at 1000 fps or beyond.... However, that is only because the Drag models we typically use (G1 or GA) do not reflect the huge increase in drag at transonic velocities.... If the model matched the drag, then the BC would be a constant, even though the large increase in drag (and loss of velocity) would still be taking place.... I dealt with that a couple of pages ago....
Pellets with a soft, thin skirt can deform quite differently at different pressures, as the skirt obturates to fill the rifling.... This change in shape can easily affect the BC when shot from different guns.... The increasing nose-up angle of attack is very small, even at 100 yards, that was touched on in an earlier post in this thread.... In fact, if the rifling twist is not too fast for the pellet, it doesn't occur, and the nose of the pellet follows the trajectory.... Spiraling can increase or decrease, depending on if the pellet is dynamically stable or not.... If it is, the spiraling decreases with range, if unstable, it increases.... There is a thread in the PCP gate dealing with those cases at this point in time....
Bob
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Why wouldn't this pellet design be one of the best for rifled barrel pellet rifles. Especially in the .177, and .22 cal lines. Is it true that this one was only available in .20 cal? Was it ever available in .22 cal?
It has a very slight diablo style waist, that basically allows two rings of contact with the rifling. Seems sorta silly that the air pellet industry has held on to tiny waist high drag pellet design. Especially when just about every pellet rifle these days has a rifled barrel that can spin and stabilize the pellet instead of depending on a 'birdie' style wasp waist design to stabilize pellets fired from smooth bore barrels.
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You would have to answer your own question by testing it at various velocities to find out what the actual BC is.... My guess is that the relatively pointed nose, compared to a true hemi-spherical nose like the JSB Exacts, will hurt the BC more than having a larger waist might help it.... As I said above, I haven't found a larger waist to improve things much, if any....
For the most part, the BC is tied to the SD, which is the weight in lbs. divided by the caliber squared.... In fact, the BC = SD / FF , and the Form Factor doesn't vary as much as you might think, being 1.0 for the 3 caliber long spritzer G1 Model (1st page), and 1.55 for a roundball, with most good pellets lying in between.... Wadcutters are worse, of course, and so are most pointed pellets, and domes that are not hemispheres, because of the sharp corner at the back of the head.... Weight is still the most important contributor to BC....
Part of the reason to hold onto the Diabolo design may be the desire to limit maximum range, and the terminal velocity and energy at that range, for downrange safety on high angle shots.... If you want to really allow an airgun to stretch it's legs, forget about pellets, and use a good bullet design, in a barrel chambered for it, with enough power to push it.... .22LR performance is available in modern PCPs....
Bob
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I think that a good 'bullet' design is in order here. I'd love to see a line of air rifle 'bullets' in .22 cal. Could be just what the sport needs. As you said, I'd love to have these air rifles be able to really stretch their legs. As I said in another thread I really like your 'boat tail' design. I think something that could work well. Is it possible to produce that bullet in a lighter weight? Has anyone considered some sort of hollow core in order to reduce the weight, but still get the right profile?
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Boattails are not great in short, and therefore light bullets.... The bearing area needed to keep the bullet straight in the bore simply gets too short.... Since the weight is the dominant factor in the BC and not the shape, there is no more point in making a hollow bullet than one made from zinc, like the lightweight pellet designs around today.... It might be possible to make, say, an 18 gr. bullet with a fractionally higher BC than, for example a JSB Exact Heavy.... but I don't think you will find anyone willing to put in the effort to make something like that because of the cost.... Any type of hand casting or swaging can't compete price wise with the mass produced pellets in .22 cal.... For the foreseeable future, I think bullets will remain practical only at the upper range of weights for a given caliber, in the range of twice what the common pellets weigh.... That means 35-45 gr. in .22 cal and with the new 34 gr. JSB coming out in .25 cal, likely in the 45 gr. and up weights in .25 cal.... Really powerful PCPs only need apply....
Bob
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I wonder if a hollow bullet could be swaged then reswaged to give it a hollow chamber inside. Or if there were some sort of polymer inserted to fill the cavity then swaged in order to give it the desired shape. That way weight is down but profile is more boattail for better BC than diablo pellets.
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Boy am I late on this topic......let me read all the pages and see what I can add.
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The .177 JSB heavies have a much less pronounced waist similar to the photo than other pellets and a BC of .0310 in Chairgun compared to the JSB Exact at .0210.
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https://www.pyramydair.com/product/jsb-diabolo-exact-heavy-177-cal-10-34-grains-domed-500ct?p=388 (https://www.pyramydair.com/product/jsb-diabolo-exact-heavy-177-cal-10-34-grains-domed-500ct?p=388)
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But fit really tight and don't group as well at the 12-20 yards that I usually shoot in the yard as the Crosman lights in either of my .177 Walther barrels.
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Well there is not much that I can add but this pellet data base of some old pellets that are not made any more as well as today's pellets. I would like to try a few of them, one pellet that I did try that to me beat out the JSB pellets was the Logun Penetrators.
http://www.photosbykev.com/wordpress/2009/01/20/air-rifle-pellet-database/ (http://www.photosbykev.com/wordpress/2009/01/20/air-rifle-pellet-database/)
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I've considered getting some Eun Jin 28 gr pellets, and removing the skirt to see how that performs. I'd leave the top section of the wasp waist to give it sort of a boat tail profile. It may not do well, but ya never know till you try it, right.
I found a couple pictures where a guy had a mold that would produce lead pellets exactly like what I just described. He never had a chance to go test them out and the thread just went cold, so I have no idea if it worked well or not.
I'll include a picture I found of the pellet and mold. I found these over at http://castboolits.gunloads.com/ (http://castboolits.gunloads.com/)
The pellet on the left is the one that looks like the Eun Jin 28 gr with the skirt removed. Below there are two images of the mold used to make the pellet on the left. The pellet on the left is about 23 gr 22. cal, the middle pellet is .20 cal 15 gr, and the ball is .185 round ball about 9.5 gr.
Actually the pellet in the middle looks like it could be a real performer:-)
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It's been a while since I added any data to this thread.... Today I received 4 sets of data from jhm757 on the brand new 34 gr. JSB King Heavy, shot from his SynRod.... After correcting to NTP, here are the BC's for that pellet, using the G1 Drag Profile.... Average velocities between the 1 yard and 25 yard Chrony distances are shown....
678 fps - 0.0327
770 fps - 0.0441
832 fps - 0.0477
880 fps - 0.0457
The muzzle velocity for the 880 fps data was 917 fps and if we start at that velocity, we could use a BC of 0.0457 out to 17 yards, then change to 0.0477 out to 40 yards, then use 0.0441 out to about 65 yards.... That averages out to using about 0.046 out to 65 yards with a MV of 917 fps.... After that, the BC seems to decrease, but bear in mind this is just one set of data, from one gun.... Here is a chart showing how the new pellet compares to the other JSBs I have data for....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drag%20Coefficients%20JSB_zpslgxqqktp.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drag%20Coefficients%20JSB_zpslgxqqktp.jpg.html)
While a BC of 0.046 is pretty respectable, the Drag Coefficient, from this set of data, seems to show that the new pellet has more drag than the other JSBs we have data for.... Anyone who has additional data can send it to me to be added to the database.... Don't forget to record the temperature, altitude, barometric pressure, and humidity.... So far, we seem to be showing the same trend as the other JSB Exact series pellet towards least drag (and best BC) at around 800-850 fps....
Bob
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Why would the BC be so much worse at 700 fps?
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I have seen the BC with JSB pellets decrease at low velocities before.... You will notice that we don't have data down at 678 fps for any of the others tested (yet).... The best set of data I have (most complete) is for the AA 16 gr., and you can see the drag increasing below about 830 fps, but the lowest data point is 740....
As to the REASON for the BC to decrease at low velocities, I don't have the answer, but that is part of what I am trying to do here is establish a new Drag Model for pellets, in particular for JSB Exacts.... Even the G1 Drag Profile has higher drag below 600 fps....
Bob
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All of this is about to become obsolete, if you can afford it.... A new Doppler Radar for ballistic use, called LabRadar, is coming on the market, supposedly priced at $559.00.... It will work out to about 100 yards with a flat based .30 cal, less range with a smaller caliber (I have heard about 40 yards with a .177), and can be set up to give a plot of velocity vs. distance in increments as small as about 1 yard or less.... Here is a plot of a 34 gr JSB King Heavy, starting at 785 fps, out to 65 yards (which I assume is where it lost acquisition).... The plot of actual measured velocities is laid over a constant Cd of 0.251, and the agreement is amazing....
http://www.network54.com/Forum/79537/message/1433191509/Lots+of+good+data+there%2C+Harry (http://www.network54.com/Forum/79537/message/1433191509/Lots+of+good+data+there%2C+Harry)
I would expect that at transonic velocities the Cd would no longer be a constant, but this device should be able to plot the entire Drag Model for any pellet you want to shoot, at any velocity.... By using a few velocity increments, say 100 fps steps, it should be possible to plot the entire Drag model for a given pellet.... We are on the verge of a complete change in how we can measure downrange velocity and BCs.... All it is going to take is deep pockets.... For now, that leaves me out, unfortunately....
Bob
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Interesting that radar can pickup such a small object like that.
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and the best part is.... Made in Canada....
Bob
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and the best part is.... Made in Canada....
Bob
By an inventor that was probably educated in America :)
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Bit of an arrogant comment, when you consider that Radar was invented by the British, don't you think?....
Bob
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LOL, Doppler Radar chronographs have been around for years although they haven't been available to the hobbyist until now. Some hobbyist. I've read about military surplus chronys before but it seems the US government no longer auctions of stuff like they used to. And yes, the credit goes to the British.
Tom
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Good grief, I was only kidding. Didn't you notice the smiley face? Thanks for the history lesson, but I already knew that. :)
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The investigation of Cd changing with velocity using LabRadar on the Yellow continues.... http://www.network54.com/Forum/79537/message/1433252500/Old+Kings+at+high+speed+--+interesting (http://www.network54.com/Forum/79537/message/1433252500/Old+Kings+at+high+speed+--+interesting)
The Cd for the new 34 gr. and old 25 gr. Kings is similar at similar velocities, as expected.... and the Cd increases at higher velocities.... Seems like they are working on the same thing I am.... parallel discovery is always interesting.... Like I am finding, the actual Cd values are slightly higher than the G1 or GA profiles in the subsonic region.... They haven't played with transonic or supersonic yet (at least not in that thread), so they may be in for a shock when they do, as I found the drag skyrockets....
Bob
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Where in these graphs is showing the drop in BC below 750fps that you have been measuring?
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Most plainly shown in Post #83, but there are other examples as well if you read back.... Michaelthomas has studied it quite a bit with Exacts and 16 gr. AA pellets for his 25 yd. Benchrest shooting, there is a sweet spot where the wind drift is at a minimum somewhere in the 800s....
I notice that the testing with the LabRadar, so far, hasn't shown it, and in fact the Cd is pretty much a straight line below about 750 fps (in .25 cal), so there is still much to learn.... The most important things are still to be learned, exploring the Cd at lower and higher velocities to fully develop the Drag Profile....
Bob
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That is what is a little surprising. CD is continually improving at lower velocities but BC is known to get worse again below 750 fps.
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Does the formula for BC have any multiplying factors based on the energy?
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If you look at the G1 drag model, you will note that the Cd is actually higher at low velocities, it has a minimum at 600-650 fps.... The BC is only a valid concept when you compare one bullet to a standard with a known Cd profile, such as the G1.... That is why if you use the G1, GA, GS, or G7 models, you get a different BC each time.... The idea here is that I would like to develop a new drag profile that is closer to reality for airgun pellets than what we have been using (G1 or GA).... None of them account for the huge increase in drag in the transonic region we get with Diabolo pellets....
The BC for a bullet that exactly matches the G1 model is 1.000.... It has a Sectional Density of 1.000, so if you have an SD of 0.15, then if the Form Factor is the same (1.000), you would expect a BC of 0.15 as well.... If the Form Factor is 2.000, with an SD of 0.15, the BC would be 0.075.... Use a different model, everything changes....
Bob
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Have you thought about sabots? Just a question.
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Nope.... never seen any accurate results with them....
Bob
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Nope.... never seen any accurate results with them....
Bob
They are popular in the muzzle loading world. I have no idea one way or another about how they might fit into the air gunning world. They probably won't. Also shotgun slugs are often carried in a sabot. This allows more powder to burn in the same space thus pushing a longer slimmer and sometimes lighter projectile to a higher velocity. Again I have no idea how this might apply in the airgun world. Hypothetically a gun designed to shoot a 9mm pellet could shoot a .257 which weighed the same in a sabot. It would achieve the same muzzle velocity but it would have a much better BC. Bob, this is just me rambeling... maybe it is worth thinking about.
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I hate stealing other guys data, but this supports what I have been trying to achieve, and gives an idea just how much information can be found using the Doppler Radar....
http://www.network54.com/Forum/79537/message/1433753419/Here+is+a+Drag+Coefficient+comparison+from+some+data+I+collected+at+the+farm. (http://www.network54.com/Forum/79537/message/1433753419/Here+is+a+Drag+Coefficient+comparison+from+some+data+I+collected+at+the+farm.)
The graphs clearly shows the trend I have been finding with the Cd going through a minimum at about 700-750 fps, and a large increase in drag at 900 fps.... They haven't examined the transonic region yet, hopefully that will come.... I'm really wishing I had a LabRadar setup....
Bob
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You have shown us how BC falls rises and falls again as it goes through the peak from 750 to 830 fps but it is very surprising to see CD actually getting worse as you get slower than that. There must be a different skin effect or changing reynolds number or a standing wave effect filling in the skirt at the minimum CD.
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I hate stealing other guys data, but this supports what I have been trying to achieve, and gives an idea just how much information can be found using the Doppler Radar....
http://www.network54.com/Forum/79537/message/1433753419/Here+is+a+Drag+Coefficient+comparison+from+some+data+I+collected+at+the+farm. (http://www.network54.com/Forum/79537/message/1433753419/Here+is+a+Drag+Coefficient+comparison+from+some+data+I+collected+at+the+farm.)
The graphs clearly shows the trend I have been finding with the Cd going through a minimum at about 700-750 fps, and a large increase in drag at 900 fps.... They haven't examined the transonic region yet, hopefully that will come.... I'm really wishing I had a LabRadar setup....
Bob
Nice to see your (Bob's) findings supported by another group with a completely different method of measurement :) Yes we are all waiting for the tests to move to the transonic.
You have shown us how BC falls rises and falls again as it goes through the peak from 750 to 830 fps but it is very surprising to see CD actually getting worse as you get slower than that. There must be a different skin effect or changing reynolds number or a standing wave effect filling in the skirt at the minimum CD.
Having some experience with Doppler systems in the past, I wonder how the data is being integrated and if the last bit a data just before the return is lost is reliable. I'm not saying it isn't but a weak (sporadic) return could explain the rise in cD at the end of contact.
Tom
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The data measurements are about two per yard, and part of the datastream is the Signal to Noise Ratio, you can see it deterorating in the last few measurements.... However, with that many data points (150ish), so what if you have to throw out the last couple.... Unfortunately the range of the LabRadar is about 100 yards on a .30 cal, and less for smaller calibers.... so the only way to get a large range of velocities is to do like I am doing an launch them at a series of velocities that overlap and then try and blend the results.... at least that would be my approach....
I don't think it's a Reynolds number effect causing the rise in Cd at low velocities.... Even the G1 Model shows increasing Cd below 600 fps (although not as drastic), and it's 1" caliber, over 3" long, and weighs a pound....
Bob
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What do you think about starting a funding pot to get Bob a new toy?! ;D
I'm not sure how we can get this going, but I have learned so much from him and would be very happy to chip in a few bucks. What do you say??
Btw, no strings attached. He can do whatever/whenever he wants to do with it.
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Hey rjorge,
I'd be more than happy to help fund such a pot 8) -----> "The Cookie Man's R&D fund."
Definitely, No Strings Attached :D.
Kirk
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I would also generously donate to that cause! Keep us updated on when and how ...
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Thats very interesting seeing the lowest drag@ 715fps for a 34gr pellet? The whole idea of going to a much heavier pellet is to gain ftlb... The graph only shows to 900fps I am wondering does the drag began to drop back down at an higher velocity? further down the graph?
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While the lowest drag is in the 700s, the difference in BC is extremely small between say, 750 and 850 fps.... However, I would expect the drag to continue to increases with the King Heavies just as it does with the smaller caliber Exacts, showing about a four-fold increase in drag by the time you push the pellet to Mach 1.... It is understanding and recording that increase in order to develop a new Drag Model for pellets that this thread is all about....
One of the nice things about using the LabRadar is that we should be able to record the entire drag curve with much fewer shots required.... I would expect that a single shot at about 1300 fps would supply all the data needed for the transonic range, down to about 900 fps, possibly even lower.... because the pellet slows so quickly in that speed range....
Bob
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Where can I buy a LabRadar?
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Seems that it does have some limitations, wondering how well will it work with pellets....
Different bullets can be read at different ranges. Preliminary testing has shown these approximate range limitations for some popular cartridges. I was told that these are conservative, and the Labradar may read them further out:
22 LR: 50-60 yards
223 Rem: 40-60 yards
270 Win: 50-70 yards
308 Win with boattail bullet: 60-80 yards
308 Win with flat base bullet: 100 yards
9mm Luger: 100+ yards
40 S&W: 130 yards
45 ACP: 140 yards
- See more at: http://www.alloutdoor.com/2015/02/02/chronograph-labradar-personal-doppler-radar/#sthash.d4dUVXkQ.dpuf (http://www.alloutdoor.com/2015/02/02/chronograph-labradar-personal-doppler-radar/#sthash.d4dUVXkQ.dpuf)
Great info on it:
http://www.alloutdoor.com/2015/02/02/chronograph-labradar-personal-doppler-radar/ (http://www.alloutdoor.com/2015/02/02/chronograph-labradar-personal-doppler-radar/)
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How far the LabRadar (or any radar) can take accurate measurements is dependent on the area of the base of the bullet available to reflect the radar waves back to the unit.... A .177 pellet may only work out to 30-40 yards.... They were getting measurements on the .25 cal pellets out to 75-95 yards.... One of the things measured and recorded is the SNR (signal to noise ratio) and once that drops below a set value, the unit no longer records data.... eliminating any worthless data....
Bob
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I do not see any for sell?
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They hope by August, according to the email I got from them....
Bob
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They hope by August, according to the email I got from them....
Bob
Thats a must have for me ;D
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While the lowest drag is in the 700s, the difference in BC is extremely small between say, 750 and 850 fps.... However, I would expect the drag to continue to increases with the King Heavies just as it does with the smaller caliber Exacts, showing about a four-fold increase in drag by the time you push the pellet to Mach 1.... It is understanding and recording that increase in order to develop a new Drag Model for pellets that this thread is all about....
One of the nice things about using the LabRadar is that we should be able to record the entire drag curve with much fewer shots required.... I would expect that a single shot at about 1300 fps would supply all the data needed for the transonic range, down to about 900 fps, possibly even lower.... because the pellet slows so quickly in that speed range....
Bob
So for the time being, all we need to do is supply Harry a properly potent pellet shooter....:) My first .25 Marauder will do the trick, and the .30 cal I built would take care of it nicely...heh-heh-heh Or one of Doug's condors.
cheers,
Douglas
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Hey rjorge,
I'd be more than happy to help fund such a pot 8) -----> "The Cookie Man's R&D fund."
Definitely, No Strings Attached :D.
Kirk
Check out the 'cloud funding'...ought to be a pretty easy set up and drop it into a PayPal account to supply the goodies.
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Yes I'm sure Harry would find out things change rapidly at supersonic and transonic velocities.... It would take a pretty potent .25 cal to push the 34 gr. at 1300 fps, which would then give you the entire flight down to 900 or so, I would think, in one shot.... Perhaps using Helium for a few high velocity shots would be a good idea....
I've been working on a program (spreadsheet) to calculate the Cd for every data point returned from the LabRadar.... I saw a similar graph in one of Harry's posts that was a nice smooth curve.... I have NO idea how he did that, because some of the LabRadar datapoints (they are every 2 milliseconds, which is about 2 per yard) are faster than the preceeding ones, which calculates out to a negative Cd (impossible, of course).... The reason for the velocity swings is not hard to explain.... LabRadar claim a 0.1% accuracy, which at 750 fps is 0.75 fps.... Since in the datastring Harry published for the 34 gr. King Heavy, the pellet lost about 100 fps in 65 yards, which is about 130 data points, that is a drop of only 0.77 fps per datapoint.... Therefore if one velocity is 0.75 fps low, and the next is 0.75 fps high, the velocity would increase by ~0.73 fps.... In Harry's data, the drop per reading varied from 2.46 fps decrease to a 1.38 fps increase (should have been relatively constant at 0.77 fps decrease).... When I plotted out the Cd vs Velocity, I got a line that zig-zagged all over the place, from negative Cd values to ridiculously high.... Even if I used a moving average over 5 to 9 datapoints (the velocity swings were greater as the pellet travelled downrange), I still got a zig-zag plot as below....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%20Plot_zpselgo9iyh.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%20Plot_zpselgo9iyh.jpg.html)
The dotted black line is a polynomial trendline, compliments of Excel.... Both the shape of that trendline, and the Cd values I calculated, are wayyyyyyyyyy different than the results Harry published on the Yellow, so I've definitely got some work to do on analyzing the data.... I think there may be some spurious returns that I should throw out, but have no idea where to draw the line on doing that.... Certainly when the velocity increases from one datapoint to the next there is a problem, but which one should you throw out, or both?.... There is going to be a lot of headscratching before I come up with a way to analyze the output of the LabRadar and turn it into a smooth and accurate depiction of the Cd as the pellet travels downrange.... I'd really like to know how Harry did that.... It is interesting how smooth a line the actual velocities are, when plotted against the downrange distance....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%20Distance%20vs%20Velocity_zpsnfjip8hx.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%20Distance%20vs%20Velocity_zpsnfjip8hx.jpg.html)
Hard to imagine that those tiny wiggles in the measured velocity cause such wild swings in the calculated Cd, isn't it?.... The practical solution may be to only take data every 10 yards or so, but even then I wouldn't trust one datapoint, I'd want to use an average of 5 or so.... maybe average the one you want plus 2 either side of it?....
Bob
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I think I figured out how to smooth the Cd curve.... RonB suggested that I plot Velocity vs Distance from the LabRadar output, and that didn't work because the distances wander around slightly, so I plotted Velocity vs Time, which is in 0.002 second increments.... I then used the Trendline feature in Excel to generate an equation of the line that fits best through all the points.... The initial attempt was linear, but I got a better fit with a 2nd order Polynomial.... Here is that chart....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%20Velocity%20vs.%20Time_zpslbym7tjk.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%20Velocity%20vs.%20Time_zpslbym7tjk.jpg.html)
The blue dots are the datapoints from LabRadar.... The red line is the linear approximation, you can see that it is too low at the beginning and end and too high in the middle.... The black line is the 2nd order Polynomial, and the equations are shown on the graph.... If you click on the graph you should get a larger version that is easier to see.... Once I had the equation, I created a new column in the spreadsheet with velocities taken from that, and then used those velocities to calculate the Drag Coefficient.... The results are below.... They incorporate the correction to standard atmosphere, which I didn't do in the previous (zig-zag) graph above....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%20vs%20Velocity_zpsypymerou.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%20vs%20Velocity_zpsypymerou.jpg.html)
So, we now have a smooth curve showing how the Cd varies with velocity for the 34 gr. JSB Heavies, from 683-784 fps.... What is still somewhat confusing to me is why the values I have calculated are quite a bit lower than what Harry got on the yellow, and why the curve is inverted compared to his (albeit the Cd is nearly constant in practice).... He found a low point in the drag at about 740 fps, whereas I have a high point at about 725 fps....
Bob
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I thought I made it reasonably clear but apparently not, so lets try this
again........smooth the values for velocity and distance by plotting them
vs time or, since the time increment is uniform, they are just as easily
plotted vs point number (1,2,3,etc). Then use the smoothed values (those
calculated from the equation) to compute Cd.
BTW, what equation is being used for Cd ?
Ron
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Distance is not necessary, and as you say, that curve would have to be smoothed as well.... Therefore I plotted the LabRadar velocity datapoints vs. time (as you say, the increments are conveniently constant), and used Excel to produce the trendline equation shown on the graph.... I then used that equation to produce the smoothed velocities for each time increment, which I used to compute the rest.... I converted everything to Metric units for simplicity, and the steps I used are as follows:
Convert the temperature, humidity and pressure to air density D in kg/m^3 using this calculator.... http://wahiduddin.net/calc/calc_da_rh.htm (http://wahiduddin.net/calc/calc_da_rh.htm) ....
Calculate the speed of sound in m/s for the test temperature (in *C) using Vs = 331.3 x SQRT((C+273.15)/273.15)....
ICAO standard atmosphere values (15*C, 0%H, 29.92"Hg), for reference, give D = 1.225 kg/m^3, and Vs = 340.3 m/s....
Convert the smoothed velocities to m/s by multiplying the fps by 0.3048....
Convert the pellet weight in grains to mass M in kg by multiplying by 0.0000648....
Calculate the area A of the pellet and convert to m^2 by using (cal.^2)/4 x PI x 0.000645....
Compute the incremental acceleration a = (dV/dT) for each smoothed velocity by taking one velocity (in m/s), subtracting the previous, and dividing the difference by the time increment (0.002 sec. except for the first increment).... result in m/s^2....
Use F=Ma to compute the drag force F in Newtons for each increment....
Determine the average velocity of each increment by adding the start and end (smoothed) velocities together and dividing the sum by 2, this is used for V in the Cd calculation below....
Calculate the Cd for each increment using the following formula....
Cd = 2 x F / (D x A x V^2)
I checked the units, and they all cancel, leaving the Cd as a dimensionless number the way it should be.... If you see something wrong in my approach, please point it out.... Incidently, I have two more columns, one to compute the local Mach number for each Cd calculation by dividing the average increment velocity V used by Vs for the test conditions, and then another one to convert that back to fps corrected to ICAO for the graph by multiplying the Mach # by 1116.45 fps.... The "X" axis on the graph above is fps in ICAO conditions, not the fps as recorded by the LabRadar....
Bob
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I'm not accustomed to having time as a variable so I did not use it. The "two chrony"
approach, my normal mode of operation, uses (dV/dx)(dx/dt) and therefore an entirely
different equation. What you have outlined is textbook perfect, yet the answers are
incorrect. Obviously, as the saying goes,..........the devil is in the details. I have cross
checked your method with mine and get complete agreement. As an example, using
data posted on June 1 for 34 gr......... at ~ 770 f/s both will give a Cd value of .303
and a drag force of .0645 lb (based on an air density of .0677 lb/cu ft). Does this
help?
Ron
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Well, we are obviously getting completely different results, nice to know mine is wrong.... but better if I knew why....
CORRECTIONS IN RED, I USED THE WRONG PELLET WEIGHT.... DUH!....
From the following thread on the Yellow.... http://www.network54.com/Forum/79537/message/1433166096/A+sample+one+shot+data+ToF%2C+Velocity%2C+range+to+65+yd%2C+JSB+Heavy+Kings+34+gr (http://www.network54.com/Forum/79537/message/1433166096/A+sample+one+shot+data+ToF%2C+Velocity%2C+range+to+65+yd%2C+JSB+Heavy+Kings+34+gr)
For the LabRadar velocity increment from 770.18 fps down to 769.31 fps, ie from 0.035021 to 0.037021 sec. and 9.07 to 9.58 yards, my numbers are as follows,
Specified conditions, 13*C, 58%H, 890hPa.... which gives me an air density of 1.080 kg/m^3 = 0.0674 lb/ft^3.... You used 0.0677, close enough....
Smoothed velocities.... 769.91 to 769.07 fps.... average velocity 234.541 m/s
Time delta = 0.002000 sec.
Acceleration is (769.911-769.071) / 0.002 = 0.84 / 0.002 = 420.0 f/s^2, my spreadsheet uses 0.25618 / 0.002 = 128.09 m/s^2
Mass is 25.4 gr. = 0.001641 kg.... If I did the conversion correctly, you should have 0.0001128 slugs....
Mass is 34.0 gr. = 0.002203 kg.... which is 0.0001510 slugs....
Diameter is 0.250", so the area is (.25)^2 / 4 x PI= 0.04908 in^2, which is 0.0000317 m^2
Drag force F = Ma = 128.09 x 0.001641 = 0.2108 N.... That converts to 0.0474 lbf, yet you have 0.0645 lbf.... so there we have completely different values, the obvious source of our difference....
Drag force F = Ma = 128.09 x 0.002203 = 0.2822 N.... which is 0.0634 lbf.... slight variation from your 0.0645 lbf, likely because of different smoothing equations....
My calculation for Cd is as follows....
Cd = 2 x F / (D x A x V^2)
= 2 (0.2108) (0.2822) / (1.080 x 0.0000317 x (234.541)^2)
= 0.4216 0.5644 / (0.0000342 x 55009)
= 0.4216 0.5644 / 1.881
= 0.2241 0.3001
I would appreciate it if you could do a similar detailed description of your calculations so that I can see where my error is.... It would appear to be in the calculation of the drag force....
Bob
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Perhaps this will explain it.........
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*LOL*, YA THINK ? ? ?
Classic case of GIGO.... Here is the correct graph for the 34 gr. JSB King Heavy....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%20vs%20Velocity_zpsihclrqzs.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%20vs%20Velocity_zpsihclrqzs.jpg.html)
Thanks for picking that up, Ron.... sometimes we overlook the obvious.... :-[
I'm curious, did you use a linear trendline, as I notice our Cd value at 770 fps (773 fps ICAO) is different by about 1%.... I have 0.300 and you got 0.303.... I would love to see a plot of your Cd vs Velocity results....
Bob
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Third order polynomial will offer a better fit, have
even used fifth order at times.
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Really interesting our Cd curves are opposite, yours low at ~750 fps, and mine high at ~725 fps.... Yours also has a lot larger range, (4.2%), compared with mine at only 1.5% (if I drop the first reading with the large delta T).... I assume we are both using the same LabRadar data from the thread I linked above, so I have no explanation why we have different smoothing curves.... I tried a 3rd order polynomial, and there was basically no difference.... (note, see below)....
Bob
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Well I found a small problem in that I forgot to revert the datapoints from which I took the trendlines to the original raw data.... That makes hardly any difference in a 2nd order Polynomial, but it changes the 3rd order Polynomial to closely resemble yours, Ron.... Here are all the Cd graphs, using from a linear trendline to a 5th order Polynomial, it makes a HUGE difference in which trendline you choose....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%20Linear_zpsti9do6zk.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%20Linear_zpsti9do6zk.jpg.html)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%202nd%20Order_zpsogtx8na6.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%202nd%20Order_zpsogtx8na6.jpg.html)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%203rd%20Order_zpsjvbvrn4l.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%203rd%20Order_zpsjvbvrn4l.jpg.html)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%204th%20Order_zpsxa9tmkyp.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%204th%20Order_zpsxa9tmkyp.jpg.html)
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%205th%20Order_zpsgwf83mj1.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%205th%20Order_zpsgwf83mj1.jpg.html)
This leaves me with a slight problem about which trendline to choose, of course.... I hate it when it becomes more art than science.... Fortunately, logic tells us that the correct one is the one that is going through a very shallow minimum, which I'm sure is why you chose the 3rd order one, as will I.... It bears in mind that once we have all the data right up to Mach 1.2, the curve we are seeing here will be virtually a straight line compared to the huge increase in drag to come in the transonic region....
I am now confident that I have a spreadsheet that will provide a workable solution to analyzing the LabRadar data.... and I look forward to the day when I have one.... Thank you for your patience and allowing me to work through my spreadsheet until we are getting consistent results....
Bob
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I'm unable to produce graphs such as yours, something still isn't correct(?).
Second, third and fourth order should be nearly identical. Fifth and higher.....
not so much........the very thing you're trying to filter out begins creeping back
in. To make some sort of check, greatly expand the graph.......I blow it up to
at least several feet wide whereby it requires considerable scrolling to see
everything. Granted, it's a pain in the butt, but at least you know where you
stand. And, I guess it probably goes without saying, ........knowing what the
graph should look like ahead of time is indeed a big help.
Ron
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As you are aware, I have no control over how Excel calculates the trendline equations, only the number of terms.... As I understand it, as you increase the number of terms in the trendline equation, it follows the velocity fluctuations more and more closely.... That is why it has more peaks and valleys.... As you said, the raw velocity data wanders around a fair amount, with some values being higher than previous ones (ie the pellet is speeding up in that half yard increment), which we know is impossible, that is the instrument margin of error creeping in.... This is particularly noticeable the further downrange you go.... As I explained earlier, without smoothing the data, the calculated Cd varies over such a huge range to be useless, at times going negative.... Here is the last part of the data (Velocity vs Time) expanded as you suggest.... Blue dots are the raw data, red line the linear trendline, black line the third order trendline....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%203rd%20Expanded_zpsv5osn1g0.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%203rd%20Expanded_zpsv5osn1g0.jpg.html)
I think we are stretching the limits of the equipment, and our ability to analyze the data it is producing... The good news is that it won't matter in the long run, because once we look at the big picture, all the little lumps and bumps will disappear.... Once we move up to the transonic range, the pellet will be losing velocity so quickly that the instrument margin of error will be insignificant, or at least greatly reduced.... We will be measuring Cd up in the region of 1.0, if my previous testing is any indication, so when the vertical scale on the graph reflects that, the small swings we are currently seeing will all but disappear.... This is what this data will look like in the big picture, with the scales set to what will be necessary to cover the range of values I expect....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Cd%203rd%20Compressed2_zpsjrddrxkb.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Cd%203rd%20Compressed2_zpsjrddrxkb.jpg.html)
I am confident that we are on the right track, and look forward to being able to process more data (without having to type in and proof read every number)....
Bob
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May I ask a really dumb question?
Is the Drag Coefficient 'inverse' of the Ballistic Coefficient??? So as the Drag Coefficient goes up the Ballistic Coefficient goes down. Is that right?
I opened the Custom profile in Chairgun and while looking at the different profiles in the edit profile window I noticed the graph and was trying to make sense of it.
Have you guys concluded the the GA pellet profile in Chairgun Pro is wrong? If so what should it be? Or is that what this discussion hopes to answer once and for all?
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They move in the opposite direction, yes, but the BC is a comparison of the Cd for your bullet compared to the Cd for the "Standard" bullet.... If the drag profile of your bullet doesn't match the selected profile, then the BC will change at different velocities....
From the measurements I have made so far, I think the GA profile in ChairGun is too low in terms of Cd at virtually all velocities, in other words the pellets I have tested have more drag.... If you compare the GA profile to the widely used G1, you will note that they used the G1 for Mach 1 and above, but reduced the drag slightly below Mach 1.... While this reflects the larger increase in drag seen in the transonic region, it isn't an accurate representation of reality.... Our pellets have more drag than the G1 profile subsonic, and a LOT more drag supersonic....
Using the GA profile is probably better than using the G1 profile, but the BC you use will have to be lower to reflect your pellet behavior.... If you look back at Post 83 on Page 5 of this thread, you will see how steeply the drag increases in the transonic range compared to the G1 profile.... Note that it is slightly higher in the subsonic range, while the GA profile is even lower than the G1 there.... Therefore none of the profiles used are very good, and the purpose of this thread is to improve on that....
Bob
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I'm digging up an old thread here but since the question is directly related to this data I'll give it a go. In case of that JSB Heavy King pellet, what would be the ideal speed in order to minimize the wind drift? Would it be 750 fps that's faster end at the bottom of the curve or would the increase in speed negate the increase in drag (and thus decrease in BC) making somewhere around 900 fps optimal (assuming the linear increase lasts to that point)?
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It will depend on the range you are shooting.... If at very close range, then about 750 fps would be optimum, but the further away the target, the faster you need to start, so that the AVERAGE drag is the least across the entire distance.... This is complicated further by the fact that the wind has more effect nearer the muzzle than the target, because once the pellet is deflected, it carries that new (angled) path downrange, with the offset distance from the line of sight increasing with distance.... If you plot muzzle velocity vs. drift, you will get a curve like this....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drift_zpslmoraeck.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drift_zpslmoraeck.jpg.html)
As you increase the distance, the optimum muzzle velocity increases.... That curve used the G1 Drag Model....
Bob
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Thanks, Bob - I knew I had forgotten something - the decrease in velocity in this case. So for 100Y shooting with Heavies it would make sense to start in the 800-850 fps range so that the pellet will spend most of it's flight in the lowest drag area speedwise.
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Possibly even 900 fps or close for 100 yard work.... Only once the entire drag curve is determined will we have the exact answer to that question.... Like anything else that goes through a minimum, some distance either side of that carries little penalty, so even if the optimum is 880 fps, 900 or even 920 may be so close that the flatter trajectory is worth it.... eg. on the above graph, 850 and 900 have the same drift, so may as well choose 900.... and 950 is only 1/8" more.... At 1000 fps, the drift is 3/8" more, however....
Bob
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Possibly even 900 fps or close for 100 yard work.... Only once the entire drag curve is determined will we have the exact answer to that question.... Like anything else that goes through a minimum, some distance either side of that carries little penalty, so even if the optimum is 880 fps, 900 or even 920 may be so close that the flatter trajectory is worth it.... eg. on the above graph, 850 and 900 have the same drift, so may as well choose 900.... and 950 is only 1/8" more.... At 1000 fps, the drift is 3/8" more, however....
Bob
Thank you Bob, this IS valuable engineering you are doing here. Thank you for your time.
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Did the Ballistic Coefficient / Modified Drag Model come to end or move to a new topic thread?
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Died for lack of data at the moment....
Bob
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Are you still looking for 1000fps+ data or are concentrating on normal pellet speeds and slower data? If its the latter I may be able to supply some data if that is the case (like Harry's data) when I get the time? Tell me what exactly we need in simple black and white terms. LOL
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Bob that is good stuff and just the info we need to get things right. I sure would like to see the chart for the .30 and .357 pellets. My testing have me setting up the .30cal at two different speeds, 890fps, and again at 930fps. Those are the two speeds that they seem to shoot the very best. I am thinking that barrel length and twist will play a role as well. 22inch barrel and a 1:17 twist.
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I have pretty much put the project on hold until I can afford a LabRadar.... Knitting together data collected by different people, guns, and conditions is nearly impossible....
Baxter, I have no data on .30 or.35 cal pellets at this time.... If you are finding two sweet spots 40 fps apart, I suspect barrel harmonics.... Using a moving weight, or other harmonic tuner, may allow you to tune for any velocity between, or beyond those....
Bob
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Bob,
Okay and that makes sense but if you decide other wise I do own a Labradar so just let me know.
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Just found this thread and will read it completely when time permits and can concentrate fully on the info provided. Likely will be over my head for the math and theory but still good usable info.
Mike
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Hi Bob,
Could you please upload a graph of BC vs Fps for the .22 pellets? I have the strelock app and would like to calculate the fpe at different distances to see at what range you will still have a viable kill shot when hunting.
Would love to see data from lower fps because the bullet slows down and its BC changes... Or maby not? Could give better info about longer range shooting.
Thanx
Ps. I love reading your posts and I am learning a lot.
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The "standard drag model" that pellets are being compared to, to calculate their BC, is gradually improving.... ChairGun originally used a "constant drag" model, which resulted in a huge change of BC like this (chart from measurements I made a decade ago)....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/JSBBCs.jpg) (http://s378.photobucket.com/user/rsterne/media/Important/JSBBCs.jpg.html)
Then they changed to using the "G1" model, which is a bullet that looks like this....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/g1_zps09zm9zd2.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/g1_zps09zm9zd2.jpg.html)
It has a drag curve like this.... Note the HUGE increase in drag in the Transonic region (Mach 0.8-1.2, or 900-1350 fps)....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/G1%20Drag%20Model%20Net_zpsopno7nwx.jpg.html)
Since BC is calculated by dividing the measured Drag Coefficient of your pellet by the Cd of the standard model at the same velocity.... obviously using the G1 model as the basis for your calculations is FAR better than using a constant Cd of about 0.2, which is what was used originally.... Note, however, that below 800 fps, the drag is RELATIVELY constant, between 0.20 and 0.23, but even in that range, using the G1 drag model will "flatten" the BC values.... Now ChairGun uses the "GA" drag model for pellets, which has an even bigger dip around 600-700 fps, so the BC of pellets is even more constant when you use that model.... Here are some other drag models....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Drag%20Coefficients%20of%20Interest2_zpsjqnyzjal.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Drag%20Coefficients%20of%20Interest2_zpsjqnyzjal.jpg.html)
At the moment, the GA drag model is the best we have for Diabolo pellets.... I have made some measurements in the Transonic region (Mach 0.8-1.2) that indicate the drag increases even faster than the GA model.... and I have also found that below about 600 fps there also seems to be higher drag (note my original chart).... but using the GA model and the BC values in ChairGun is the best we have to work with currently.... Alternately, there are many BCs here.... https://hardairmagazine.com/ballistic-coefficients/ (https://hardairmagazine.com/ballistic-coefficients/) .... They have been measured using a LabRadar, but I don't know what drag model was used to calculate them, or if they are corrected to ICAO standard atmospheric conditions....
Bob
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The .25 pellet speeds on that site look very low, the BC would probably be higher at least for heavy pellets if muzzle velocity was higher. I remember seeing a labradar graph where Exact King Heavy had lowest drag at around 750-800 fps and in this case the starting velocity was much lower.
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Yes, the velocity can certainly change the BC value calculated.... I got a response from the Editor of HAM, and at least they are using the GA Drag Model (and in fact that is now on their BC web page).... The GA model does take into account to some extent the lower Cd in the "middle" of the range of typical airgun velocities (note the red line on the above graph).... It won't agree perfectly with every pellet, but the better the drag model used, the more constant the calculated BC will be.... If I recall the LabRadar data on the King Heavy, the graph you are referring to was the Cd, not the BC.... When the BC is calculated using the GA model, the natural tendency is to make the BC more constant over a wider range of velocities....
Until we get an even better drag model, we are stuck with using the GA model for pellets as the best one currently available....
Bob
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This is the one I was referring to, may require that embedded image fix for browser for it to show:
(http://img.photobucket.com/albums/v392/Kyogle/Labradar%20Superimposed%20graphs%20for%20Heavy%20and%20light%20JSB%20Kings%20Cd_zpski6bkrwx.jpg)
Graph shows drag but it more or less corresponds to your BC graphs showing that heavier pellets have lowest drag at higher speed and for all pellets the drag increases quite fast as the velocity drops below the lowest drag area. As I see it, if I were to shoot King Heavies for 100 yards and tried to minimize the wind drift - then I should shoot them at around 900-920 fps to keep the drag as low as possible over the entire range. For lighter pellets that speed could be lowered but drift would increase due to increased drag, as shown by regular Kings where BR shooters typically use about 850-880 fps.
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Yes, those are what I saw, and they do indeed show the Cd.... To arrive at the BC, you have to divide those Cd numbers by the Cd for the GA model, and correct for the SD.... Therefore, the better the match to the drag model used, the more constant the BC number.... You are correct that there is an optimum MV for any pellet to minimize wind drift at a given range....
Bob
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Hopefully I can still post here. It is the topic I'd like to ask about.
How much does lower velocity affect big bore bullet BC?
I am wondering about how the manufacturer listed BC (I assume it is for powder burners) compares to the same bullet at a lower airgun velocity. I can shoot a 44 caliber 310 gr bullet made in a Lee lead mold at 700 fps. The website lists the BC at .218 (probably about1300 fps PB velocity?).
Using Chairgun what BC should I use? I am just comparing bullets trying to determine the retained energy and drop. I only have about a 60 yard hunting area (5 wooded acres) but determined with Chairgun that you need to have really heavy balls to shoot round balls. My .58 at 283 gr is probably OK. It's going to definitely be bullets for the 44.
https://leeprecision.com/bullet-casting/hand-gun-bullet-molds/
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You can get a rough idea of the Subsonic BC by calculating the Sectional Density.... A "typical" bullet will have a BC of about the same value.... The SD of a 310 gr. bullet that is 0.44" in diameter is 0.229.... I would think that the 0.218 BC quoted is probably close enough, particularly at ranges of only 60 yards.... The actual value will depend on the shape of the bullet....
Bob
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You can get a rough idea of the Subsonic BC by calculating the Sectional Density.... A "typical" bullet will have a BC of about the same value.... The SD of a 310 gr. bullet that is 0.44" in diameter is 0.229.... I would think that the 0.218 BC quoted is probably close enough, particularly at ranges of only 60 yards.... The actual value will depend on the shape of the bullet....
Bob
Thanks! Ok that is great to know. That means if I use the bullet as is from the mold (310 gr) there is a little more retained energy. I have a HP pin that I have to try out that will lower that SD but not sure how to figure out the form factor. It would have a little more meplat (nose cut off .1 or so) and probably more of a faster shooting deer bullet. The 310 gr bullet is .429 so that SD/BC is probably correctly calculated.
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If the bullet is 0.429" diameter, the SD of a 310 gr. bullet would be 0.241....
Bob
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If the bullet is 0.429" diameter, the SD of a 310 gr. bullet would be 0.241....
Bob
Sorry. Yes less diameter would be higher SD. The differences must be in the metplat then. And only way to test is with several chronos or lab radar I guess.
Thanks
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As I said, using the SD is only an approximation.... The actual BC depends on the shape of the bullet....
Bob