Velocity vs. Choke.
During testing with my 32 inch Winchester 37 I have noticed that I consistently get velocities higher than published velocities both for reloads and factory loads. There can be many reasons but three obvious possibilities come to mind. Either it's due to the barrel length, the tight choke or a chronograph that has a positive bias. Could be the chronograph as it is a bargain priced unit but lets use this opportunity to examine several truisms and at the same time narrow down the actual reason for the increased velocity.
Myth - The velocity of a shell fired from a tight choked gun will be greater than the same shell fired from a gun with a more open choke.
This myth has also been around forever with little or no proof. This should be an easy thing to test so first I'll test to see if it is true. Then if it is true I'll try to see how important the relationship really is. Here I would also hope to determine if speed variation caused by choke constriction is important enough to consider when choosing a load or choke constriction.
Theory and physics:
Theory would say that this is probably a true hypothesis. The shot charge (blob) leaving the barrel must be able to be compressed and/or modified else the result would be a catastrophic event. If we assume the moving shot charge is somewhat like a non-compressible liquid like water or compressible liquid like air we should be able to apply nozzle theory to the shot charge as it passes through the choke. Conservation of energy demands that as the shot blob passes through the choke that energy into the choke region (Q1) must equal energy out (Q2). So the blob with area a1 (unchoked bore area) moving down the pipe at velocity v1 (Q1=(a1)x(v1)) will change in the choke region to an area a2 (choked area) with velocity v2 (Q2=(a2)x(v2)). However some energy, L, will be lost due to increased friction and any work used to compress the blob (this quantity is hard to measure but is always >0 and would increase with choke constriction). So we would expect (a1)x(v1)=(a2)x(v2)-L. Since a2<a1 then v2>v1 would be expected.
1. Shoot and collect patterns and velocities using 4 chokes of different constrictions.
2. Evaluate and calculate 70 % circle diameters - use these in other studies.
3. Run simple statistics on tabulated results to test hypothesis
4. Try to get a statistically significant relationship between velocity and Choke constriction.
5. Draw conclusions.
Technical precautions and procedures:
1. Eliminate as many variables as possible.
2. Gun and choke differences and other thoughts.
By running a simple multiple linear regression program against the data we can see if Choke constriction is significant in determining velocity. Here variable 1 is velocity as measured by the chronograph; variable 2 is choke constriction beyond .720 in thousands. By this I mean a .690 choke is rated as 30 = (.720-.690)x1000 and .705 = 15 etc. A 3rd variable shows up in the results and is a constant term.
Here again variable 1 is measured velocity and variable 2 is choke diameter tighter than .720 in thousands of an inch.
VARIABLE MEAN VARIANCE STD DEV 1 1183.366 609.7878 24.69388 2 18.65854 55.03049 7.418253 MATRIX OF SIMPLE CORRELATION COEFFICIENTS 1 1 2 .6237 1 DEPENDENT VARIABLE NO. 1 381.641 14884 39 VARIABLE COEFFICIENT STD.ERROR T-VALUE 2 2.076191 .4163858 4.98622 3 1144.628 8.346736 137.1348 MEAN SQUARE STD ERROR MULT CORR F-TEST ON R 381.641 19.53563 .6243298 24.91218
From this analysis we see that choke diameter (variable 2) is significant in predicting velocity as is variable 3 (a constant). Significant is determined by a T-value of greater than 2 or less than -2 in the results for each variable in predicting velocity. Likewise we also can say we are 95% sure the actual f/s multiplier for each thousandths of an inch constriction is between 2.08 - .83 (1.25) and 2.08 + .83 (2.91) with the best estimate at 2.076 f/s.
Chart with regression line drawn in:
If you have trouble seeing this graph click on the graph itself.
These results indicate that choke has a significant impact on velocity at least for this gun, chokes and type loads tested. A quick explanation of the results: the velocity starts at 1145 feet/sec and increases 2 feet/sec for each thousandth of an inch of extra constriction beyond our base of .720 inch.
An estimate would be for any given velocity would be:
Velocity in ft /sec = 1145 + 2.08*constriction.
So shooting the AA light loads (1145 f/s by the book) would have a muzzle velocity of 1190 for a .700 choked barrel. That is 1145+(.720-.700)*1000*2 = 1145+20*2 =1190 . A .690 choked barrel would result in a 1210 velocity. Note that the constant term just happens to be 1145 and has nothing to do with the AA shells used. However it is nice that the velocity generated from this model approaches published velocity as the choke goes to zero (.720).
Note: This analysis includes all shots fired. I have not averaged the shells and have not selectively thrown out obvious outlyers. A much better estimate of actual speed expected for any given increase in choke constriction can be determined by being more selective in which shots I use to derive the model and averaging groups etc.
It appears that the choke constriction has an important and very significant impact on velocity and that our hypothesis is correct. The model gives a quick estimate of the increase in velocity that could be expected with an increase in choke. The model is a simple linear estimate. The actual relationship is probably much more complicated than that. As the choke constriction increases so will the friction encountered at the choke and energy lost to manipulating the blob. This will cause the additional increase in velocity per choke constriction to diminish. I could speculate on the form and amount but with no way to measure such a loss of energy it would only be speculation. The linear model works statistically for the chokes tested and works for the target guns for which I am concerned.
Should I worry about the speed increase with tight choke? Yes! Required lead will be affected and so will the energy per pellet. An increase of 50 or 60 f/sec could allow the use of smaller shot and still give good breaking power with the benefit of greater pellet numbers. Shot string may also be affected but I can't say anything about shot strings without having a way to see them or even if long or short is better.
Real eye opener:
Still having problems with consistency in measured velocity even with AA factory shells. The standard deviation is greater than should be expected though the averages seem reasonable. I suspect the chronograph or my setup. For future I think published velocities + 50 would be a good estimate for the 32 inch test gun when I can't get a reasonable velocity or simply don't have one.