First 8th vs second 8th in a quarter mile

[hamza123]

So I've heard that any 0.1 seconds saved in the first 8th mile is equal to 0.2 seconds at the end of a quarter mile. Is this true? If so, what's the science!/mechanics/physics behind it?

[Some Gump]

Dunno if true, but it makes sense.

Presuming it's the reaction time. Presume cars and traction identical.

Car a starts. It's now accelerating at it's max rate.
0.1s later. Car b starts. Car a (which has been accelerating) now at x mph.

Rest of run (any time) car b travelling at y mph. Car a travelling at (y+x) mph. We're assuming the cars accelerate identically so the gap should be quite constant.

The whole run, car a is increasing the gap between it and car b. It starts the run 0.1 s ahead, so by the end of the run it's more than 0.1s ahead.

Then apply "Anecdote rounding" and 0.1s becomes 0.2.

[Driver101]

Isn't it the first 60ft and not 1/8 mile?

[hamza123]

Driver101 said:

Isn't it the first 60ft and not 1/8 mile?

No idea. I heard it was the first 8th from cleetus Mc farland lol

[SpeckledJim]

I can see it being approximately true.

If you imagine the shape of the speed curve over time, the rate at which speed is added gradually tapers off, so you'd want as much of the distance covered to be done at as high speed as possible, so I can imagine that 0.1 second dawdling at around 0-30 mph is worth 0.2 seconds once you're going much faster.

0.1 second's dawdle at the start will shift the entire graph to the right, and your highest potential speed won't be attained before the line, but after the line, where it's useless.