simonshack wrote:*
HOW DID THE SHUTTLES ACHIEVE ESCAPE VELOCITY?
The Space Shuttle, weighing 2million kg at launch, apparently used the most advanced liquid fuel (hydrogen/oxygen) propellants known to mankind -
with an exhaust velocity of 4.4km/s.(15.840km/h)
NASA told us that a Space Shuttle would detach itself from its main tank at 110km altitude ("MECO" - Main Engine Cutoff) at which point its rockets were switched off -
having reached a velocity of approx 8km/s.(28.800km/h)
"The most advanced liquid-fuelled chemical rockets today produce an exhaust velocity of, at best, 4.5 km/s. There is nowhere else to go: this is close to the theoretical limit of chemical energy extraction."
(source: see link to book below)
So the obvious question is: how did the Shuttle achieve a speed of 8 km/s with a max exhaust velocity of 4.4 km/s?
The only 'explanation' I've been able to find so far is from a book called
"Rocket and Spacecraft Propulsion: Principles, Practice and New Developments". However, it is clearly meant to be referring to a rocket "performing in the vacuum of space" - and cannot possibly apply to a 2million kg spacecraft still battling against gravity and aerodynamic drag :
http://books.google.it/books?id=xBYYasV ... .6&f=false
To be sure, here it is once again...
Newton's 2nd Law:"Force is equal to mass times acceleration (for constant mass). An object will accelerate in the direction of any net force applied to it. The greater the force, the greater the acceleration. The greater the mass, the slower the acceleration."
Hello again, simon!
I shall try to answer your question about the rocket moving faster than it's exhaust, with the caveat that I'm only talking about rockets traveling through the atmosphere of course
First, an observation about the book "Rocket and Spacecraft Propulsion: Principles, Practice and New Developments" which says:
exhaust [...] once it has left the nozzle of the rocket engine has no further effect on the rocket
This, I agree is the case with rockets in a vacuum.
However, this statement doesn't agree with the
sceppy model of rockets in the atmosphere, which I believe has legs.
http://www.cluesforum.info/viewtopic.ph ... &start=300
OK, here we go
Using (and
not abusing) our man Newton we see that
F=MA (Force = Mass x Acceleration)
If, in our rocket, Force = 1, Mass = 1 and Acceleration = 1 then:
1 = 1 x 1
If the rocket mass drops to .5 while the exhaust still produces the same amount of force then:
1 = .5 x 2
The rocket has doubled it's acceleration and can start to move faster then the exhaust velocity
Given that a rocket is something like 95+% fuel this analysis is reasonable
Now, what happens when the rocket's velocity surpasses its exhaust speed?
Via the Sceppy Model
If a rocket is going up at 1,000 m/s and the exhaust is shooting out at 500 m/s, just to pick some easy numbers, the "sweet spot" of the exhaust plume, where the most work is done by the atmosphere to equalize the low pressure exhaust gas with the high pressure air around it (the
sceppy model), will have moved 500 m farther back from the rear of the craft.The exhaust plume shoots out 500 m in one second but the ship has moved an extra 500 m ahead of it.
This means that the force of the thrust will be diminished accordingly because the source of the thrust is farther away from the rear of the ship.
Going back to Newton, the way he was meant to be used, we find that F=MA still holds and that
Force is now, say half = .5
Mass is half = .5
Acceleration must be 1
And the ship's high rate of acceleration is retarded
.5 = .5 x 1
So it seems that once you get your rocket out in front of it's exhaust plume the rocket is going to slow down.
Via the NASA model
https://www.grc.nasa.gov/WWW/k-12/airplane/thrsteq.html
Thrust = Massflow + Difference in pressure between exhaust and atmosphere
When the rocket is accelerated to faster than the exhaust velocity the rocket:
1. the massflow component of thrust is constant because amount of fuel exiting the nozzle per second is constant
2. The pressure differential component increases the higher up the rocket goes because of lower atmospheric pressure
NASA rockets will continue to accelerate and in fact do better the higher up they go (until they run out of fuel)
NB: the NASA model assumes that when the external pressure is 0 (in a vacuum) the pressure differential component is maximized and hence gas-exhaust rockets are perfect for space travel. According to NASA.