DeltaV of multistage rockets

[vchamp]

What is the easiest way to calculate a deltaV of a multistage rocket, when the first and the second stages are firing simultaneously?

If I know the mass before a separation, can I still use the Tsiolkovsky rocket equation and sum up the deltaVs calculated separately for the first and the second stage?

I tried this method for HLLV Energia and the result seems to be too high even though the Isp value was for vacuum. Before separation I got 10.3 km/s, and the total deltaV is 14.3 km/s. Is it possible?

 

[Urwumpe]

You need first to split the rocket flight into phases of constant structural mass.

Then, you need to calculate the effective specific impulse, which is total thrust / total mass flow.

So, when you have 10 kN at 4500 m/s ISP and 50 kN at 2500 m/s ISP, the sum is

[math]I_{sp, total} = \frac{F_{total}}{\dot{m}_{total}} = \frac{10 kN + 50 kN}{\frac{10 kN}{4500 \frac{m}{s}} + \frac{50 kN}{2500 \frac{m}{s}}}[/math]

 

[garyw]

I don't suppose that there is a calculator out there that can do this for people...?!

 

[vchamp]

Thank you, Urwumpe. Total Isp is what I needed :thumbup: Now the total dV for Energia is more plausible - 8.6 km/s.

 

[Grover]

how do we calculate how much is "Lost" through gaining altitude and aero. drag in the atmosphere? or do we just guess its around 1km/s?

 

[C3PO]

how do we calculate how much is "Lost" through gaining altitude and aero. drag in the atmosphere? or do we just guess its around 1km/s?

With great difficulty. :lol:

You need to simulate some test flights. I found that out the hard way when experimenting with XR-1/air launch. It depends very much on the profile and especially on the acceleration (time@suborbital vel).
The Alpha angle (the angle between +Z and Velocity vector) is is a good indicator of how efficient your flight profile is. Keeping it as small as possible gives the best acceleration. Weaker engines means you need a larger angle, and you have more gravitational losses.
Get a good autopilot for those flights because small differences can have a great impact on performance. Especially the initial turn to heading and pitch-over can have a big impact on performance if you're using realistic ISP and thrust.

 

[Urwumpe]

I don't suppose that there is a calculator out there that can do this for people...?!

Would be no problem to write a software for multistage rocket design and optimization... it just takes time. :facepalm:

The mathematics, algorithms and theory behind it all is pretty simple.

 

[C3PO]

Would be no problem to write a software for multistage rocket design and optimization... it just takes time. :facepalm:

The mathematics, algorithms and theory behind it all is pretty simple.

There have been a few attempts to make such a calulator, but they never went beyond single stage in vacum.

When you get to ambient pressure dependant ISP and drag with non-zero alpha/beta angles, things get complicated real fast.

So yeah, time is the limiting factor.

 

[Urwumpe]

There have been a few attempts to make such a calulator, but they never went beyond single stage in vacum.

When you get to ambient pressure dependant ISP and drag with non-zero alpha/beta angles, things get complicated real fast.

So yeah, time is the limiting factor.

Yeah, that is what I mean with time... you can also do a simple spreadsheet for a rocket configuration, but this is pretty limited.

 

[C3PO]

Yeah, that is what I mean with time... you can also do a simple spreadsheet for a rocket configuration, but this is pretty limited.

Exactly. You can get close using simple calculations, but not close enough.

If you use realistic performance, static and dynamic pressure plays a large enough role to make the simple model useless. If you use "magic" engines and materials, you have enough DV to stop caring about a super-efficient ascent profile. So there's not much incentive to make such a simple model calculator. (unless you enjoy the math challenge )

 

[Urwumpe]

Exactly. You can get close using simple calculations, but not close enough.

If you use realistic performance, static and dynamic pressure plays a large enough role to make the simple model useless. If you use "magic" engines and materials, you have enough DV to stop caring about a super-efficient ascent profile. So there's not much incentive to make such a simple model calculator.

well, depends on what you call simple. if you do a Phase 0 study of a two stage launch vehicle, a spreadsheet will be all that you really need.

If you want to have a perfected Orbiter add-on with optimized launch profile and stage design, you need some kind of a CAE solution together with special optimization and simulation tools.

But really...who does that in that accuracy? You take the spreadsheet data and use the test flights to refine the accuracy. :lol:

 

[C3PO]

If you want to have a perfected Orbiter add-on with optimized launch profile and stage design, you need some kind of a CAE solution together with special optimization and simulation tools.

I have a great tool for just that. It's called Orbiter. :lol:

But really...who does that in that accuracy? You take the spreadsheet data and use the test flights to refine the accuracy. :lol:

You could cut down on the test flights wit such a spreadsheet, but when people venture into making that kind of quality addons they usually have enough flights in their log book to guesstimate a good starting point for the test flights.
I look at this from a "Darwinistic" POV. If it was a great advantage to use a spreadsheet for this, we would have a few circulating in the forum. And AFAIK we don't.

 

[Urwumpe]

If it was a great advantage to use a spreadsheet for this, we would have a few circulating in the forum. And AFAIK we don't.

Well, I always make a new spreadsheet for every kind of launcher, and only rarely reuse one. :lol:

Also I often write special 5 minute software in Java for doing the optimization calculations, when using SciLab is too complex.