Delta-V on Rocket with Multiple Engines that Cutoff at Different Times.

[lethalparadox0]

I want to know how to calculate the Delta-V of a rocket that uses multiple engines at launch and that cutoff at different times during the launch. For example, if I had a rocket with a liquid fuel engine in the center and two SRBs attached to the side. The SRBs would cutoff and detach before the liquid fuel rocket is done burning. What I've been doing is calculating the full mass as the entire rocket and the dry mass as the rocket without its fuel and with the SRBs detached from the rocket. The ISP is the average ISP of the three engines. I was just wondering if my calculations were correct or if I should do it another way.

Edited May 18, 2015 by lethalparadox0

[adinfinitum]

The best way to do it would be to take the average Isp of the two boosters and the main engine, and use the mass minus solid fuel and however much liquid fuel is burned before the boosters burn out. That'll give you deltaV for that piece, and then you just find the deltaV after boosters detach, using however much liquid fuel remains, and add the two together.

[Xannari Ferrows]

You should factor in your staging, since the proper formula is ÃŽâ€V = Stage1(Isp • 9.8065) • Ln(M1/M0) + Stage2(Isp • 9.8065) • Ln(M1/M0)

For the first stage Isp, a very simple method of calculation is to do Isp = (((SRB1 + SRB2)/2) + LFO1)/2

When you drop your SRBs, it changes your structural mass, which effectively changes both M1 and M0.

It's also true that your end readings can depend on your liquid fueled engine's thrust while the SRBs are firing. This will determine the amount of fuel left, which will effect your M0; something that changes with staging.

By using a 1 step calculation, as you suggest, the end result factors in the weight of the SRBs as part of M1 through the whole equation, even though they leave after a certain time.

Edited May 21, 2015 by Xannari Ferrows

[lethalparadox0]

Is there a way to calculate how much liquid fuel will be left after the SRBs burn out?

Edited May 18, 2015 by lethalparadox0

[OhioBob]

You have to treat each portion of the burn as a separate stage, compute the ÃŽâ€v separately for each stage, and then add up the results. For example, let's say you have a liquid core with SRB strap-ons:

A = total initial mass

B = mass of solid propellant

C = dry mass of SRBs

D = mass of liquid propellant

t1 = burn time of SRBs

t2 = burn time of liquid core (where t2>t1)

For the first stage,

Initial mass = A

Final mass = A - B - D*t1/t2

For the second stage,

Initial mass = A - B - C - D*t1/t2

Final mass = A - B - C - D

The above assumes you're not adjusting the throttle so that the propellant flow rate of the liquid engine is constant.

The Isp is not a simple average (or even a weighted average). When you have different engines operating at the same time, the combined ISP is

Isp = ΣF / Σ(F/I_sp)

Let's say you have one engine with a thrust of 1000 kN and an Isp of 250 s, and another with a thrust of 500 kN and an Isp of 300 s. The combined Isp is

Isp = (1000+500) / ((1000/250)+(500/300)) = 264.71 s

Edited May 18, 2015 by OhioBob

[Xannari Ferrows]

Is there a way to calculate how mush liquid fuel will be left after the SRBs burn out?

That depends on your thrust. Take the fuel consumption rate per second, multiply it by the percentage of your throttle, as a decimal [100% = 1. 50% = .5].

Leftover fuel = (Rate of fuel consumption • Percentage of throttle) • Number of seconds in stage 1.

[Red Iron Crown]

Surely you mean "Consumed Fuel" rather than "Leftover Fuel", Xannari?

[Xannari Ferrows]

Surely you mean "Consumed Fuel" rather than "Leftover Fuel", Xannari?

Oh crap, that totally slipped past me. Umm... let's see...

Leftover fuel = Original tank capacity - ((Rate of fuel consumption • Percentage of throttle) • Number of seconds in stage 1)

I think that works...