Ballistics Coefficients Changing with Velocity

[Jay]

LOL I started a new folder and tagged it "Bob's AG Info", Thank's Bob great stuff!!!

[rsterne]

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

[PelletsForPests]

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?

[rsterne]

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....



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

[rsterne]

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....



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....



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

[PelletsForPests]

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.
(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?

[Jr007]

Thank You rsterne.

That why I like coming to the airgun school.

[rsterne]

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

[PelletsForPests]

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

[rsterne]

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

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

[rgb1]

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

[rsterne]

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

[rgb1]

"..... 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

[rsterne]

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

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

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

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

[PelletsForPests]

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)

[rgb1]

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

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

[rsterne]

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

[PelletsForPests]

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

[K.O.]

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/

 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

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/


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...

[Taso1000]

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

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,     , 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