On Oct/21/2017 at 12:36 AM, Fred J. McCall wrote :
Alain Fournier wrote:

On Oct/19/2017 at 9:48 PM, JF Mezei wrote :
On 2017-10-19 20:15, Alain Fournier wrote:

It was my claim from the very start that LH2/LOX does NOT offer better
performance for the first stage.

If discussing engine performance only, would it be correct to state that
SSMEs with higher ISP would offer better performance then RP1 engines or
SRBs since it has better Isp?

Performance is a somewhat vague term. Higher ISP shouldn't be your
measure of performance. If you measure performance by ISP, SSME
is better, but it will cost you dearly if you measure performance
by cost in dollars.


That applies to all stages, though, so if LH2/LOX has poor performance
(in dollars) on the first stage, it will have equally poor performance
on all other stages.

No. Assume a rocket where the first stage and the second stage are
identical except that the first stage has 9 engines and the second
stage has only 1, and that the rocket uses RP-1. Somewhat like the
Falcon 9, the Falcon 9 isn't exactly like that but assume a rocket
that is like that.

Let's divide the cost of a stage into 3 parts. E = cost of an engine,
T = cost of empty tank and F cost of fuel. For the fuel, the cost
should be in kg, the dollar cost of the fuel is not important, for
the engines and tank using dollars or weight for costs doesn't
make much difference. So the costs of the the first stage is
S1 = T + F + 9E
and the cost of the second stage is
S2 = T + F + E.

Now someone comes along and says, we could save by using LH2 on
the second stage. Now we have to see if you really save overall.
The tank would cost more, the fuel would be lighter and the engine
would cost more. So cost of stage with LH2 becomes
S2LH2 = T + delta T + F - delta F + E + delta E.
So the difference in cost between the RP-1 second stage and the
LH2 second stage is
S2LH2 - S2 = delta T - delta F + delta E.
People at SpaceX looked at that and figured it's not worth it
meaning at SpaceX they think that
delta F delta T + delta E.
Other rocket people looked at that and said yes we would save
by having LH2 for the second stage, so others think that
delta F delta T + delta E.
What is important to know is that it isn't obvious which is
true. That is because we have approximately
delta F = delta T + delta E.

Now let's look at the first stage. If we go to LH2 we get the
cost for the first stage with LH2
S1LH2 = T + delta T + F - delta F + 9(E + delta E).
And the difference between a first stage with RP-1 is
S1LH2 - S1 = delta T - delta F + 9(delta E).
We just said that we have approximately
delta F = delta T + delta E. So we have approximately
S1LH2 - S1 = 8(delta E).
And no sane person would pay 8(delta E) for nothing.

The difference comes from the fact that the first stage
has more engines because you need more thrust on the
first stage.


Alain Fournier