On this slide, we have collected all of the equations
necessary to calculate the thrust of a rocket engine.
In a
rocket engine,
stored fuel and stored oxidizer
are ignited in a combustion chamber.
The combustion produces great amounts of exhaust gas at high
temperature
and
pressure.
The hot exhaust is passed through a
nozzle
which accelerates the flow.
Thrust
is produced according to Newton's
third law
of motion.
The amount of thrust produced by the rocket depends
on the mass flow rate through the engine, the exit
velocity of the exhaust, and the pressure at the nozzle
exit. All of these variables depend
on the design of the nozzle.
The smallest crosssectional area of the nozzle is called the
throat of the nozzle. The hot exhaust flow is
choked
at the throat, which means that the
Mach number
is equal to 1.0 in the throat and the
mass flow rate
m dot
is determined by the throat area.
mdot = (A* * pt/sqrt[Tt]) * sqrt(gam/R) * [(gam + 1)/2]^[(gam + 1)/(gam  1)/2]
where A* is the area of the throat, pt is the total
pressure in the combustion chamber, Tt is the total temperature
in the combustion chamber, gam is the ratio of
specific heats of the exhaust, and
R is the
gas constant.
The
area ratio
from the throat
to the exit Ae sets the
exit Mach number:
A/A* = {[(gam+1)/2]^[(gam+1)/(gam1)/2]} / Me * [1 + Me^2 * (gam1)/2]^[(gam+1)/(gam1)/2]
We can determine
the exit pressure pe and exit temperature Te from the
isentropic relations
at the nozzle exit:
pe / pt = [1 + Me^2 * (gam1)/2]^[gam/(gam1)]
Te / Tt = [1 + Me^2 * (gam1)/2]^1
Knowing Te we can use the equation for the
speed of sound
and the definition of the
Mach number
to calculate the exit velocity Ve:
Ve = Me * sqrt (gam * R * Te)
We now have all the information necessary to determine
the thrust of a rocket.
The exit pressure is
only equal to free stream pressure at some design condition.
We must, therefore, use the longer version of the generalized
thrust equation
to describe the thrust of the system.
If the free stream pressure is given by p0, the
rocket thrust equation
is given by:
F = m dot * Ve + (pe  p0) * Ae
You can explore the design and operation of a rocket nozzle with
our interactive
thrust simulator
program which runs on your browser.
The thrust equation shown above works for both
liquid rocket
and
solid rocket engines.
There is also an efficiency parameter called the
specific impulse
which works for both types of rockets and greatly simplifies
the performance analysis for rockets.
Guided Tours

Rocket Thrust:

Propulsion System:

Combustion:

Rocket Thrust Simulator:
Activities:
Gas Temperature Activity: Grade 1012
Related Sites:
Rocket Index
Rocket Home
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