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
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
9
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.
-
$\begingroup$ That assumes 100% efficiency and ignores the fuel required for the turbopump, though. $\endgroup$– HobbesCommented Sep 6, 2018 at 11:41
-
2$\begingroup$ 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] en.wikipedia.org/wiki/Falcon_9#cite_note-falcon9-2015-3 [2] uigi.com/o2_conv.html [3] en.wikipedia.org/wiki/RP-1 [4] spacex.com/falcon9 $\endgroup$ Commented Sep 6, 2018 at 12:19
-
2$\begingroup$ 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. $\endgroup$ Commented Sep 6, 2018 at 12:20
-
1$\begingroup$ BlueCoder's approach is the one I had in mind as well, but couldn't find the numbers for on short notice. $\endgroup$– HobbesCommented Sep 6, 2018 at 12:40
-
1$\begingroup$ @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." $\endgroup$– uhohCommented Sep 7, 2018 at 0:43
$\begingroup$
$\endgroup$
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.
