and/or deliver the largest Payload?Conclusion: the same value of Vsp.
And substituting...
Gives....
Giving the left hand side to be
= [Kinetic Energy into payload and ship] / [Energy into propellant]
The right hand side is just a function Fcn (d, t, u) of three
dimensionless
numbers (d,t,u). Only d is related to the optimum Vsp. When the value
of
d is found that maximizes the function, then d=delta_V/Vsp gives the
optimum
Vsp.
Maximizing the term which is Fcn (d, t, u), maximizes the term . This maximizes P+S, or it maximizes delta_V, or it minimizes E.
When d = 1.59xxxx, and u and t are 0.000, this function is about .647 xxx.
The optimum Vsp is about 2/3 delta_V (about 1/1.59....).
The propellant is about 3.95 times the payload.