Math Is Fun Forum

Hi,

I have a problem I am keen to get some advice on.

Basically I'm tweaking the handling parameters for some cars in a computer game (Grand Theft Auto: San Andreas) in an attempt to make them as true to real life as possible.   (See, maths IS fun!!)

I've got some 'real world' data based on my manual tests of different settings and their affect on the vehicles in the game, and I'm trying to derive a formula to help me calculate the expected results rather than manually testing every possible setting (of which there are thousands)

The sample data I have collected is listed below.  Note that 'EA' is the game parameter that I am working with at the moment.  It stands for Engine Acceleration and the higher the setting, the higher the car's acceleration rate is.  I have done slightly more tests to 200km/hr than to 400, because it's hard to find enough straight road in the game world to get to 400 with an EA less than 30.  I might be able to do it if anyone needs the figures, but it's a hard ask

EA    Seconds to 200km/hr
10    12.5
20    6.25
30    4.25
40    3.50
50    2.75
60    2.50
70    2.25
80    2.00
90    2.00
100    2.00
   
EA    Seconds to 400km/hr
30    14.00
40    10.75
50    8.50
60    7.50
70    6.50
80    6.00
90    5.50
100    5.25

Unfortunately, the only method of timing that I have at my disposal is a manual stopwatch, which isn't very accurate, but I've generally done a number of runs and compensated for my reaction times etc.  In any case, the times I list below need to be viewed with a certain amount of flexibility and I would say that you could adjust them by at least 0.25 seconds either way if you see that they would fit a pattern / formula by doing so.

I have spent a number of days using Excel to work with these numbers and while I have been sucessful in determining a pattern and deriving formulas for other game parameters, I have been unable to do so with EA.  The best I've been able to do so far is to graph the numbers, the result being that and they show up as a relatively smooth, non-linear curve.  This confirms in my mind that there must be some pattern or formula somewhere in the bowels of the game engine, however working with the numbers, I can't determine what this could be.  I have tried variations on simple ratios, differences and combinations of, but when it comes down to it, I don't really have any idea on how to approach this problem

I can use the graph to (approximately) predict an outcome, for example, looking at the results on the 400km/hr graph and using them to estimate what the time would be for an EA of 55 showed up as 8 seconds on the graph, and was confirmed as being accurate after in game testing.

If anyone can give me some idea of how best to approach this problem I would be MOST appreciative!  And of course if you just happen to be a GTA:SA player, then you are more than welcome to a copy of my realistic car setups once they are completed

And in case you're wondering, yes, I MUST be a nerd as I seem to spend more time working on a spreadsheet with game data than I do actually playing the game (at least for the moment anyway)

Teach me oh wizened ones!

Thanks in advance,

Sam.