- #1

Ozen

- 41

- 2

- TL;DR Summary
- I have two equations for thrust on a muzzle brake, however they each yield different results, which is correct?

Let me start off by saying I decided to post this in the aerospace engineering thread because it directly deals with thrust, even though it is not for a plane or similar.

I have two equations that I can use to calculate the force on a baffle of a muzzle brake, Equation 1, from The Engineering Design Handbook Series, and Equation 2, from Armament Engineering, a computer aided approach. But both yield different results with the same inputs (even when converted to there correct counterpart. Equation 1 yields significantly higher results than equation 2. Below is a run-down on solving them both for the same given system, note that they don't use the same variables always.

Ae = .000029 m^2 (bore area)

mc = .00169 kg (charge mass)

mp = .00402 kg (projectile mass)

Vt = 9.2E-06 m^3 (16in barrel volume); 3.5E-06 m^3 (7in barrel volume)

vo = 892 m/s (muzzle velocity); 650 m/s

pe = 5.52E+07 PA; 1.17E+08 PA (chamber pressure)

lambda = 1.64 (factor)

Ct = 2.21 (correction factor)

RT0 = 700119 m^2/s^2 (gas constant * average temperature of gas at shot ejection)

pmz = pe * (1 - (mc / (2 * mp +mc)) (pressure at muzzle exit)

Fb = 0.26 * lambda * Ct * (mc / Vt) * Ae * RT0 * (1 + (mc / 6 * mp))

***Units must be in imperial, all were converted to their correct correspondent before computing

16in barrel: Fb = 9385 N

7in barrel: Fb = 29389 N

Doesn't this seem rather odd? Almost triple the force for a system that has lower velocity, lower volume, and higher pressure.

Fb = pmz * Ae * lambda * Ct

***Units must be metric, same as above

16in barrel: Fb = 4794 N

7in barrel: Fb = 10162 N

Which equation should I use? I lean towards Equation 2 since that seem more realistic, but if that is wrong, the material may yield and break when I would test a design. Or worse, the design could work for testing but have a bad fatigue life and end up breaking not long after.

***Supplemental question: Why do shorter barrel systems produce more thrust on the baffle than the longer barrel systems?

I have two equations that I can use to calculate the force on a baffle of a muzzle brake, Equation 1, from The Engineering Design Handbook Series, and Equation 2, from Armament Engineering, a computer aided approach. But both yield different results with the same inputs (even when converted to there correct counterpart. Equation 1 yields significantly higher results than equation 2. Below is a run-down on solving them both for the same given system, note that they don't use the same variables always.

**Givens:**Ae = .000029 m^2 (bore area)

mc = .00169 kg (charge mass)

mp = .00402 kg (projectile mass)

Vt = 9.2E-06 m^3 (16in barrel volume); 3.5E-06 m^3 (7in barrel volume)

vo = 892 m/s (muzzle velocity); 650 m/s

pe = 5.52E+07 PA; 1.17E+08 PA (chamber pressure)

lambda = 1.64 (factor)

Ct = 2.21 (correction factor)

RT0 = 700119 m^2/s^2 (gas constant * average temperature of gas at shot ejection)

pmz = pe * (1 - (mc / (2 * mp +mc)) (pressure at muzzle exit)

**Equation 1:**Fb = 0.26 * lambda * Ct * (mc / Vt) * Ae * RT0 * (1 + (mc / 6 * mp))

***Units must be in imperial, all were converted to their correct correspondent before computing

**Solved:**16in barrel: Fb = 9385 N

7in barrel: Fb = 29389 N

Doesn't this seem rather odd? Almost triple the force for a system that has lower velocity, lower volume, and higher pressure.

**Equation 2:**Fb = pmz * Ae * lambda * Ct

***Units must be metric, same as above

**Solved:**16in barrel: Fb = 4794 N

7in barrel: Fb = 10162 N

**My Question:**Which equation should I use? I lean towards Equation 2 since that seem more realistic, but if that is wrong, the material may yield and break when I would test a design. Or worse, the design could work for testing but have a bad fatigue life and end up breaking not long after.

***Supplemental question: Why do shorter barrel systems produce more thrust on the baffle than the longer barrel systems?