How throttle changes affect calculations of thrust?

Question

So, for constant throttle setting equation to calculate thrust looks like

$ \ F = \dot{m}_\mathrm e V_\mathrm e + (p_\mathrm e - p_0) A_\mathrm e$

But if we are looking at flightclub.io simulation, the graph of throttle for first stage changes with time. What do we need to do then in the equation to get the right thrust?? Do we need to just multiply the resulted thrust by throttle coefficient in the current moment of flight?

(Stage 1 is the blue graph)

Flight - GPS III SV04
Rocket - Falcon 9 Block 5

Organic Marble · Accepted Answer · 2020-10-07T19:09:05.797

5

For a first approximation, just reduce the mass flow in the equation by the % throttled down.

So if they reduce the throttle by 10%, cut down the mass flow by 10%.

An advantage of doing it this way versus just cutting the thrust down is that your simulation will reflect the reduced mass flow during the throttle-down, not just the reduced thrust.

edited Oct 07 '20 at 19:09

answered Oct 07 '20 at 18:35

Organic Marble

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Equations both are the same, arent they? – mad.redhead Oct 07 '20 at 18:37
@mad.redhead There's V0M0 term in this one that is not needed. That's for jet engines. – Organic Marble Oct 07 '20 at 18:40
Oh yeah, my bad. Anyway, thanks for the fast reply!! I may now close the question. – mad.redhead Oct 07 '20 at 18:40
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But I just want to know (if its possible to answer without creating a new question), why does throttle on graph drops from 0.95 to 0,75 at 57th second? What causes that change? Or shoulld I create another question? – mad.redhead Oct 07 '20 at 18:44
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@mad.redhead I don't know specifically for Falcon, but some vehicles throttle down as they pass through maximum dynamic pressure. Based on the time, I would guess that is what is going on here. See https://space.stackexchange.com/a/16963/6944 – Organic Marble Oct 07 '20 at 18:46
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@mad.redhead also https://space.stackexchange.com/q/24252/6944 – Organic Marble Oct 07 '20 at 20:22
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@mad.redhead Besides throttling down to limit max Q, some launchers also throttle down or shut down engines to reduce the maximum G-load on the upper structure and payload late in a stage burn. As propellant is consumed, the mass of the rocket decreases, and acceleration and thus G-load increase; throttling back reduces it. – Russell Borogove Oct 07 '20 at 21:49
@mad.redhead for more on that cf. What is BECO? (Gemini) Same as MECO? and Has an object ever been put in orbit where the first stage was always at maximum thrust? and Is it possible to calculate Max-Q without having to input an altitude and especially Launch Accelerations: Values, history and What G-forces do different launchers cause? – uhoh Oct 09 '20 at 12:37
@uhoh will definitely check this out and write you back – mad.redhead Oct 09 '20 at 14:48

How throttle changes affect calculations of thrust?

$ \ F = \dot{m}_\mathrm e V_\mathrm e + (p_\mathrm e - p_0) A_\mathrm e$

1 Answers1