Yaw Induced BC changes.

One of the things which often gets mentioned is that pellet wobble will affect the BC of a pellet, leading to large differences in measured BCs. I have never been comfortable with this simple and logical conclusion, the reason being that, while pellet wobble will affect BC values, it also affects a whole lot of other things in the pellet flight which should make it obvious. I have never seen anyone mention seeing anything about strange about their pellet’s behaviour when low BCs have been measured.

Since firing pellets with a known yaw angle to get consistent wobble is rather difficult, I used the usual easy way out of the problem by modelling the effects. The trajectory program is the usual one I use on pellets with the same data from the 15.9 grain .22 AA Field pellet. The modelling was simple with trajectories calculated for pellet yaw angles from zero up to ten degrees in two degree steps, with a muzzle velocity of 850 ft/sec. I took readings for the velocity at 30 and 50 yards along with the calculated error in the pellet position at the same ranges. I then used Chairgun for each range to calculate the average BC based on the calculated velocity.

The first figure shows the calculated velocity drop in ft/sec over 30 and 50 yards for each yaw angle.

yawbc1.jpg


The figure below shows how the calculated BC varies with yaw angle for both the 30 and 50 yard ranges.

yawbc2.jpg


So there is a demonstrable effect on the value of BC from pellet yaw angle. In this case, the value fell from .029 with no yaw down to .023 with ten degrees of yaw. So far so good.
Below is a graph of the pellet impact point error in inches at 30 and 50 yards range for the different yaw angles.

yawbc3.jpg


Group size can be expected to be twice the error value, as the error can be in any direction. Now, I think that most shooters would notice a group size of 34 inches at 50 yards range. Even a four-inch group size would be considered completely unacceptable, but you can get that with just over one degree of yaw at 50 yards, two degrees of yaw at 30 yards. Yaw angles of one or two degrees made no difference to the calculated BC value. For those who don’t like graphs, the table below sums the results.

yawBC4.jpg


So the problem I have is that you cannot have a yaw angle large enough to cause a measurable change in BC without having a large error at the target, in many cases too large for the pellet to be in any way usable. All the work I have done in the past suggests that pellet angles have to be below one degree for an acceptable group size. My feeling is that the reason for BC variations is far more complex than some pellets having more yaw (wobble) than others.

The modelling may have errors in it, however the most important variables have been derived from experimental results. The fact is that even if the modelling is 50% in error, it still seems unlikely that pellet wobble which is sufficient to cause significant differences in BC will not produce large errors and groups at the targets.
 
Are you using the physics definition of ballistics coefficient?


If so, there's a clear link, as cross-sectional area is explicitly mentioned in the definition. If the projectile wobbles, that cranks its cross-sectional area up.
First of all, forget most of the things Wikipedia tells you about external ballistics.

BC is based on sectional density and form factor. Sectional density is defined as mass in pounds divided by projectile calibre in inches squared, so the projectile area does not come into it.

The drag increase when a projectile yaws at subsonic speeds is not because of any area increase, that is not how subsonic aerodynamics work. Subsonic aerodynamics work through the low pressures generated on the leeward side when the air flows around the projectile, not the pressures on the windward side. Windward side pressures only come to dominate at hypersonic speeds. The drag increase with a subsonic projectile at yaw is caused by the normal force generating a component in the drag force direction. I show normal forces as opposed to lift and drag forces in the OP on pellet stability.
 
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First of all, forget most of the things Wikipedia tells you about external ballistics.

BC is based on sectional density and form factor. Sectional density is defined as mass in pounds divided by projectile calibre in inches squared, so the projectile area does not come into it.

The drag increase when a projectile yaws at subsonic speeds is not because of any area increase, that is not how subsonic aerodynamics work. Subsonic aerodynamics work through the low pressures generated on the leeward side when the air flows around the projectile, not the pressures on the windward side. Windward side pressures only come to dominate at hypersonic speeds. The drag increase with a subsonic projectile at yaw is caused by the normal force generating a component in the drag force direction. I show normal forces as opposed to lift and drag forces in the OP on pellet stability.

I was asking you what definition of ballistic coefficient you are using. This seems like a non-answer.
 
I was asking you what definition of ballistic coefficient you are using. This seems like a non-answer.
There is only one definition of ballistic coefficient, and I have told you what is used in all calculations. I have also pointed out a fundamental mistake in your assumption that a yawing projectile has a bigger reference area with pressures acting on it.

As I said, cross-sectional area is not used in the BC calculations, it is the projectile calibre squared, so Wikipedia cannot even get that right. But even if Wikipedia was correct, you will still use the same area value irrespective of what the yaw angle is, otherwise BC would be impossible to use with a yawing projectile without a complex trajectory model. That Wiki article is mainly a historical article, full of assumptions used in the past which no one would dream of using now. In fact, no one should be using ballistic coefficients at all, particularly for long range shooting.

Perhaps the Wiki article was written by a physicist rather than an aerodynamicist, the two are not the same. ;)
 
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One of the things which often gets mentioned is that pellet wobble will affect the BC of a pellet, leading to large differences in measured BCs. I have never been comfortable with this simple and logical conclusion, the reason being that, while pellet wobble will affect BC values, it also affects a whole lot of other things in the pellet flight which should make it obvious. I have never seen anyone mention seeing anything about strange about their pellet’s behaviour when low BCs have been measured.

Since firing pellets with a known yaw angle to get consistent wobble is rather difficult, I used the usual easy way out of the problem by modelling the effects. The trajectory program is the usual one I use on pellets with the same data from the 15.9 grain .22 AA Field pellet. The modelling was simple with trajectories calculated for pellet yaw angles from zero up to ten degrees in two degree steps, with a muzzle velocity of 850 ft/sec. I took readings for the velocity at 30 and 50 yards along with the calculated error in the pellet position at the same ranges. I then used Chairgun for each range to calculate the average BC based on the calculated velocity.

The first figure shows the calculated velocity drop in ft/sec over 30 and 50 yards for each yaw angle.

View attachment 507913

The figure below shows how the calculated BC varies with yaw angle for both the 30 and 50 yard ranges.

View attachment 507914

So there is a demonstrable effect on the value of BC from pellet yaw angle. In this case, the value fell from .029 with no yaw down to .023 with ten degrees of yaw. So far so good.
Below is a graph of the pellet impact point error in inches at 30 and 50 yards range for the different yaw angles.

View attachment 507915

Group size can be expected to be twice the error value, as the error can be in any direction. Now, I think that most shooters would notice a group size of 34 inches at 50 yards range. Even a four-inch group size would be considered completely unacceptable, but you can get that with just over one degree of yaw at 50 yards, two degrees of yaw at 30 yards. Yaw angles of one or two degrees made no difference to the calculated BC value. For those who don’t like graphs, the table below sums the results.

View attachment 507916

So the problem I have is that you cannot have a yaw angle large enough to cause a measurable change in BC without having a large error at the target, in many cases too large for the pellet to be in any way usable. All the work I have done in the past suggests that pellet angles have to be below one degree for an acceptable group size. My feeling is that the reason for BC variations is far more complex than some pellets having more yaw (wobble) than others.

The modelling may have errors in it, however the most important variables have been derived from experimental results. The fact is that even if the modelling is 50% in error, it still seems unlikely that pellet wobble which is sufficient to cause significant differences in BC will not produce large errors and groups at the targets.
Nicely presented analysis.

Can actual yaw be measured using high speed cameras? (Or have I watched too many episodes of Mythbusters?). I imagine a Labradar combined with high speed video could get both yaw and ballistic data out to at least 50y.

I suspect it would take exceptionally detailed and crisp photos to detect yaw in the required fractions of a degree.
 
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There is only one definition of ballistic coefficient, and I have told you what is used in all calculations. I have also pointed out a fundamental mistake in your assumption that a yawing projectile has a bigger reference area with pressures acting on it.

What definition of Ballistics Coefficient are you using? Yes, you have told us what inputs you are using, but you have not told us what definition you are using.
 
Nicely presented analysis.

Can actual yaw be measured using high speed cameras? (Or have I watched too many episodes of Mythbusters?). I imagine a Labradar combined with high speed video could get both yaw and ballistic data out to at least 50y.

I suspect it would take exceptionally detailed and crisp photos to detect yaw in the required fractions of a degree.
There is a system called flight follower which can take film of bullets in flight showing yaw behaviour which should be able to do it for pellets, if you have the odd £25000 to hire it.
 
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