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Q: Upper bound on rocket speed ( Answered 3 out of 5 stars,   2 Comments )
Subject: Upper bound on rocket speed
Category: Science > Physics
Asked by: mr_spock-ga
List Price: $8.00
Posted: 09 Aug 2005 19:48 PDT
Expires: 08 Sep 2005 19:48 PDT
Question ID: 553833
I read somewhere (sorry, no link) that the velocity of a rocket
vehicle (in a vacuum) was limited to approximately twice the velocity
of it's exhaust.  This didn't make sense to me.  After thinking about
it, I realized that perhaps the claim is making an assumption about
the underlying propulsion technology (theoretical limits on ISP, etc).
 What's the story?
Subject: Re: Upper bound on rocket speed
Answered By: hedgie-ga on 10 Aug 2005 00:43 PDT
Rated:3 out of 5 stars
Dear Spock 

 There is no limit on speed of a rocket, imposed by physics
 (other then speed of light, of course).

 Practical limits are given first 
                  by amount of fuel and then
                  by method of propulsion.

Here is an overview from NASA:
Rocket technology is fundamentally limited by its need for propellant.
The farther, faster, or more payload carried, the more propellant that
is required. This limit cannot be overcome with engineering
refinements. This limitation is based on the underlying physical
principles of all rocket propulsion - the very physics of its

 Note, this "physical principles" refer to amount of fuel.

The Relativistic Rocket is possible:

main question still is:
How much fuel is needed?

The secondary questions is: method of propulsion:

EP is faster then CP

The ejection of gases from this reaction provides thrust to the
rocket. The energy provided in chemical propulsion is limited because
it takes a relatively large mass of fuel to achieve the needed levels.
That limits the exhaust velocity. In the space shuttle, for example,
the natural limit imposed by CP is less than three miles a second or
about 10,000 miles per hour."

"In one form of electric propulsion, electro thermal, we use an arc
that has about the energy density of a lightning bolt in heat. So the
speed limit jumps to about 45,000 miles per hour." Ion propulsion
introduces even more energy and can go to 100,000 mph now, with faster
speeds on the horizon.

In conclusion:

The short answer: a rocket's speed is limited by the fuel it can carry. 

The long answer: read hear:

The  final proof (in case of argument) that there is no such limit
(even if slow method, such as CP, is used) comes from physics: 

 Conservation of momentum:
If you expel a mas m at speed v  from moving body (a rocket),
 then momentum of that body (rocket) MUST increase by m*v .
 No matter how small that v was, it is a positive increase of velocity.

Of course:
If v is small, then we are wasting resources.
If speed of rocket is [very] high  (relativistic) ,
then adding of momentum and relation of momentums and velocity
has to use relativistic formula.

 Contribution is still positive. That's all.


Clarification of Answer by hedgie-ga on 11 Aug 2005 01:05 PDT
Mr Spock

 I do prefer any rating to no rating, since it provides a feedback
 which helps to be a better researcher.
In this case I would prefer a Request for clarification before rating:
as I really am at loss what is there to explain on a claim, which is not valid. 
 I provided proof that claim is wrong. That should satisfy a logical person.
 I added few supporting links to 'authorities'  like NASA and 'mad scientist'
 for general consumption, as general public which is not always logical.

 Does 'to explain an invalid claim' means to scrounge up some arguments 
in support of it? In some cases there are arguments on both sides of an issue,
but this one is not that kind of a question. It looks like yes or no question.


You can still clarify that - if you wish.
In anycase, thank you for question and rating,
mr_spock-ga rated this answer:3 out of 5 stars
You made no effort to explain the claim I heard.

Subject: Re: Upper bound on rocket speed
From: racecar-ga on 10 Aug 2005 11:31 PDT
The claim you heard about maximum rocket speed was most likely a
verbal statement of the rocket equation

V = v*ln(M/m),

V = rocket speed
v = exhaust speed
M = initial mass of rocket (ship + fuel)
m = final mass of rocket (ship only)

(I left the Vo off the equation because I'm assuming the rocket begins at rest.)

So, if the initial mass of the rocket is 7.4 times its final mass
(that is, 86% of the initial mass is fuel), then the top speed of the
rocket is the exhaust speed times the natural log of 7.4, which is 2. 
It is probably difficult to build a rocket whose starting mass is over
95% fuel, which is what you would have to do to reach 3 times exhaust
speed.  That is likely the reasoning behind the statement you recall.

The formula above ignores gravity, and is for a single stage rocket,
but it still works as an upper bound for ship velocity even with
gravity and multiple stages.  You just let m be the mass of the last
stage, and M the total initial mass.
Subject: Re: Upper bound on rocket speed
From: mr_spock-ga on 10 Aug 2005 12:18 PDT
Thank you.  That is perhaps where the 2x came from.  I think I read
that in this article, but I can't access it now to verify.

If so, shame on Discover Magazine.

I only gave 3 stars because I though I would be able to rate each
answer seperately.  The last answer was better.

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