Specific impulse(inverse of specific fuel consumption) is defined as F mg We want high Isp(high c), since AV=cIn dt Using mo =mp +ms +m (mp =propellant, ms structure, m, payload) ms or m=moe-ms So, for given mp, ms, the higher c (Isp), the higher m; this dependence is at least linear( for small c,m=mp av -ms), but it becomes exponentially fast for high energy mIssions(》1) For chemical rockets c is limited by chemical energy/mass in fuel Cm=v2E In general, since u (Accounting for work of expansion leads to a replacement of e by H, the enthalpy. For ideal expansion, Brayton cycle, so nd H=CPTo(ideal gas) 2CpTo1 16.522, Space P pessan Lecture 1b Prof. Manuel martinez Page 4 of 616.522, Space Propulsion Lecture 1b Prof. Manuel Martinez-Sanchez Page 4 of 6 Specific impulse (inverse of specific fuel consumption) is defined as * F sp F c c c I= = = g g m g i We want high Isp (high c), since 0 f dv dm m m =- c ∆V = c ln dt dt m → Using m =m +m +m , 0 PSL ( ) m = propellant, m = structure, m = payload P SL ∆V P c L S L0 S ∆V c m m = - m or m = m e - m e -1 − So, for given mP, mS, the higher c (Isp), the higher mL; this dependence is at least linear (for small LP S ∆V c ,m m -m c ∆V  ), but it becomes exponentially fast for high energy missions ( ∆V 1 c  ). For chemical rockets, c is limited by chemical energy/mass in fuel max c 2E. = In general, since 2 e th th 1 mu = E= mE 2 η η i ii e th u 2E = η (Accounting for work of expansion leads to a replacement of E by H, the enthalpy.) For ideal expansion, Brayton cycle, so -1 e 0 th P =1- P γ γ ⎛ ⎞ ⎜ ⎟ ⎝ ⎠ η and H=cPT0 (ideal gas) -1 e e P0 0 P u = 2c T 1 - P γ γ ⎡ ⎤ ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎢ ⎥ ⎣ ⎦