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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

UndefinedUsername
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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.

$$F = \frac{dp}{dt}$$

Momentum is mass times velocity:

$$p = mv$$

So

$$F = v \frac{dm}{dt} = v \dot{m}$$

where $\dot{m}$ 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.

$$ 7,607,000\,\mathrm{kg\, m/s}^2 = 2570\,\mathrm{m/s} \ \dot{m}$$

Solve for $\dot{m}$.

$$ \dot{m} = \frac{7,607,000}{2570} \mathrm{kg/s} = 2960\,\mathrm{kg/s} $$

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.

Piotr99
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uhoh
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  • That assumes 100% efficiency and ignores the fuel required for the turbopump, though. – Hobbes Sep 06 '18 at 11:41
  • @Hobbes interesting, how is efficiency defined? If you can add to this answer, or post something better, please go for it! OP's "thousand tab" situation sounded like they needed something soon more than they needed three significant digits. – uhoh Sep 06 '18 at 11:43
  • @Hobbes I've just asked In the context of calculating mass flow rate from thrust and Isp, how would an additional efficiency be defined? That might be a better place to explain than comments. – uhoh Sep 06 '18 at 12:18
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    I think uhoh's answer 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 280424 Kg of Oxygen and 133608 Kg of RP-1. First stage burn time is 162s [4]. So (280424+133608)/162 = 2555 Kg/s. [1] https://en.wikipedia.org/wiki/Falcon_9#cite_note-falcon9-2015-3 [2] http://www.uigi.com/o2_conv.html [3] https://en.wikipedia.org/wiki/RP-1 [4] https://www.spacex.com/falcon9 – BlueCoder Sep 06 '18 at 12:19
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    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. – BlueCoder Sep 06 '18 at 12:20
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    BlueCoder's approach is the one I had in mind as well, but couldn't find the numbers for on short notice. – Hobbes Sep 06 '18 at 12:40
  • @2012rcampion your edit has changed my answer from an answer to the OP's question "...how to calculate..." to an answer to "..what is the value of...". I thought I'd leave a bit unsaid to give the OP the satisfaction of doing a little math and finding out the answer themselves, since they asked specifically for how to calculate something. Your edit makes it look like I believe the actual number 2960 kg/s, which I'd intentionally left out because I did not want to report or advocate a specific number. – uhoh Sep 07 '18 at 00:34
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    @2012rcampion Since (at)BlueCoder's answer chooses to do the numbers, the've already reported a value for this there, so it's not necessary to do here. And while we don't have a specific homework policy as some sites do, I feel that there's a certain comradely cordiality to not over-answering a question that specifically asks only for how to do something rather than "tell me what the answer is." – uhoh Sep 07 '18 at 00:43
  • Does this fuel performance account for weight? I forgot to ask before, but how would you calculate between a full payload and an empty payload in fuel performance? Lower weight payloads can surly go further and last longer than heavier payloads to LEO for example. – UndefinedUsername Sep 08 '18 at 15:59
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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.

  • I just took as good the first sources I found around. To make a better estimate, I would at least verify more carfully the actual RP-1 density and also have a look at the thrust level during the whole 162 seconds. Also note that some of the first stage fuel is kept for landing.
BlueCoder
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