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

100 Yard Pellet Flight

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ballisticboy:
Recently I got to thinking about shooting to ranges of 100 yards and the problems with pellet dynamic stability at the longer ranges. When I had compared leaded to lead free pellets, some of the designs showed large increases in yaw (wobble) angles as ranges increased, even in the lead versions of the pellet design. I had not looked at the detailed effects of the yaw increases, as the modelling was at a relatively simple level. To keep things simple, I initially used a simple initial yaw rate as the pellet left the barrel to see what the model predicted.

The two pellet designs are JSB pellets, not because they have particularly bad problems, but because I happen to have most modelling data on those two. I started with the .177 10.3 grain Heavy pellet with its more cylindrical shape, which in previous studies had shown a tendency to increased yaw angles at longer ranges and higher speeds. I fixed on a muzzle velocity of 950 ft/sec, simply because it seemed a reasonable starting point, and a barrel twist rate of one turn in 16 inches.

The first job was to find out what the model predicted would happen if the pellet was fired as is with no flaws but with an initial yaw rate, i.e. would it show up problems at long ranges. The result can be seen below.



You can see the model is definitely predicting there is a problem after about 60 yards. If it is a perfect pellet with no yaw rate to start with fired from a perfect gun, then the resulting trajectory will be like this one here.



There are still some signs of problems, but obviously much reduced. However, the chances of being able to fire a pellet with no pellet flaws or no initial yaw rates from a perfect gun are very slim.

With a fixed twist rate and a given design of pellet, the larger the calibre, the higher the gyroscopic stability factor becomes. Having started with a .177 pellet, I then scaled up the design to .22 to see what happened. The .22 pellet came out at 19.7 grains. The muzzle velocity was kept the same.



You can see there is definitely a problem showing up here. A perfect pellet fired perfectly from the gun will give this flight profile below.



Much better but still with an obvious problem at long range.

So it looks as if there is a problem with this type of pellet design where the normally hollow parts of the pellet are partially filled in order to increase the pellet mass. The next stage is to look if other pellet designs act the same. Data is available for the JSB 15.9 grain .22 pellet, so this one was modelled with the same error inputs as the JSB Heavy design based one, i.e. with an initial yaw rate. The result is shown below.



The result is predicting much better behaviour, but there is still a tendency towards spiral type problems.

The result for a perfect pellet fired perfectly is shown below.



This round is showing acceptable behaviour.

The next stage is to see what can be done to improve the flight of a less than perfect pellet fired from a less than perfect gun.

ballisticboy:
The accepted way for reducing pellet spiralling at long ranges is to use lower twist rates and a reduced velocity. This reduces the effects of increased spin rate relative to the forward velocity. The improvements can be seen below where the .177 JSB Heavy has been fired at a muzzle velocity of 850 ft/sec from a barrel with a one turn in 32 inches twist rate. The first diagram shows the predicted behaviour of a pellet with a CG offset from the pellet centreline and with a flat spot on the front facing part of the nose, giving an asymmetry.



The effects compared to the trajectory at 950 ft/sec with a 16-inch twist rate barrel are much reduced but still present.

Using a perfect pellet and barrel, the trajectory looks like this.



This is probably a usable trajectory, but there still seems to be possible problems as the range increases, and again hoping for a perfect pellet is not a good idea.

The problem with using guns with low twist barrels which are a perfect fit to your choice of pellets, and have lower muzzle velocities, is that changes to the gun are being used to try to solve what is basically a pellet problem. In addition, not everyone can afford a new gun or even a new barrel with the fitting costs, if they do not have the necessary skills or knowledge to do it themselves.

The cause of the problems with the pellets is twofold. First is the lack of dynamic stability, which enables pellet yaw angles to increase as the pellet flies down range. Secondly, as the ratio between the forward velocity and the pellet spin rate changes, it gives increases in gyroscopic stability which causes increased yaw wave lengths, i.e. it takes a longer distance for the pellet to go through a complete wobble which leads to the pellet moving away from its normal trajectory, leading to increased spirals.

If increases in the pellet spin rate compared to the pellet forward velocity are what seems to be the major cause of problems, the logical answer is to make the spin rate slow down at a faster rate. This can be done in a number of ways, one of which is to add very small strakes to the sides of the pellet flare. A possible design would be like this one shown below, using in this case a JSB 15.9 grain .22 pellet as the basis.



There are four strakes on the pellet shown positioned evenly around the pellet flare. It is possible to estimate the approximate spin damping given by these strakes. I did not take into account the small changes in pellet inertia or aerodynamic stability. That can be included in later modelling. I also did not consider setting the strakes at a small angle to give a fixed minimum value for the ration between forward speed and spin rate.

ballisticboy:
Using strakes, the resulting trajectory for the JSB 15.9 grain .22 pellet shown previously with the strakes shown and with the pellet flaws used in the modelling before are as shown below.



Compared to the previous figure for this pellet fired without strakes, there is a large improvement with the almost complete elimination of spiral type behaviour.



The total effect can perhaps best be seen if we look at the trajectories from the back rather than the side view. The diagram below shows the trajectory as seen from behind the shooter.



Since the strakes appeared to work on the 15.9 grain pellet, they were tried on the heavier pellet in .22 size. The resulting trajectory is shown below.



There are still some spirals present, but they are much reduced compared to the same pellet without strakes.



Again, the effect can best be seen from behind the shooter.



These are the same sized strakes as used on the lighter pellet. Larger strakes could give additional spin damping and further reduced spirals.

The strakes modelled are just a first guess at the size needed and to see if it is possible to improve the pellet flight in this way. Much further modelling would be needed to optimize the strake size, position, angle to give fixed spin to forward velocity ratios and total effect. They will also increase the complication in making the pellets, but four strakes should be possible without too much difficulty.

As a first look at the possibilities, the strakes seem to show some promise, and the theory of increasing the spin damping seems to give benefits.

JuryRigger:
Absolutely fascinating!...
Thank you for what you do!..
Jesse

Nvreloader:
Miles
VERY interesting, showing good promises, following along.

The 50/60 yd mark shows very consistent start of the problem/pattern.

I have a dead tree at 85yds, and the Starling always sit in,
I have been sniping at them for several yrs and have watched 22 cal Crosmans @900fps,
start out straight looping path for the target, the do the right twist/loop circle
(at unknown range) almost making a complete full turn before losing sight of them.
No Bandits brought down yet........

Bob should be here any time........... ;)
Thanks,

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