[Math] Observations on spaceship speed

[elec0]

I've spent the last day or two whipping up something to be able to test speed in relation to the different ships and thrusters.
It's hardly complete, my data set is still fairly small and I've only really isolated thrust as a variable, but I thought you all might be interested in my findings so far.

So far it seems that acceleration is a linear function of velocity, and that each ship has a different speed cap (there is probably still a global speed cap, not sure yet though) based on thrust/mass/other factors.

By time acceleration and velocity have an inverse exponential and logarithmic relationship, respectively (or so it seems.)
I believe this type of shape is just a result of having a speed cap, since in real life velocity isn't capped.

Here is my testing area

I use a rangefinder to get distance to the back of the given ship, and a YOLOL chip reads that as quickly as possible (~0.2s) and writes it to a text panel for bulk storage. The text panel has 127 characters, and with flooring the numbers you can get 30-40 readings in a single, easy-to-copy-and-paste location.

Here's my spreadsheet if anyone wants to see more information: https://docs.google.com/spreadsheets/d/1qBADgFBPS__C_C7MhECZm8zPds-bNcVYx5by96SEhtc/edit?usp=sharing

 

[CalenLoki]

I fookin love science. Thank's for your research.

Seems that you can achieve almost top speed in 2s. IMO would be more fun to increase it (lower both thruster force and drag). And I mean double or triple. But that's up to devs.

Have you done any tests regarding drag scaling formula?
Is the presented data for the same ship, but with deactivated some of thrusters, or are those different ships?
I.e. make ship with 6 box thrusters and some extra mass. Then check top speed with 2, 4 and 6 thrusters active, but exactly the same mass.

 

[elec0]

I haven't yet, no, it's strictly just acceleration until it gets out of range of the rangefinder.
Yes, the data is for the same ship with thrusters deactivated, except where noted with the Zilan, where I just grabbed it out of the premade blueprints. I wanted to keep the mass as constant as possible.
My next set of tests is going to be keeping thrust constant while changing the mass.

 

[CalenLoki]

I'm surprised how little difference there is between 4 and 6 thrusters pushing the same mass. Top speed is of course capped, but initial acceleration should be much higher for 6.

Keeping the mass constant and changing thrust may be more accurate, as we have no way to precisely measure mass ATM. Unless you literally bolt several of the same ship modules together, just some of them with disabled thrusters.

 

[elec0]

All right, I've made observations with changing mass.
Here's what the final test with 12 mass extenders looks like

I just made a frame and slapped a lot of plates on it, figuring that plates were probably fairly heavy. It appears that I was correct.

Some preliminary findings so far:
Max velocity is decreased when mass increases.
This relationship appears to be linear:

Acceleration is also decreased as mass increases, although the relationship does *not* appear to be linear: I'm not as confident about this conclusion, though, as I don't have that many data points.

What I'm really aiming for is to try and figure out the velocity/acceleration formula they use.
I *think* that these observations are enough to get a fairly good idea of what it is, but I'm not seeing it yet. I've gotta think about it more.
If anyone else has ideas about things, please chime in. There's more data and graphs in the spreadsheet.

 

[CalenLoki]

TBH it looks linear. That grey curve in acceleration chart would match the results more if it were flat line, and the little deviations may be caused by measuring errors (yolol doesn't execute precisely every 0.2s, but has slight randomness)