Math help

[Nich]

I feel like it should be really easy but I am struggling with the algebra.

 

If you know;

TWR of the engine

Structural Mass Ratio of the tank

Payload

Desired starting TWR of the stage

You should be able to find the mass of the stage

[Nich]

I had an answer but forgot that Required TWR includes the payload.

Edited May 24, 2019 by Nich

[Snark]

Moving to Gameplay Questions.

41 minutes ago, Nich said:

I feel like it should be really easy but I am struggling with the algebra.

Can you explain what it is, exactly that you're trying to do?

I can picture a situation where you have a stage and are trying to figure out how much engine it needs.  Or where you have an engine and a required TWR, and you're trying to figure out how much payload you can move.  Or you know the engine, payload, and desired dV and are trying to figure out how much fuel to add.  And a few other things like that.

I'm having trouble picturing a situation where you're trying to "find the mass of the stage", since that's right there in the engineering report in the VAB.  Can you describe a bit more what it is you're trying to figure out and why?

[Nich]

@Snark Ha ha sorry spread sheeting.  I am planning an RP-1 play through with procedural engines and I am putting together a spreadsheet to try and optimize my 3 stage rockets.  I am just stabbing in the dark here trying to figure things out and this was my first hurdle.

I have not played with it yet but I would guess engines have a fixed TWR as you re scale them.  I am pretty sure procedural tanks have a fixed structural mass ratio as well.

My major constraint is total mass of 20t, 60t, and 150t with as much payload as possible for each pad.

Edited May 24, 2019 by Nich

[Snark]

So I'm still trying to sort this out.  If I were designing a rocket, I'd start with the payload (obviously, since that's the thing I _need_ so it's not negotiable), and then design the stage around that.  It looks like:

1. Determine payload
2. Pick an appropriate engine (e.g. TWR and Isp characteristics, based on what situation it's in, e.g. surface lifter? orbital maneuvering? etc.)
3. Decide about how much dV I want in the stage
4. Decide on how much fuel I need in order to get the specified dV

Is that (or something close to it) not how you go about designing?

[OHara]

10 hours ago, Nich said:

You should be able to find the mass of the stage

If I'm correct in how I understand that you are approaching this, 
no, the constraints you listed are not enough to know the total mass of the stage.

M = Mpayload + M_engine + M_tank + M_fuel,   where for each stage any upper stages count toward its payload.

You know Mtank = 3% Mfuel  in realism overhauls (12.5% in stock)

You like to have, say, TWR_liftoff = 1.5 Gs to lift off, so   Thrust = g × M × TWR_liftoff
You know most engines have TWR_engine about 20, so  Thrust = g × M_engine × TWR_engine

So you know what fraction of the stage-mass is going to be engines
M_engine × TWR_engine =  (Mpayload + M_engine  + 1.03 × Mfuel) × TWR_liftoff

but of course you haven't yet decided the mass of fuel until you set your delta-V needs for each stage, and there the algebra gets harder .

Both sides of the equation can still scale up or down, until final payload mass determines that scale.

[Nich]

@OHara Actually I think that was the last bit I needed.  Total mass of the stage is already known and I will be using 3D graphing to solve the M₁/M₂ and M₂/M₃ ratios.  I think I can use that bit you gave me to find the dry mass of M₁, M₂ and M₃ using.

M x TWR_liftoff/TWR_engine = M_engine and

(M - M_Payload - M_engine )/1.03 = M_fuel and 

Mfuel x .03 = Mtank