Problem 1 – You are asked to analyze the mass of the charge require to fire a 100mm
recoilless system. A 15 pound projectile is to be fired at a muzzle velocity of 1,500 f/s.
The propellant properties are listed below. Using Equation 3.171 you may assume a
typical ballistic efficiency of 33% to estimate, c, the amount of charge allocated to the
gun side of the recoilless gun. You may consider two cases. First the after effect is
computed using Equation 5.27. For the second case, use .
Specific heat ratio
Propellant force
Effective nozzle exhaust velocity
G = 32.2; % [ft/s/s] acceleration of gravity
g = 1.25; % ratio of specific heats of propellant
Q = G*F/(g-1);% [ft*lb/slug] chemical energy of propellant
eb = 0.33; % ballistic efficiency
Define projectile specific (by slug) energies,
charge mass, and impulse
KE = (1/2)*mp*V.^2; % [ft*lb] muzzle energy of gun
CE = KE./eb; % [ft*lb] chemical energy required
6.4 Interior Ballistics of Recoilless Guns
Problem 2 – We want to examine the ballistic efficiency of recoilless guns as a function
of velocity. We know the ballistic efficiency of Equation 3.171 should decline at higher
velocities because more kinetic energy must be invested in the propellant gas column to
keep up with the shot as quantified in Equation 3.20. Let us suppose we know the
efficiency for the close breech approximation to gun and propellant of problem 1 is 33%
at 500 m/s and declines to 25% at 1,500 m/s. A linear fit between these two points is
(6.10)
Using the approximation of Equation 6.9, please plot the ballistic efficiency using
equation 3.171 for the total propelling charge of a recoilless gun between 500 m/s and
1,500 m/s. You may use . What is the highest ballistic efficiency and at what
muzzle velocity does it occur?
interest
vv = 1500:5000; % [ft/s] muzzle velocity of gun
cg = CEg/Q; % [slug/slug] mass of propellant per slug
Ig = vv.*(1+cg/2); % [lb*s/slug] total launch momentum per slug
Compute nozzle propellant and then total
propellant
required per slug
title(‘Efficiency of a 100mm Recoilless Gun’)
grid on
Display maximum efficiency and the
velocity it
occurs at