Maximum efficiency

[yourfriend499]

So I had always known how to find how much delta-v a spacecraft had but what about efficiency.

The efficiency is the ratio of mass wet to delta-v relative to mass dry you can graph the relationship with v=isp*ln(1+w/d)

Final I took calculus and I've written an equation so you can find the best amount of fuel based on of payload(anything that is not fuel tanks) and the added weight of the fuel tank shells and isp also you can change the efficiency

the payload isp, isp is p, and efficiency is e

first, divide e by 10000 side note the value is just representative how close you are the curve the farther from 100 the less efficient however it is necessary to do so often

second multiple I by 9.81 (from the game given amount)

use the formula below and that is the amount of fuel you should use

i/(3√((3/4)^2-p/2))

 

 

Edited February 19, 2017 by yourfriend499
Clarification

[Bill Phil]

Efficiency in terms of... payload mass fraction...?

[Steel]

Yeah, what efficiency are we talking about here?

[yourfriend499]

6 hours ago, Steel said:

Yeah, what efficiency are we talking about here?

The relationship between the ratio of mass wet and mass dry which gives delta-v so the most delta-v for the least amount of fuel 

[Bill Phil]

1 hour ago, yourfriend499 said:

The relationship between the ratio of mass wet and mass dry which gives delta-v so the most delta-v for the least amount of fuel 

So the smallest mass ratio? Are we solving for what isp we need for a given mass ratio?

[FleshJeb]

There are no local minima or maxima in the Rocket Equation. It's not optimizable from that standpoint.

The overriding concern in KSP is the minimum useful TWR. (And in Real Life, structural and launch concerns)

Interestingly enough, there IS an optimal ISP for a given burn, but IIRC we don't even get close with chemical rockets--It's most applicable to ions and VASIMIR.

https://en.wikipedia.org/wiki/Specific_impulse#Energy_efficiency

https://en.wikipedia.org/wiki/Spacecraft_propulsion#Energy