View Question
Q: Upper bound on rocket speed ( Answered ,   2 Comments )
 Question
 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:
 ```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 operation. http://www.grc.nasa.gov/WWW/bpp/bpp_WHY.htm Note, this "physical principles" refer to amount of fuel. The Relativistic Rocket is possible: main question still is: How much fuel is needed? http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html 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. http://www.umich.edu/~newsinfo/MT/00/Fal00/mt1f00a.html In conclusion: The short answer: a rocket's speed is limited by the fuel it can carry. The long answer: read hear: http://www.madsci.org/posts/archives/may97/860795535.As.r.html 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. Hedgie``` 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: `You made no effort to explain the claim I heard.`

 ```The claim you heard about maximum rocket speed was most likely a verbal statement of the rocket equation V = v*ln(M/m), where V = rocket speed v = exhaust speed M = initial mass of rocket (ship + fuel) m = final mass of rocket (ship only) http://scienceworld.wolfram.com/physics/RocketEquation.html (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.```
 ```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. http://www.discover.com/issues/aug-03/cover/ 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.```