Racing question for the math people
 

I've challenged a neighbor to an indoor go-kart race where all the karts are identical. I out-weigh him by about 50lbs. Horsepower to weight ratio is easy to calculate but how would you factor that into a time? If we raced identical cars, the weight wouldn't be much of an issue but karts...weight is everything. The only thing my tiny mind could think of was to physically add the difference in our weight to his kart via weight belts or something....

Thanks for any and all help!

Impossible to be accurate without a detailed study of the particular track.

Your best bet is to run several laps, then switch karts, repeat.

How possible is it to be slightly inaccurate?;)
I'm not striving for super-accuracy, I just want a formula that will get me in the ballpark.

I agree. And then get another pair of karts and go again, because the karts are NOT the same. One will have newer tires, etc. When we used to go, the big game was to try to get into the kart that was obviously faster by just observing.

Yeah, impossible to tell without a ton more info on the track, etc.

I'm not sure how switching kart is going to help tell you anything. Unless when you make the switch, you leave some of your limbs behind in your kart.

When's the race? Can you lose 50 lbs by then?

The only way for me to lose 50lbs would be to remove some vital body parts (internal and/or external).

Let's say the karts weight 500 lbs each, you at 200 and he at 150.

Then you + kart = 700, he +kart = 650

650/700= 0.929 1-0.929 = about 7% faster, all things equal. Factor in acceleration, inerta, driver skill and go from there. Where would you put the 50 lbs bag of cement on his kart?

I thought the point of the race was to see who was better. Sure, one driver will be at least different than the other's style. By taking the differences in the physics out of the contest, the better driver will come out on top.

Go in with some complicated formula written out on a piece of paper, bring your calculator, after you get your times you punch in a bunch of numbers, and lookee there . . . you beat him!

How will switching karts help determine who is the better driver, when one weighs 50 lbs more than the other, or take the differences in physics out of the contest?

He will be 50 lbs heavier in Kart A, and he'll still be 50 lbs heavier in Kart B.

I thought that was explained above by averaging speeds. Did someone delete a post from above?

Here's what I thought I saw: After the first series of heats, the average difference in times/speed is x. Switch karts and the next average is y. Now we have the discrepancy of the karts out of the way. To figure the handicap now would be fair.

I though Hugh had the rest of it figured out. If not, I'm sure once the variables are equalized, a formula could be applied. It's gonna be x + y over something.

That's solving the wrong problem, though.

He's not worried about any discrepancy in the karts. I think he's willing to assume the karts are identical.

The problem he is trying to figure out is how to equalize his 50 lb weight disadvantage.

Hugh's formula is an attempt to solve the problem, but I don't think it really works. The added weight could be a huge disadvantage, or a much smaller disadvantage, depending on the track configuration.

THe other guy just needs to add 50lbs of balast to his cart. Of course the lower he places it, the lower his CG will be. A lower CG is a very real advantage.

I've driven some indoor karts. Each cart (drove 4 in a day) was completely different than the last even though they were all supposed to be the same.

If it's a "slick track" your added weight can actually be an advantage.

Just make him wear a 50lbs weight belt and be done with it.

Thanks for all the replies everyone!

Correct....I'm not too worried in the discrepancies of the karts. Simply switching karts will negate that. I like the formula that Hugh brought forth and I agree that adding weight might be a disadvantge, but wouldn't be as bad as having it higher up (raising the kart's CG). My weight would raise the CG whereas weight put on the kart would change the CG and the polar moment (if my physics knowledge is still working). Maybe I'll have to spot him some weight...maybe take 10lbs off the difference.

Assuming Hugh's calcs are correct. You have a 7% weight advantage. Compare lap times over x laps in the same cart, then repeat in a different cart as a control, then apply the 7% factor to both his average/quickest times to see who's "better". That way, driving styles are the only variables.

Sherwood

At our local indoor track the guys tell me that 10 lbs is equal to about 0.1 seconds per lap. The track is just shy of 1/4 mile and the cars have 6.5 hp briggs and stratton engines. Just as a point of reference.