Good article.
Shotgun Shell Ballistics & Penetration
December 17, 2008 by Chris Hustad
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By Marvin McDonald ( J J Mac )
I have investigated the effect of shot size and velocity on penetration in waterfowl. I decided to publish the results because others might be interested as well.
The recommendation most commonly encountered in the DHC Forums for adequate penetration for clean kills with steel shot is a velocity of 575 fps or 600 fps for all shot sizes. The implication is that all shot sizes penetrate to the same depth if the velocity is the same for all sizes. Then “maximum kill distances” are obtained from ballistics data corresponding to either 575 or 600 fps. A constant-velocity rule-of-thumb for equivalent penetration by all shot sizes is very simple and therefore desirable but it is well known that all shot sizes do not penetrate the same at a given velocity and thus this rule can’t be technically correct.
For example, people use large shot for Giant Canadas because the large shot penetrates more than small shot at the same velocity. This results in cleaner kills whereas smaller shot works great for smaller waterfowl because of better pattern density and a lesser amount of penetration. Also, hunters use buckshot to kill deer and other large game and police and military personnel use buckshot to stop bad guys. This is due to the penetration of the buckshot which will stop and/or kill the larger targets. Smaller shot size will not penetrate on a consistent basis, at least at normal ranges.
I will show later in this article that the velocity – diameter relationship for equivalent penetration is D2 V2 = D1 V1 for two different pellet sizes of the same density.
Penetration through vital organs is necessary and anything more than that is not needed. However, many hunters think it is desirable for shot to have adequate penetration to exit waterfowl so that one does not chomp down on steel shot at the dinner table.
In what follows, the shot is assumed to be spherical and non-deformable.
More on the 600 fps Rule
The Shotshell Ballistics (SSB) software by Ed Lowry and Keith Garner can be used to obtain the penetration of different shot sizes at any velocity. Pellet Penetration output is the number of inches that the pellet penetrates into ballistic gelatin and is based on experimental data. Unlike the heterogeneous nature of waterfowl (feathers, skin, bone, organs, muscle, etc), ballistic gelatin is a homogeneous material that is made up and calibrated before each use and is used under specified conditions so that reproducible results are obtained. The following table shows the penetration of steel pellets of various sizes at 600 fps from the SSB software.
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As expected, the penetration at 600 fps varies significantly for different shot sizes. For example, T pellets penetrate 2.6 times as much as #7 pellets, 1.6 times as much as #3 pellets, and 24% more than B pellets.
Ducks - SSB Software for Constant Penetration by Different Shot Sizes
Now, let’s see what the SSB program gives for the velocities and distances for equivalent penetration when shooting shot sizes appropriate for ducks. For this purpose, I will assume that #3 steel shot at 600 fps has an appropriate penetration for the type shooting that will be done. This is a completely arbitrary selection at this point just to illustrate the method and the deviation from the 600 fps rule-of-thumb. From Table 1, the penetration in ballistic gelatin for #3 shot at 600 fps is 1.28 inches so that will be the penetration used for all the different shot sizes. Since all the shot sizes will have the same penetration in ballistic gelatin they will also have the same average penetration performance in waterfowl even though it will be different than the ballistic gelatin penetration of 1.28 inches. Of course, the heterogeneous nature of a duck will dictate that the penetration will not always be exactly the same for any two pellets that penetrate in different locations so we are talking average values here. I cover the large range from #7 shot up to B shot just to see the effect even though the most commonly used steel shot sizes for ducks are #4 - #2.
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The 600 fps rule-of-thumb gives distances for that are too far for pellet sizes smaller than #3 and too close for the pellets larger than #3. Note also that the velocity required for 1.28 inches penetration in ballistic gelatin varies greatly for the different diameter shot from 847 fps at the smallest size shown to 501 fps for B shot.
Geese - SSB Software for Constant Penetration by Different Shot Sizes
Here is a look at loads commonly used for geese. Steel BBs at 600 fps (ballistic gelatin penetration = 1.80 inches) are used as the base case for demonstration purposes.
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Again, the 600 fps rule-of-thumb gives distances that are too large for the smaller pellet sizes (< BB) and too small for the larger pellet sizes (>BB). Also, the velocities vary significantly from 713 fps for #2 shot to 547 fps for T shot.
The Momentum Density Penetration (MDP) Equation
I also took a look at momentum density to see if it could be used to correlate penetration. Momentum density is defined as the pellet momentum (mass x velocity) divided by its cross-sectional area. There is a correlation. If the momentum density is the same for two different size pellets of the same density, the penetration is the same. Simplification results in:
D V = constant for a given amount of ballistic gelatin penetration where D is the diameter of the shot and V is its velocity. Thus, when comparing two different pellet sizes of the same density material, we get
D2 V2 = D1 V1 or V2 = (D1/ D2) V1 “MDP Equation”
In other words, if subscript 1 is for the smaller pellet and subscript 2 is for the larger pellet, for the same penetration the velocity of the larger pellet is reduced from the velocity of the smaller pellet by the ratio D1/ D2. This equation was checked for steel shot and gives the same velocities as obtained from the SSB software using constant ballistic gelatin penetration numbers. It clearly shows the effect that pellet size has on velocity for equal penetration. The MDP equation can be used for shot of different densities too but both pellets 1 and 2 must have the same density.
Shotgun Shell Ballistics & Penetration Summary
This study confirms that the 600 fps rule-of-thumb for steel shot does not give constant penetration for all shot sizes and thus gives erroneous results for maximum killing distances. Of course, we knew this from the start. Certainly you can find a shot size where the “rule” is pretty close, e.g., #3 shot at 600 fps (1.28 in. ballistic gelatin penetration) looks pretty good for ducks and BB shot at 600 fps (1.80 in. ballistic gelatin penetration) looks pretty good for large geese but it would be erroneous to say that two different pellet sizes of the same density have the same penetration when the two velocities are the same.
The SSB software can be used to calculate the velocity and distance for equivalent penetration by shot of different sizes. This calculation can be made for two shot sizes of the same density or the two can be of different density. This is the procedure to follow. For load 1, using the Pellet Penetration page, determine the penetration in ballistic gelatin corresponding to the velocity (or distance) that the load gives the type of performance you prefer. This field performance data can be from your own experience or from the CONSEP Chart or from other sources. Knowing this penetration, open another Pellet Penetration page and find the velocity and distance corresponding to this same penetration using the inputs for the second load. Altitude and temperature adjustments can be made by the software.
The MDP equation can be used for calculating the velocity of one pellet size with the same penetration as another pellet size at a given velocity also if the densities of the two are the same. Then the SSB software can be used to calculate the distance corresponding to that velocity.
One could argue that even though penetration is the same for two pellet sizes, some performance difference may be seen because the wound channel is bigger for the larger pellets and more damage will result. I don’t know how much of an effect this is but suspect it is pretty small if the difference in shot sizes is not large and is bigger when the two pellet sizes differ a lot.
Even though this has been about penetration, pattern density is very important also. For a centered pattern, you must have both adequate penetration and enough pattern density to hit vital organs in order to make clean, consistent kills on waterfowl.
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