conor@inmos.co.uk (Conor O'Neill) (10/23/89)
In article <1989Oct18.174154.23242@utzoo.uucp> henry@utzoo.uucp (Henry Spencer) writes: >In general, correct. For one thing, it's easier to build solid motors >in large sizes (i.e. high thrusts). For another, the average molecular >weight of the exhaust is higher, which is bad for getting maximum velocity >but good for getting maximum thrust. I've seen this said before (many times) but never with a simple explanation. My school physics seemed to imply that it is exhaust momentum which matters, not simply velocity nor molecular weight. Could someone please elaborate. -- Conor O'Neill, Software Group, INMOS Ltd., UK. UK: conor@inmos.co.uk US: conor@inmos.com "It's state-of-the-art" "But it doesn't work!" "That is the state-of-the-art".
zweig@brutus.cs.uiuc.edu (Johnny Zweig) (10/24/89)
conor@inmos.co.uk (Conor O'Neill) writes: >In article <1989Oct18.174154.23242@utzoo.uucp> henry@utzoo.uucp (Henry Spencer) writes: >>In general, correct. For one thing, it's easier to build solid motors >>in large sizes (i.e. high thrusts). For another, the average molecular >>weight of the exhaust is higher, which is bad for getting maximum velocity >>but good for getting maximum thrust. >I've seen this said before (many times) but never with a simple explanation. >My school physics seemed to imply that it is exhaust momentum which matters, >not simply velocity nor molecular weight. Could someone please elaborate. Note that the exhaust's momentum involves its velocity relative to the spacecraft's motor. There are actually 2 kinds of thrust: Momentum Thrust and Pressure Thrust. The first has to do with the momentum of the stuff going out of the motor, the other has to do with the crose-sectional-area of the nozzle and the difference between ambient pressure outside and the exhaust gas pressure. (According to the "Space Handbook", available from the US Gov't Printing Office). I can't quite hack all the Isp, TC/m, and other mumbo-jumbo. I think it boils down to the fact that the mass-flow (Kg/S) out the back of the motor gives you part of your thrust, and the interaction between what comes out the back "pressing against" the atmosphere is another. So if I have two rockets that spit out the same mass of stuff per second, but one has higher nozzle pressure, that one will give me somewhat more thrust off the launchpad (once up in space there should be no difference since there's no atmosphere). I would also be interested in a more accurate explanation, if someone who can avoid simply stating some equation and saying "see, dummy?" would care to post one. -Johnny Non-physicist
roger@telesoft.com (Roger Arnold @prodigal) (10/25/89)
conor@inmos.co.uk (Conor O'Neill) writes: > henry@utzoo.uucp (Henry Spencer) writes: > >In general, correct. For one thing, it's easier to build solid motors > >in large sizes (i.e. high thrusts). For another, the average molecular > >weight of the exhaust is higher, which is bad for getting maximum velocity > >but good for getting maximum thrust. > > I've seen this said before (many times) but never with a simple explanation. > My school physics seemed to imply that it is exhaust momentum which matters, > not simply velocity nor molecular weight. Could someone please elaborate. > > -- > Conor O'Neill, Software Group, INMOS Ltd., UK. > UK: conor@inmos.co.uk US: conor@inmos.com You're correct that it's exhaust momentum which matters. Momentum is mass times velocity; energy, however, is proportional to mass times velocity *squared*. For a given amount of power (energy per second), you can increase the thrust (momentum per second) by increasing the mass flow and reducing the exhaust velocity. The tradeoff between thrust and exhaust velocity is most relevant in optimizing the performance of ion engines for interplanetary missions. In that case, you're dealing with an external power source, as opposed to using the energy in the fuel itself. Henry's example for solid fuel rockets is a little misleading. Power, in a solid fuel rocket, is a function of the burn rate, and that's controlled by things like the fuel composition, the exposed surface area, and the grain size. It's pretty easy to design for the maximum burn rate, and hence thrust, that the rocket casings will take. There's no reason to deliberately reduce exhaust velocity in a solid fuel rocket; you want whatever the most energetic combination of solid fuel and oxidizer you can manage to develop will deliver. - Roger Arnold ucsd!telesoft!roger
davidsen@crdos1.crd.ge.COM (Wm E Davidsen Jr) (10/25/89)
In article <1989Oct23.203306.24154@brutus.cs.uiuc.edu>, zweig@brutus.cs.uiuc.edu (Johnny Zweig) writes: | I can't quite hack all the Isp, TC/m, and other mumbo-jumbo. I think it boils | down to the fact that the mass-flow (Kg/S) out the back of the motor gives | you part of your thrust, and the interaction between what comes out the back | "pressing against" the atmosphere is another. So if I have two rockets that | spit out the same mass of stuff per second, but one has higher nozzle | pressure, that one will give me somewhat more thrust off the launchpad (once | up in space there should be no difference since there's no atmosphere). Let me try to explain how this works. Picture a sphere filled with a pressurized fluid. Call it a ballon full of hot air. If you bisect the sphere with a plane (like, cut it in half), the pressure against each half will be equal. No thrust. Now open a hole in the sphere and let pressure escape (let go of the next of the balloon). If you think about the sphere pressure now, the inner pressure is P (say 10 psi), and the diameter of the nozzle is D (say 1/4 inch). That's an area of .785 square inches, which would have had a pressure of 7.85 pounds against it. Therefore the "front" of the balloon (or combustion chamber) has 7.85 lb more pressure on it than the back. There are also action/reaction effects which are independent of the pressure. Note that atmospheric pressure didn't come into any of this, except that it raises the pressure in the combustion chamber by a tiny amount and therefore raises the thrust. Since lack of atmosphere will effect either of the rockets you mentioned, there will still be more thrust for the higher pressure. Since you said the samme mass per unit time, the *velocity* may well be higher, as well, depending on the density of the exhaust. Correct or expand on this as appropriate. The guy said he wasn't a physicist so I didn't use metric. -- bill davidsen (davidsen@crdos1.crd.GE.COM -or- uunet!crdgw1!crdos1!davidsen) "The world is filled with fools. They blindly follow their so-called 'reason' in the face of the church and common sense. Any fool can see that the world is flat!" - anon
griffin@helios.physics.utoronto.ca (Prof. A. Griffin) (10/25/89)
Disclaimer: I am NOT professor Griffin. If you use "F", please check the attribution against the signature. In article <2639@ganymede.inmos.co.uk> conor@inmos.co.uk (Conor O'Neill) writes: >In article <1989Oct18.174154.23242@utzoo.uucp> henry@utzoo.uucp (Henry Spencer) writes: >>In general, correct. For one thing, it's easier to build solid motors >>in large sizes (i.e. high thrusts). For another, the average molecular >>weight of the exhaust is higher, which is bad for getting maximum velocity >>but good for getting maximum thrust. > > >I've seen this said before (many times) but never with a simple explanation. >My school physics seemed to imply that it is exhaust momentum which matters, >not simply velocity nor molecular weight. Could someone please elaborate. > All right, here's a high-school physics description. We assume that the reason the gas is moving so quickly out the back of the rocket is that the gas is hot, and that it has thermalized according to a Maxwell-Boltzmann distribution. Fancy talk which means that the average velocity (careful, not the root mean square velocity) is sqrt( 8 k T /(pi m) ) where m is the molecular weight of the particle which has been thermalized, and k is the Boltzmann constant. So, if you're going to throw one kilogram of gas heated to T degrees out the back of your rocket, you would do best to choose one with a low molecular weight, because of the m^-1/2 dependence. By the way, about that equation. I've been known to slip a decimal on occasion, as history will show, but the m^-1/2 dependence is as described in a book, and we all know that textbooks are never wrong :-) >-- >Conor O'Neill, Software Group, INMOS Ltd., UK. >UK: conor@inmos.co.uk US: conor@inmos.com >"It's state-of-the-art" "But it doesn't work!" "That is the state-of-the-art". -- Christopher Neufeld....Just a graduate student | "Scotty..now _would_ cneufeld@pro-generic.pnet01.crash | be a good time!" griffin@helios.physics.utoronto.ca | - Pavel Chekov "Don't edit reality for the sake of simplicity" |
henry@utzoo.uucp (Henry Spencer) (10/25/89)
In article <2639@ganymede.inmos.co.uk> conor@inmos.co.uk (Conor O'Neill) writes: >>... the average molecular >>weight of the exhaust is higher, which is bad for getting maximum velocity >>but good for getting maximum thrust. To get one picky issue out of the way here: I goofed slightly. To a first approximation, molecular weight is not an issue for maximizing thrust. (Should have looked it up rather than trying to figure it out myself...) >I've seen this said before (many times) but never with a simple explanation. >My school physics seemed to imply that it is exhaust momentum which matters, >not simply velocity nor molecular weight... If all you want is thrust, then momentum is the significant number, and that is determined basically by pressures and areas in the engine. But for many applications propellant consumption also matters, which puts a premium on the highest possible exhaust velocity, to get a given amount of exhaust momentum with the minimum exhaust mass. In a thermal rocket, where exhaust velocity is achieved by heating gases to high temperatures and letting them expand out a nozzle, to a first approximation exhaust velocity is set by chamber temperature and exhaust molecular weight. The significance of molecular weight is that at a given temperature, the average *energy* of gas molecules is constant regardless of their mass, so the ones with the lowest molecular weight move fastest. -- A bit of tolerance is worth a | Henry Spencer at U of Toronto Zoology megabyte of flaming. | uunet!attcan!utzoo!henry henry@zoo.toronto.edu