## Kerbal Efficiency

22 Oct

As you may know from reading my previous post I’ve recently got back into Kerbal Space Program due to the release of a career mode. In this mode you have to preform science experiments to unlock new parts for your craft. There are two ways of returning the results to your space centre, you can either transmit them from you ship which incurs losses, or you can land and manually recover the ship and all available science data on it. There has been a lot of talk between me and my friends about which way is best. I initially though that landing at home and doing a manual recovery would obviously gives the most data, but it can be inconvenient if you’re doing sample analysis on a far away planet. There is also the added complication that repeat experiments give diminishing science returns.

Luckily through reading around on the forums and doing a bit of maths I have come to the surprising discovery that if you do enough science it doesn’t matter how you get it home.

The first time you do an experiment you get the full initial science value (ISV) multiplied by the efficiency of the method of returning it.

$E_{0} = ISV\times T_{efficiency}$

Obviously in this case a landing on Kerbin is best with the highest efficiency of 1. The interesting bit comes in when you consider the diminishing returns. The second time you perform an experiment the experiment value, E, you get is reduced by a combination of 80% and the transmission efficiency of the data

$E_{n} = E_{n-1}\times (1-T_{efficiency}*0.8)$

Below I’ve calculated the returns you’d get performing some of the standard science experiments ten times assuming the ISV is 1, and at the bottom the total amount of science you would have at the end of all ten experiments. The efficiency of transmission is given under the name of the experiment.

 Crew Report EVA Goo Science Jr Temp Atmosphere 100% 50% 40% 20% 60% 90% 1 1.0000 0.5000 0.4000 0.2000 0.6000 0.9000 2 0.2000 0.3000 0.2720 0.1680 0.3120 0.2520 4 0.0080 0.1080 0.1258 0.1185 0.0844 0.0198 5 0.0016 0.0648 0.0855 0.0996 0.0439 0.0055 6 0.0003 0.0389 0.0582 0.0836 0.0228 0.0015 7 0.0001 0.0233 0.0395 0.0703 0.0119 0.0004 8 0.0000 0.0140 0.0269 0.0590 0.0062 0.0001 9 0.0000 0.0084 0.0183 0.0496 0.0032 0.0000 10 0.0000 0.0050 0.0124 0.0416 0.0017 0.0000 Total 1.2500 1.2424 1.2236 1.0314 1.2482 1.2500

As you can see from the totals the maximum amount of science you can obtain from a given experiment is 125% of the initial science value, and even the 40% transmissions get pretty close to that after ten runs. Below is the data plotted showing the results of the diminishing returns. As it is a constant reduction based on the transmission efficienct the more efficient methods get reduced faster

Kerbal Science Efficiency

Provided you have the power on your craft, and the patience necessary to do the ten or more runs of the experiment, it seems like returning samples manually offers no real bonus.