Now if your looking for specific guidance to select a powder I am afraid you will be disappointed with this article. This article is to explore some of the interesting dynamics that happens between the time the primer ignites to the time the wad/shot column leaves the muzzle. There will be no grand life changing conclusion, but hopefully some interesting insight into how pressure affects the wad/shot column while traveling down the barrel.

One of the arguments that always come out of the powder burn-rate argument is that powder X feels softer than powder Y for the same resulting shot mass launched at the same velocity. Since both loads have the same total recoil impulse they are arguing they can feel the difference in the acceleration vs time curve caused by the difference in pressure vs time. Many claim that the slower burning with lower peak pressure of powder X is the reason. Others argue that you cannot sense the difference because if they both have the same mass and the same velocity then they have the same total recoil and feel the same.

Again I don't think I will definitively bust either of these notions as much of the "feel" of recoil is very subjective and particular to each person. What I do believe I can show is that although two loads might truly have the same total recoil impulse that the events that happen over that incredibly short event of setback can actually be different. Whether the average human can feel that differences in an event that takes 2-3 milli-seconds is questionable.

Back in 2002 a man by the name of Neil Winston published two interesting studies on shotguns. The second study looked at pressure and recoil. I am going to borrow some data from and build on his study. The studies can be found at the following web address: http://www.claytargettesting.com/

In the past I have been very critical of his second study on recoil. {http://www.claytargettesting.com/study2/pages/study2.html} As I have revisited the information several times since my initial criticism of the study; my opinion has become less harsh but I still believe the Mr Winston missed a very good opportunity to tell a more complete story.

In the third part of his study, he presents the pressure curve for two loads that have the same total recoil impulse. The two loads have the same mass and velocity well within any reasonable engineering standard. The two loads have velocities that are less than 0.7% different. The interesting thing is the two loads use two dramatically different powders. One is using the fast burning Red Dot (Alliant). The other is using the relatively slow burning PB (IMR). Therefore, the loads have pressure profiles that look noticably different.

In

I hope to use that data to show what the wad/shot column experienced during the setback event.

So next, I am going to explain how I set up a numerical simulation of the setback event and walk through the results. All the programming was writen in MatLab.

First thing I did was to extract the pressure curves from Mr Winston study. I simply digitized the curve shown in

With those functions created and tested, I set about creating a dynamic simulation of the setback event. Start with Newton Second law, from this we will derive the equation of motion for the shot charge moving down the barrel.

The mass is 1 1/8oz of shot.

The force is a function of time and is the result of the pressure (

So now if we substitute our time dependent force function into the

We now have an equation of motion that describes the acceleration of the wad/shot column as a function of time. Since acceleration (a) is the second derivative of position with time we have a differential equation.

Divide the equation through by mass (

From this equation we can create a simple simulation. By numerically integrating the equation of motion twice with respect to time we can create, the acceleration vs time, velocity vs time and position vs time profiles of the load as it moves down the barrel.

In the MatLab code I did just that. My integration was a very simple brute force methode. I had the computing horsepower and the pressure curves were smooth with no discontinuities so a moderately fine time step and simple rectangular integration resulted in acceptable good integration.

The original test data was taken using a 30inch test barrel so I integrated until the position reach 30 inches.

The results were promising but off. Both loads resulted in nearly identical velocities but the velocity was high ~1405fps. Given the pressure data coming from digitizing a plot from another paper I was encouraged the velocities were so close to each other.

I reasoned that the cause for the velocity being high was due to the fact that the above model has no friction in it along with a few other secondary forces like crimp opening, the additional friction in the forcing cone and so on. Friction being the highest of all the secondary force action on the wad/shot column as it moves down the barrel.

Therefore, I derived a simple friction model. Sliding friction is normal modeled as a normal force times a coefficient of friction. I did not have a good value for the coefficient for friction between polyethylene wad and a steel barrel. More so, I did not have any idea the magnitude of the normal force between the wad/shot column and barrel would be.

I conjectured that the normal force generating the friction would be proportional to the force the pressure was putting on the base of the wad/shot column. My reasoning here is that the shot under acceleration of this force would try to spread out. Image trying to pile up shot on the top of your reloading bench the shot under just 1g of acceleration would rather spread out than stack. How hard that shot tries to spread out should be proportional to how hard the pellets are being pushed down. Using those assumptions we come up with a friction model that would look like the following starting with the traditional model for sliding friction.

We already know that

So our friction model looks like:

The catch here is that we do not know what

And this actually worked reasonable well. With a fudge factor of

Now we get to the interesting stuff. First position data. This is the results of double integrating of the resulting acceleration resulting from the force of the pressure and force of friction.

The

Here we see more differences in the characteristic of the velocity profile of the two loads. We can see as expected the slower burning PB takes its old sweet time to get rolling but slowly and surely catches up to the Red Dot load. Its harder to see the difference in the Velocity vs Position plot so I made one more graph (

The thing to see take away from

Now we move on to some more dramatic differences in the acceleration of the shot column. First verse time and second verse the position in the barrel.

From the acceleration plot in

Finally I would like to plot pressure and acceleration (

Conclussion: Recoil is a nasty little thing to quantify in a complete and indepth manner. The easiest and probably most objective way it to simply state it as the total recoil impulse (ie change in momentum) which would be Mass times Velocity. It's simple and for comparison sake accurate enough assuming all other factors are the same, such as the same weight firearm same action type, same shooter, similar clothing, and so on. As I stated earlier that althought the wad/shot column experience dramatically different forces in the two loads exaimed above there is probably only a few exceptional individuals that can "feel" the difference between two loads that have the same total recoil impulse but have different pressure vs time curves. Temporally the setback event is so fast that it is at the edge of our ability to resolve, but human tissue has properites that change fairly dramatically with the rate at which they experience loads so I think its possible but rare to find such an individual.

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