Author Topic: Saturn rocket engine theory  (Read 5348 times)

Offline ka9q

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Saturn rocket engine theory
« on: April 05, 2013, 05:24:17 PM »
This should be a question for Bob B. but I haven't seen him here in over a month.

The only good reason I engage hoaxers is for what I learn in the process of researching answers to their claims. Arguing with some Youtube idiots who insist rockets push on air and therefore can't work in a vacuum prompted me to finally study the thermodynamics of rocket nozzles.

With the formulas in Sutton & Biblarz ("Rocket Propulsion Elements") I plugged in the numbers I could find for the F-1 engine to see how close I could come to its performance figures.

My source numbers:

From Wikipedia on RP-1, for 2.56:1 mixture ratio:
Specific heat ratio: 1.24
Combustion temp: 3670 K

From Wikipedia on F-1:
Mixture ratio: 2.27:1 LOX/RP-1
Chamber pressure: 7 MPa
Expansion ratio: 16
Throat area: 0.6788 m2 (back-calculated from nozzle exit diam of 12.2' and 16:1 expansion ratio)

Mol wt: 23.42 g/mol (computed from a mix of 34% CO, 34% H20, 17% CO2, 15% H2 taken from fig 5-3 of S&B, nozzle exit gas ratio for RP-1/LOX at 1:2.25)

From this I compute the following sea level (101325 Pa) performance:

Combustion gas density: 5.37 kg/m3
Combustion gas Mach 1: 1271 m/s
Mass rate: 2732 kg/s
Throat temp: 3277 K
Throat pressure: 3.9 MPa
Throat density: 3.35 kg/m3
Throat Mach 1: 1201 m/s
Nozzle exit temp: 1362 K
Nozzle exit pressure: 41800 Pa
Nozzle exit density: 0.086 kg/m3
Nozzle exit Mach: 3.76
Nozzle exit Mach 1: 774.3 m/s
Nozzle exit velocity: 2910 m/s
Total thrust: 7.3 MN (7.95 MN mass thrust - 646 kN pressure thrust; overexpanded)
Isp: 272.6 sec (2673 m/s effective exhaust velocity)
Carnot efficiency: 62.9% (heat -> exhaust K.E. conversion)

These are the nominal sea-level numbers for the post-Apollo 8 F-1:
Isp: 263 sec
thrust: 6.77 MN
mass rate: 2625 kg/s

And this is what I get in a vacuum:
Isp: 314 sec (3076 m/s)
Thrust: 8.4 MN (7.95 MN mass thrust + 454 kN pressure thrust)

I notice my calculated numbers for sea level performance are on the high side. Is this what I should expect given that I didn't account for the propellant diverted to operate the gas generator and turbines, or heat losses through the walls of the combustion chamber and nozzle? What about my source numbers? E.g., the mixture ratio for Wikipedia's RP-1/LOX numbers doesn't exactly match that of the F-1.

I'm also not sure if the combustion temperature I used accounts for the oxygen starting as a cryogenic liquid.

« Last Edit: April 05, 2013, 05:44:43 PM by ka9q »