David.Smith@CMU-CS-IUS.ARPA (06/15/84)
n mass. In the rifle analogy, the reaction mass comprises not just the combustion products, but also the rifle and the person holding the rifle. There is a limit to the rate of expansion of combustion products, even if uncontained in space. A rifle ensures that most of that rate gets transferred to the bullet. A rocket lets most of it get away, since the exhaust is only confined by its own inertia. A rocket in the atmosphere gets a little bit of assistance in confining the exhaust. David Smith
jheimann@BBNCCY.ARPA (06/15/84)
From: John Heimann <jheimann@BBNCCY.ARPA> The bullet/rocket analogy is specious because in fact the bullet is part of the material which is being ejected from the rifle; i.e. is analoous to the exhaust gasses, not the rocket. It is the rifle that is analogous to the rocket. If one were to have a rocket engine with a combustion chamber that was open at the front, analogous to an open breech rifle, then we would expect the rocket engine to have far less thrust (if any at all) than a closed chamber engine. Alternatively, as we would expect a bullet fired from a gun in space to have a higher velocity than one fired in the atmosphere since there would be no viscous drag on the bullet, and hence to impart a greater impulse to the rifle, so we would expect a rocket in space to eject its exhaust gasses at a higher rate than in the atmosphere and hence have greater thrust. Another way to look at it: the exhaust gasses escape rearward at a rate which is dependant on the difference in pressure between the engine throat and the end of the exhaust nozzle. The atmospheric "backpressure" that you refer to is just atmospheric pressure on the rear of the rocket, which is cancelled out by atmospheric pressure on the front of the rocket. At every moment I experience something like 5000 pounds of force on my back due to atmospheric pressure, yet I don't accelerate forward since there also happens to be the same force on my chest. John
David.Smith@CMU-CS-IUS.ARPA (06/16/84)
The bullet/rocket analogy is specious because in fact the bullet is
part of the material which is being ejected from the rifle; i.e. is
analogous to the exhaust gasses, not the rocket. It is the rifle
that is analogous to the rocket.
I am not yet convinced that the analogy is specious. The gases
push laterally on the sides of the barrel, as on the sides of the
rocket. To a first approximation, it doesn't matter whether the barrel
is fixed to the breech or travels with the bullet (or it wouldn't if
the barrel had zero weight but retained it strength). The gases push
equally on both bullet and breech, and it doesn't matter which one you
consider to be engine and which exhaust.
But suppose we go ahead and consider the rifle to correspond to the engine.
Which way will you get a bigger kick in the shoulder?
1. Fire the charge without a bullet, producing maximal exhaust velocity.
2. Obstruct exit of the exhaust by forcing it to drive a bullet out.
Alternatively, as we would expect a bullet fired from a gun
in space to have a higher velocity than one fired in the
atmosphere since there would be no viscous drag on the bullet,
and hence to impart a greater impulse to the rifle, ...
To the extent that the air being accelerated ahead of the bullet drags
on the barrel, OK. But besides that (and it's not applicable to the
rocket anyway), I'll still argue that it does not impart greater impulse
in space, even though the bullet velocity is higher.
At every moment I experience something like 5000 pounds of
force on my back due to atmospheric pressure, yet I don't
accelerate forward since there also happens to be the same
force on my chest.
You would if you applied pressure to the air on one side which was not
matched on the other. The rocket exhaust does this.
David SmithREM%MIT-MC@sri-unix.UUCP (06/17/84)
From: Robert Elton Maas <REM @ MIT-MC> Your argument has a serious flaw. If exhaust gas is slowed by frictin with air, it's transferring momentum to the air it slides against, thus total momentum isn't decreased by this friction. In fact if the chemical reaction in the engine resists this backpressure by pushing harder on the exhaust gas to try to foce them to keep their original velocity, the total momentum of the exhaust&FrictionnedAir will be greater.
David.Smith@CMU-CS-IUS.ARPA (06/18/84)
Let's look at the impulse (momentum transfer) derived from burning a small
parcel of fuel/oxidizer. The parcel has mass m and chemical energy E
(which we assume is used with perfect efficiency). Equate the chemical
energy to the kinetic energy of the parcel as it exits the engine (in
the frame of the rocket). This gives us the exhaust velocity,
v = sqrt( 2E/m ).
The impulse to the engine is the same as the momentum imparted to the
exhaust:
I = mv = sqrt( 2mE )
>From these equations, it is clear that throwing extra inert mass into
the engine (raising m without raising E) will lower the exhaust
velocity, while increasing impulse (and thrust with it). This is the
reason that turbofans (and turboprops) are more fuel-efficient than
turbojets, at least up to the speed at which shock waves form on the
blades. Suppose that m is raised not by dumping mass into the
chamber, but by putting the rocket into the atmosphere and letting
the exhaust entrain the air. More thrust, no?
Of course, if the vehicle has to carry the extra mass to the point of
use, it would be better to have it in the form of propellant, so that E
is also raised. Carrying dead mass is pretty expensive. And in space,
you have to carry your dead mass with you.
David Smith
P.S. As I stated in my original message, rockets really do generate
more thrust in space than in the atmosphere. Nasa has stated this, and
they ought to know, having operated engines in both places. I am still
hoping that someone can either show the flaw in my reasoning or tell
what other effects are operating. Perhaps energy is lost to sideways
turbulence?
DRSeder@ssc-vax.UUCP (Dani Eder) (06/20/84)
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