linear t/w conversion for comparison of engines?

[GoSlash27]

I'm trying to come up with a linear "figure of merit" that scores all the engines in KSP for t/w, efficiency, and price. Clearly, Isp and price are easy to pin down, since they are linear to relative worth. All things being equal, an engine that does the same thing for half the price is twice as good. Likewise, all else being equal, doubling the Isp doubles the worth of an engine.

But this is not the case with t/w ratio. Doubling the t/w of an engine won't make it twice as good. Depending on where it was to begin with, a doubling could have a much more dramatic effect or no noticeable gain at all in the performance of the vehicle.

Basically, doubling the t/w is saying I'm carrying half the mass of engine for the amount of thrust, leaving more payload and fuel, but that won't be twice as much. For it to be truly linear and scalable, we'd have to take a natural log of the (engine mass+full fuel tanks+payload)/(engine mass+empty fuel tanks+payload)

The question is where to set fuel vs. payload and where to set the sum total of both for an apples-to-apples comparison.

Would setting the fuel+tanks in a stage equal to payload at 1G generate a useful ballpark datum for Kerbin launches?

Open to suggestions,

-Slashy

Edited November 4, 2014 by GoSlash27

[Jouni]

You can compare thrust, specific impulse, and price, as they are all linear quantities. Even the product of thrust and Isp is a somewhat meaningful linear quantity. TWR, on the other hand, is a normalized quantity, so comparing it with linear quantities doesn't really make sense.

You could do price-optimal engine charts similar to tavert's mass-optimal engine charts. Select minimum TWR, payload mass, and delta-v requirements for a rocket stage, and the charts compare the prices for stages using different engines that can fulfill the requirements.

Edit: Now that I think of it, specific impulse is also a normalized quantity, but in a different way than TWR. You can compare thrust vs. price and thrust x Isp vs. price, but even the latter is somewhat problematic.

Edited November 4, 2014 by Jouni

[Tsevion]

You could perhaps use a fixed mass (say 100t), and figure out how many engines to add to get to a specific TWR (0.5?, 1.0?, 2.0?). The score is then the weight of those engines. This is a direct calculation from TWR, so effectively ignores the other factors, while still giving a number that is more linearly representative of capability.

The problem is very low TWR engines can't make the minimum goal (Nuclear has trouble making 2.0, the ship needs to be 80% engine... Ion struggles to make 0.5). Of course, if rating engines for launch capability this makes sense... nukes ARE terrible launch engines, an ions simply can't launch at all. On the flip-side, both are really handy in space.

Another thing to consider is you probably want to normalize the price to something like price per kN of thrust... otherwise smaller engines are getting a bit of an unfair advantage.

[cantab]

Mass, cost, and thrust are like extensive properties. Double the engine up and you double all of them.

Isp is an intensive property. TWR and thrust per kuid are also intensive properties. Double the engine up and they stay the same.

TWR per kuid is going to pop out as an extensive property, since a pair of engines would have twice the price but the same TWR.

To have a level playing field between small and large engines, you need to only consider intensive properties. It's pretty simple to check - if your figure of merit changes when you consider a pair of the engine, it's not a valid figure of merit.

Ultimately I think a simplified version of tavert's approach is best. Impose a required delta-V and initial TWR, assume for simplicity that you can use fractional engines, and work out the price per ton of payload for the various engines.

There is though a gotcha. A multi-stage rocket where each stage is mass-optimal will be mass optimal in total, but a multi-stage rocket where each stage is price-optimal may not be price-optimal in total because if the upper stage is cheap but heavy it becomes a bigger payload for the stage below. This may limit the use of these figures.