Cillian Thomas - 26/01/2022

The F1 rocket engine was the engine aboard the Saturn V rocket that brought humans to the moon for the first time. Rocket science and design can be complicated, but designing a nozzle for a specified thrust can be done on a napkin with some assumptions. Isentropic gas relations can be used to relate different points in the nozzle, and these relations can be used to calculate the expected key performance characteristics of any nozzle.

I decided to estimate the theoretical performance of the F1 rocket engine under ideal conditions, and compare it to the reported figures for the engine. I used a book called The Saturn V F-1 Engine by Young [1] to get the chamber pressure, chamber temperature, mixture ratio, area ratio, and exit diameter. From here I was able to use the NASA CEA calculator [2] to get average specific heat ratios and use Rocket propulsion Elements by Sutton [3] to gather the isentropic gas relations in the nozzle to ultimately calculate the performance.

The F1 rocket engine nozzle

Image source

Comparing these values to the reported figures in The Saturn V F-1 Engine by Young [2], it can be seen that a fairly reasonable estimate of the performance of the rocket can be concluded in a matter of very simple calculations.

I calculated the specific impulse to be about 12% higher than the minimum reported specific impulse, the thrust to be ~8% higher, and the mass flow rate to be ~3% less.

Of course, the reported specific impulse and thrust will not be as high as calculated due to heat loss through the walls, boundary layer effects, the gases not behaving as ideal gases, non isentropic expansion of the gas, and many more complexities of real engines. The mass flow rate is lower in the ideal engine may need some explaining, however. Sutton [3] explains that in a real engine, the mass flow rate is usually higher than the calculated ideal. This is due to many reasons including heat transfer that causes density changes, incomplete combustion causing more dense particles to be exhausted, and the specific heat ratio and molecular weight values changing along with the nozzle.

The calculations shown here can be reverse-engineered in order to design an engine. Starting with a desired thrust and data from the propellents, the details of the area of the throat and area ratio of the nozzle can be calculated. While this mathematical analysis is quite basic, the real challenge in rocket design is developing the open cycle thermodynamic cycle that can produce the specified performance while also not melting (the combustion chamber at 3500 k is 60% as hot as the sun). Despite the complex engineering that goes into the development of an engine, it is still interesting to find that the performance characteristics can be estimated fairly accurately with a first analysis.

[1] - Young, A., 2008. F-1 engine description and operation. In The Saturn V F-1 Engine (pp. 77-105). Praxis, New York, NY.

[2] Cearun.grc.nasa.gov. 2022. CEARUN rev3a. [online] Available at: https://cearun.grc.nasa.gov/ [Accessed 26 January 2022].

[3] - Sutton, G.P. and Biblarz, O., 2016. Rocket propulsion elements. John Wiley & Sons.