Cadence and the Crack Shot

A few matches ago, I noticed a phenomenon in my shooting.  Every so often, I would notice my shots starting to move.  I’d make a small sight change and immediately see a large motion in the hit location.  I always passed it off as a possible issue with my sight.  Then I was reading a book on high power shooting by G David Tubb.  He talked about maintaining a steady cadence and the idea that heating of the cartridge in the chamber can change the muzzle velocity.  My thought was that if I chamber a cartridge before fiddling with the sights, then that one shot would heat soak in the chamber for longer than all the other shots.  This would throw the shot high, or at least wild.

So, off for a test.  I made up 20 test rounds.  I set up 2 targets side by side.  After shooting a number of rounds to warm the barrel, I then shot at the 2 targets alternating right and left.  Every shot to the left I shot at normal cadence.  Shots to the right I sat on for a measured 30 seconds, then shot at my regular cadence.  My expectations were a similar group size for each style with the slow cadence side grouping higher than the fast cadence.

Wrong.

The variation in elevation of the 2 groups was .06 inches at 200 yards.  Essentially nothing.  However, group sizes were very different.  Fast cadence had a standard deviation of 4.27  while the slow cadence had a standard deviation of 2.99.  This is a big chunk.  Both of these might be a bit higher than normal because I went about 10 shots longer before cleaning than normal.

The next question was what the shortest reasonable wait time would be.  I wired up a cartridge with a thermocouple run in through the primer hole.  I built it up with powder and a bullet, just like the real thing.  Then, after each string at a match, I’d pop the wired shell in and record the temperature rise over time.  

 

The shell is a bit dirty, but I've been pushing it into dirty chambers all day.

The chart below shows the various data strings.  The temperature was rising throughout the day, so the starting point is a bit off for each.  I also was a little slapdash on getting started promptly when the shell went in.  Overall, it was a bitterly cold day.

 Temperatures are degrees F and time in seconds.

Clearly the heating steadies out after about 30 seconds.  My normal cadence would have a cartridge in place for 10-15 seconds, so there was probably a lot of variation at that pace.

I'll probably do a similar test on a hot day, but for now, I'll just be patient when I need to take that Crack Shot.

End-Over-End me through trouble and strife.

I’ve recently added to my monthly 200 yard silhouette match.  I’ve gone out to a mid and long range match starting at 300 and going out to 1000 yards.  Now I’ll admit, I don’t use the 38-55 Trapdoor beyond 600 yards, but it does get to reach out a bit.  Besides the eye opening challenge of shooting long range in a 25MPH side wind, I discovered an additional issue.  My .38 bullets seem to be going unstable at the longer range.  I knew they were OK at 300 yards because I can do a lot of testing at that range locally, but 600 yards is harder for me to get time at.

A book was suggested to me.  “Understanding Firearm Ballistics” by Robert Rinker.  It was pretty straight forward and came with one formula on basic stability that would help me compare my current “OK” bullet with any new bullet I want to try.  The formula basically compares the moment of inertia of the bullet in the spin direction with the moment of inertia in the tumble direction.  It also has a term for the RPM of the bullet spin, which turns out to be a fairly heavy player.

So labeling:

N=RPM

A=MOMENT OF INERTIA IN SPIN

B=MOMENT OF INERTIA IN TUMBLE (OR YAW-it should be the same either way).

S=”STABILITY”.  I will be treating it as a dimensionless number as long as all my input numbers use the same units from one bullet to the next.

U= A shape factor.  I have no way of calculating this, so I choose to ignore it.  Easy, eh?

The basic formula is:

S=A^2*N^2/(B*U)

I apologize for my poor math text layout. 

The important thing to notice is that stability goes up as the square of the moment of inertia in spin and the square of velocity.  So a short squat fast bullet should be highly stable.

The next step is to compare my current bullet with my new bullet.  A little time with a cad program and some calipers and I had my numbers.  The pictures below show my two bullets.

My current bullet is a Postell style that weighs 336 grains. It is a Lyman 378674DV

The Round Nose Flat Point weighs 305 grains.  It is a Redding Saeco 65571  #571.

The Postell has a CG that is 6.3% of the length back of the center.  The RNFP CG is 4.1% back of the center.  This in itself will add some stability as the tendency of the nose to lift is reduced.

The Postell “A” value is .0007675 LB*in*in compared to .0007279 for the RNFP. 

The Postell “B” value is .005918 as compared to .004374 for the RNFP.

So, assuming the muzzle velocity is unchanged (which, sadly, seems to be the truth despite the lower weight) I get an increase of stability of right at 20%.  Which is sizeable, but is it enough?

Well, off to the range.  At 300 yards, the new, shorter, bullet throws a 10 shot group with a standard deviation of 1.56.  The older, postell, bullet throws a standard deviation of 3.76.  This is a big chunk and the smaller bullet has become my baseline.  However, at 300 yards, it doesn’t really answer my question.  Is it more stable at 600 yards?  Unfortunately, the data acquisition at 600 is a little tougher.  In matches, each shot is marked by a target puller and can be viewed from a scope, but that’s a lot less accurate than measuring paper.  So my answer right now is “I don’t know.”  Hopefully, sometime in the spring, I can get to a test range during low wind and shoot some test targets.