Ballistic Theory Twist Rate Related Posts

Miles_M

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This was the first of the 12 FPE threads I created years ago for UK forums. They tend to follow on from each other, so I will post them all in this thread in the order they were created, or some may not make sense. It may take me a while to do it.

There are plenty of videos on YouTube which will tell you anything you want to know about your gun and pellets, including rifle twist rates, but they cannot go into the detail. Scientific experiments on twist rates are virtually impossible to carry out since you cannot eliminate the other sources of error which will have a primary effect on your results. This is where modelling has to take over, as we can set up any experiment we want inside a computer.

The data was produced using a six degree of freedom program which, at the time of the original post, was new and had metric output. There are some problems with the output for pellets where the units are only to the nearest millimetre, but we can get some preliminary results.

I have been modelling the effects of the centre of gravity (C of G) not being exactly on the centreline of the pellet. In fact, I assumed it was 0.1mm (around 4 thou in real units) off the centreline and then carried out a lot of runs to see the effect on the group size at 50 metres range. I had to use 50 metres and not 50 yards, as the model works in metres and I hadn’t had time to change it. The aerodynamic data was the same as I have used for other modelling work I have posted, and is strictly only applicable to the AAField type pellets in .22 calibre. The muzzle velocity was 585ft/sec, which gives just barely over 12FPE.

If you fire a pellet which is a perfect fit in your barrel but with an offset C of G there are two sources of error. One is the effect of the G of G offset during the pellet flight, and the other is due to what happens to the pellet as it leaves the barrel. Now, what happens to the pellet as it leaves the barrel is not exactly clear. When the front of the pellet leaves the barrel, the C of G will start to move sideways due to the rotation of the pellet and the offset distance from the centreline. The back of the pellet is still in the gun barrel and cannot move sideways, so the pellet will start to yaw away from pointing in the straight ahead direction. At some point the back of the pellet will also leave the barrel and is free to move sideways, but it will not move sideways if the yaw rate of the pellet is high enough for the sideways movement of the C of G. Someone, who knows far more than me about theoretical ballistics, suggested that the best approximation is to assume the rotational momentum of the offset C of G is entirely transferred into the yaw momentum so that we can calculate an initial yawing rate for the pellet. This is what I have done for the following results involving yaw rates.

The first set of results are for a pellet which leaves the barrel perfectly, i.e. no yaw rate, but which has an offset C of G (I would like to see someone try to set that up in an experiment). So this is purely down to the effect of the offset C of G on the pellet flight. The figure shows how the error at 50 metres will change depending on the barrel twist rate. Each point represents a result from the model, and the line is just a best fit for the data. In this case, a straight line represents it fairly well. It shows how as pellet spin rates get higher, i.e. fewer inches per turn, the error due to the offset itself gets to be insignificant.
Off1.jpg
As I said above, the pure offset error is only half of the total effect. There is also the effect of the initial yaw rate created as the pellet leaves the barrel. The second figure shows the effect of barrel twist rates on the error caused by the initial yaw rate.
Off2.jpg
In this case, the best line fit is a curve which is very close to being proportional to the reciprocal of the barrel twist rate. In this case, again as you would expect, the error gets worse as we increase the spin rate of the pellet and thus the initial yaw rates on barrel exit.

So it would appear that there are two conflicting results from the two components of the total error. If we combine both the C of G offset effects and the initial yaw rate effects, we get the result shown below.
Off3.jpg
In this case the line is a not very good best fit as the relationship is fairly complex. It does show that there is a range of values for barrel twist rates which will minimize the effects of pellet offset C of G. The area of interest which encompasses most of the current barrel twist rates is shown in more detail below.
Off4.jpg
It would appear that there is a fairly flat area for twist rates between about 16 inches per turn up to 50 inches per turn. These values coincide well with the currently used common twist rates, which have evolved over time. It looks like very small gains could be made by going for twist rates around 35 inches per turn, but the gains are very small. You must remember that the results are for only one pellet type, calibre and one velocity. Changing any one of these variables could change the optimum value.

You should also remember that, going to the lower twist rate, could reduce the variety of pellet designs which could be used in the gun and would eliminate the possibility of many gyroscopically stabilized slugs. Finally, an offset C of G is not the only source of error in a gun pellet combination, others may require greater or lesser twist rates and have a bigger effect at the target.
 
This is a short follow up to the previous post, after a request to repeat the exercise for .177 pellets. I have also briefly compared the two calibres.

Following on from the post on the effects of an offset CG on a .22 pellet, I have had time to do a little work on the same make .177 sized pellets. I have only looked at the total effect this time, not the separate components of the error as before, as I simply have not had time to perform all the computer runs necessary.

Below is the result for the .177 pellets fired at just under 12 FPE. The CG offset I used this time is slightly less than .1mm. I did this to keep the CG offset the same percentage of the pellet diameter as for the .22 results.
177off.jpg
You can see that the result for the .177 pellets is very similar to the previous .22 result, but the optimum twist rate range seems to be narrower. It is interesting that again the optimum twist rate appears close to, though just above, the commonly used values.

The diagram below shows the results for both the .177 and the .22 pellets. It shows that for this particular design, the .22 appears to have slightly less error than the .177 over much of the range. The .22 though is worse at the high twist rates, which is what you would intuitively expect.
17722off.jpg
The twist rates of most interest are shown in more detail in the last diagram, again comparing the .177 and .22 results.
17722off2.jpg
Remember, these results are only for one design of pellet with one type of error source. There are plenty of other designs and error sources to consider for an optimum overall twist rate.
 
This one is very technical and not easy to follow. It will not improve your shooting, but it may help to understand the effects some pellet faults can have on your group sizes and how fliers can occur. It is the last of the pellet based posts looking at the effects of spin rates for pellets with defects.

The previous two posts show how an offset centre of gravity (CG) position can give an error at the target, which varies according to the twist rate of the rifle barrel. The diagram appears to show that the error is a minimum for barrel twist rates of between 15-50 inches per turn. The diagram was based on data for one pellet design at one muzzle velocity and an offset CG as the only error source.

One more obvious pellet based source of error is small external asymmetries. These may be caused by pellet shape production errors or post-production damage. When the pellet flies through the air any asymmetry will normally have one result which is the production of an imbalance in the aerodynamic forces about the pellet central axis producing an aerodynamic overturning moment. It is well known with wind tunnel models that even the slightest flaw in the shape of a model will produce an aerodynamic imbalance, so any flaw on a pellet can give the same effect.

The asymmetry I can use in the model I have is the ability to put the nose or the tail at an angle to the rest of the pellet. For the first part of this exercise I have put an angle on the nose which produces the same effect as the nose having a small high drag area off the centreline. This could be a rough surface or a small flat area such as a dent or pit. The angle chosen is 1.72 degrees.

The pellet being used was in .177 calibre and had a muzzle velocity of 795 ft/sec. The input data is based on the AA Field 8.4 grain pellet and has been derived from measured and estimated sources. Some of the estimated aerodynamic data may not be entirely accurate. However, while any inaccuracy may affect the group size the general trend should not be affected. All the results are at a range of 50 yards in still air conditions.

The first diagram shows the trend in group size with pellet spin rate at the muzzle.
assf1.jpg
Many people will not be familiar with their pellet spin rates so the same data is in the diagram below using barrel twist rates.
assf2.jpg
It can be seen that the group size falls dramatically as the twist rate increases. By the time the twist rate is in the normal range of values the group size is relatively small (less than one inch). This is because the spin rate is high, around 3700 radians per second for a twist rate of one turn in sixteen inches. The high spin rate means that any side forces or moments are only pointing in one direction for a fraction of a second and do not have time to cause the pellet to have a significant change in direction.

The nose angle used for the results so far is a fairly large. I deliberately chose a largish value in order to show up the effects of spin rate. To show up the effect of the size of the pellet damage I considered a small circular flat area facing directly into the airflow and then varied the size of the flat area and its distance from the pellet centreline. Having worked out the size of the aerodynamic moment from the flat I then produced a nose angle to give the same aerodynamic effect. The table below shows the values used.
assf3.jpg
For this exercise I used just one twist rate which is one turn in sixteen inches. There appears to be a direct relation between the size and position of the asymmetry and the resulting group size. This is shown below.
assf4.jpg
When I previously looked at the effects of offset CG on pellet dispersion I was mainly concerned with spin rate and did not look at the effect of varying the size of the offset. This time I have filled in that gap with the diagram below. I have used the same spin rate as for the asymmetry calculations.
assf5.jpg
One thing you can be sure of is that any particular pellet you fire will not have just one fault. It will probably have a large number of faults but for the moment I will just look at the combination of offset GG and nose asymmetry. The same asymmetry angle is used and the CG offset is the same as used in the previous work at just over 3 thou. I have calculated the resulting group size throughout a range of spin rates.

The diagrams below show the group size for all the separate components and, for the higher spin rates, the combined total group size when both problems exist. For the offset CG there are two components, one due to the flight of the pellet with the offset CG giving a small yaw angle (CG in the diagram) and the other for the yaw rate caused by the offset CG as the pellet leaves the barrel (Yaw).

The first diagram shows the results at low spin rates for the separate CG components, the combined CG effect and the asymmetry. It does not show the CG and asymmetry combined, as the predicted pellet yaw angles were too high for accurate modelling using the data available.
assf6.jpg
The next diagram shows the group sizes for the higher spin rates. This time the combined CG offset plus asymmetry results are included as the yaw angles were much lower.
assf7.jpg
The same results based on barrel twist rates are presented below.
assf8.jpg
assf9.jpg
Looking at the results above, it appears that at low spin rates the asymmetry will dominate, but that is just a function of the relative sizes of the assumed pellet problems. If the size of the asymmetry is reduced, a slightly different shape will be obtained for the total CG+Yaw+asymmetry curve. It is interesting to see though that the optimum barrel twist rates are still appearing to be around 15 to 18 inches per turn.

For all the computer runs for the total effect of all the error sources, the orientation between the CG offset, and the nose asymmetry was kept the same. To see if orientation has a significant effect on the group size the sixteen-inch twist rate modelling was repeated at four different orientations i.e. the CG offset, and the external asymmetry were at 0, 90, 180 and 270 degrees to each other, as shown below where the small circles represent the asymmetry and its different positions, each orientation being modelled separately.
assf11.JPG

The diagram below shows the resulting group sizes at the different orientations.
assf10.jpg
As can be seen, unfortunately, orientation has a significant effect on the group size. This means that two pellets with the same flaws could give very different results because of the relative positions of the flaws.

In the end the shooter is dependent on the manufacturers to produce accurate consistent pellets with no external damage. A CG offset by a few thou or a damage area 1mm in diameter on the front of the pellet can give large group sizes, particularly if they are in the worst positions relative to each other.
 

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