Calculating Exhausted Mass Velocity in Rocket Thrust Manipulation

[xphysics]

Hey everyone, so I'm just wondering if you guys can articulate the term "velocity of lost mass" from the rocket. After a few massaging on the equations(derivatives and integrals stuff) i found that to manipulate the thrust, one must manipulate the burn rate AND the "velocity of loss mass". all i know about the velocity of loss mass is that it's well the velocity of the mass that's being exhausted from the rocket itself. So my question is: How could you experimentally calculate the velocity of lost mass(notes: this is not the burn rate but the speed of the mass that's being exhausted)

These are the equation if you wondered:
F=(dm/dt)u (u is the velocity of lost mass)
or this:
http://ocw.mit.edu/courses/physics/...anics-fall-1999/lecture-notes/supplement8.pdf

 

[tiny-tim]

hi xphysics!

Hey everyone, so I'm just wondering if you guys can articulate the term "velocity of lost mass" from the rocket.
…
all i know about the velocity of loss mass is that it's well the velocity of the mass that's being exhausted from the rocket itself. So my question is: How could you experimentally calculate the velocity of lost mass(notes: this is not the burn rate but the speed of the mass that's being exhausted)

i'm not sure what you're asking

the "velocity of lost mass" is the speed of the mass relative to the rocket

 

[xphysics]

"How would you experimentally calculate..."

 

[D H]

Hey everyone, so I'm just wondering if you guys can articulate the term "velocity of lost mass" from the rocket. After a few massaging on the equations(derivatives and integrals stuff) i found that to manipulate the thrust, one must manipulate the burn rate AND the "velocity of loss mass".

For all practical purposes, a rocket has zero control over the exhaust velocity. The only thing that is controlled dynamically is the burn rate, and for many rockets, even that isn't controllable. Solid rocket engines are "on" until they run out of fuel. Simple liquid fueled rocket engines can be turned on or off, but they aren't throttleable. It's only the more sophisticated rockets that can control the amount of mass consumed per unit time, and even most of them can't control the exhaust velocity.

The exhaust velocity of a rocket is determined by the nature of the fuel being burnt, the geometry of the rocket's combustion chamber and nozzle, and by the ambient pressure of the atmosphere into which the exhaust is being propelled. You can't switch fuel mid-flight, and you have no control over ambient pressure. The only thing that is controllable is the geometry of the rocket, and it's only a very, very tiny fraction of rockets (mostly experimental) that somehow control their geometry. For most rockets, the geometry is fixed at the time the rocket is built.

How could you experimentally calculate the velocity of lost mass(notes: this is not the burn rate but the speed of the mass that's being exhausted?

By putting the rocket on a test stand.

 

[xphysics]

Can you tell me more about the test stand? I thought of enforcing it horizontally and then record it frame by frame to measure how fast the flame is coming out since it's the lost mass( if I'm correct)

 

[D H]

People want to measure thrust, not exhaust velocity. The amount of thrust generated by a rocket is what is of utmost concern. Exhaust velocity? Not so much. While it is ultimate what generates thrust, measuring it isn't all that meaningful. The exhaust velocity can be back-calculated from measurements of the thrust generated by the rocket.

 

[Sunfire]

Analysis becomes simpler if you'd consider a primitive rocket comprising an adiabatic duct and a compressed gas tank attached to its inlet. Then you'll need to look at Fanno flow analysis of the flow in the duct to determine the exit flow velocity.

This is a simplified system though. Just my 2 cents.

 

[xphysics]

Ahhh I see! You can obtain the velocity of the rocket (at a certain time ofc) then use Tipler's derivation to obtain the exhausted mass velocity. Oh and the reason why I consider the exhausted mass velocity because it affects the velocity greatly IMO if you look at the derivation, same goes for burn rate
Anyway thank you for suggesting that method, it'd great if I can obtain more suggestions from you guys about obtaining the exhausted mass velocity, also what do you think about the method I mentioned above?