Optimizing my commute III

[asterroc]

I was reminded by mathsex people that (1) if I assume gas mileage and speed are equally important, that I could just average the optimal speed for both and I get around 65mph for the ideal driving speed, or (2) a potential way of giving a more realistic value to my time as compared to the gas mileage is to put a dollar value on my time - according to my salary that's around $20/hr. More math to come...

Comments

[gemini6ice.livejournal.com]

I think in other posts I've stated my support of time-money as the driving unit of value.

So your commute costs you:
t(v) = 20 * Distance / v
g(v) = Av + Bv^2

and we want to minimize t(v) + g(v). Fun. :)

Do you have any fuel efficiency stats for your car so we can solve for constants A and B?

[gemini6ice.livejournal.com]

Sorry, fuel efficiency g(v)= Av + Bv^2 + Cv^3

[gemini6ice.livejournal.com]

oh, wait , +D.

http://auto.howstuffworks.com/question477.htm

[zandperl.livejournal.com]

That formula is for POWER, not fuel efficiency. We need a quadratic (or at least an even power function) b/c we need an absolute maximum. A cubic equation implies that as you drive infinitely faster, you can get infinite fuel efficiency.

[zandperl.livejournal.com]

Yeap, I was thinking about exactly that as I drove in this morning. The stats I have are rough. What I'm willing to use are that at 74 mph I get 36 mpg, and at 55 mph I get 40 mpg, and 55 mph gives the absolute maximum. I'm going to check with jethereal later, I'm pretty sure that's sufficient information to solve for those constants. Though actually it'd be more standard to write g(v) as follows

g(v)=Av^2+Bv+C

Don't ever forget the +C. ;) And also, I'd rather express it all in minutes so I don't have to deal with decimal hours, but that's a trival conversion. But what's less slightly less trival is that the total time should have a +20min b/c regardless of how fast I drive on the highway I still have local streets and traffic at the end. I should have something whipped up by the end of the day.