I am an inveterate driver of “back ways” to places. My preferred route to campus involves driving through a whole bunch of residential streets, rather than taking the “main” road leading from our neighborhood to campus. I do this because there are four traffic lights on the main-road route, and they’re not well timed, so it’s a rare day when I don’t get stuck at one or more of them. My preferred route has a lot of stop signs, but very little traffic, so they’re quick stops, and I spend more time in motion, which makes me feel like I’m getting there faster.
That’s the psychological reason, but does this make physical sense? That is, under what conditions is it actually faster to take the back route, rather than just going down the main road?
Some parameters: the main road route covers 1.7 miles and contains four traffic lights. The back way covers 2.2 miles and has nine stop signs. The speed limit on all of these streets is 30mph, but I usually drive more like 35mph, or 16 m/s to put it in round numbers. I don’t really gun my car after any of the stops, so the acceleration is around 2 m/s/s (I’m enough of a dork to have checked this with the accelerometer in my phone, as well as counting “one thousand one, one thousand two…” while accelerating up to speed).
Given that information, how can I estimate the conditions under which it makes practical sense, rather than just psychological sense, to take the longer route rather than the main roads?