Does anyone know how to calculate the KG per second of RP-1 and LOX from the 9 Merlin 1D engines?

as can be seen from the title, I have been through at least 1,000 chrome tabs in the last few hours trying to find some form of definitive answer, but I've found absolutely nothing. Could anyone help me with a calculation from its 7,607kn to Fuel consumption KG/s

2 Answers
2

As @RussellBorogove points out in his excellent answer, Isp or "mass-specific impulse" is the number that expresses the relationship between thrust and mass flow rate.

Mass specific impulse with units would be Newtons per kg/sec. While that has units of m/s, and may be identical or at least quite close to the average velocity of the exhaust (which will have a distribution), the derivation below is a handy way to either remember how things are related, and/or to get the units to work out.

Force can be equated to change in momentum per unit time.

$$F = fracdpdt$$

Momentum is mass times velocity:

$$p = mv$$

So

$$F = v fracdmdt = v dotm$$

where $dotm$ is the mass rate.

The specific impulse of a Falcon 9 Merlin 1D is about 262 seconds in the atmosphere. Multiply that by standard gravity of about 9.81 m/s^2 to get an exhaust velocity of about 2570 m/s.

$$ 7,607,000 = 2570 dotm$$

Solve for $dotm$.

$$ dotm = frac7,607,0002570 $$

That's one way how to calculate the kg/sec of RP-1 and LOX. If you want to know each one separately, find the the ratio between the two. Search this site for oxidizer fuel ratio or similar terms if you can't find it on the internet.

I think uhoh's answer (7607000/2570=2959 Kg/s) is in the ballpark.

Here's another (less precise) approach:

First stage has 245,620 L of liquid oxygen and 146,020 L of RP-1 fuel (1)

Let's assume oxygen density as 1,1417 (2) and RP-1 density as 0,915 (average of 0.81 and 1.02 in (3)).

So we have 245620*1,1417 = 280424 Kg of Oxygen and 146020*0,915 = 133608 Kg of RP-1.

First stage burn time is 162s (4).

So (280424+133608)/162 = 2555 Kg/s.

Considering that the engines won't be at their maximum thrust for the whole 162 period (they slow down at least during Max-Q I think) and the uncertainties on these numbers*, I think uhoh's answer is correct at the very least in the order of magnitude.

By the way, using this calculation we get 1731 Kg/s for the Oxygen and 824 Kg/s for RP-1.

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