Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site ssc-vax.UUCP
Path: utzoo!watmath!clyde!floyd!vax135!cornell!uw-beaver!ssc-vax!eder
From: eder@ssc-vax.UUCP (Dani Eder)
Newsgroups: net.space
Subject: Re: Rocket thrust
Message-ID: <215@ssc-vax.UUCP>
Date: Wed, 20-Jun-84 13:10:54 EDT
Article-I.D.: ssc-vax.215
Posted: Wed Jun 20 13:10:54 1984
Date-Received: Thu, 21-Jun-84 07:56:28 EDT
References: <988@sri-arpa.UUCP>
Organization: Boeing Aerospace, Seattle
Lines: 48

June 20, 1984

     This is an attempt to explain how rocket motor thrust varies with
atmospheric pressure, and why.  For more details, I refer the interested
individual to "Rocket propulsion and spaceflight dynamics", Cornelisse
et al, Pitman Press, 1979, or any of a number of books to be found under
Dewey Decimal classification '629.411' in your local library.

     Definitions: 

     Thrust=F, mass flow rate=propellant consumption rate=mdot, exhaust
velocity=v(e), nozzle area at base of nozzle=A(e), pressure at base=p(e),
atmospheric pressure=p(a).

     The basic relation of rocket engines is F=(mdot)(v(e))+A(e)[p(e)-p(a)].
The first term arises from conservation of momentum.  Mass moving out the    
back times velocity equals rocket body moving forward times velocity.
To get the most use from a given amount of fuel, you want v(e) to be as
high as possible.  Imagine a fixed exit pressure.  As you raise the
chamber pressure relative to it, the gas has more energy available in
pressure drop to be converted into velocity. 
 
     The second term in the relation is the one which raised questions.
   \    /     The exaust gases and atmosphere both exert their forces
   /    \     through the wall of the rocket nozzle.  The exhaust gas
  /      \    produces pressure from the inside and the atmosphere from
 /        \   the outside.  Gas pressure acts perpendicular to a wall,
/          \  so the exhaust on the right wall of the nozzle to the left
||||||||||||  pushes to the right and upward.  If the nozzle is symmetrical,
              rightward component is matched by an opposite force on the
left side of the nozzle, but the upward components add.  This is a net
positive upward thrust.  Similarly, the atmosphere presses inward on the
nozzle, with the left-right components canelling and the down components
adding, producing a negative upward thrust.  The net thrust depends on the
difference between the two, or p(e)-p(a). 

     Some comments have been made about the atmosphere acting on the
bottom of the exhaust bell.  The physical situation is that the pressure
upward on the nozzle end is balanced by an equal pressure downward on the
nose of the rocket.  In an airplane sitting motionless on the ground,
atmospheric pressure is balanced, hence there is no tendency for the
airplane to accelerate off in any direction.  Wings are designed to
create a lower pressure over the top surface than the bottom when air 
flows over them.  It is the pressure difference that holds the plane up.
In a rocket also, it is the pressure DIFFERENCE that provides thrust.

Dani Eder / Boeing Aerospace Company / ssc-vax!eder