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Old November 5, 2008, 01:41 AM   #1
rbb50
Senior Member
 
Join Date: November 2, 2008
Location: Deep in the Heart of Texas
Posts: 169
Reloading Science and Mathematics

This is called the Greenhill Formula.to determine the optimal rifle twist rate twist for a given bullet in any rifle. The formula is T=150(d/r) for velocities from about 1500 to 2800 fps. Substitute 180 for the 150 value for velocities exceeding 2800 fps. "T" is the twist rate. "D" is the bullet diameter. "R" is the bullet length to diameter ratio (length of bullet divided by diameter).

When V=1500fps-2800fps T=150(D/R)

When V is greater than 2800fps T=180(D/R)

Example with a known:

V=1500fps-2800fps
L=1.19
D= 0.311
R=L/D=3.83
D/R= 0.081
150(D/R) =12.180
T=12.180

With this calculation one can find a 180 grain .311 diameter bullet that is 1.19 inches long will work optimally in a rifle barrel with a 1 in 12 twist rate when fired at a velocity of between 1500 fps to 2800 fps.

This does not take into account the RPM of any given bullet but does work as a way to calculate the velocity needed on other size bullets that have another optimum twist rate slower or faster than the given twist rate in the rifle used.

Calculation to find Revolutions Per Minute (RPM):
“V” is the velocity in feet per second. “I” is 12 inches the amount the bullet will travel in one second. “T” is the twist rate. “RPM” is revolutions per minute. Notice the velocity is in feet per second "FPS" so FPS(I/T) is multiplied by 60 to obtain revolutions per minute (RPM).

RPM= V(I/T)60

Example with a known:
V=2,200fps
I/T=1
RPM=2,200fps(I/T)60
RPM=132,000

The bullet is spinning 132,000 revolutions per minute when fired at 2200 foot per second from a barrel with a 1 in 12 twist rate.

What if the value of T equals a 1 in 15 twist rate?

V=2700fps
L= 0.9
D= 0.311
R= 2.89
D/R=0.1
150(D/R) =15
T=15

The 125 grain .311 bullet that is 0.9 inches long takes a slower twist rate of 1 twist in 15 inches than the longer 180-grain bullet of the same diameter to be optimal for accuracy.

Since the given twist rate of the rifle it is being fired from cannot be changed then to make it an accurate stable bullet the RPMs of the 125 grain bullet need to be slowed down in order for it not to become unstable in flight from too fast of a twist rate.

Normally a lighter bullet will be fired at a much faster velocity as is seen in the reloading manuals and because it is lighter and shorter which allows the case to hold more powder also.

In this case when I find the bullet is not optimal to the twist rate of the particular rifling twist rate it is fired from I can achieve greater accuracy by not loading it to a maximum and loading it to a reduced load as a way to slow down the RPMs there by making a bullet that is optimal for a 1 in 15 twist rate work in a barrel with a 1 in 12 twist rate accurately.

This means I have to use another calculation to find what the RPMs would be normal to the smaller bullet in a barrel with a 1 in 15 twist rate to calculate the velocity it needs to be fired from a barrel with a 1 in 12 twist rate to obtain those same RPMs to make it stable and accurate.

Example with known:

V=2,700fps
I/T=0.8
RPM=2,700fps(I/T)60
RPM=129,600

Imagine that in a 1 in 12 twist rate barrel

V=2,700fps
I/T=1
RPM=2,700fps(I/T)60
RPM=162,000

Let’s slow that bullet RPM down some with a slower velocity in the 1 in 12 twist rate barrel

V=2,160fps
I/T=1
RPM=2,160fps(I/T)60
RPM=129,600

Now we have the same revolutions per minute as in a 1 in 15 twist rate barrel and have a load for the smaller bullet we can calculate to be optimized in a barrel with a 1 in 12 twist rate by using the velocity needed and comparing it to loadings for that particular bullets estimated velocity in reloading manuals.

Kind of seems odd that a 125 grain bullet in that particular caliber would have to be fired at a slower velocity than the heavier bullets to obtain an optimum accuracy for it but believe me when I say it works very well and you will not find a load for that 125 grain bullet in any reloading books published today for the 7.7mm and yet I shot a ½ inch group in the bulls-eye with it at 100 yards just last week using those calculations.

However if I load that same 125-grain bullet to a much faster velocity of 2,700 fps I can see it all over the target with 1-foot groups.

I found the same formula worked with my 7mm-08 concerning the shorter100 grain bullets of which I slowed down to the lowest load in the book still getting about 2,600-2,700fps and saw them hitting one-hole groups from a barrel they should not be optimum in to begin with.

Usually I will load nine rounds for testing with three each of 1/2 grain charge differences and find one of three test loads to give me those 3 shots through one hole groups I am looking for by using the math above and calculating a load for that particular bullet weight for an approximate velocity.

I read a lot of articles about people trying to explain why certain bullets are optimum for certain rifle twist but I have never seen an article explaining much as to why that is.

So I decided to write this little article explaining why that is and how everyone can learn how to make all weights of bullets more accurate in the caliber they are shooting.

Now that I look back on the article I do wonder if it is just like a friend that look at it and then at me and said, “I lost you when you said something about mathematics”. LOL

The other thing I never explained in this article is bullet expansion and how although one can get a certain weight bullet that is not normally optimal for accuracy in a certain rifle twist to become accurate on a target by using mathematics it does not mean that the particular bullet they achieved accuracy with using these formulas will end up with a proper expansion for hunting certain game animals.

Depending on the caliber being used there is a whole other article with more mathematics I would have to write explaining how to calculate energy of any given weight bullet at a given velocity while also calculating the game being hunted weights also.

In short when someone ask me how I make those hand loads that are so accurate while I’m at the rifle range most of the time my answer is just, “Reloading is a science that takes a lot of education in mathematics”.

Yet I did think if I posted this article in this forum that there would be some that would pull out a caliper and measure bullets then find the twist rate of their own rifle barrel while scratching their heads and reading the math and think, “Hummmm…This gives me some new good ideals at the reloading bench now”.

After all you are never going to be able to change the twist rate on your rifle so you might as well do the math if you want to shoot a shorter or longer bullet than what is optimum for the twist rate for that particular rifle accurately.

Just be sure to do the math on the ballistics, expansion and energy for that weight of bullet before you decide to use it for hunting also.

Another part of the math is that a 100-grain bullet is much cheaper than a 180-grain bullet in every case when one just wants to go plinking at the target range for fun of which can turn into not much fun at all if it is not even hitting the target.
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