Friday, April 10, 2009

Accelerating to 100

I made a guesstimate in the post about slow drivers regarding the time it takes to accelerate back up to 100 from a stop to join back in the traffic. The guesstimate of 10 seconds was based off my own evaluation of how far away a car would be before I'd decide to pull out from a standing start, and then relating that distance to the time based method used for shadowing cars. I'd guessed that about 6 seconds would be the limit for me, so about 10 seconds would be comfortable for most people.

10 seconds sounds a short amount though. Most cars wouldn't accelerate to 100 in 10 seconds comfortably, but while you're accelerating away you are also putting distance between you and the car behind. So how much time is gained by the increase in speed? Some quick math:

100km/h = 27.2m/s (since we're going to be working in seconds)
Assuming constant acceleration to reach 100km/h in 10 seconds, you'd get a graph like this:

The actual distance travelled is the area under the graph, which, as it's a right triangle is simply length*breadth/2.
= 27.7m/s*10s/2
= 138.8m

The approaching car has another 138 metres to cover, which it can do in distance/speed.
= 138.8m / 27.7m/s
= 5s

5 seconds, or exactly half the time. That's what I thought immediately, but a couple of math dead-ends while watching the footy had me looking up all sorts of parabolic complexities.

So with 1/2 the time given back to the merging driver, that would mean my guess of a 6 second gap for merging would mean going from 0-100 in 12 seconds. That's achievable even in my corolla, but doubling the 10 second gap to 20 seconds for 0-100 certainly sounds achievable by the majority of the population. Can't seem to find any average acceleration for general driving conditions tho :/

So that's for merging, the same goes for rejoining from pulling over. The time lost compared to continuing on at the driver's original speed is the time taken to get to the original speed minus the time it would have taken to cover the distance used to get to that speed. So, the same result. 1/2 the time. 20 seconds to get back up to speed means you have only lost 10 seconds. This also goes for decelerating, so the figures of 10 seconds for deceleration, 10 seconds for letting them pass, and 10 seconds to rejoin would seem highly achievable.