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All Springer/NP/PCP Air Gun Discussion General > "Bob and Lloyds Workshop"

External Ballistics of Pellets by Ballistician Miles Morris

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Spacebus:
Thanks for the data, Miles. It very much reinforces what I am seeing with my .177 lead free pellets. I wanted very much for the Dynamic 9.5 grn pellets to be as accurate as my H&N 10.64 grn copper plated pellets, but they are nearly unusable. Some groups come out at .5" at 25 yards and then I'll get two groups that are over an inch. They look very much like well made pellets, but I suspect that lead pellets do a better job of expanding and filling the barrel. My anecdotal evidence is seeing dented skirts on my copper plated lead pellets still hit exactly at the POA. I hope the big pellet manufacturers get better with their lead free options, as so far only H&N and Predator seem to make competent lead free ammo.

The below groups are from testing with H&N .25 Barracuda Green 19.91 grain pellets. The far right is with my Seneca Eagle Claw on max power and all eight shots. The third from the left is at two "clicks" less than max power and the "flier" is my attempt at Kentucky Windage to compensate for the different POI between the Green pellets and my NSA Slugs.

Spacebus:
I'm hoping manufacturers will start making zinc and tin pellets with all new designs rather than just substitute materials.

ballisticboy:
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 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.



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



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.



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.



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.

ballisticboy:
There is a lot of advice and information available on the internet regarding the way projectiles fly high or low when fired into a crosswind. Unfortunately, when it comes to pellets, most of the information is wrong. Here I hope to try to explain why pellets fly high or low in a crosswind and why bullet derived diagrams are not suitable for the majority of pellets.

When a pellet is fired from a gun with a crosswind blowing across the trajectory, there are two distinct effects. The main effect is the downwind drift, which was described in this post:-
https://www.gatewaytoairguns.org/GTA/index.php?topic=169459.20
Reply No35

There is a second effect, usually called the vertical error or vertical effect. Contrary to popular myth, despite what you may read on the internet, it is not caused by Magnus. It is simply a result of gyroscopic stability. It will help to understand what causes vertical error if you have seen the previous posts on pellet stability:-
https://www.gatewaytoairguns.org/GTA/index.php?topic=169459.0
The original post, reply No3 and reply No31

When a pellet leaves the barrel of an air gun, it is pointing more or less in the same direction as the gun barrel. If there is no wind then the airflow, due to the pellets speed, is coming directly at the pellet. If there is a crosswind, the airflow direction is changed slightly so that now it is coming at a small angle to the pellet, as shown in this figure. The airflow the pellet sees is in the direction of the green arrow.



A stable pellet will always try to face into the direction of the airflow it sees, this is the definition of a stable pellet. It does not try to keep pointing in the direction it is facing when it left the barrel. Because, on leaving the barrel, the pellet is not facing into the airflow, the air passing around the pellet will create a side force on the pellet.

The side force actually acts all over the pellet with many separate small forces, the size and direction of each force at each point depending on the shape of each part of the pellet. For convenience, we only consider the total side force and the point through which it has to act to reproduce the same effect as all the separate forces. The point through which the aerodynamic side force acts is known as the centre of pressure (CP), which on most pellets lies behind the centre of gravity (CG).  When the CP is behind the CG, a pellet is said to be aerodynamically stable as the aerodynamic moment created by the aerodynamic side force is trying to turn the pellet to face the airflow.



This is where most pellets differ from bullets and slugs, in that for bullets and slugs the CP is in front of the CG, creating a destabilising aerodynamic moment which moves the pellet away from the direction of the airflow.



This is just an illustration, as not many pellet designs are aerodynamically unstable.

The aerodynamic moments are important because objects which are spinning at high speeds will only change their orientation as a reaction to a moment, not a force. Side forces will move a spinning body sideways but, unless they are also producing a moment about the CG, forces will not change the orientation. The gyroscopic reaction to an aerodynamically unstable projectile is in the opposite direction to that of an aerodynamically stable one. This is what makes most pellets react differently to a bullet/slug in a crosswind, and is the reason charts for bullets cannot be used for pellets.

Combining two of the above diagrams shows how the crosswind produces a side force on the pellet which, because it acts through the CP, produces an aerodynamic moment about the CG.



The gyroscopic reaction to the aerodynamic moment is to cause the pellet nose to rise in the case shown where the wind is blowing left to right from the nine o’clock position. Looking at the front of the pellet along the green line above, we see it as the airflow will see it.



As mentioned previously, if we have a bullet or a slug the gyroscopic reaction will be in the opposite direction i.e. nose down, due to them having a destabilising aerodynamic moment.

The nose up reaction of the pellet will produce a vertical force slightly changing the direction of the pellet, which is what produces the vertical error at the target. If the wind is coming from the right, i.e. three o'clock, the pellet will turn nose down and the force direction will be downwards.



The vertical force in turn produces a stabilising aerodynamic moment which causes a gyroscopic reaction on the pellet, turning it to face into the airflow, which will reduce the aerodynamic forces and moments allowing the pellet to face directly into the airflow.

Because the vertical force only acts on the pellet for a short time immediately after it leaves the gun barrel, the deflection in the trajectory is linear, i.e. it increases directly with range. The down wind drift however increases in a non-linear fashion, getting much greater as the range increases.

The vertical error is often expressed as a percentage of the down wind drift. This is a very simplified way of looking at it and is not correct, as the ratio between the vertical error and the down wind drift changes depending on the range. Below is a diagram showing how the ratio changes with range for a .22 pellet fired at 900ft/sec.



Don’t take too much notice of the predicted values, as it was a rifle with a relatively high twist rate that was modelled, and it is the shape of the curve that is of interest. The waviness of the curve is the result of heave and swerve (spiralling) giving small changes in the pellet position. At short ranges the ratio is very high, but the actual drift figures are very low, so you are unlikely to notice it. The short range ratio values are also heavily distorted by the effects of heave and swerve, and the modelling is least accurate here as it is trying to predict the rate at which the pellet turns to face the airflow. It is only at longer ranges that the vertical error may become a problem, despite being a smaller value compared to the down wind drift. The main point of showing the curve is to show that it is not a constant ratio between the downwind drift and the vertical error over the entire range, as sometimes claimed.

The size of the vertical error and the ratio between the vertical and down wind errors from a crosswind will depend on your chosen rifle and pellet. Practising with your chosen rifle and pellet will show you if it is something you need to take into account at longer ranges. Some shooters notice it, others have never seen any change. Long range target shooters seem to be the ones who mainly notice it, and who sometimes go to extreme lengths to try to reduce it to a minimum.

ballisticboy:
You will often see claims that, based on observation, a wind from one side will give a larger drift than the same wind from the other side, but is this true? Is there a physical mechanism which can cause this effect?

The modelling of the effect of wind on projectiles is one of the most accurate ballistic effects there is, if you know what the wind speed and direction is at the moment of projectile flight. This is the tricky bit, knowing what the wind is doing, not what the effect will be on the projectile, so we can reasonably expect modelling to tell us what will happen if we assume a wind value and direction.

To look at the effect of wind direction, I assumed a constant wind of 5mph at 90 degrees to the line of the trajectory over a 75 yard range. The projectile was the 15.9 grain .22 JSB fired at 900ft/sec. The wind was modelled blowing from left to right and from right to left. In order to enhance any projectile effects, a relatively high twist rate barrel was assumed.

The first thing to do is to model a trajectory with no wind. This will be the zero baseline for comparison. Then two more trajectories have to be modelled with the wind coming from the two different directions. The wind drift is obtained simply by subtracting the zero wind trajectory figures from the trajectory figures with the wind. The result can be seen in the figure below, which shows the wind drift in each direction as range increases.


 
It can be seen that for the same wind, the drift is identical for a wind from left to right (LR) or from right to left (RL). So it would seem that the claims of different drift are not true, but there is another factor to consider.

When looking through a scope or open sights, you are looking in a straight line. Unfortunately, projectiles with a high spin rate, pellets or slugs, do not fly in a straight line, either vertically or horizontally. There is spin drift and this could be an explanation for some of the claims, particularly where the range being shot is much more than the zero range.

In setting up your zero, you are already taking into account any spin drift at the zero range. Beyond the zero range, the drift will be greater than the line of sight. This is shown here, the blue line is the pellet spin drift with no wind and the red line is the sight line for a 50 yard zero.



Don’t forget, this is only a demonstration with a high twist rate barrel. The majority of shooters will see much smaller spin drift values.

Now the wind moves the pellet relative to the spin drift line, not the sight line. The wind drift figures above are relative to the spin drift line, which is the zero wind trajectory line. If we now plot the wind drift relative to the sight line, we get the figure below.



Now to anyone looking through a scope or over open sights the pellet will appear to drift more in a right to left wind than it does in a left to right wind for ranges greater than the zero range. Conversely, for ranges less than the zero range the pellet will appear to drift more for a left to right wind than it does for a right to left wind, but the drift here is so small that you will probably not notice the difference, or it will be hidden by other errors.

The difference is still small, at 75 yards you are still talking about something less than an inch, but it may be enough under some circumstances to make someone think there is a difference in the drift. It is around 20% difference in this case, but remember I have deliberately chosen a high twist rate barrel, which will exacerbate the difference.

I am not saying this is the reason some shooters think that wind drift is worse in one direction than the other. I am only trying to suggest a possible reason why some may think they are seeing differences.

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