How Wind Causes Pellets to Drift

One thing which affects all shooters, but in particular the air gun shooter, is the effect of a cross wind giving downwind drift. Here I will try to explain in a simple way how downwind drift is produced and how it varies with range and speed so that readers may understand better how their pellets are affected. I will not look at the vertical effect of a cross wind as that is much more complicated, but I will say that contrary to popular myth it is not due to Magnus.

When a pellet is fired in the air, as everyone knows, it slows down. To reach a certain range from the gun, because it slows down, it will take longer to reach that range than it would have done if it had just kept on going at the same speed. Because the pellet starts to slow down almost immediately after it has left the barrel, it will always take longer to travel a certain range, no matter how large or small the chosen distance is.

Suppose we choose a fixed range, say 30 yards, and a .22 pellet with a muzzle velocity of 585ft/sec. To reach 30 yards, that pellet will take 0.1635 seconds (AA Field pellet). Now if that pellet did not slow down at all but just kept on going at the same speed it would take 0.1538 seconds to travel 30 yards, so we can say that in the air it takes 0.0097 seconds longer to travel 30 yards than it would have done if it had kept going at the same speed. This time difference, the 0.0097 seconds, is called the lag time. The downwind drift at 30 yards for our pellet fired in the air is then given by the cross wind speed multiplied by that time difference. So in our case, for a 5mph cross wind, which is the same as a 88inches/sec cross wind, the downwind drift will be 0.0097 X 88 which comes out to 0.8536 inches. But the question is, why is downwind drift dependent on how much the pellet slows down?

The most popular misconception is that a crosswind blows on the side of a pellet. It is not surprising that this myth is popular, before now I have seen it written down in magazines, stated in videos and on forums. The wind will not blow on the side of the pellet if the pellet is stable (unless the pellet is grossly gyroscopically over stable, in which case you will have much more than a cross wind to worry about). A stable pellet, by definition, will always turn to face the direction from which the air is coming when it meets the front of the pellet. If there is no cross wind, the only thing giving a direction for the air to come from is the pellets own speed as it moves through the air, so the pellet will face in that direction.

When there is a cross wind, the air direction is not just due to the pellet speed. There is also the wind speed to think of. The pellet though does not see two separate wind directions, it sees a combination of the directions of the cross wind speed and the wind speed from the pellets own movement creating a relative airflow. Again, by the definition of a stable pellet, the pellet will turn to face the direction of the relative air flow from the cross wind and the pellet speed. The diagram below shows what is happening.


wind3a.jpg


If the pellet is facing into the combined relative airflow, then there cannot be any flow on the side of the pellet to push it sideways down wind.

Since the pellet is facing the airflow, the only force acting on it is drag, and it is part of the drag force which produces the downwind drift. The next diagram shows how this happens.


wind2.jpg


It all comes about because the pellet is not actually pointing in the direction in which it is travelling, so the drag force is at an angle to the pellet's direction of travel, which makes some of the drag act in the direction of the wind. It is this small component of the drag which produces your downwind drift.

But what proof is there that the above is true? From the diagram above, if there is no drag there should be no downwind drift and if the drag is negative then the projectile should drift upwind, not down wind. These effects can be seen with rockets. If a rocket is fired with a motor which exactly equals the drag giving no overall force, a crosswind has no effect on it, whereas an accelerating rocket can be seen to drift upwind. Projectiles fired at the same speed and weight but with different drags have also been shown to have downwind drift proportional to the drag, so the theory is well proven.

While the drag provides the force for the downwind drift, the pellet weight will decide on the acceleration rate of the sideways velocity, producing the rate of the downwind drift. This is where BC becomes useful, as it combines a factor for the pellet drag with the pellet weight. The BC also determines how much the pellet will slow down, and thus contributes to the time difference we looked at before.

The other factor which will determine what the time difference calculated above will be is the pellet velocity. The velocity will affect the size of the drag force as well as the time taken to reach the range of interest.
 
Last edited:
Thank you, Miles, for taking the time to explain something in as simple terms as these complex things can be broken down into.

Sadly, my physics teacher never bothered to do that same service that you have done.
So I almost flunked my physics courses. (And consequently never considered becoming a ballistician like you.)

Thanks again! 👍🏼😊
Matthias
 
So are you saying if we shoot it faster there will be less wind drift
No, as said, it is the difference between the actual time of flight and the time of flight if the pellet does not slow down, called the lag time. This is why the drag coefficient is important. It is the rapid rise in the drag coefficient as speeds approach the speed of sound which cause the wind drift to start to increase.

So if you increase muzzle velocity, the wind drift will decrease until you reach a point where the rise in drag coefficient overpowers the increase in velocity and starts to increase the wind drift
 
I just received my pellet sizer last week and already did some modifications to it. Finished and working well now.
My intention is to fix or try to fix some anomalies with .22 MRD's (25gr), these groups reasonably better @50 in milder windy conditions then the lighter pellets but doesn't group well at 100 even without a wind, and that bothers me.
In mean time the Canadian winter started at my place, so intensive testing or paying full and undivided attention outdoors - these days - is not for my liking.
So tinkering only in my room in front of a PC ... sizing pellets (meaning making a flat ring on the head where is a blue line shown) - would that improve on aerodynamics?

sized pellets.JPG
 
I just received my pellet sizer last week and already did some modifications to it. Finished and working well now.
My intention is to fix or try to fix some anomalies with .22 MRD's (25gr), these groups reasonably better @50 in milder windy conditions then the lighter pellets but doesn't group well at 100 even without a wind, and that bothers me.
In mean time the Canadian winter started at my place, so intensive testing or paying full and undivided attention outdoors - these days - is not for my liking.
So tinkering only in my room in front of a PC ... sizing pellets (meaning making a flat ring on the head where is a blue line shown) - would that improve on aerodynamics?

View attachment 310772
It will not make any noticeable change to the aerodynamics. Depending on the pellet fit in your barrel, there may be an improvement in the pellet yaw behaviour after leaving the barrel, or it may get worse and open up your groups. You are unlikely to see any large change in the cross wind behaviour.
 
@Ballisticboy, would it be possible for you to write a general function that explains this phenomenon. I do comprehend your theory in this explanation.

Depending on the degree of the drag and/or force, whether from the relative wind direction or pellet direction, would help me better master the art of shooting in the wind.

Picture me having an equation in my head while assessing every pellet that's shot from my gun. Thanks!
 
The only relatively simple equations are the ones below, which will only apply for short ranges and low angle fire, where Cd can be assumed to be constant.

For long ranges, Cd and V1 are both changing and are interdependent, so an analytical solution is not possible. Then you need a trajectory model.

You can get a rough idea of the Cd from the form factor of the pellet used in the BC and the reference drag law.


cross wind equation.jpg


That will give the tech haters a headache. ;)
 
The only relatively simple equations are the ones below, which will only apply for short ranges and low angle fire, where Cd can be assumed to be constant.

For long ranges, Cd and V1 are both changing and are interdependent, so an analytical solution is not possible. Then you need a trajectory model.

You can get a rough idea of the Cd from the form factor of the pellet used in the BC and the reference drag law.


View attachment 311046

That will give the tech haters a headache. ;)
Arrrggghhhhhhn thinking hard, stop please.
 
@Ballisticboy, thanks this is a good start to the theoretical model. I'm glad you provided the definitions to the variables. However, there's one left. What's the definition to "k"? I assume it must be related to the general model of bullet coefficient (BC).

In long range shooting, BC is not constant.

In all of this, I'm just being unscientific by applying the theoretical model in a practical manner from observing my own shooting. I enjoy the math just as much as I enjoy shooting.
 
@Ballisticboy, thanks this is a good start to the theoretical model. I'm glad you provided the definitions to the variables. However, there's one left. What's the definition to "k"? I assume it must be related to the general model of bullet coefficient (BC).

In long range shooting, BC is not constant.

In all of this, I'm just being unscientific by applying the theoretical model in a practical manner from observing my own shooting. I enjoy the math just as much as I enjoy shooting.
K is defined in the second equation.