Wind drift - theory vs reality

[Keith Glasscock]

I have watched intently as a variety of discussions have drifted toward a single question:

Do we really know how BC and wind drift interact?

Background:

In reading several volumes written by Bryan Litz, I've found that the operative method for determining BC is to plot the drag function by measuring the residual velocity at varying distances from the muzzle (Doppler, downrange chronograph, etc.). By assessing the residual velocity, a model is created of the bullet's velocity retention behavior. From this model, the BC of the bullet is derived.

The theory on wind drift, as calculated by many ballistic calculators, is that the lag time determines the wind drift. However, there are a number of substantial accounts of bullet behaviors that do not follow the lag time model. Some theorize that the bullet mass is an unaccounted for component of the bullet's wind-drift performance. I might suggest one more variable - wetted area.

Since it is virtually impossible to fire a bullet over a long distance and have adequate datapoints as to the exactly air velocities all along the range, comparative testing seems to be the only way to economically ascertain the actual differences between bullets.

Is anyone doing, or has anyone done real-world, side-by-side , simultaneous fire testing?

 

[Papa Charlie]

Keith, are you suggesting that the greater the surface area of the bullet the greater the impact impact on the bullet from the environment as it travels along the path?

 

[tvaught]

Is anyone doing, or has anyone done real-world, side-by-side , simultaneous fire testing?

How would you conduct a valid "side by side" test without the use of a closed/constant test environment ie wind tunnel?

How could you possibly eliminate enviro noise from your test results?

 

[Keith Glasscock]

The concept of simultaneous fire would allow the bullets to generally encounter the same conditions.

For example, one could fire a significant number of simultaneous shots from two rifles over a period of time that allows the wind to change significantly.

Then an assessment could be made about differences in wind drift between the two bullet designs. From there, assertions could be made regarding the likelihood that our current wind drift math is valid.

 

[dcali]

BC accounts for weight already (and the various components of drag- including skin friction). The myth that heavy bullets with equal BC will have materially different wind performance is just that - a myth.

The only things that matter are BC and muzzle velocity. The G7 model is a very good fit for our bullets at realistic supersonic velocities. Once you hit transonic, things get different, but that’s still not a BC thing. It’s just the limits of standard drag models.

Why are people so loathe to believe this when they are perfectly fine using BC as as an accurate predictor or drop? Both wind and drop are drag phenomena. I think it’s because we are poor judges or wind and we think we see things that we don’t. Simple as that. To believe otherwise is to doubt some fundamental laws of physics. We’re taking F=ma level stuff.

 

[Keith Glasscock]

Interesting opinion.

I appreciate your input.

The question was whether anyone has or is doing real-world testing to validate the BC to wind drift relationship?

 

[dcali]

Yes, there has been tons and tons of testing validating the application of drag models to flight trajectories in all kinds of conditions.

 

[Ballisticboy]

The maths regarding projectiles behaviour in cross winds is already extremely well tested and proven in large, medium and small calibre weapons. In fact down wind drift is considered to be one of the most accurate calculations in ballistic modelling. Having said that though there are a number of problems in comparing calculated and observed behaviours.
One of the first error sources is the use of BC. No matter which reference drag law is used it will never be an exact match to the actual drag law for which ever bullet you are using. The differences may be small or large in some conditions but you will need to use a purpose made drag law for the bullets you are firing to eliminate this error. Even then the drag will vary from bullet to bullet, I have seen drag coefficient differences of +/- 10% or more on some bullet designs. On top of this there will be some bullet mass variability as well which will further complicate matters.
The lag time method assumes the bullet immediately turns into the combined air flow (zero yaw position) and stays pointing in that direction. In real life of course this does not happen and there will be some induced yawing of the bullet about its zero yaw position. This will lead to some movement of the bullet about its trajectory (heave and swerve) which will move the POI in one direction or the other. Depending on the wind and bullet speeds this movement of the POI may be very small but may combine with other accuracy problems.
As has been pointed out though the biggest problem in any tests is knowing what the wind is doing at any one time both at different ranges and at different times. I have obtained records of wind speeds and directions measured every second over one hour time periods and the variation from one second to the next can be significant. The average wind speeds on the day were not particularly high 5 to 10 mph but the speeds could easily change by 3-4 mph every second with 20-30 degree direction changes.
One proof of the theory is with rockets. A rocket with a sustainer motor will have no wind drift where as a rocket with a high thrust boost motor will drift upwind. Both effects have been observed and well documented over the years.

 

[Lbart]

Interesting opinion.
I appreciate your input.
The question was whether anyone has or is doing real-world testing to validate the BC to wind drift relationship?

Keith, I and some friends did a non scientific test back in 2006 comparing the 6.5/7 and 30 cal bullets. It was published in the April 2007 Precision Shooting magazine.
The test was limited to 14 shots for each cal. in summery the 7 won by a small margin. I would love to see a test of this nature done again. Wind speeds were calculated to be from 12-23 mph.

 

[chromatica]

With a background in physics and engineering, I thought I’d take a stab at answering this question. Pour yourself a cup of coffee and sit down…

Modern day ballistics calculators do not calculate wind deflection based on the lag time as you described. They calculate the three dimensional forces on the bullet at every point along its trajectory. These forces include gravity, drag, lift, and the coriolis force. (Some advanced products include angular momentum but let’s ignore that for the moment). Right now we will also ignore lift and the coriolis force and focus only on gravity and aerodynamic drag.

Velocity is expressed as a vector with three different components Vx along the axial direction (downrange direction), Vy along the lateral direction (drift), and Vz along the vertical direction (drop). [Some authors choose Vy in the vertical direction and Vz in the lateral direction.] When a bullet leaves the muzzle of a level barrel at 2700 fps, Vx = 2700, Vy = 0, and Vz = 0. Downrange however, the bullet picks up vertical velocity as it drops and picks up horizontal velocity as it responds to a crosswind. In the old days a “Flat Fire” assumption was used to simplify the problem, namely that Vy and Vz were always so small that they could be ignored. This was a helpful approximation before the days of computers. With the advent of computers and now that ELR shooting is now a possibility, the Flat Fire approximation is not only a hindrance but it leads to the wrong answers.

The bullet in flight senses a flow field that is a composed of its forward motion combined with the external wind. The aerodynamic drag on a bullet can also be expressed as a vector with three components ion the x, y, and z directions. There is an equation in physics to describe the force that a body feels when it is in the midst of a flow field. That equation is:

F = ½ rho V^2 Cd A

where V is the total magnitude of the velocity of the air rushing past it

rho is the density of the air
Cd is the coefficient of drag
A is the frontal area of the bullet

In the example of a bullet leaving a barrel in level flight, V = 2700 fps. If there is no wind, then all of the air flow felt by the bullet is in the x direction and all of the drag is also in the x direction. However, downrange this is no longer the case. The bullet begins to pick up z velocity from the action of gravity. This z velocity then leads to drag in the z direction (that counteracts the force of gravity). With a little geometry you can convince yourself that the drag resolves into three components:

Anywhere along the trajectory, the drag force can be expressed as:

Fx = - ½ k Vx V
Fy = ½ k (W - Vy) V
Fz = - ½ k Vz V

Where W is the magnitude of the pure crosswind.

If we want to include the force of gravity, then:

Fz = - ½ k Vz V – m g
Where m is the mass of the bullet
g is the acceleration of gravity

In level flight, at the muzzle, the equations become:
Fx = - ½ k (2700 fps)^2
Fy = 0
Fz = - mg

Now let’s add wind to the physics. If there is a pure crosswind coming from the left t 10 mph (14.66 fps), the bullet aligns itself so that the nose is facing into the oncoming flow. We say that the bullet is “weathervaning” into the apparent wind. The nose will face a direction slighty to the left of the target. The bullet begins to feel a drag in the y direction as well as in the x direction immediately after leaving the barrel.

Again at the muzzle, the total force on the bullet (drag plus gravity) becomes:

Fx = - ½ k (2700 fps)^2
Fy = ½ k 14.66 fps * 2700 fps
Fz = - m g

As soon as the bullet leaves the muzzle, it begins to slow down. Vx will continue dropping below its initial 2700 fps. However, the bullet starts picking up velocity in the y direction from the force of the wind and begins to drift off to the right. The projectile will also begin to feel drag in the y direction due to its newly found y velocity. And it picks up velocity in the z direction from the action of gravity.

Newton’s famous equation is F = ma (or a = F/m). If you divide these forces by that we have quantified by the mass of the bullet, then you have the acceleration of the bullet at any instant along its trajectory. Modern day calculators know how to solve these equations by taking small steps (often .001 seconds) and calculating the forces, acceleration, velocity and position at the end of each time step. The position in the y direction at any point along the trajectory describes the wind deflection and can be expressed in any unit of length.

If I haven’t totally confused everybody, I’ll explain the relationship of the coefficient of drag (Cd) to BC in a future post…

 

[M995]

So if I understand this correctly. The bearing surface works as a wind vain & pushes the nose into the wind. If that's the case, it explains why wind drift really isn't linear.

 

[Keith Glasscock]

Yes, there has been tons and tons of testing validating the application of drag models to flight trajectories in all kinds of conditions.

That is excellent news. Would you be kind enough to direct me to some that directly address equal BC with different masses? I’m curious what was found.

 

[dbduff]

With a background in physics and engineering, I thought I’d take a stab at answering this question. Pour yourself a cup of coffee and sit down…

Modern day ballistics calculators do not calculate wind deflection based on the lag time as you described. They calculate the three dimensional forces on the bullet at every point along its trajectory. These forces include gravity, drag, lift, and the coriolis force. (Some advanced products include angular momentum but let’s ignore that for the moment). Right now we will also ignore lift and the coriolis force and focus only on gravity and aerodynamic drag.

Velocity is expressed as a vector with three different components Vx along the axial direction (downrange direction), Vy along the lateral direction (drift), and Vz along the vertical direction (drop). [Some authors choose Vy in the vertical direction and Vz in the lateral direction.] When a bullet leaves the muzzle of a level barrel at 2700 fps, Vx = 2700, Vy = 0, and Vz = 0. Downrange however, the bullet picks up vertical velocity as it drops and picks up horizontal velocity as it responds to a crosswind. In the old days a “Flat Fire” assumption was used to simplify the problem, namely that Vy and Vz were always so small that they could be ignored. This was a helpful approximation before the days of computers. With the advent of computers and now that ELR shooting is now a possibility, the Flat Fire approximation is not only a hindrance but it leads to the wrong answers.

The bullet in flight senses a flow field that is a composed of its forward motion combined with the external wind. The aerodynamic drag on a bullet can also be expressed as a vector with three components ion the x, y, and z directions. There is an equation in physics to describe the force that a body feels when it is in the midst of a flow field. That equation is:

F = ½ rho V^2 Cd A

where V is the total magnitude of the velocity of the air rushing past it

rho is the density of the air
Cd is the coefficient of drag
A is the frontal area of the bullet

In the example of a bullet leaving a barrel in level flight, V = 2700 fps. If there is no wind, then all of the air flow felt by the bullet is in the x direction and all of the drag is also in the x direction. However, downrange this is no longer the case. The bullet begins to pick up z velocity from the action of gravity. This z velocity then leads to drag in the z direction (that counteracts the force of gravity). With a little geometry you can convince yourself that the drag resolves into three components:

Anywhere along the trajectory, the drag force can be expressed as:

Fx = - ½ k Vx V
Fy = ½ k (W - Vy) V
Fz = - ½ k Vz V

Where W is the magnitude of the pure crosswind.

If we want to include the force of gravity, then:

Fz = - ½ k Vz V – m g
Where m is the mass of the bullet
g is the acceleration of gravity

In level flight, at the muzzle, the equations become:
Fx = - ½ k (2700 fps)^2
Fy = 0
Fz = - mg

Now let’s add wind to the physics. If there is a pure crosswind coming from the left t 10 mph (14.66 fps), the bullet aligns itself so that the nose is facing into the oncoming flow. We say that the bullet is “weathervaning” into the apparent wind. The nose will face a direction slighty to the left of the target. The bullet begins to feel a drag in the y direction as well as in the x direction immediately after leaving the barrel.

Again at the muzzle, the total force on the bullet (drag plus gravity) becomes:

Fx = - ½ k (2700 fps)^2
Fy = ½ k 14.66 fps * 2700 fps
Fz = - m g

As soon as the bullet leaves the muzzle, it begins to slow down. Vx will continue dropping below its initial 2700 fps. However, the bullet starts picking up velocity in the y direction from the force of the wind and begins to drift off to the right. The projectile will also begin to feel drag in the y direction due to its newly found y velocity. And it picks up velocity in the z direction from the action of gravity.

Newton’s famous equation is F = ma (or a = F/m). If you divide these forces by that we have quantified by the mass of the bullet, then you have the acceleration of the bullet at any instant along its trajectory. Modern day calculators know how to solve these equations by taking small steps (often .001 seconds) and calculating the forces, acceleration, velocity and position at the end of each time step. The position in the y direction at any point along the trajectory describes the wind deflection and can be expressed in any unit of length.

If I haven’t totally confused everybody, I’ll explain the relationship of the coefficient of drag (Cd) to BC in a future post…

 

[dbduff]

This is why this site is so cool. While I don't begin to understand 90 percent of what have discussed, the fact that you will take the time and effort to use your expertise to describe how bullets react to wind variances is just superlative. Thanks so much. I shot today in 20-40 mph gusts at,300, 200 and 100. I can relate!

 

[Ballisticboy]

So if I understand this correctly. The bearing surface works as a wind vain & pushes the nose into the wind. If that's the case, it explains why wind drift really isn't linear.

Not really as bullets are generally aerodynamically unstable with the centre of aerodynamic pressure somewhere on the nose. It is the gyroscopic response to the aerodynamic moment from the aerodynamic force on the bullet nose which causes the bullet to turn to face the combined air flow. The wind drift is not linear because the component of the drag force acting in the wind direction is working continously throughout the trajectory increasing the down wind drift speed.

 

[dcali]

That is excellent news. Would you be kind enough to direct me to some that directly address equal BC with different masses? I’m curious what was found.

I don't think anyone would do that exact test, because there wouldn't be much of a point. We already know the impact of drag on trajectory and we know the impact of weight. They're independent of each other - one is the F and the other is the M in F=MA. So specifying a combination of drag and weight (a BC, in other words) that exactly matches that of a different weight and drag doesn't tell you anything that you didn't already know - that A will be the same. It's inherent in the definition of BC. That's the math angle.

But another way to put it is that if there is a difference in trajectories between two bullets with identical BCs and muzzle velocities, there must be a force acting on one of them that is not acting on the other, and it has to be something that isn't accounted for in a drag function - something the math wouldn't catch. But the math is pretty good and agrees more or less with the better 6DOF math which accounts for every significant force. It's the same math responsible from all manner of technology from sniper rifles to missiles to A-10's to rockets to... you get the picture. We know it works with a very high degree of accuracy when the inputs are well known. It predicts things like aerodynamic jump, epicyclic swerve and yaw limit cycle. That's pretty damn good.

Is it credible to think that something as fundamental as a difference in wind deflection been overlooked in the last 150+ years of ballistics research? I don't think so. But there has to be a missing piece if there is a difference between two bullets with the same BC and muzzle velocity. And that missing piece has to be significant enough that a shooter without instrumentation can detect it, but insignificant enough that it doesn't show up meaningfully in a 6DOF simulation. I don't see how that's possible.

 

[IdahoSharpshooter]

I've always believed that the bullet actually flew in a bit of a corkscrew path instead of straight arc to the target. There are things that may not be accurately represented in software. Inertia, for instance, barrel twist direction, and the Coriolis Effect.

Much smarter people than I proved during the early days of WWII that the Hydrogen Bomb could not produce nearly the destructive energy it does, and that Bumble Bees are waaaaay too unaerdynamic to fly.

 

[Keith Glasscock]

I do note that all of the math includes one basic assumption. That is that the wind will be continuous and consistent from muzzle to target. I'm wondering if some of the observations of drift differences are a matter of turbulence reactions.

A previous poster noted that the bullet immediately turns into the resultant flow as a result of the aerodynamic forces upon muzzle release. Since instantaneous realignment is virtually impossible with a spin stabilized projectile, I wonder if we are gaining an initial Vy as the bullet weathervanes (for lack of a better term).

 

[C.E.Smith043]

This is why this site is so cool. While I don't begin to understand 90 percent of what have discussed, the fact that you will take the time and effort to use your expertise to describe how bullets react to wind variances is just superlative. Thanks so much. I shot today in 20-40 mph gusts at,300, 200 and 100. I can relate!

This is also one of the reasons i miss P.S. Magazine. There were always pages of data and formulas you could try to follow if that was your cup of tea.

The great thing about this site is some of its writers are here in some form or fashion.

 

[Ned Ludd]

IMO - this topic is at the very heart of another current thread regarding the wind drift of two bullets of markedly different weight, but fairly similar BCs. More specifically, a relatively new 131 gr .257 cal Blackjack bullet is being offered with an advertised G7 BC of 0.345. In theory, this bullet would exhibit almost identical wind drift at 1000 yd when launched with a muzzle velocity of ~2940 fps as compared with a 180 Hybrid at 2820 fps. As you might imagine, many naysayers have chimed in with purely anecdotal information suggesting that lighter bullets do not always behave in terms of wind drift as may be predicted by ballistic calculators.

The problem with using anecdotal information to support the argument that lighter bullets behave aberrantly with regard to "predicted" wind drift as compared to heavier bullets of comparable BC is that rarely, if ever, are the bullets compared side-by-side in an empirical manner. There are a few different ways you could conduct reasonable tests to assess the wind drift of two different weight bullets with fairly comparable BCs, but ideally, it would take two shooters of fairly equal ability, each shooting a different rifle/bullet, side-by-side, concurrently. One approach would be to center POI for both rifles on the targets at some specified distance under essentially calm conditions (i.e. no wind zeroes), then shoot them again at some point later in the day after the wind had picked up, with both shooters still holding dead center. It wouldn't take more than 10 or 20 shots each to form a couple nice groups with each load, the center-points of which could then be directly measured for horizontal/vertical deflection and compared.

The conundrum involved in the use of light, high BC bullets is not new. Years ago, I came up with the idea of shooting the Berger 90 VLD in a .223 bolt rifle in F-TR. A few years prior to that time, several individuals in Canada and the UK had had some success using that combination. They had posted some specifics of the setups they used and the whole idea intrigued and appealed to me. As a result, I ordered a .223 Rem rifle purpose-built to shoot the 90 VLDs. At the time this occurred, I was aware of only one other shooter that was routinely using the .223 Rem with 90s in F-TR here in the States. There may have been a few more that I didn't know about, but my point is that it wasn't a commonly-used setup at the time. There were more than a few rolled eyes among my F-Class shooting friends, but that did not dissuade me. To make a long story short, it didn't take long to make believers of them. On paper, the performance of a 90 VLD at ~2850 fps is predicted to be just a tick better than a typical 185 Juggernaut load, which was considered to be the "go-to" bullet for F-TR shooters using .308 Win rifles at the time. Note that the 200+ gr bullets did not yet enjoy widespread in .308 Win/F-TR use at that point. I have used that rifle in F-TR matches from 300 yd to 1000 yd in the time since, and not once have I ever observed the 90 VLDs behaving differently in terms of wind deflection than is predicted by the JBM ballistic calculator. Yet there are people that still claim the 90s "don't shoot right" at 1000 yd. IMO - the most likely reason they incorrectly believe that has to do with recent advances made in the 30 cal bullets commonly used in F-TR over the last few years.

As I mentioned, the 90 VLDs from a .223 Rem are predicted (on paper) to have ever so slightly less wind drift than a typical 185 Jug load. In my hands, my scores at 1000 yd reflected that directly over some period of time. I would always score just slightly better with the .223 than with my Juggernaut loads. However, there are now several very good 200+ gr 30 cal bullet designs that are commonly used in F-TR. Not surprisingly, the 90 VLDs give up quite a bit to loads with those bullets at 1000 yd. But so, too, do 185 Juggernauts. That's why you rarely, if ever, see the very top F-TR shooters using 185 Juggernauts at big matches. They'd simply be giving up too much as compared to the newer, high BC 200+ gr bullets. It's not that the 90 VLDs behave aberrantly, it's simply that they (and the 185 Juggernauts) have been surpassed by better 200+ gr bullets with higher BCs. Unless I knew with absolute certainty that the conditions would be relatively mild, I would not use one of my .223 F-TR rifles shooting 90s as a first choice at an important long-range match. In fairness, the 90s do have an additional issue in that it's very difficult to load the relatively small .223 Rem case to the same low ES/SD values that are readily achievable in .308 Win loads. So they give a tad more vertical at 1000 yd. However, in my hands that's usually a minor concern relative to the amount of wind deflection they are giving up as compared to the 200+ gr bullets in .308 Win. It's not that you can't shoot the 90s with almost sickening precision under fairly benign conditions, it's that your competitors shooting 200s will have a marked advantage at 1000 yd when the wind comes up. That is exactly the same reason that few top F-TR competitors are using 185 Juggernauts at 1000 yd in this day and age. Nonetheless, the value of the .223 with 90s has become much better appreciated in the last few years, especially for MR competitions, where you will often find a lot more of them on the firing line than there were several years ago.

However, the 131 gr .257 Blackjack bullet is a whole different animal, IMO. With an advertised G7 BC of 0.345, the predicted wind deflection for a Blackjack with ~2940 fps muzzle velocity at 1000 yd compares very favorably to that of a 180 Hybrid pushed at 2820 fps. The 180 Hybrid G7 box BC is ~0.349, its pointed G7 BC should be a little over 0.360). A 2940 fps velocity should be readily achievable with the 131 gr Blackjack using either the 6.5 Creedmoor or 6.5x47 parent cases.

It has always been my understanding that when loaded to equal pressure, the heavier, higher BC bullet will always show less wind deflection than the lighter, lower BC bullet, even though it will have a slower muzzle velocity. However, the Blackjack bullet is a different scenario. Here we have a lighter bullet with almost, but not quite equal BC to the 180 Hybrid. More importantly, the difference in BCs is close enough that the lighter bullet's slight BC deficit can be compensated for by its greater velocity. So on paper, wind deflection at 1000 yd should be identical, which brings us back to the question of whether the lighter bullet will behave aberrantly with respect to ballistic calculator predictions, solely because of its lesser mass. My experience and intuition suggests that in fact, this does not happen. I believe that bullets generally behave as their BC suggests they should, regardless of their mass, because the relative bullet mass is already taken into account in the BC. Nonetheless, I'm sure that others may have a different opinion, and keep their belief that the heavier bullet will generally win out.

Ultimately, it may be that only empirical side-by-side testing of rifles/loads with the two bullets will answer the question to everyone's satisfaction. I'd really love to see some side-by-side testing with the Blackjacks and 180 Hybrids. I've been watching this bullet since it was first advertised with the idea of of having my first F-Open rifle purpose-built to shoot it, much the same as I did with my first .223/90 VLDs. However, in my mind there is an even more critical question regarding this bullet than its apparent BC and wind behavior. Specifically, can they be loaded with the equal precision to the ~180 gr .284 bullets against which they would be competing? Not to take anything away from the Blackjack bullet or its manufacturers, but it is still somewhat of an unknown, at least to me, with regard to how easy it is to load and tune. There are at least two recent 30 cal bullet offerings with exceptionally high BCs for which many F-TR shooters have had extreme difficulty developing consistent loads/precision. At this point, it's very difficult to pinpoint the exact cause for this behavior, but the number of people that have experienced it suggests it's not an anomaly. In my mind, only time will tell how easy to load/tune the Blackjack bullet is with regard to an anticipated use in F-Class. shooting.