This is a study of some of the whys and wherefores associated with using a gas turbine engine rather than a liquid fuel rocket, or solid booster, for the first stage of a vertical take off spacecraft, or as a booster for the Shuttle.
Specifically I have chosen to repeat the Apollo mission, as it is well documented. The aim of the LEO insertion was to get approximately 120 tonnes into LEO, at an altitude of 180 km.
Currently civilian gas turbines for aircraft are becoming more efficient by using high bypass designs, which are only really suitable for subsonic designs. This is not really suitable for a rocket's first stage, which is likely to see at least M3. Another issue I'll carefully avoid in this first look is that gas turbine engines tend to top out around 20 km.
One obvious example of a gas turbine engine suitable for that speed range, approximately, is Concorde's Olympus engine. For reasons I don't understand its performance on afterburner (aka reheat) was only a 20% boost in thrust, at a cost of more than doubling its fuel consumption. This is atypical, military jets often see a 50% improvement thrust, admittedly in exchange for a 125% increase in fuel flow. Therefore I have also included an Olympus using a generic military afterburner system.
The Saturn launch vehicle used F1 engines in the first stage, and J2s in the second.
Here's a summary of the engines considered.
| Units | Saturn | Concorde | Concorde | Concorde | |
| F1 | Dry | Reheat | Military a/b | ||
| Engine Mass | kg | 8391 | 3175 | 3175 | 3175 |
| Thrust at Sea Level | kgf | 708093 | 14000 | 17000 | 21000 |
| Thrust in Vacuum | kgf | 789324 | |||
| Fuel consumption | kg/s | 2672 | 2.9 | 6.3 | 6.6 |
| Specific Impulse | kgf/kg/s | 265 | 4800 | 2720 | 3200 |
The rocket data was taken from www.astronautix.com , Concorde figures from here , and the afterburner stuff from NASA. Obviously for a first stage performance at sea level is more important than performance in a vacuum. Here are the 4 first stages capable of getting 117 tonnes into some sort of orbit above 180 km and 7.8 km/s.
| Engine type | F1 | Dry | Reheat | Military a/b |
| Number of engines | 5 | 183 | 135 | 97 |
| Engine mass | 8391 | 3175 | 3175 | 3175 |
| Body and tank | 93263 | 4272 | 6847 | 5154 |
| Hence Empty Mass | 135218 | 585297 | 435472 | 313129 |
| Fuel | 2150999 | 85443 | 136931 | 103072 |
| Total stage Mass | 2286217 | 670740 | 572402 | 416201 |
| Seconds of fuel | 161 | 161 | 161 | 161 |
As can be seen, there is a complex interaction between the number of engines, the specific impulse of each one, and the fuel flow rate, to get the same performance. There seems very little disadvantage in going for the Military afterburner version of the three gas turbines shown, and superficially it seeems like a reasonable alternative to the Saturn.
Here's the output of my simulator program, written in Scilab . It is not a true orbital mechanics program, as may be seen in at least one of the following plots.
The top plot is the angle of the rocket relative to vertical. An autopilot routine tries to keep the motion of the rocket within sensible bounds.
The next down shows the altitude against time, as the green line, and against distance downrange as the turquoise one.
The third plot shows the mass and the thrust (in tonnes of thrust).
The fourth shows the speed up (blue) and along (black), and the total speed (green).
The final plot is really diagnostic and tells me which stage is firing when, and what mode the autopilot is in.
The next plot shows the total non-chemical energy of the rocket, in Joules, and the payload that reaches orbit.
As each stage is dropped off the kinetic and gravitational energy invested in that stage is 'lost' to the system.
The difference between the two curves shows, in some complex fashion, the inefficiency of the rocket. It is interesting
that the energy invested in the second stage considerably exceeds that of the first, much heavier, stage and I
am gently wondering if there would be any benefit in 'balancing' them a bit.
Incidentally the offset at zero seconds is correct, it is the kinetic energy due to the rotation of the Earth.
Strictly speaking there should be an enormous negative offset as we are at the bottom of a gravity well, but that
does not affect the shape of the plot.
That's all mildly interesting, so how does the gas turbine proposal shape up against the Saturn?
Advantages
Well that sounds too good to be true...
Disadvantages
There is no room for 97 engines, each of which needs air, unless they are arranged 3 deep around the circumference of the fuel tank. It seems unlikely that they would get enough air, especially at high altitude.
Gas Turbines are precision built machines - this proposal needs 300 tonnes of precision machining. The F1s have some precision parts, but mostly they are pipes and pumps and pressure vessels. They only weigh 42 tonnes altogether, and do not need air, so they can be mounted under the fuel tank, and will not particularly interfere with each other.
At stage 1 burnout the altititude is in excess of 60 km, and the speed is around 1.6 km/s, or M4.5. In practice gas turbines do not work at such high speeds or altitudes, ram jets or scram jets are preferred, neither of which will work at low speed.
Here are more sensible proposals for gas turbines and scramjets .
Just for the sake of completeness I've put together a first stage that obeys a realistic restriction on Mach number, say 3, (or 1.0 km/s in groundspeed) and altitude, say, to be 20 km, or rather more than 60000 ft. In practice altitude is the main issue, so I've reduced the initial angle of climb to give a higher speed for a given altitude, which will incur problems for the rest of the rocket.
Conclusion
OK, this is a stacked deck. Next I'll try SRB replacements for the Shuttle, which might make a lot more sense.