This shows we want high Po/Pe. This means large area ratio., not necessarily high Po. In fact, for vacuum operation, higher Po simply means higher Pe, with no increase of ue (or Isp). In a closer look, higher Po can increase To by inhibiting dissociation-> higher Isp But the main reason to go to high Po is to reduce weight for a given thrust(also for boosting, where Pe cannot be much lower than Pa, so high Po/Pe means high Po) M4πR2tp 2πRtG=πR2po At 2R M4xR2P。Rp A=KR2 F2σcP。K M 2I PwR F = CPK R R F KC CoOk M (Kcn)。v Thus, for a given thrust level the engine mass scales like For a given total impulse(not thrust), it may be better to reduce Po, reduce thrust, operate longer. In boosters there is a complex tradeoff, involving gravity losses, drag penalties, improved Isp at high Po, etc. In general, for boosters it is found advantageous to go to high Po, limited mostly(in liquid rockets by turbomachinery For space engines the result is less clear, but they do tend to optimize at much lower The power of a rocket can be extremely high For the shuttle F=3000ton=3×10Nt, C=3300 m/sec 3×10×3.3×103=5×100wat=50GW! Thus, if one step in the power chain involves electrical power the engine is likely to be very heavy. Why then electrical? Because it breaks the ue limit, allowing any Isp, or, in other words, it gives very fuel efficient rockets. With EM forces one can increase ue almost arbitrarily however looking at the power requirements, Pro f a spa martine ssn Lecture 1b Page 5 of 616.522, Space Propulsion Lecture 1b Prof. Manuel Martinez-Sanchez Page 5 of 6 This shows we want high P0/Pe. This means large area ratio e * A A , not necessarily high P0. In fact, for vacuum operation, higher P0 simply means higher Pe, with no increase of ue (or Isp). In a closer look, higher P0 can increase T0 by inhibiting dissociation higher Isp. But the main reason to go to high P0 is to reduce weight for a given thrust (also for boosting, where Pe cannot be much lower than Pa, so high P0/Pe means high P0). Roughly 2 w 2 0 F0 t M 4 R t 2 R t = R p F cPA π ρ  πσ π 0 R t=p 2σ 2 0 w 2 2 t F 0 M 4 R PRρ A = K R F 2 c P K R π σ  w 2 F 0 F F 0 M2 F R F = c P K R R = F Kc c P K π ρ σ  ( ) w 32 32 0 F M2 1 = F K c P π ρ σ Thus, for a given thrust level, the engine mass scales like 0 1 P . For a given total impulse (not thrust), it may be better to reduce P0, reduce thrust, operate longer. In boosters, there is a complex tradeoff, involving gravity losses, drag penalties, improved Isp at high P0, etc. In general, for boosters it is found advantageous to go to high P0, limited mostly (in liquid rockets) by turbomachinery. For space engines the result is less clear, but they do tend to optimize at much lower P0. The power of a rocket can be extremely high. For the Shuttle 7 F 3000 ton = 3 ×10 Nt ,  c 3300 m/sec  1 11 mc Fc 3×10 3.3 10 =5 10 watt =50 GW!! 2 7 3 10 2 22 = = ×× × i Thus, if one step in the power chain involves electrical power, the engine is likely to be very heavy. Why then electrical? Because it breaks the ue limit, allowing any Isp, or, in other words, it gives very fuel efficient rockets. With EM forces one can increase ue almost arbitrarily; however looking at the power requirements