Glad to see new activity here. I did a lot of independent research and calculations on this stuff a few years back, and my conclusion was basically that the propulsion team should think about designing one stage of a hypothetical three stage rocket - that is, a stage with a delta-v of ~3.2km/s when the payload mass is based on the non-propulsion components of previous launch vehicles. Achieving such a thing would go a long way toward gaining credibility, and it'd make one hell of a sounding rocket on its own. A really conservative rough estimate, assuming 50% kinetic energy lost due to drag effects, still puts the rocket at more than 200km altitude.
An actual three stage orbital LV would benefit from not having each stage contribute an identical amount of delta-v. Specifically, it makes sense for the first stage to be very high acceleration for a short amount of time, and the last stage to be a longer, slower, high- efficiency burn. The reason for this is that high acceleration is desirable when lifting off vertically because you're losing 1 g just to overcome gravity. However, if your mass ratio for that stage mo/mf is, say, 0.5, this means your total accelerating mass is going to drop in half over the burn, and in the absence of throttling (a recommended absence) your acceleration is going to be twice as high. Therefore the limiting factor on the delta-v contributed by any stage is that the initial acceleration must be great enough that the 1g loss is not significant, but the final acceleration must not tear the vehicle apart. This leads to a more realistic estimate of perhaps 2 to 2.5km/s delta- v from the first stage, as a design goal. This is doable with an exhaust velocity of 2500m/s and a fuel/total mass ratio of 63%. Still pretty technically challenging, but within reason. Keep the design as simple as possible, consider doing some test launches without the full avionics and recovery package - just having the nose cone pop off and deploy a streamer to spoil the aerodynamics is a lot more reliable than a parachute recovery system deployed by a computer running Java. By now it should be obvious that the Shuttle is the opposite of good design practices in terms of reliability, infrastructure required to launch, frequency of launch, &c. Some things to consider. Richard Campbell On 25 Oct 2007, at 06:53, rq17zt wrote: > Hey all, > > Since Andrew was talking about re-starting the propulsion list > recently, here's post ;) > > --- > > Tom and i were discussing scaling laws for Isp at the > Wed. meeting. I'll give a summary, but this is just from my memory, so > receive it with some skepticism. > > As a simple 1st approach to designing a motor for orbit, we estimate > the mission requirement as a vehicle capable of achieving a certain > minimum delta-V. Meaning the relative speed the vehicle would achieve > absent losses such as gravity and air friction. For our 1st guess we > selected the minimum delta-V as ~9 km/s, around 20% more than the > orbital velocity, which is about 7.6 km/s. > > (I went back and looked up our old requirement estimate, > it was 9.46 km/s.) > > Delta-V can be computed in terms of the mass ratio and propellant > exhaust velocity as > > 1) delta-V = c * Log[m0 / mf] > > Where (c) is the propellant exhaust velocity, (m0) is the initial > vehicle mass, and (mf) is the final vehicle mass at burn out. > > For the record, > > 2) c = gee * Isp > > Where (Isp) is the specific impulse, defined as Thrust/(mass flow > rate), and (gee) is the Earth's gravity, which i believe by convention > is assumed to be 9.8066 m/s^2. For calculations never use Isp > directly, always use exhaust velocity. > > --- > > The important thing about the 1st equation is that there is an > exponential relationship between (c) and the fraction of the initial > vehicle mass that must be propellant. Further, for a given structural > technology there is an upper limit on how large the propellant > fraction can be. Therefore given the structural technology there is a > minimum Isp needed to reach orbit. > > When talking with Tom at the meeting i forgot that all this applies to > single stage vehicles. Staging improves the situation somewhat, so we > should take that into account in our calculations. > > --- > > In the rocket biz there is a standard way of expressing the propellant > fraction etc. > > (mL) is the mass of the payload > (mp) the propellant mass > (md) is the dead 'weight' (Useless stuff like motors and tanks, > etc. ;) > > I'm not sure how well it works, but it's common to attempt to separate > the effects of payload mass from propellant and vehicle structure, > which motivates the definition of the "propellant mass fraction" > > Lp === mp / (mp + md) > > Eq(1) can be rewritten in terms of (Lp) > > [ Lp mL + mp ] > 3) delta-V = c * Log[-----------------] > [Lp mL + (1-Lp) mp] > > > ------ > > It would be nice if as part of exploring propellants we could get this > info up on the Wiki in a semi-polished form. > > ------ > > The rest of this info is taken verbatim from my old notes, much of > which were based on the talk we got from Ranier Anacker. > > Typical propellant exhaust velocities: [m/s] > Hydrogen + Oxygen 3700, 4500 > Kerosene + Oxygen 2700, 2800 > Gasoline + Oxygen 2600, 2700 > Alcohol + Oxygen 2500, 2700 > Shuttle SRBs 2500, 2600 > Most Solids 2200, 2500 > > "Realistic Lp values are between 0.7 and 0.9." > > Mass fraction of real rockets: > Vehicle mp[kg] md[kg] Lp mL[kg] > V2 (1945) 8482 3082 0.7335 1000 > > Shuttle SRB 502700 81900 0.8599 - > Shuttle External Tank 703100 35000 0.9526 - > Shuttle E.T.+Orbiter 703100 178300 0.7977 - > Shuttle (1995) 1708500 342100 0.8332 13000 > > DeltaII (1995) 207706 19359 0.9147 2000-5000 > DeltaIII (2000) 262749 27468 0.9054 8000 > > _______________________________________________ > psas-propulsion mailing list > psas-propulsion@lists.psas.pdx.edu > http://lists.psas.pdx.edu/mailman/listinfo/psas-propulsion > _______________________________________________ psas-propulsion mailing list psas-propulsion@lists.psas.pdx.edu http://lists.psas.pdx.edu/mailman/listinfo/psas-propulsion
