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