Author Topic: last of the internal ballistics formulae (Read 743 times))

Poorman Plinker · « **on:** August 08, 2017, 02:50:51 PM »

Bore Volume determines the maximum potential amount of propellant usage that will be available to be applied to the base of the pellet, depending on the power plant.

BV = (Pi*r^2)L
Where:
BV = Bore volume (cubic inches)
Pi = 3.14159
r = Radius (inches)
L = Length of barrel (inches)

.177 - 10 inch = .25 cubic inches (ci), 18 inch = .44 ci, 24 inch = .59 ci.
.22 - 10 inch = .37 cubic inches (ci), 18 inch = .67 ci, 24 inch = .89 ci.

Revolutions per-second of a barrel with a rifle twist 1 turn in 14 inches is said to have a twist rate of 14. The MzV (muzzle velocity) times 12 divided by twist rate equals the rate of rotation per second:
RR = MzV*12 / tr
Where:
RR = Rotational rate per second
tr = Twist rate
MzV = Muzzle velocity (FPS)
With twist rate of 14, a projectile traveling at 450 FPS rotates at 337.5 revolutions per-second. To determine revolutions per minute simply multiply by 60 (60 seconds per minute). For the 450 FPS pellet in the 16 twist barrel is rotating at 20250 rpm.

rsterne · « **Reply #1 on:** August 08, 2017, 03:13:47 PM »

In addition to the bore volume determining the amount of air (propellant) used, the other factor is the pressure of that gas.... In fact, you can calculate the MAXIMUM POSSIBLE FPE of any PCP by the following formula....

Max. FPE = Bore volume (cu.in) / 12 x Pressure (psi)

This is broken down as follows....

Bore area (sq.in) x Pressure (psi) = Force available to accelerate the projectile (lbs.)....
Barrel length (ft.) = length through which that force can act....
Bore volume (cu.in) is of course Bore area (sq.in) x Barrel length (in.).... The divisor of "12" converts inches to feet in the formula above....
Energy (ft.lb) = Distance (ft.) x Force (lbs.)

Note that this is the MAXIMUM FPE that it is possible to produce, actually it is the Energy Input into the system.... Some of that energy goes into accelerating the mass of the gas (propellant) itself, some into overcoming friction and all the other losses, and some is lost as heat as the air cools during expansion.... It also assumes that the pressure is a constant throughout the travel of the projectile down the barrel, which would require a reservoir of infinite volume.... In the real world, if you reach 50% of this number as the FPE that ends up in the bullet, you are really doing a good job....

Bob

Poorman Plinker · « **Reply #2 on:** August 09, 2017, 03:27:27 PM »

Mr. Sterne,

Thanks for the new formula. I did not have that one to share with the group. The FPE formula you have there is absolutely clear to me.

Everything I have read says that 30% is the norm. One study sighted as little as 29% in .177 caliber but more in .22. All this by math theory, of course.

Thank you sir,

Poorman Plinker · « **Reply #3 on:** August 09, 2017, 03:42:32 PM »

Actually...

This is what I found:

For illustration, here is a theoretical energy balance of a typical factory pneumatic airgun:
35% Barrel friction/heat
34% Heating of the gases
31% Muzzle velocity

On the other hand, the Cardews had a theoretical energy balance of a typical piston airgun:
6% Spring rebound
3% Piston rebound
5% Muzzle blast
23% Transfer port turbulence
34% Barrel friction/heat
29% Muzzle velocity

Mark Denny "The Physics Teacher" theorized that the energy losses are not universal but are caliber and barrel length dependent. He concluded for barrels between 6 and 19 inches that:
71% of the initial gas pressure was lost in a .177 airgun,
29% for muzzle velocity in .177
56% of the initial gas pressure was lost in .22 caliber
44% for muzzle velocity.

Doug Wall · « **Reply #4 on:** August 09, 2017, 04:34:47 PM »

"34% Heating of the gases"

I always thought that expanding gasses from PCPs and CO2 guns cooled on expansion, not heated!

As for gas pressure lost in the barrel, - It depends on how much air the valve is letting through, and a range of 6-19 inches is a factor of 3! How can you generalize with a factor of 3 involved?

rsterne · « **Reply #5 on:** August 09, 2017, 10:47:40 PM »

The gas released from the valve in a PCP cools.... The air compressed in a Springer heats up.... You can't even begin to compare the Internal Ballistics or Internal Physics of the two types.... TOTALLY DIFFERENT !!!

Bob

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last of the internal ballistics formulae

Author Topic: last of the internal ballistics formulae (Read 743 times))

Poorman Plinker

last of the internal ballistics formulae

rsterne

Re: last of the internal ballistics formulae

Poorman Plinker

Re: last of the internal ballistics formulae

Poorman Plinker

Re: last of the internal ballistics formulae

Doug Wall

Re: last of the internal ballistics formulae

rsterne

Re: last of the internal ballistics formulae