How to calculate delta-v of parallel staging?

[Pipcard]

If you're calculating the delta-v of something, you only need the wet mass, dry mass, and specific impulse. Then you plug in those numbers into Tsiolkovsky's equation. Simple enough.

But how would you calculate the delta-v of a rocket with one stage in the middle, and two smaller boosters on the side, all burning at once?

I'm using parameters of the L-4S rocket (first stage and boosters) here:

First stage:

• Wet mass: 9399.0 kg
• Dry mass: 4507.0 kg
• Propellant mass: 3887.0 kg
• Burn time: 27.8 seconds

Boosters:

• Wet mass: 1005.0 kg
• Dry mass: 381.0 kg
• Propellant mass: 624.0 kg
• Burn time: 7.1 seconds

Remember, they all begin burning at the same time. And the boosters separate after 7.1 seconds.

 

[MaverickSawyer]

Simple. Split it into two equations: one with the boosters (t-0 to t+7.1) and one without (t+7.1 to t+27.8). Then, add the two of them together for the complete dV. You'll need the amount of fuel burned in those first 7.1 seconds, but simple arithmatic should get that for you.

 

[Pipcard]

Simple. Split it into two equations: one with the boosters (t-0 to t+7.1) and one without (t+7.1 to t+27.8). Then, add the two of them together for the complete dV. You'll need the amount of fuel burned in those first 7.1 seconds, but simple arithmatic should get that for you.

Yeah, I already knew how to do the dV without boosters (t+7.1 to t+27.8).

I forgot to tell you that, the first stage and boosters have different specific impulses (215 and 220 s, respectively). This is what is causing me problems.

 

[Phil Smith]

So I dont know still you need answer for your question, but here some formulas (btw you need to know massflow of your core stage engine):

dV1(from 0 to 7.1 sec) = (Isp(b) + Isp(c))* LN * (Total vehicle launch mass/(2*381+(9399-3887)+left core stage propellant));

dV2(from 7.1 to 27.8 sec) = Isp(c) * LN * ((9399-3887)+left core stage propellant)/(9399-3887));

Total dV = dV1+dV2.

where Isp(b) - booster specific impulce;
Isp(c) - core stage engine's specific impulse;
Total vehicle launch mass = 9399+2*1005;
left core stage propellant = 3887 - mdot*7.1.

So I hope it helps you

 

[Urwumpe]

Yes, for calculating this, you always need to split the flight into logical stages of constant structural mass. Even dropping the fairing is a new stage.

For mixing multiple engines with different specific impulse and total thrust, you simply need to apply the thrust equation (F = mdot * isp). Calculate mass flow for all engines, and calculate total thrust, and you can calculate total effective specific impulse for a stage.

What is needed is the mass flow of the rockets. But this can be calculated from your data.

mass flow 0: 624 kg / 7.1 seconds = 87.89 kg/s
Thrust 0: 87.88 kg/s * 215 m/s * 9.81 m/s² = 185.367 kN
Mass flow 1: 3887 kg / 27.8 s = 139.82 kg/s
Thrust 1: 301.759 kN

Total mass flow is 315.6 kg/s

Thus, for the first 7.1 seconds you have a specific impulse of

isp1 = (301.759 kN + 2 * 185.367 kN) / (315.6 kg/s) = 2130 Ns/kg or 217.22 s (for those with prehistoric units of measurement)

dv1 = isp1 * ln(11409 kg/(11409 kg - (315.6 kg/s * 7.1 s)))
= 2130 m/s * ln(11409 kg / 9168.27 kg) = 465.92 m/s

Sorry, Phil Smith, but your calculation is horrible wrong. What ever you expected to get as result, this should not be DV. Just adding the specific impulses of engines or engine classes is a stupid guess, but not knowing what to do with a specific impulse.

 

[Phil Smith]

sorry, i get it! you just found total thrust and total mass flow and after that found total isp. sure. my bad!:facepalm:
i'm just sitting at my job:uhh:

 

[Pipcard]

I now think 215 and 220 were the specific impulses at sea level, not in vacuum. But the method was all that I needed. Thank you.

edit: Also, I interpreted the chart wrong. 9399 kg was the mass of the whole L-4S, not just the first stage. 1005 kg was the wet mass of both boosters (so 502.5 kg per booster).

4507 kg is the mass of the whole rocket minus the mass of both boosters, and the fuel of the first stage.

 

[RGClark]

Yes, for calculating this, you always need to split the flight into logical stages of constant structural mass. Even dropping the fairing is a new stage.

For mixing multiple engines with different specific impulse and total thrust, you simply need to apply the thrust equation (F = mdot * isp). Calculate mass flow for all engines, and calculate total thrust, and you can calculate total effective specific impulse for a stage.

What is needed is the mass flow of the rockets. But this can be calculated from your data.

mass flow 0: 624 kg / 7.1 seconds = 87.89 kg/s
Thrust 0: 87.88 kg/s * 215 m/s * 9.81 m/s² = 185.367 kN
Mass flow 1: 3887 kg / 27.8 s = 139.82 kg/s
Thrust 1: 301.759 kN

Total mass flow is 315.6 kg/s

Thus, for the first 7.1 seconds you have a specific impulse of

isp1 = (301.759 kN + 2 * 185.367 kN) / (315.6 kg/s) = 2130 Ns/kg or 217.22 s (for those with prehistoric units of measurement)

dv1 = isp1 * ln(11409 kg/(11409 kg - (315.6 kg/s * 7.1 s)))
= 2130 m/s * ln(11409 kg / 9168.27 kg) = 465.92 m/s
...

And for your second exercise in parallel staging ;-), take a look at the SpaceLaunchReport.com page on the SLS:

Space Launch Report - Space Launch System Data Sheet.
http://spacelaunchreport.com/sls0.html

Calculate the payload to LEO for the data in "SLS Block 1 2011 Baseline" and for the data in "SLS Block 1 with ICPS". I think you'll be surprised by how high is the payload you get.

Bob Clark

 

[Urwumpe]

I actually can't calculate the payload by only calculating DV.

For the payload, I would also need to include trajectory.

 

[Capt_hensley]

I wonder if IOS has any data on their Neptune launch systems? They all use parallel staging. Of course at the rate they are moving they may never get the first rocket off the ground let alone the Nep1000...

 

[Urwumpe]

I wonder if IOS has any data on their Neptune launch systems? They all use parallel staging. Of course at the rate they are moving they may never get the first rocket off the ground let alone the Nep1000...

AFAIR, they don't use parallel staging, but linear staging. The stages are just installed approximately concentric.

 

[Capt_hensley]

Heres what I found...

NEPTUNE 9 (N9)
The modular N9 rocket is a three stage (parallel staged) satellite launch vehicle capable of launching 70-Kg payload into polar low-earth orbit. It is composed of 9 Common Propulsion Modules. The engine count breaks down to 6 stage-1 engines, 2 stage-2 engines, and 1 stage-3 engine (a total of 9 engines). N9 was designed specifically to support the TubeSat, CubeSat, and general small-sat community.

NEPTUNE 36 (N36)
The N36 is a three-stage (parallel staged), medium-lift launch vehicle capable of placing a 1000-Kg payload into polar low-earth orbit or accelerating a 190-Kg payload to Earth-escape velocity. The rocket is composed of 36 Common Propulsion Modules. The engine count breaks down to 24 booster engines, 8 stage two engines, and 4 stage three engines. The N36 is slated to launch the Google Lunar X PRIZE SYNERGY MOON lander/rover to the Moon. It will also be utilized to launch a two-person crew module into low earth orbit for short orbital tourism missions. The crew module (CM-2) is presently in development.

http://www.interorbital.com/Neptune Modular Page_1.htm

 

[Urwumpe]

Yes, I know. I have read it too some while ago. I just don't find much sense in starting all engines parallel and have most of them throttled down to minimum.