Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site petrus.UUCP Path: utzoo!watmath!clyde!burl!ulysses!bellcore!petrus!karn From: karn@petrus.UUCP (Phil R. Karn) Newsgroups: net.space Subject: Re: Scramjets Message-ID: <34@petrus.UUCP> Date: Thu, 27-Feb-86 20:57:47 EST Article-I.D.: petrus.34 Posted: Thu Feb 27 20:57:47 1986 Date-Received: Sat, 1-Mar-86 04:20:14 EST References: <344@vger.UUCP> <617@smeagol.UUCP> Organization: Bell Communications Research, Inc Lines: 115 > 1. Specific impulse (Isp): thrust per pound of propellant. At least, > that's the way I learned it, a carry over from non-metric > engineering. (Thrust per unit mass is probably more meaningful.) > Propellant naturally includes both fuel and oxidizer. You are > correct that in the case of air breathers, they get their oxidizer > from the atmosphere. Thus, their Isp's are higher. Rockets tend > to have Isp's in the low 100's; turbojets in the 3000's (?), and > ramjets somewhere in between.... I have several problems with this. Specific impulse is often erroneously specified in "seconds"; the correct units should be "meters/sec", i.e., velocity. The error occurs because Isp is usually defined in English units as pounds-force of thrust x seconds -------------------------------- pounds-mass of propellant and somebody made the mistake of "cancelling out" the pounds-force factor with the pounds-mass factor. A good example of how the English system of measurements befuddles thinking, but I digress... In metric units, things are much clearer: newtons of thrust x seconds --------------------------- kilograms of propellant Since a newton is the force required to accelerate 1 kg by 1 meter/sec^2, it has dimensions Kg-m/sec^2. When the other factors are included, this all reduces to meters/second. This way of expressing specific impulse has a much more elegant and straightforward meaning: it is simply the velocity of the rocket exhaust relative to the rocket. The faster the exhaust, the higher the specific impulse and the less mass (i.e., propellant) that must be ejected to gain a specified impulse (momentum). Since momentum is simply mass times velocity, this is a linear relationship. You only need half as much propellant mass if you kick it out twice as fast. However, the energy that must be imparted to the exhaust increases as the SQUARE of the exhaust velocity (the kinetic energy of the exhaust is 1/2 m v^2). If as a measure of the "energy efficiency" of a rocket you divide the energy imparted to the exhaust by the impulse obtained, you get: energy = 1/2 mass x velocity^2 ==> 1/2 x velocity ------- --------------------- impulse = mass x velocity This means that the amount of power required to sustain a given amount of thrust goes up linearly with exhaust velocity (i.e. specific impulse). This is why people don't generally use rocket motors to propel automobiles. If to cruise down the road at a nice legal 55 mph you need X newtons of "thrust" to balance air and road drag, it is much more energy efficient to do this by exerting a force of X newtons against the road at 55 mph than it is to push with the same force against a stream of hot gases traveling at several thousand meters per second. Similarly with airplanes, it is much more efficient to scoop up as much of the air mass around you and push on that than it is to push solely on the combustion products of your engine. So what this says is that for anything other than spacecraft, where you're not surrounded by something you can grab and push on, you want the LOWEST specific impulse you can attain. Hence propellers and high-bypass turbojets are more fuel-efficient than low bypass jets or rocket engines for air travel. It's not clear to me that "specific impulse" has any meaning, though, for an air-breathing (and air-pushing) aircraft, nor for an automobile. With chemical rockets, the combustion products of the reaction that produces energy are used as the ejection mass on which the rocket "pushes". This means that the specific impulse of a chemical rocket is theoretically determined by the propellants' energy density, i.e., joules per kilogram. (I've neglected some other effects here such as the molecular weight of the combustion products and other, non-useful ways that the combustion energy is dissipated, but suffice to say that there is a theoretical exhaust velocity associated with each propellant combination.) Unlike airplanes and cars, spacecraft must carry all their reaction mass with them. Since work must be done to carry this mass to the point where it is finally ejected, for any specified total delta-vee there is an OPTIMUM specific impulse if your goal is to minimize energy requirements. Below this point less power is needed to generate each unit of thrust, but this is outweighed by the extra thrust (and power) needed to loft the extra ejection mass required. On the other hand, above this point you can carry less reaction mass, but the extra energy required to eject it at the higher velocity more than counteracts the savings in lofting propellant mass. So why do rocket designers always seem to be striving for higher specific impulse? One reason is that other considerations besides energy efficiency are important. Rockets are mechanically easier to build if they have lower fuel-to-payload mass ratios; in particular, fewer stages may be needed. The other reason is that in most situations, chemical rocket propellants always seem to have less than the optimum specific impulse, so an increase is almost always desirable. If you go away from chemical rockets, however, the rocket's energy no longer need be stored in its reaction mass. For example, in a nuclear rocket engine energy from a nuclear reactor is applied it to an inert (for the purposes of thrust) material such as hydrogen gas. It is then possible to vary the specific impulse of the engine as an operating parameter. If you want more specific impulse, feed less mass to your reactor (operating at a constant power level), or alternatively, crank up the reactor while feeding it mass at a constant rate. Either causes the mass to be ejected at a higher velocity, increasing specific impulse (and the amount of power required for each unit of thrust). Other engines in which this is possible include the ion engine, the plasma engine and the electrothermal thruster. In many cases, the engine has to be operated at a LOWER specific impulse than it is capable of because it is easier to carry additional reaction mass than additional energy for accelerating it. Unfortunately, all of these non-chemical engines, with the exception of the nuclear engine, are currently incapable of generating enough thrust to overcome their weight; they are useful only in space when you've got plenty of time to accumulate momentum. Phil