B = burning rate coefficient
C = weight of unburned propellant
Cd = orifice discharge coefficient of oil damper
Cv = specific heat of gas at constant volume
f = fraction of web remaining unburned
K = oil damper velocity coefficient
K1 = heat transfer coefficient
K0, K1, K2, K01, K1', K2, = constants for geometrical form function
m = propelled mass
N = weight of burned propellant equal to weight of gas produced at time t
n = burning rate exponent
P = propellant gas pressure
P* = oil damper oil pressure
R = gas constant
T0 = propellant adiabatic flame temperature
T = space mean temperature of propellant gas
v = velocity of propelled mass
w = propellant web
s = travel
s0 = initial displacement
α = maneuver load factor
ρsp = density of solid propellant
ρdf = density of damping fluid
2
(7) The value of the heat transfer coefficient, K', in thrusters is of the order of 100 to 200 ft-lb/sec-ft = .
F
(8) Because of the interdependence of the many variables in the equations describing the interior ballistics of
a damped thruster, an electronic analog usually is set up to solve the equations as a function of time. The
coefficients and other factors in the equations are then varied on the analog computer to match as best as
possible an experimental pressure time curve from a workhorse (heavy-weight) developmental thruster.
One or more of the coefficients (B, n, form function coefficients, etc.) which define the rate of gas
production can be varied until an "ideal" pressure-time curve is defined. The propellant charge design can
then be refined to meet the "ideal" coefficients. The refined charge would then be tested in an actual
device for verification of the computer study.
b. Bypass Requirements.
(1) Bypass conditions are specified for some thrusters at the end of stroke in order to obtain a required
pressure at the end of a fixed length of high pressure hose. Assume that a minimum bypass pressure, Pt,
is required at the end of a fixed hose length, Lt, and is to be supplied at the end of function of the thruster.
It is necessary to know the pressure in the thruster when the bypass port is uncovered, Pf; it is also
necessary to know the volume of the thruster, Vd.† For a hose with volume, V,t, and surface area, S., an
estimate of the hose pressure is given by:
Where:
β = fraction heat loss due to flow through the orifice and additional heat loss in the thruster after
ports are uncovered.
†Vt includes volume of the end block or any other volume attached to hose, in addition to the hose volume.
‡ See app. V for derivation of equation (49).
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