GTA
All Springer/NP/PCP Air Gun Discussion General => "Bob and Lloyds Workshop" => Topic started by: rsterne on June 29, 2011, 08:12:25 PM
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In another thread I mentioned that I had done some testing of pellets at various velocities to determine the Ballistics Coefficient.... What I found was quite interesting as it was NOT a constant but in fact a curve with a definite peak.... The peak was at a higher velocity with heavier pellets.... Here is a graph of the trends I found....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/JSBBCs.jpg)
Those results are smoothed to show the trends, and should not be relied on to predict the BC at a given velocity.... I did not have a powerful enough gun to propel the 25.2 gr. Monsters fast enough to see their dropoff.... The BCs were calculated by measuring the velocity at the muzzle and 25 yards and then using the BC Calculator in ChairGun.... I used the JSB Exact series of pellets as they are designed to have a high BC and there was a good range of weights available.... Once I realized that there was a big drop in the BC at the higher velocities I did more testing at much shorter range, just 5 yards....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/JSBTransonic.jpg)
Note how low the BCs get when the velocity approaches the speed of sound.... At 600 fps I measured a BC of 0.035 for the 13.4 gr Exact RS but at 1100 fps it had dropped to only 0.010.... It lost over 11% of its energy in just 5 yards.... With the 18.1 gr. Exact Heavy I measured the BC at 0.040 at 800 fps and at 1000 fps it was down to 0.020.... If you are looking for an explanation of what is happening, then check out what happens to the Ceofficient of Drag in the transonic region (which starts at Mach 0.85 - 950 fps)....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/TransonicDrag.jpg)
After these experiments I concluded that there is no point in pushing a pellet past about 950 fps.... It takes a lot of energy to accelerate it that last bit.... and then it turns around and loses all that extra energy in the first few yards.... In addition, once you start pushing over about 1050 fps then you can be dealing with locallized shock waves which can initiate tumbling or other loss of accuracy.... If you need more power, once you hit 950 fps go to a heavier pellet....
Bob
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Interesting... I was thinkin a 950 plus 22 would be good, but...
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Great post!Whats funny to me is that I just got into airguns 7 days ago and I already had come to the very same conclusion!Thanks for the work in getting this done you may save a lot of people tons of trouble.
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Are these diabolo, waisted pellets? What are you shooting them out of? Do you think that, at the higher velocities, they are over-stabilized?
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JSB Exact Series (diablo, waisted).... Shot from a PCP (24" Crosman barrel) with variable power.... The gun will produce sub MOA groups with 18.1 gr. JSB Exact Heavies at 25 yards when shot at 950 fps (36 FPE).... My twist calculator (Miller Rule) indicates a stability factor of about 1.5 with these pellets at subsonic velocities.... so that would indicate they are not over-stabilized.... in fact near optimum....
Here is the raw data for the 18.1 gr. JSB Heavies.... MV and BC (over 25 yards)
566 fps : BC = 0.030
710 fps : BC = 0.036
819 fps : BC = 0.040
899 fps : BC = 0.032
967 fps : BC = 0.027
1004 fps : BC = 0.022
Bob
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Bob just want to say I have enjoyed reading(really guess studying) the work you do with AGs, it is fantastic Brother having you around to drop these golden nuggets of knowledge(and formatting so its seeable/understandable) for us so we can find the gold mine in the use of our guns. THANK's for your work.
P.S. Hope you don't mind that I save most of your work to my files.
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Anyone is absolutely welcome to save any of my posts.... I do them to share my results with the airgun community.... When I started back into airguns 4 years ago when I retired I was frustrated by the lack of detailed information available.... Now, when I do an experiment or project I try and document it and share it.... Glad it helps....
Bob
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Excellent post, and very interesting! Really appreciate the information.
I look forward to any additional chonro work you do on this in the future!
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I can't test every possible combination, guys!.... JSB Exacts seem to work well in most of my guns in one weight or other.... that's why I tested them.... Anyone with a Chrony, some time, and some pellets can get in on the act.... You need to set up your Chrony at two measured ranges from the muzzle and fire 5-shot groups and record the average velocity.... I used 1 yard and 25 yards for most of my testing.... When you get into the area where the BC is really tanking then to get better data you really need to shorten up the range.... You could use as little as 5 yards or as much as 10 yards.... The problem is that the pellet loses so much velocity in the first 5 yards when it starts out near the speed of sound.... that if you measure it at 25 yards you are only getting an "average" and the calculated BC will be higher than it really is....
When you think about what is happening when you shoot at near sonic velocities.... it's pretty complex.... The BC starts out low and then increases.... If you shoot at really long range then it peaks and starts to fall again.... The actual trajectory will be more curved on the ends and flatter in the middle than the "average" value would indicate.... Some of the best FT shooters in Canada have remarked to me that they have observed this and previously didn't have an explanation until they saw my data....
Incidently, I tried an RWS 11.9 gr. Hobby that was just supersonic (1131 fps) just out of curiousity.... In just 5 yards, it lost 96 fps and the energy dropped from 33.8 FPE to 28.3 FPE... a loss of 16.3%.... The BC was a feeble 0.007....
Bob
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Well, even if you cannot test ever pellet.... still a good (excellent) post. :)
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Here are some Ballistics Coefficient measurements I did a couple of years ago.... The "Non-PAL" numbers are using a gun that shoots under 500 fps with "normal weight" pellet as required by Canadian law to not be classified as a Firearm and require a "Possession and Acquisition License".... They were done with Crosman pumpers (1389 / 2289).... The "PAL" numbers were done using a Diana 34 in .177 and a Crosman based PCP with regulator in .22 cal.... 5 shot groups were fired to collect the muzzle velocity and the velocity at 25 yards and then the BCs calculated using ChairGun....
(http://i378.photobucket.com/albums/oo221/rsterne/Important/BallisticsCoefficient177Cal.jpg)
(http://i378.photobucket.com/albums/oo221/rsterne/Important/Web177PALBalCoef.jpg)
(http://i378.photobucket.com/albums/oo221/rsterne/Important/BallisticsCoefficient22Cal.jpg)
(http://i378.photobucket.com/albums/oo221/rsterne/Important/WebPALBalCoef.jpg)
You will note that in general terms, wadcutter (flat nosed) pellets performed poorer at the higher velocities (ie the BC dropped).... while round nosed pellets had a better BC at the higher velocities than they did at under 500 fps.... Most pointed pellets were also not quite as good at the higher speeds with the notable exception of Predators.... The numbers in bold in the second set of data indicated that the BC improved at the higher velocities.... Note that there aren't that many pellets that did that.... This is not a comprehensive study of each type of pellet as there are only two velocity data points.... It clearly shows, however, that the BC of pellets is affected by the velocity....
Bob
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Thanks again for your work , very informative layout.
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Bob, very good post!
Thanks for the charts and data at the two different velocities !!! Great Stuff!
Solid data and science really help prove, or not, so many of the myths and "common knowledge" that gets passed around in many sports.
I have enjoyed you lessons on BC on this post and the other these last few days.
One question, maybe very much off track, keeps popping into my head.
My other pastimes are racing sailboats and flying RC sailplanes (gliders).
When self teaching the aerodynamics and hydrodynamics to design and build
the planes and the centerboards and rudders for my boats, there is a number
in the aero and hydo-dynamic world that may be the equalivent of BC, ...
...but I am not sure.
Are "Reynolds Numbers" used in BC calculations ?
They are a function of speed, form drag, viscosity of the fluid, and length of the object.
When reading your other post, I wondered if assuming the form drag would behave
the same in .177 vs .22 (for the same shape) would account for some of the BC
differences at different velocities. Given the same fluid (air); speed, viscosity, humidity,
pressure...etc, a larger cross section will have to have a higher drag.
In the airplane world, a 50k Reynolds Number might apply to a wing at 100 mph.
The same wing at 500 mph will have a RN in the millions, when calculating lift/drag ratios.
(not actual #'s in my example. Just foggy memories from years ago)
In water, a boats rudder might have the same 50k RN at 3mph. Viscosity really affects this number.
I also remember how the factor of RN affected my gliders preformance.
When practicing and tweaking trim, the gliders flew much better in winter temps
and humidity, than they did in summer temps and dryer air. One way the RN
factor was explained to me was that the thickness (# of air molecules for a given volume)
of the air improved the lift of the wings noticably. Drag would have also
been increased, but at the slower speeds was not as big a part of the RN calculation.
I wonder if the top FT and BR guys find the same issues with their accuracy in different air conditions ?
If you are a trained engineer, please forgive my layman's explaination.
Just trying to put outside experience into practice in my airgunning.
One of my scratch designed/built gliders placed in the top 10 at a Nationals in the '80's. My sailboat preformance in the last 15 years.....much better)
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I too spent much of my life doing R/C yachts and sailplanes.... in fact my business for 30 years was R/C racing yachts.... My designs have won a World Championships in 1980 and many US National Championships over the years.... I had a website which I tried to take down when I retired but couldn't contact the webmaster so it's still around if you want to take a look....
http://www.myrc.org/bobsterne.htm (http://www.myrc.org/bobsterne.htm)
Anyway, I'm VERY familiar with Reynolds Numbers.... but I never though of doing a calculation to see if there was something going on with pellets.... The critical Rn is 50,000 where all sorts of weird things change.... Sooooooooooo.... let's see where that happens with pellets.... Here is a calculator that will take into account all the possible atmospheric variables....
http://aero.stanford.edu/StdAtm.html (http://aero.stanford.edu/StdAtm.html)
It turns out that a pellet only 0.0158 ft. long (0.190") moving at 500 fps has a Reynolds Number of just over 50,000 (at sea level).... What that means, in practical terms for airgunners, is that most pellets will be moving fast enough to be above the critical Rn.... However, there are still signiifcant changes in how air flows past an object up to a Rn of about 400,000.... A pellet that is 0.75" long travelling at 1000 fps would have a Rn of about 400,000.... Therefore, significant changes in the flow around almost all pellets will exist at different velocities.... just not critical ones....
Bob
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Thanks for the Rn info for airgunning...I had a feeling you knew about them.
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Wow, excellent post. Thank you so much for the information.
Based on your information, I think I will try the JSB exacts (15.7 grain) as it looks like they may help me during my long range shooting (I do a lot of 50-70 yard stuff and have been shooting Premier Domed). Intersting how much better they are at high FPE (.037 vs .028) but it is actually slightly worse (.020 vs .022) at low velocities. I think overall though for my shooting, based on your data, they will be better. I would expect them to be at least as accurate as the Premiers but only one way to find out!
I am not sure they will have such a good BC in my 22-23 FPE Disco but should be fairly close. I may also try the 18.0 grain JSBs and Kodiak's... though fear shooting a pellet too slow at those ranges as it will be harder to compensate.
Thanks again!
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My Disco loved the 15.9 gr. JSB Exacts.... shot them at a whisker over 800 and they were the most accurate pellet in that rifle....
Bob
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I cannot wait to try them! I also cannot wait to get a chrono to play with... maybe for Christmas.
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Love the sharing of your impressive knowledge Bob and glad you chose this forum to educate. For the first time you've really got me thinking about the science behind the simple numbers i pull off a chrony and the science behind some of the best ammo available for our respective guns. Your posts are often simply brilliant.
Knew there was another reason i loved JSB's so much 8)
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Thanks for the kind words.... I love to learn and love to share....
Bob
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LOL I started a new folder and tagged it "Bob's AG Info", Thank's Bob great stuff!!!
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Since I wrote this post, I have learned a lot more about Ballistics Coefficients.... It turns out all they are is a comparison between the Drag Coefficient of your projectile at your velocity, with that of a "standard projectile".... Therefore, which standard you select will give a different result for the BC.... Currently, the best standard for Diabolo pellets at airgun velocities is the "GA" standard used in ChairGun.... Although the drag of the pellet still varies wildly with velocity, the BC is more constant because the model your pellet is compared to more closely represents what you are shooting....
I'm not sure of the Drag Model used by ChairGun in 2011 when I wrote this thread.... but judging by the shape of the curves in my data, I suspect it was a "constant drag" model.... which is about as far from reality as you can get.... If I duplicated the measurements today, using the more modern GA model, I would expect the BC to be more constant over a wider velocity range.... That doesn't mean the pellet doesn't slow down any less violently at Transonic velocities.... only that the model is now better....
Bob
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Given wind drift at the muzzle has the greatest external effect on trajectory: if a subsonic projectile's BC is highest between 600-800 fps, doesn't that mean the most accurate possible shots would start around said velocities rather than around 900 where most tune their .22s?
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Here is my "old" data (yep, still had the raw data), reworked using the new GA drag model in ChairGun.... It also incorporates my altitude of 2500 ft., which I did not allow for in 2011 (My calculated BC's were too high then).... The other thing that is different is that I plotted the BC vs the AVERAGE velocity between the muzzle and 25 yards, instead of using the MV.... This makes no difference in the results, just makes the BC match the velocities more accurately....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/JSB%20%20GA%20BCs_zpsywkwbmlu.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/JSB%20%20GA%20BCs_zpsywkwbmlu.jpg.html)
You can see the same trends, with the BC a bit higher in the mid-range and lower on the ends.... and the peak of the curve being at a lower velocity for lighter pellets.... but notice that the "range" of BC values is much tighter.... ie it varies less than on my original graph.... This shows that in the 6 years since I did my original work, the understanding of the drag model for Diabolo pellets has improved quite a bit.... For instance, for the 18.1 gr. JSB Heavies, my calculated range of BCs varied from 0.022-0.038, but now the range of BCs, over the same range of velocities, is much tighter, from 0.024-0.034.... If the drag model matched the JSB Exact series perfectly, then the BC for each pellet would be a constant over all velocities.... so there is still room for improvement in the GA model.... However, it is a LOT better than whatever was being used 6 years ago....
Bob
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Rick, that is a good observation, but there are several things to consider.... Generally, where you are most concerned about the effect of wind, you are shooting at longer ranges, and with heavier pellets, with a pretty decent BC.... Since the pellet slows a lot during it's travel to the target, you will want a muzzle velocity higher than the optimum, so that the pellet is spending more time closest to the optimum BC.... You are correct that the wind deflects the pellet more near the shooter, because that angle of deflection gets magnified all the way to the target, though, so that would lower the optimum velocity back towards where the lowest BC occurs....
If we use a Drift Calculator, and input various MVs, and using a constant windspeed from muzzle to target, we should be allowing for all those variables, if we simply graph the actual drift at the target range.... Here is such a graph for the 18.1 gr. JSB Exact, using the GA drag model at 50 yards....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Wind%20Drift%20JSB%2050_zpsio6vbeef.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Wind%20Drift%20JSB%2050_zpsio6vbeef.jpg.html)
Note that there is very little difference in total wind drift at 50 yards between 750 - 900 fps (about 0.1"), and even at 950 fps it is only 0.2" more than the minimum.... Since the trajectory flattens out significantly as you increase the velocity, I think that is a reasonable compromise.... Pushing 1000 fps MV and beyond, however, results in increasing wind drift.... What people don't realize is how good we have it, shooting at subsonic velocities, in terms of minimizing wind drift.... Here is a similar graph, for 200 yards, for four widely different BCs....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Wind%20Drift%20G1_zps5d7eem8a.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Wind%20Drift%20G1_zps5d7eem8a.jpg.html)
Note that in every case, the wind drift goes through a minimum at 900-1000 fps, and you have to drive any of the bullets between 2200-3200 fps to get back down to the same deflection.... Velocities of 1400-1800 fps have at least 30-50% more drift than the best case scenarios.... The greatest reduction in wind drift, however, comes from achieving a better BC....
Bob
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Fascinating. I figured the answer the answer would be along the lines of "no, you want more time near the apex of the BC", but that provided excellent insight. Thanks
Ted made an explaination on his win at EBR and said based on his research, faster pellets destabilize easier in unideal conditions.
https://youtu.be/TNONcrNmWDE (Skip to 7:52)
Do you know what causes this? Is it a phenomenon due to the Impact's design (strange harmonics when regulated at high pressure, etc.), or is there a general truth to this?
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Thank You rsterne.
That why I like coming to the airgun school.
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Rick, I see no reason for pellets to "destabilize" within a velocity range.... too slow, or too fast, for the twist rate of the barrel, then yes.... However, I can certainly see the accuracy being worse when the barrel harmonics are not aligned with the pellet velocity.... ie at the instant the pellet leaves the muzzle, is it in the middle of a vibration, moving quickly (small velocity change produces large departure angle change), or reversing at the end of a swing, and hence almost stationary (smaller groups).... Certainly if a pellet is spinning marginally too fast, when it loses forward speed (at longer range) it is now spinning too fast for the lower forward velocity.... This can lead to Dynamic Instability and spiraling, with consequently larger groups....
I suppose if a pellet is marginally stable (Gyroscopically or Dynamically) then a crosswind might send it over the edge?.... What is fascinating is how much vertical component a crosswind causes from two completely separate things.... "Aerodynamic Jump" (a sudden crosswind induced yaw, causing the pellet to pitch up or down) as it leaves the muzzle, and the "Magnus Effect" which causes a vertical force from spin in a crosswind.... Then of course there is also "Spin Drift" where the pellet effectively "rolls downwind", causing a different deflection right or left in the same strength wind.... The direction of all of these depend on twist direction and wind direction....
Bob
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Thanks Bob.
I spent a good while reading about what you talked on, and have been trying to calculate sample equations to prove to myself I understand out the concept of Aerodynamic Jump (using Don Miller's formula, atmospheric conditions normal to my home 70ft above sea level, and JSB .303 44.75).
I understand the premise in general, but I'm having a hard time calculating SG. I believe this is because twist rates are calculated for generic spitzers when using custom parameters on the programs I've tried, but I can't really be sure, and have no idea what the safe value of pellet gyroscopic stability.
Is airgun twist ratio science a manufacturer secret or am I just using the wrong programs? The more I try to find out about airguns, the more I realize how right you are about the rapid advancement in models/tech pertaining to them
NOW as far as the Magnus effect goes, pretty easy to understand the basic concept as it pertains to things like a baseball...but when it comes to actually calculating it..... LOL! Overwhelming. Is the Magnus effect something ultra accurate long range shooters (aka Canadians) actually calculate into shots, or something that is only considered when designing barrels to work efficiently with a specific projectile?
I feel like I should be paying you for the record. If only my high school physics teacher had done the entire course using air gun ballistics instead of hypothetical vehicles... lol. Thanks.
Rick
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Rick, I wouldn't even attempt to calculate Jump or Magnus (which depends on surface roughness, like dimples on a golfball).... so what you are attempting is wayyyyyyy beyond my abilities.... Good Luck !!!
You are correct, none of the ballistics programs I have seen allow for waisted (Diabolo) projectiles.... IMO, they need MUCH less twist rate, and in fact if you calculate the recommended twist using their length, I have a feeling many pellets will spiral because at that RPM you run into Dynamic Instability downrange.... If you want to read about that, try this link....
http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/stab.htm#Dynamic_stability (http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/stab.htm#Dynamic_stability)
If you back up to the Main Index on that site "How do Bullets Fly" (bottom left corner, the arrow with the bar above it).... there is LOTS of good stuff there....
Bob
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Bob, in reply #27 you said...." the "Magnus Effect" which causes a vertical force from spin in a crosswind"....
this is a common misconception.
Magnus force isn't due to a cross wind, it is generated because of yaw angle. Moreover, the equation for
the force magnitude has no crosswind term. HTH.
Ron
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I understood that it was the Magnus effect that was responsible for the lift on a golf ball due to it's backspin.... It is interesting that there can be a "yaw effect" on a sphere, resulting in a lift force.... Thanks for the clarification, Ron, apparently I still have a lot to learn.... If there is no "crosswind term", does that mean that the Magnus effect is the same in no wind, 100 mph wind from the right, or 100 mph wind from the left?....
Bob
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"..... If there is no "crosswind term", does that mean that the Magnus effect
is the same in no wind, 100 mph wind from the right, or 100 mph wind from the left?....
Yes......simply because it's a product of spin and yaw.......and not crosswind.
It takes less than one precession cycle for a gyroscopically stable projectile
to align it's coning motion axis with the relative wind vector. The time frame is
very short. Once that happens, the yaw angle is due only to precession and the
projectile no longer "sees" the crosswind with regards to Magnus. On the other
hand, golf balls/tennis balls and such don't have the same gyroscopic capability
and as a consequence will sail along with their spin axis at a nearly constant
angle relative to the initial flight path ......which is a whole different situation.
Ron
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I want to make sure I understand.... If the wind is XXX mph from the right, with a RH twist, the top of the bullet is rotating towards the wind.... as per this diagram....
http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig9.htm (http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig9.htm)
This results in a downwards Magnus force, according to that article.... I would assume that if the wind was from the left, the force would be upwards, would it not?.... If after travelling 50 yards, the wind shifted 180*, would not the trajectory change, due to the Magnus force shifting from down to up (or vice versa)?.... While the lift or depression of the trajectory may be technically due to "yaw", is not the original source of that yaw the FORCE acting on the bullet upwards or downwards, due to the Magnus effect?.... Does not the change in wind direction change the Magnus force from "down" to "up", which then causes the bullet to alter its yaw angle, which in turn changes its trajectory.... ie a chain of events, which STARTS from the up or down force on the bullet due to the Magnus effect of a spinning bullet in a crosswind?....
Further, from the same site....
http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig10.htm (http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig10.htm)
The Magnus force is applied at the Center of Pressure, which can either be at, behind, or forward of the CG.... If they are not aligned, this creates a Magnus moment about the CG, causing the bullet to pitch up or down.... depending on the direction of the Magnus force, and the position of the CP relative to the CG....
http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig11.htm (http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig11.htm)
This can stabilize (CG forward of CP) or destabilize (CG aft of CP) the bullet.... Further, since the CP moves around, the bullet may gain stability at one velocity and lose it at another.... What I did not realize is that in addition to a vertical component to the bullet trajectory, there is a horizontal component as well, due to the Magnus effect.... in addition to the yaw caused by the crosswind which produces our normal "downwind drift"....
or have I got it totally wrong?....
Bob
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Bob that is my understanding as well.
I'm sure the effect is incredibly minimal considering the smooth nature of projectiles, however it is definitely affected by the direction of wind flow relative to the axis and direction of spin.
That's a cool website you mentioned earlier. Makes me wonder if there is a perfect spin + projectile combo that could give stability through transonic speeds, yet not over stabilize (which would keep the projectile pointed up rather than down after the apex of trajectory.. if I understand right)
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Bob, you don't have it totally wrong but there is one key aspect that
you're not grasping. The diagrams and text in the link you provided.....
http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig9.htm (http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig9.htm)
are somewhat misleading, as are a number of other things on the site.
My personal preference is McCoy.......I'm sure you know that.
Perhaps a sketch will make things more clear. Pictured on the left are
the conditions when our bullet first encounters a crosswind.
V is the velocity due to forward motion
Vw is wind welocity
Vr is the resultant of these two and is what the bullet actually experiences.
As you can see it flys at a small angle of yaw. The bullet now will very quickly
adjust so as to align with the relative wind vector Vr as pictured on the
right. This behavior is a key part of gyro stability. Now the bullet no longer
experiences any side wind component ........there is no "yaw caused by crosswind".
The crossflow that generates Magnus force comes solely from the normal precessional
motion as the bullet corkscrews it's way down range. And, if you hadn't already guessed,
it's a rotating vector which affects dynamic stability by damping.
Ron
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OK, I get what's in the diagram, many thanks for that.... Now since a Gyroscope creates a force at 90* to any change in the position of it's axis (in this case yaw), does that mean there is a corresponding upwards (or downwards) pitch change in response to the crosswind as well?....
It's a difficult concept to grasp that even though the bullet in the diagram above is yawed into the crosswind (until it no longer see it).... it still drifts along with the wind at a rate governed by how quickly it is slowing down....
One thing remains unclear to me however.... Does the Magnus effect change the trajectory of the bullet?.... upwards in a crosswind from one side, and downwards from the other?.... or not?....
Bob
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I don't understand how it could be any other way. Consider Newton's third law. The spinning pellet is always going to be "pushing" air into uneven resistance unless in an airless vaccum. With increased wind speed, the Magnus is magnified because of the equal and opposite reaction of wind pushing air into the pellets turbulence. Granted the Magnus effect is constant even in a windless environment, wind direction has to be the determining factor in whether the Magnus is normal or inverse
This PDF explains it better than I can I'm sure. Let me know if I'm way off course
http://tfc.snu.ac.kr/jboard/file_down.php?tid=11&file_name=99.pdf&data_file=136_1407714252.pdf (http://tfc.snu.ac.kr/jboard/file_down.php?tid=11&file_name=99.pdf&data_file=136_1407714252.pdf)
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I have given thought to pellets and B.C. and since there are so many different pellets of differing nose shapes lengths and so on, the the only real accurate model to use with pellets would be a Custom Model for each based on real world result... could be from the manufacturers... but then they might not sell as many "gizmo pellets...
http://appliedballisticsllc.com/ballistics-educational-resources/custom-drag-curves/ (http://appliedballisticsllc.com/ballistics-educational-resources/custom-drag-curves/)
we should be able to develop drag profiles like from Harry's LabRadar generated cd plot in the .25 JSB MK II thread...
https://www.gatewaytoairguns.org/GTA/index.php?topic=124298.msg1264458#msg1264458 (https://www.gatewaytoairguns.org/GTA/index.php?topic=124298.msg1264458#msg1264458)
It sure would be more useful and not really that hard to do...
could be tested both ways long distance and at various muzzle velocities...
I personally right now am more interested in shifts in how much drag stabilization a pellet feels compared to the gyro stabilization at different speeds it looks to me to show up in the long vs short pellets in their B.C. curve also....
so
JSB Hemispherical .22
Length in calibers
Express 14.3
Exact J 15.9 1.4
Heavy 18.1 1.4
Monster 25.4 1.55
JSB .25
King 25.4 1.25
MK II 33.9 1.43
so I am borrowing a computational fluid dynamics model... I added the vertical lines are at 1 and 1.5 calibers the tail ends at 2 calibers... It is a drag model of a shotgun pellet at about 1000 fps pic is from this thread...
http://www.trapshooters.com/threads/pic-of-air-flow-and-force-on-a-moving-pellet.42053/ (http://www.trapshooters.com/threads/pic-of-air-flow-and-force-on-a-moving-pellet.42053/)
Now look at how the pellets skirt would ride in the low velocity bubble or not or partially not...at different speeds... that is if you think about double the speed quadruple the drag... then since at 1000 fps we serendipitously have a low velocity area 2 calibers long... so at 500 fps it is .5 calibers long and you can see that at slower speeds the skirt feel more drag... then is riding in turbulent air while more and more (cd falling and bc rising) then the shorter pellet the skirt is totally in the low velocity bubble and the drag on the head is rising... same happens to the longer pellets at a higher speed...
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Bob, you don't have it totally wrong but there is one key aspect that
you're not grasping. The diagrams and text in the link you provided.....
http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig9.htm (http://ffden-2.phys.uaf.edu/212fall2001_Web_projects/Isaac%20Rowland/Ballistics/Bulletflight/fig9.htm)
are somewhat misleading, as are a number of other things on the site.
My personal preference is McCoy.......I'm sure you know that.
Perhaps a sketch will make things more clear. Pictured on the left are
the conditions when our bullet first encounters a crosswind.
V is the velocity due to forward motion
Vw is wind welocity
Vr is the resultant of these two and is what the bullet actually experiences.
As you can see it flys at a small angle of yaw. The bullet now will very quickly
adjust so as to align with the relative wind vector Vr as pictured on the
right. This behavior is a key part of gyro stability. Now the bullet no longer
experiences any side wind component ........there is no "yaw caused by crosswind".
The crossflow that generates Magnus force comes solely from the normal precessional
motion as the bullet corkscrews it's way down range. And, if you hadn't already guessed,
it's a rotating vector which affects dynamic stability by damping.
Ron
Thank you All for all this educational discussion! I have nothing scientific or formulas to add, ;D , just an observation.
If the projectile is flying yawed isn't the bc drastically reduced for the remainder of the flight? Or does the yaw eventually auto correct due to bullet spin?
Thank you,
Taso
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Actually, Taso, the bullet is aligned with the wind that it is seeing at all times.... It may be yawed in relation to its path to the target, but it is always pointing into the "local wind" (in yachting you would call it the apparent wind), a combination of real wind and bullet motion.... This means that the bullet is always flying "point first" relative to the air surrounding it.... After the first instant when the crosswind hits it, the bullet turns into the apparent wind, and the wind no longer presses on the sides of the bullet.... The bullet drifts "downwind" in this "sea of air" as it travels to the target....
Bob
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"You are correct that the wind deflects the pellet more near the shooter, because that angle of deflection gets magnified all the way to the target"
Just wanted to clarify this so that those just beginning to study these concepts fully understand. The wind doesn't deflect the projectile most near the bore (when it is at maximum velocity) but it causes point of impact to move more at a distance relative to bore or point of aim due to the change in angle that the wind causes the projectile to follow. The same column of wind velocity will deflect the projectile less from 50 to 100 yards than it would from 450 to 500 yards. Any angle of deflection that occurs nearer the bore continues to add to projectile movement along its entire flight. But more time in any given wind speed will move the projectile more and it will spend progressively more time in that wind as it gets further from the bore (it's slowing rapidly). But the angle caused by the nearer deflection is a cumulative effect out to target distance.
Another way to think of it. Consider shooting at an Alka Seltzer tablet at 100 yards with a .204 Ruger (probably 4000 fps average MV over the 100 yard distance) in a 10 mph wind on flat terrain. You would have relatively less movement of the projectile and might not have the bullet move enough to miss with a center hold. Now shoot at the same Alka Seltzer tablet at 300 yards near the end of a canyon with no wind movement out to 200 yards but the same 10 mph wind velocity working from 200 to 300 yards (probably 2000 fps avg MV over that 100 yard distance). It's the same 100 yards of 10 mph wind body that the bullet must pass through as the nearer shot but you might well miss since the same wind speed would move the bullet relatively more due to it's slowed velocity.
This is the major issue with real world shooting. We can measure and quantify all the relevant factors discussed and we can know practically exactly the ballistic arc of our specific projectile. And if we have a wind speed meter in our hand we can determine wind speed and direction where we are standing. But knowing what the wind effect is at some distance from us is not even remotely quantifiable in most cases (assuming one does not have remote sensing instruments along the flight path).
One other factor to consider along with Magnus, spin drift, and the others that I haven't seen mentioned yet. Coriolis effect. The projectile is moving through the air. The target is (in most instances) on the ground. The rotation of the earth can move the target out of the line of flight of the projectile.
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Firstly, thank you to all contributors to this thread. I am now better informed and will read this yet again. Well done.
The trouble is now knowing about many but not all the variables, there is not a lot I can or want to do about them.
For the average back yard shooter I would suggest reading this but not get too concerned about it. Real life plinking dictates that the ordinary shooter will hit some and miss some so revel in the hits and ponder the misses and then have another go. A score of 100.10 on a small bore range would be an excellent achievement but really hard to score even in the controlled conditions.
As long as it is fun and interesting keep at it.
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Bob asks " Does the Magnus effect change the trajectory of the bullet?.... upwards in a
crosswind from one side, and downwards from the other?.... or not?...."
It doesn't change the trajectory, up or down, because it doesn't "see" the crosswind.
Is it possible that folks are confusing Magnus with aerodynamic jump?
Ron
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Your clarification may, or may not apply to airguns, although for the most part it would apply to a high velocity CF rifle bullet, which as it slows is deflected more by the wind.... An airgun, because it is shooting in the Transonic and Subsonic ranges, might actually see LESS wind deflection between, say 75-100 yards, than between 0-25 yards.... This would certainly be the case if the muzzle velocity is around or over 900 fps.... The fact remains that once it is deflected by a wind between 0-25 yards, it carries that ANGLE of deflection all the way to the target, and it would require more wind in the opposite direction downwind to bring it back to the POA.... In the simple case, where the Cd is constant from muzzle to target, this is the result if the wind shifted 180 deg. (from 3 o-clock to 9 o-clock) at the 50 yard point, at the same velocity.... (chart is top view)....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Windage%204_zpsrfsn9jh1.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Windage%204_zpsrfsn9jh1.jpg.html)
In reality, if the pellet started out at 1000 fps, and by the time it reached 100 yards was down to 700 fps.... the deflection in the first 50 yards (Cd higher) would be even greater, while the deflection in the last 50 yards (Cd lower) would be less.... resulting in the impact even further to the left than on that chart....
The "Coriolis effect" actually has two components.... a vertical one (Eotvos effect), because gravity is slightly less at high altitude, causing bullets shot towards the east to hit higher than ones shot to the west (greater effect at the equator).... and a horizontal one, that shows up when shooting to the north or south, because the surface of the earth rotates out from under the trajectory (greater effect at the poles).... For CF rifles, both are nearly insignificant (< 0.4 MOA) at ranges less than 1000 yards, but the lower velocity of an airgun (longer time to target) may make these somewhat important at less range than that (300 yards?).... I would personally rank this as EXTREMELY UNIMPORTANT compared to other reasons to miss your target.... I actually did a chart a while back on potential error factors and plotted them vs. range....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Trajectory%20Errors_zpsyjgic01f.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Trajectory%20Errors_zpsyjgic01f.jpg.html)
If your rifle is capable of 1 MOA, that itself introduces a possible error of 1" at 100 yards.... If your velocity string has a 4% ES, that can induce a vertical dispersion of about 1.4".... If you make a 2% error in estimating the range (ie 98 yards or 102 yards) that introduces a vertical error of about 1.6".... and a 2 mph wind can cause the pellet to drift about 1.8".... (all these depending on BC and velocity of course, but relatively speaking).... With such relatively large errors already built into airgunning, it is amazing we can shoot as well as we do.... ::)
Bob
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Ron, you're probably right.... Jump does indeed cause a vertical deflection as the bullet leaves the muzzle in a crosswind, that much I understand.... I would assume a "similar" effect must occur if the crosswind does not occur until the bullet has already travelled, say, 10 yards?.... or is there only a vertical deflection if there is a crosswind present AT THE MUZZLE, and if so, why would that not occur further downrange?....
Let me ask you this.... Compared to a trajectory in a complete absence of crosswind.... what would the trajectory do with the following (admittedly extreme) wind profile?....
Muzzle to 25 yards no wind.... MV 1000 fps....
25 to 50 yards, 100 fps wind from 3 o'clock....
50 to 75 yards, 100 fps wind from 9 o'clock....
75 to 100 yards, no wind....
What would the bullet be doing, relative to its "no wind" trajectory, in each segment as it travels downrange?.... I'm talking vertical deflection only here, not drift.... I don't expect hard numbers, just a description of what the bullet is doing, and how the vertical trajectory differs in the two cases....
Bob
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You are certainly correct about the dual coriolis effect-haven't thought about that aspect in years. Also right about it being extremely insignificant in "real world" terms. But so are BC, Magnus, spin drift, and all the others discussed. You can probably never give any of them a second thought and it would not effect shooting a pellet once you had chosen one.
The angle issue is also correct, assuming you had a way to verify that the wind was constant downrange (which it almost never would be in actual shooting conditions).
As to the wind drift issue we'll have to disagree. You may be entirely correct but I can't see the wind drift ever being less at any time as velocity is falling (again making the large assumption that the wind is always constant). Seems to me that almost any pellet would be more affected than almost any rifle bullet. As noted, I could be wrong. In any event, a very comprehensive body of information you have compiled. Have a Happy 4th of July.
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bandg.... I'll refer you back to Reply #24 for a detailed explanation of wind drift vs. muzzle velocity.... The drag coefficient of any projectile peaks at around Mach 1.2, so above that your "more velocity, less drift" is correct.... below that, not so much....
(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)
Bob
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Still disagree Bob. Am I incorrect in assuming that drag coefficient is related almost entirely to velocity loss? Please enlighten me on how this relates to physical lateral movement imparted by a body of air moving perpendicular to the flight path.
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Gentlemen,
I have a request. Could all the previously mentioned effects be listed in order of severity of bc change relating to air rifle velocities and ranges?
Maybe two lists, one for diabolo pellets and the other for non-diabolo lead bullets/slugs whichever the proper name is?
I think the biggest effect would be drag from the diabolo waist.
Taso
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The wind drift is proportional to the "lag time", which is the difference in flight time between the real world and in a vacuum.... So yes, the higher the Cd, the greater the velocity loss, and the greater the lag time and hence wind drift.... There are many good sources to understand this, the best probably Brian Litz' book on Applied Ballistics.... I realize this is a difficult concept to accept, but is in fact the case.... Here is a link from Sierra Bullets that explains it....
http://www.exteriorballistics.com/ebexplained/4th/532.cfm (http://www.exteriorballistics.com/ebexplained/4th/532.cfm)
HTHs....
Bob
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Taso, the Ballistics Coefficient of a bullet has two major components, the Sectional Density and the Form Factor.... You are correct that Diabolo pellets tend to have a poorer FF (greater drag) than a bullet.... However, since BC = SD / FF a heavy pellet could in fact have a better BC than a light bullet in the same caliber.... While a list would be a good idea, I think it might have to be too "specific" to a particular pellet or bullet to be of much use....
Bob
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Bob,
How much do Coriolis, Bernoulli, Magnus, earth rotation etc. effects really effect a pellet shooter? Wouldn't the shuttle cock/drag stabilization of waisted pellets cancel out or minimize the aforementioned effects?
Thanks,
Taso
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I think they have very little effect.... Aerodynamic Jump certainly has an effect (which I guess I was blaming on Magnus), because you can see pellets hit higher or lower depending on if the wind comes from the left or right.... That causes this effect for different crosswind directions.... Notice that with the wind at 3 o'clock the pellet hits low, and with it at 9 o'clock it hits high.... with the most "unexpected POI" occurring when the wind is at 4:30 or 10:30....
(http://i378.photobucket.com/albums/oo221/rsterne/Ballistics/Pellet%20Drift%20Chart%2012%20FPE%203%20mph%2025m_zpsikrbnsvd.jpg) (http://s378.photobucket.com/user/rsterne/media/Ballistics/Pellet%20Drift%20Chart%2012%20FPE%203%20mph%2025m_zpsikrbnsvd.jpg.html)
My understanding is that rimfire bullets and pellets react oppositely, even if they have the same twist direction.... I would suspect that is because with a rimfire bullet, the CP is ahead of the CG, while with a Diabolo pellet it is behind.... causing the opposite "jump" in pitch to occur....
In the lower chart in Reply # 44 above I tried to quantify various major error factors.... IMO, the greatest variable is the wind, and unless you are shooting at known range (eg. target) the next greatest variable is your ability to estimate the range to target.... The ES of your rifle, if small enough for the range you are shooting at, can largely be eliminated as a major concern, as it can usually be brought down to the point that the MOA capability (basic accuracy) of the gun itself overwhelms it.... "Jump" is a factor of the wind, and the other factors (Magnus, Coriolis, etc.) are so minor I think they are insignificant, certainly at all normal airgun ranges.... Bullets can stand more windspeed before the drift becomes as important as it is with a pellet....
Bob
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Using bullets, ie spin stabilized ...... and considering
only the effect of aerodynamic jump
A) Muzzle to 25 yards no wind.... MV 1000 fps....
B) 25 to 50 yards, 100 fps wind from 3 o'clock....
C) 50 to 75 yards, 100 fps wind from 9 o'clock....
D) 75 to 100 yards, no wind....
A) no vertical deflection from crosswind
B) bullet gets a one time upward modification to the
existing flight path as it enters this segment of travel
C) bullet gets a one time downward modification to the
existing flight path as it enters this segment of travel
D) same as B
Ron
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Thanks, Ron.... exactly as I figured.... So if the velocity was constant, with each segment being the same 25 yd. length, the POI would be (nearly) the same as without any wind, because the angular change upwards in bullet path at 25 and 75 yards would be the same, and that at 50 yards downwards would be twice as great?.... The trajectory would be identical from 0-25 yards and 75-100 yards, but with a "peak" in the middle at 50 yards.... more or less....
This also means that if the crosswind is constant from muzzle to target, relative to the no-wind trajectory there would only be one "jump" near the muzzle, and the new path would diverge from the original by a constant angle.... This is completely different from the sideways drift, which keeps increasing all the way to target if the wind is constant, the angle of divergence continually increasing (in a parabola?)....
Bob