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Old October 24th 17, 01:20 AM posted to sci.space.policy
Alain Fournier[_3_]
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Default Were liquid boosters on Shuttle ever realistic?

On Oct/23/2017 at 5:01 AM, Fred J. McCall wrote :
Alain Fournier wrote:

On Oct/21/2017 at 10:56 AM, Fred J. McCall wrote :
Alain Fournier wrote:

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.


Yes, you can always rig the numbers by the problem statement.


Which number was rigged? The only slightly dubious thing in my
example is that I was assuming the same size for the second stage
as for the first stage, which would be unusual for a rocket. But
it doesn't change the idea of the outcome if you divide by two
the size of the tanks in the second stage of my example. It only
makes the computations a little more complicated.


Why does the first stage need nine engines?


You should ask SpaceX why they put nine engines on their first stage.

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.


It's not 'nothing'. It's more payload to orbit, which is sort of the
goal of the thing (and what you've ignored with your rigged numbers).
Explain Delta IV.


In my example I was assuming the same functionality for the stages.
Meaning, the stages would put the same mass at the same altitude
and same speed whether it was the RP1 variant or the LH2 variant.

For the Delta IV, there are several variants. Let's look at the
one with one CBC as a first stage and the 5m diameter second stage.
The first stage has one RS-68A engine with a dry weight of the
engine of 6740 kg and 3137 kN thrust, the gross mass of the booster
is 226400 kg. The second stage has one RL10B-2 engine weighing
277 kg and providing 110 kN thrust, the gross mass of the second
stage is 30710 kg.

The example I gave above applies with only minor modifications.
Instead of putting 9 times more engines on the first stage, they
put only one engine as for the second stage but that engine
weighs 24 times more. Saving on the mass and cost of the RL10B-2 by
replacing it with a RP-1 engine isn't much worth the trouble even
if you include the weight saved on the dry weight of the tank.
The added weight of the fuel would approximately counter balance
your gains. Different people will come to different conclusions
on this but the gains or losses by going to RP-1 wouldn't be great.
But for the first stage, you have *much* more to gain by going
to RP-1, the engine is 24 times bigger, I don't know how many times
more expensive it is but it should also be much more expensive
than the second stage engine (which is more important than the
fact that the engine is heavier). Even if you take into account
the fact the the first stage is bigger than the second stage,
the first stage's engine is comparatively bigger. The gains you
can get by going to RP-1 would be more important on the first
stage.


And an RP1/LOX engine with equivalent thrust will weigh about the same
as the LH2/LOX RS-68A, so you save nothing so far as weight goes.


Four Merlin 1D engines will give more thrust (4x845 = 3380 kN) than one
RS-68A (3137 kN) but they will weigh 1880 kg which is much less than
the 6740 kg of the RS-68A. But that is not really very important here.

The
fuel to get equivalent performance will weigh much more, so your
RP1/LOX engine needs higher thrust because it has to lift more mass in
fuel.


Yes. The fuel will weigh much more. You don't use RP1/LOX engines
instead of LH2/LOX engines to save weight. I'm glad to see that we
now agree on this.

Why didn't they go to RP-1 for the first stage of the Delta IV? I
don't know. But what I have said before is that if you use LH2
for the first stage, it will work but it will cost you. I
don't consider Delta IV to be a low cost launcher.


But it's comparable to most other launchers of its generation. Both
Atlas V and Delta IV cost about $13k/kg to get stuff into orbit. Atlas
V is RP1/LOX while Delta IV is LH2/LOX for the 'core stage'.

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


And because you rigged the problem by assuming you only have a low
thrust engine that you use everywhere.


No, I was assuming the same engine everywhere like on the Falcon 9.


Which rigs your result.


Hum! are you claiming that SpaceX designed their Falcon 9 that way
to rig the results of this conversation? I can assure you that I
did not collude with SpaceX on that (nor on anything else for that
matter).

The Merlin engine on the Falcon 9 has a thrust to weight ratio of 180
which is much more than what you have on the Delta IV.


And it has a lower Isp and lower thrust. So what? Engine weight is
trivial unless you rig the numbers.


Engine weight isn't the important thing here. I'm glad to see we agree
on this. But the cost of the engines is important. If you need nine
on the first stage against only one on the second stage, you can see
that saving on engines on the first stage is more important than on
the second stage.

And if you have a design such as the Delta IV, it isn't as obvious but
the same argument applies. The RS-68A on the first stage weighs 24 times
the RL10B-2 on the second stage. Also the RS-68A has 28.5 times more
thrust than the RL10B-2. I don't know what's the price tag of neither
the RS-68A nor the RL10B-2, but I would expect it to cost many times
more. So once again, you can see that saving on the first stage engines
is more important than on the second stage engines.

This argument still holds even if you take into account that the second
stage is smaller than the first. The second stage of the Falcon isn't
nine times smaller than the first stage and the second stage of the
Delta IV isn't 28 times smaller than the first. You want to have
proportionally more thrust on the first stage than on the second stage
and you have to pay for that one way or another.


Alain Fournier