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Author Topic: External Ballistics of Pellets by Ballistician Miles Morris  (Read 3454 times))

Offline JohnnyPDX

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #40 on: May 15, 2020, 10:52:52 AM »
To make it more appealing to the average person perhaps this simplification will help:




Offline rsterne

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #41 on: May 15, 2020, 12:25:21 PM »
Miles, thanks for sharing the development of that pellet with Gerald Cardew.... The one in Figure 2 looks similar to the idea of the BBT's I have developed, but with a hemispherical nose instead of the tangent ogive with Meplat I settled on.... I can see that for lower drag the RN would be better in the Subsonic range....

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #42 on: May 15, 2020, 12:36:19 PM »
Wow, WOW!
Thanks, Miles, for all your efforts at teaching us who haven't had the chance to study this. 👍🏼😊
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Re: Early Experiments on Low Mass Subsonic Bullet Type Designs
« Reply #43 on: May 19, 2020, 05:45:03 PM »
Just a small note. In an idle moment today I used Chairgun to calculate the BC of the .22 final design we tested. Based on the average velocity drop of five pellets the BC was 0.053 based on the GA drag law. Now the GA drag law is not a suitable shape for ths type of projectile but it does give a direct comparison with diabolo pellets.
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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #44 on: May 19, 2020, 07:33:51 PM »
Interesting, you didn't say how you made these, but there are low cost DIY injection molding machines that would work well for this. I'm envisioning a two step cast and mold process.
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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #45 on: May 20, 2020, 07:18:40 AM »
Interesting, you didn't say how you made these, but there are low cost DIY injection molding machines that would work well for this. I'm envisioning a two step cast and mold process.

Gerald cast the metal first then molded the plastic with the lead in place. The plastic was not to touch the barrel in a production version, the plastic mearly acts as a lightweight aeroshell with the lead core providing the weight and the bearing surface in the barrel. In this way the inertias and the aerodynamic moments could be controlled.
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Examples of data simple tests can tell you.
« Reply #46 on: June 08, 2020, 08:08:40 AM »
To start this one a warning, it is very technical and specialist and as such will not be of interest to the vast majority. Hopefully one or two may find it of interest.

This one is about analysing measured data from trials results to try to obtain some of the aerodynamic coefficients which govern pellet flight. When I was working one of the things I had to do was to analyse trials results. The trials were carried out according to strict trial plans which I usually had to write and which usually involved the use of extensive instrumentation including meteorological systems, survey equipment, and multiple radar systems one of which was a multimillion pound/dollar tracking Doppler system. To go with all this we also had the supporting instrumentation engineers. For most shooters this instrumentation will not be available when they are testing but that does not mean that the same analysis methods cannot be applied to some carefully measured results.

There are plenty of ways in which the aerodynamic properties of pellets, slugs or any other gun launched projectile can be calculated, so that pellet flight can be modelled. The problem with pellets is trying to find suitable measured data in order to confirm, or otherwise, the calculated data. For many aerodynamic coefficients it is very difficult to obtain measured values without very extensive instrumentation and facilities. However, if tests are carefully thought out it is sometimes surprising what can be derived from the resulting data.

Perhaps the easiest aerodynamic coefficient to obtain is drag coefficient and how it varies with projectile speed. It can be done with a couple of chronographs which have been calibrated against each other if they are used at different discreet ranges. The best method available for many shooters is to use the LabRadar to obtain a downloaded data file of measured pellet speeds at a large number of distances.

The problem with many radars is the amount of data from a number of shots (I would always recommend a minimum of ten shots), making sure there has been no form of smoothing applied to the data to make it look better and how best to analyse it. Using unsmoothed data and simple analysis, assuming you are firing as flat as possible and combining the analysed measured data from a number of shots, you may get data which looks a bit of a mess (figure 1).


Figure 1
 
It is at this point that you can start using different data smoothing techniques such as running average values etc. The reason you should not use smoothing before analysing is that the shape of the drag curve you obtain from the smoothed data will be mainly dependent on the smoothing method used rather than the true data derived shape. Excel can be used to give a curve fit to the data but I always found it more accurate to just put a line through the centre of the data by eye avoiding the limitations of the curve fit methods. Using this method the data above gives the fitted curve below (figure 2) for the Cd curve.


Figure 2

Some years ago Harry Fuller in Australia produced some interesting firing data when he fired some marked .25 JSB King pellets over a range of 200 yards through paper targets. For each of the data distances ( 2 feet, 75, 100, 150 and 200 yards) there were two targets a measured distance apart. The marks on the pellets left a mark on each of the paper targets so the angle through which the pellet had turned between the two targets could be measured and the effective twist rate at each range could be calculated. The initial and final pellet velocities were also measured. The twist rate data is shown here.

2 feet = 1: 18.9
225 feet/ 75 yards = 1:15.9
300 feet/ 100 yards = 1:14.9
450 feet/ 150 yards = 1:13.2
600 feet/ 200 yards = 1:12.8

One of the aero coefficients I had tried to calculate before was the aerodynamic spin damping coefficient. Because of the shape of a pellet and its Reynolds numbers it is not an easy calculation. However Harry’s data provided a possible method of obtaining measured spin decay data. Using the two measured velocities and a calculated Cd drag law I obtained estimates of the pellet velocity at each data point and from that and the measured effective twist rate the pellet spin rate in radians per second. Once we have the pellet speed and spin rate it is then relatively easy to derive the spin damping coefficient. The resulting spin damping coefficients obtained from the data are shown below after smoothing.



The estimated drag law is a possible source of error in the calculations of the spin damping coefficients so the exercise was repeated using a different very simple drag law. The new spin damping coefficients were practically identical to the previous set suggesting the drag law was not a major error source.

One aerodynamic coefficient which most shooters have never heard of but which is arguably the most important coefficient of all is the aerodynamic overturning moment coefficient slope, usually called Cma which is a lot easier to write. This one coefficient is important since it is a major factor in aerodynamic stability, gyroscopic stability, spin drift, vertical cross wind effect and group size, amongst other things. It is however very difficult to measure without major facilities.

One of the things Harry Fuller did years ago, on a day when the wind direction was steady but the wind speed was varying, was to fire 15.9 grain .22 JSB Exact pellets over a range of 60 yards at a pan and compare the results with 25 grain JSB Monsters. Harry was interested in showing that the vertical crosswind effect is different for pellets and bullet shaped projectiles. Harry’s results can be seen in his photograph below (figure 3).


 
This test, which Harry carried out, is a brilliant example of what can be done with the simplest of instrumentation, in this case a chronograph and an old pan. Harry’s results clearly show the difference in the vertical cross wind effect between aerodynamically stable and aerodynamically unstable spinning projectiles. But there is more information there as well.

When I was looking at the vertical cross wind effects on pellets to try to help incorporate this effect into Chairgun one of the things which stood out was that the angle between  the line of pellets  and the horizontal was largely independent of muzzle velocity for speeds below 900ft/sec. Years later, looking at the theory again, it was obvious that one of the main factors in deciding the magnitude of the angle shown above was the distance between the centre of gravity and the centre of pressure which is a major component of Cma. Thus by comparing modelled results with the angle seen in figure 3 a good estimate for Cma can be obtained. The original estimated Cma for the JSB exact pellet and the values derived from Harry’s firing results can be seen below.



Now those numbers won’t mean a lot to most people but they are highly significant being negative rather than positive and being a factor of 5-10 smaller than many projectiles.

This post is not meant to be a “look how clever I am” post. It is an attempt to show there are probably many other results around which could be used for simple analysis to at least get some idea of the values of certain important aerodynamic coefficients. It is however vital that the tests are carried out carefully and methodically in the right atmospheric conditions to be usable. The analysis also needs some idea of the atmospheric conditions, things such as air temperature and pressure.
 
The more we can find out from tests the greater our understanding of pellet flight can become and the more we will be able to say what is good, what is bad and maybe why.
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Offline JungleShooter

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #47 on: June 08, 2020, 03:51:47 PM »
Miles,  😊

you are showing us that the deep dark HOLE that we have fallen into is far deeper than most of us imagined....

Keep writing! Thank you! 👍🏼


Now, you brought up some stuff that I've seen on my ballistic calculator, Strelok Pro.

🔶There are several settings in Strelok that I didn't know what to do with — and now I want to KNOW...! 😄

▪Vertical Deflection of Crosswind, with an optional manual setting (here set to 1.2345679 for fun)
▪Coriolis Effect
▪Spin Drift▪Twist direction of the barrel

For the first three of the four, see the attached screen shot....



Once the Peruvian government allows us to leave our homes again after this covid craze I finally want to really get into 100 yard shooting and shooting slugs....
➔ And I have an inkling that these four settings in Strelok might have a sufficiently large effect to be important....   


🤔 So, what do I do with these settings? Will there be a difference between pellets and slugs?

If this thread is not the place, I gladly start a new one.... 😊
 
Matthias
« Last Edit: June 08, 2020, 03:54:30 PM by JungleShooter »
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Offline ballisticboy

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #48 on: June 08, 2020, 07:18:00 PM »
Matthias

Vertical deflection of a crosswind is a difficult one to use. When a pellet is fired into a wind at 90 degrees to its direction of travel it will not only be deflected down wind it will also be deflected up or down depending on a number of things. In Chairgun, and it appears Strelok, a simple method was used which set the vertical deflection as a percentage of the downwind drift. The trouble is the percentage is not a constant with range and will be different for different pellets and slugs. (as can be seen in Harry's pan picture) For long ranges (50 yards or more) with conventional pellets a figure of around 30-40% would be a first guess but it will be heavily design dependent. For slugs figures closer to 10-20% are probably better but again design dependent. The barrel twist rate and twist direction will also change the vertical deflection in size and direction.

As for coriolis effect for airguns I am not convinced it will be relevant. For rifles shooting 1000 metres or more yes, but air rifles? If you want to include coriolis then you should have to include the direction in which you are firing and where you are on the Earth's surface.

Spin drift for pellets will be in the opposite direction to that for slugs. Pellets will normally drift to the left and slugs to the right assuming a barrel with right hand twist. If the barrel twist is in the opposite direction the spin drift will also be in the opposite direction. The program will again need extra input, gyroscopic stability factor as a minimum to give a crude guess with sweeping assumptions. To calculate it properly will need axial inertia, Cma, spin rate, spin damping and lift coefficient in a modified 4DOF program. Some of the old fire control systems used to use a fiddle based on, I think, time of flight but they needed to know what projectile and gun was being used. I am not at all sure the data to create such a system for pellets and slugs exists. Work may need to be done in the future if air gun ranges keep increasing.

Sorry I cannot be more specific. The main problem is people are trying to use point mass trajectory models for things which need extra abilities in the program and, with that, much more input data. This is a very similar situation to that which existed in the 1960s for artillery fire control systems. For pellets and slugs the necessary data simply does not exist or is not made available. I have created limited data on one or two pellet designs and some slug designs but it is not of much use without the specialised trajectory programs to use it.
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Offline JungleShooter

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #49 on: June 10, 2020, 09:49:01 PM »
Thanks a lot for your time and input, Miles! 😊

Matthias

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #50 on: September 15, 2021, 01:43:18 PM »
Does a tin pellet require a different twist rate than a lead pellet? I found the tin slug thread before this one and saw that tin slugs require a much faster twist rate. I'm getting very inconsistent groups with my .177 regulated Bandit firing Dynamic TM-1 9.5 grn tin pellets. Sometimes my groups will be 1/2" or less, but other times up to 1.5". The TM-1 pellets also aren't shaped quite like the traditional Diabolo pellet, they look like a pellet/slug hybrid. I remember it being much more accurate with H&N Barracuda copper plated 10.64 grn pellets, but I can't test right now due to a tropical storm moving through our area.
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Offline ballisticboy

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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #51 on: September 15, 2021, 08:00:24 PM »
I have looked at non-lead pellets compared to lead pellets, and the ideal twist rates seemed to be much the same for the two. This is probably because the pellets I looked at were aerodynamically stable and thus less dependent on spin stabilisation.

One thing which did stand out was that the non-lead pellets were much more affected by any pellet defects than lead pellets of an identical design. This would suggest that non-lead pellets need to be made to a greater degree of accuracy and consistency, and also are more critical of pellet barrel fit for good group sizes.

If there is any interest, I could put the modelling results in a thread.
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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #52 on: September 15, 2021, 08:27:17 PM »
I have looked at non-lead pellets compared to lead pellets, and the ideal twist rates seemed to be much the same for the two. This is probably because the pellets I looked at were aerodynamically stable and thus less dependent on spin stabilisation.

One thing which did stand out was that the non-lead pellets were much more affected by any pellet defects than lead pellets of an identical design. This would suggest that non-lead pellets need to be made to a greater degree of accuracy and consistency, and also are more critical of pellet barrel fit for good group sizes.

If there is any interest, I could put the modelling results in a thread.

If you don't mind I would like to see the modeling.
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Modelling Comparing Lead and Non-Lead Pellet Group Sizes
« Reply #53 on: September 16, 2021, 06:26:15 PM »
With all the discussion of banning lead pellets in the future, I have had a look at a direct comparison of the group sizes between two pellets, one made of lead and the other made of zinc. I chose the usual 0.22 15.9 grain JSB type pellet and just substituted zinc for the lead. The zinc pellet weight came out at 10.04 grains, a bit lightweight but ok for this comparison. The results should be much the same for tin pellets, as the densities of zinc and tin are very similar (7.13 for zinc and 7.31 for tin).

Stability and group sizes are affected by a very large number of things, but one of them is the balance between the physical properties of the pellet, such as mass and moments of inertia, and the aerodynamic properties. If the aerodynamic and physical properties are balanced for a given design of lead pellet and you change from lead to zinc, then you are changing the all important balance, which should change how the pellet works. I am trying to see how much the group sizes change and if different twist rates are needed for the different pellet materials.

Many of the non-lead pellets appear to be the same or similar designs to the lead ones. This work compares the groups sizes for a lead and a zinc pellet of identical shape, fired at the same muzzle velocity (900ft/sec) and with the same defects present in the pellets. As the pellet designs are identical, the same aerodynamics have been used for both the lead and zinc pellets, but with the different mechanical properties.

The defects are based on some work I did some time ago looking at the effect of twist rates on group sizes for non-perfect pellets. For this exercise the pellets have a centre of gravity which is 0.1mm (4 thou) away from the pellet centreline, and a 1.25mm diameter flat spot on the front of the nose close to the pellet edge representing a dent or cavity. The barrel twist rates used range from one turn in 82 inches up to one turn in 7 inches.

The aerodynamic data is based on experimentally derived data as far as possible, with some extra coefficients estimated using standard aerodynamic estimation techniques. The pellet physical characteristics have been calculated using a simple program which has been tested for accuracy against standard shapes with known mass and inertial properties. The trajectory modelling program is a six degree of freedom model which has been fully tested to government standards.

The group sizes at 30 and 50 yards for both the lead and zinc pellets have been calculated and compared. The resulting variations in group sizes with barrel twist rate is shown in the two diagrams below for 30 and 50 yards range. Each dot represents two trajectory runs, one with no pellet defects to give a zero error point and one with the pellet defects to give the error size and thus the predicted group size.





Don’t worry about the size of the groups predicted, that is just a function of the size of the pellet defects used, which were pretty severe, for this exercise in order to show up the differences. The important things are the relative sizes of the lead and zinc groups and how they vary with barrel twist rates.

The 30 yard results are the easiest to look at first, as the lead (pb) pellet results are always better than the zinc (zn) results. The zinc group sizes are generally 30% or more larger than the lead ones. The results at 50 yards are largely the same, but there is something strange happening at twist rates around one turn in 50 inches, where the zinc pellet suddenly looks much better. Looking at the variation in the pellet yaw angle with range for this twist rate, the maximum yaw seems to increase to a much larger angle than normal, indicating a dynamic instability which then to slowly damps down. This can be seen in the diagram below, showing the vertical yaw angle as a function of range for this particular case
.


One possible explanation is something known as spin yaw resonance producing spin yaw lock in, which happens when the yaw and spin frequencies are the same or very close. The yaw wave length shown above is close to the barrel twist rate, which would support the resonance theory. Resonance usually gives larger errors. In this exercise though, the orientation of the pellet defects used produced a vertical error giving a high impact point. The extra drag produced by the yaw angles shown above caused the pellet to fall as the range increased, so it may just be a coincidence that the error is small at the chosen range because the extra fall of the pellet due to the increased drag counteracted the vertical error of the pellet defects.

The best twist rates for both the lead and the zinc pellets seem to be similar, with the zinc having a slightly smaller bandwidth of suitable twist rates.

The results do not mean that a lead pellet will always give smaller groups than a zinc pellet. A zinc pellet with no defects which is a perfect fit in a barrel will be as good as a lead one in terms of group size. What it does mean is that a zinc pellet is much more sensitive to defects and is much more fussy about the barrel fit than a lead one. A zinc pellet will have to be made much more accurately and be a better fit in the barrel to match the lead pellet group sizes. Using lead pellet designs and production methods as a basis for zinc pellets is unlikely to give suitable results in a wide range of guns and barrels due to the above sensitivity.

The effects of cross winds have not been included in the above results for group sizes.
« Last Edit: September 16, 2021, 07:15:18 PM by rsterne »
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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #54 on: September 16, 2021, 08:10:13 PM »
Miles,

Very interesting!

You are an amazing guy. Your research, and your way of putting the results and implications into words that are comprehensible — great! 👍🏼

Thank you.

Matthias
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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #55 on: September 17, 2021, 08:55:19 AM »
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.
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Re: External Ballistics of Pellets by Ballistician Miles Morris
« Reply #56 on: September 17, 2021, 11:17:04 AM »
I'm hoping manufacturers will start making zinc and tin pellets with all new designs rather than just substitute materials.
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Pellet Wobble Effects on BC and Accuracy (Groups)
« Reply #57 on: September 23, 2021, 05:20:06 PM »
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.
  • Maidstone, Kent, UK, England
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