Optimal Mass Efficiency Charts for the Low TWR Range

[Cunjo Carl]

Just updated some mass efficiency charts to help out a challenge I'm interested in, and I figured I'd drop them off here as well in case someone else might get some use out of them. They're especially for the low thrust range. Cheers!

(posted in the Direct Assent Challenge)

In the charts below, Dawn is in blue, NERV is in green and Wolfhound is in orange. The line for a staged rocket is the brightly colored one, and the fainter lines coming off of it are for asparagus rockets. The closest faint line is for 2 stages burning simultaneously, then after that is for 5 stages burning simultaneously, and finally is the mathematical limit of infinite asparagus. To use the chart, pick your TWR on the bottom axis and then look up. The higher the line, the more efficient the engine at this TWR in its most mass optimal configuration. The effective Isp can also be used for the following handy equation for planning purposes:  DeltaV = Effective Isp * ln(m_payload/m_fullrocket), which can be used on any stage or set of stages using the same approximate configuration.

In order to get the most mass-optimal configuration, you need to choose the optimal deltaV per stage. These values are shown below. Note that you don't lose much efficiency by being off a few percent, and it's typically better to go a little high in deltaV rather than a little low. Being off by 8+% is where the efficiency really starts to tail off.

  

I hope this helps take a bit of the guesswork out of some of those slower missions. Best of luck out there!

[Jestersage]

Okay, I am still not too certain what you mean by staged rocket vs an aspargus.

Do you mean staged as in, if a craft is of a given mass, staged means "nothing get dropped", using 1 of the thrusters, 2-simul means a orkcet with similar construction to KerbalX,  2 thrusters burned, before 1 of them get dropped off along with the fuel tank?

Or are you talking about, say a clone of Constellation MTV (all of them same mass except the thrusters, they are for 1 thrusters, 2 thrusters, 5 thrusters)? This is the more common build method for Low TRW high Delta V builds AFAIK.

Edited July 3, 2019 by Jestersage

[Cunjo Carl]

23 hours ago, Jestersage said:

Okay, I am still not too certain what you mean by staged rocket vs an aspargus.

Do you mean staged as in, if a craft is of a given mass, staged means "nothing get dropped", using 1 of the thrusters, 2-simul means a orkcet with similar construction to KerbalX,  2 thrusters burned, before 1 of them get dropped off along with the fuel tank?

Or are you talking about, say a clone of Constellation MTV (all of them same mass except the thrusters, they are for 1 thrusters, 2 thrusters, 5 thrusters)? This is the more common build method for Low TRW high Delta V builds AFAIK.

Sorry, I'm not familiar with those rockets and couldn't find them with a search. A staged rocket would be a standard rocket like the Saturn V where the stages burn one at a time. So: stage 1 fires, runs out of fuel, decouples, then stage 2 starts up. On the other hand asparagus rockets are more like the delta IV heavy or the falcon heavy where all of the 'stages' light at the same time, and the outer ones get dropped only as they run out of fuel. In real life there's no fuel crossfeed on these rockets, but in KSP people can go nuts and have 5 stages all crossfed and all burning at once. For some reason it's called asparagus!

To put numbers to it, counting stages from the top of our asparagus rocket,

Stage #	Thrusters in this stage	Total firing thrusters
1	1	1
2	2	3
3	4	7
4	8	15
5	16	31

The above numbers aren't optimal for anything, but should convey the idea. The line names in the efficiency charts refer to how many of the 'stages' are firing simultaneously. So in the above example, the 5th stage would get the efficiency of the "5 simul" line, and the 2nd stage would get the efficiency of the "2 simul" line. For the math's sake, this assumes each stage starts with the same TWR, because otherwise we'd need a spreadsheet. Generally speaking we'd never make a rocket exactly like this, there's always practical issues in the way. But, the lines should make a good square one in planning a rocket.

 

Edited July 4, 2019 by Cunjo Carl

[Jestersage]

1 hour ago, Cunjo Carl said:

Sorry, I'm not familiar with those rockets and couldn't find them with a search.

KerbalX is the Stock Asparagus Staging Rocket: https://wiki.kerbalspaceprogram.com/wiki/Kerbal_X

Constellation MTV (Mars transfer Vehicle), aka Copernicus, is the planned Vehicle to take Astronauts to Mars during constellation period (pre-2001). google "Constellation Mars transfer", and you will eventually come across teh MTV in 3 different configuration: The initial 3 NTR, then 4 NTR plus extended inline and dropable fuel tank, then 4 NTR with  "Star-truss" fuel tank.

Around here, due to capability to build an actual Asparagus staged rocket, if it's normal rocket with no crossfeed, you can just call them Core+Booster. However, for NTR, the closest Architecture is actually Von Braun-Mars - not asparagus, but the side NERVA boosters get dropped off and return to Earth Orbital station.
www.astronautix.com/i/imis1968.html
www.astronautix.com/v/vonbraunmarpedition-1969.html

So how it translate to KSP is that, since people based it on these two designs:

Design 0: No drop off at all. Typically used for SSTO.
Design 1: Constellation approach: Put desire amount of NERVA at one end, and then put dropable fuel tank. Drop off tank when empty
Design 2: von braun parallel-design: Strap a bunch of NERVA-booster on it in parallel. May or May not have crossfeed. Drop off the stage as needed while core stage burn. ay or may not have addition stage in serial.

I really do not see other variant regarding Nerva.

---

So your table is crating confusion because we do not know if they  are hook up to each other in series, which is the second aspect of Von braun (second and thrid stage are serial-connection).

The only conclusion that I can reach from your table is that, Assuming it is asparagus and counting from Bottom, there is a core stage, plus 15 other parallel somehow, then not sure what get dropped off each time. Then once the bottom's core stage is burned, 4th stage comes about, which have 1 core stage + 7 parallel...

Otherwise, if they are all lit, then it's just your standard serial.

---

If you cannot show your picture, my suggestion: just do one parallel stage. 

Design 1 Will be a certain size fuel tank with x number of NERVA at the bottom. Nothing get detach

Design 2 is asparagus staging; 1-Core+2x. Drop 2 (balance issue) each time. No more than 1 parallel stack, but can attach as many around the core if needed. Eg: An asparagus with 1 core stage + 8 side stage. Using KerbalX construction, Fuel path will be in S shape (as seen in https://wiki.kerbalspaceprogram.com/wiki/Asparagus_staging)

 

Edited July 4, 2019 by Jestersage

[Cunjo Carl]

Ah, it's been a while since I've been able to do KSP! Now I know what I'm looking at and squinted at a picture of it, KerbalX does appear to be an asparagus rocket, though its stages look very small.

I look forward to reading about the MTV later!

The chart's context is all of the rocket's boosters are lit at the start, and each stage crossfeeds into the next stage. Then, as each stage runs out of fuel it's dropped (both engines and tanks).  Here's an example of what that might look like, viewed from the top down onto the 'moar boosters'.

But in an ideal world how big should each stage be relative to the next? And how much more mass efficiency do you get for increasing the number of stages? That's what the plots show with the "simul" lines. Arrows show fuel flow, numbers show the stage.

Then there's normally staged rockets like this one viewed from the side.

What's the best engine at your TWR? How much deltaV should each stage have for optimal mass efficiency? That's that the "staged" lines shows.