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.

Process:

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.

1. Use the same a gun when shooting the 4 sets.
2. Use interchangeable choke from same manufacturer.
3. Use the same shells for each set. -- AA light target (2.75 dram, 8 shot, 1.125 oz, 461 by count).
4. Pull all shells from same box.
5. Shoot - a whole set at one sitting.
6. Same distance - 14 yards (see earlier discussion on pattern evaluation).

2. Gun and choke differences and other thoughts.

1. Gun --- Winchester 37 - 24-inch barrel, 2.75 chamber, .729 bore, fitted with Winchoke screw in choking system. Use four Winchoke tubes. No other special work has been done to the barrel or choke except for the addition of the choking system.
2. Four chokes were used. Three are factory Winchoke tubes that measure 1.82 inch in length and are choked .690, .700 .705. One is an after market tube extended job which measures 3 inches in length with a choke measuring .710. Note about choke differences. The Winchoke tubes measure .740 at the point where the shot enters the choke. This is larger than the bore. I suppose this is to guarantee a smooth transition from bore to choke tube. However this also allows the shot to expand for a short time before being compressed by the rest of the choke. It could very well act like a jug choke and give a pattern result greater than the indicated constriction alone would indicate. Here all 4 choke tubes are of equal construction so a valid comparison should result. Choke construction can make a measurable difference in velocity.
3. The four choke constrictions used should be different enough to detect any effect on velocity if any exists. Here again I use all shots fired (41 in all) making no judgment to the "goodness" of the data points.
4. A note about the choke variable used in analysis. In the discussion above notice it's the surface area of the bore and choke used in the energy conservation formulas. When calculating the choke area vs the bore area proportions for the various choke diameters I found that these proportions, although slightly different, are very close to simple diameter proportions between bore and choke. This is due to the small differences in diameter size at the choke. Using the differences from a base bore diameter is much easier to comprehend and is very close to actual theory.

Statistics:

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.

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.

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.

 Conclusions:

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.