How To Calculate Velocity For Different Barrel Lengths

I found these equations online; they were developed by Homer Powley. They seem to work well for rifles, and handguns, with the exception of revolvers.

Also, they may not be accurate when calculating the velocity of barrel lengths where most of the powder is wasted, for example, a .45-70 from a 4-inch barrel will most likely produce an inaccurate value.

However, a .223 from a 3-inch barrel was accurate to within 3 ft/s (it estimated 1,150 ft/s).

Alright, here's how to do it.

You need to know these values for your load.

Also, remember you can calculate velocities for longer, as well as shorter, barrels.

Vo = the original muzzle velocity (ft/s)

B = the bullet weight (gr)

C = the charge weight (gr)

Lc = the cartridge overall length (in)

Lb = the bullet length (in)

Lbbl = the barrel length (in)

D = the bore diameter (in)

I'll do an example.

.30-'06 Springfield 150-gr SP at 2,900 ft/s from a 24-in barrel.

We'll see how it does from a 16.5-in barrel.

Vo = 2,900 ft/s

B = 150 gr

C = 54.0 gr

Lc = 3.34 in

Lb = 1.10 in

Lbbl = 24.0 in

D = 0.308 in

First we find the expansion ratio, Ro.

Ro = 1/(1-([(B+C/3)(Vo/8000)^2]/C))

Ro = 1/(1-([(150 gr+54.0 gr/3)(2,900 ft/s/8000)^2]/C))

Ro = 1/(1-([(168)(0.131)]/C))

Ro = 8.19

The expansion ratio is 8.19.

Now we want to find the expansion ratio for the new barrel.

First find the Bullet Travel for the original barrel, To.

To = Lbbl+Lb-Lc

To = 24.0+1.10-3.34

To = 21.8

Now find the bore volume, Sbo.

Sbo = To*0.773*D^2

Sbo = 21.8*0.773*0.308^2

Sbo = 1.60

Now we need to find the "chamber volume", Sc.

Sc = Sbo/(Ro-1)

Sc = 1.60/(8.19-1)

Sc = 0.222

Now we can use Sc to calculate the expansion ration for the new barrel.

Find the bullet travel and bore volume of the new barrel.

T = Lbbl+Lb-Lc

T = 16.5+1.10-3.34

T = 14.3

Sb = T*0.773*D^2

Sb = 14.3*0.773*0.308^2

Sb = 1.05

Use the bore volume to find the new expansion ratio.

R = (Sb/Sc)+1

R = (1.05/0.222)+1

R = 5.70

Now use this equation and solve for velocity.

V = 8000*sqrt((C*(1-(1/sqrt(sqrt(R)))))/(B+(C/3)))

V = 8000*sqrt((54.0*(1-(1/sqrt(sqrt(5.70)))))/(150+(54.0/3)))

V = 8000*sqrt((54.0*(1-(1/sqrt(2.39))))/168)

V = 8000*sqrt((54.0*(1-(1/1.55)))/168)

V = 8000*sqrt((54.0*(1-0.65))/168)

V = 8000*sqrt((54.0*0.35)/168)

V = 8000*sqrt((54.0*0.35)/168)

V = 8000*sqrt(19.1/168)

V = 8000*sqrt(0.113)

V = 8000*0.337

V = 2694 which rounds to 2690 ft/s.

The velocity of the load from a 16.5-in barrel is estimated to be 2,690 ft/s.

If you are likely to use this, I suggest saving the equations before they disappear.

That's something I had a problem with.

Any questions, send me a PM.

After all those formulas you may be in need of a little levity. Enjoy!

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