3 ms·
One thing to note is that this shortest path won’t typically be much shorter. Consider a circular ring road. The circumference on the inside is pi * d and on th
by dan-robertson 7y ago
One thing to note is that this shortest path won’t typically be much shorter. Consider a circular ring road. The circumference on the inside is pi * d and on the outside is pi * (d + w), where w is the width of the road, so the amount you save by driving on the inside is pi * w which is probably less than 100m.
In a more general simplified case where you always stick to the inside of every curve and jump from left to right for free, the amount you save compared to sticking to the middle lane is the line integral:
\frac14 w \int k \mathrm ds
where k is the curvature (strictly speaking k should be an adjusted curvature of 1/((1/K) - (w/2)) where K is the actual curvature).
Because roads are not very curvy, the integral of k will be small and so the distance saved is very low. And note this is an overestimate because it doesn’t cost in changing from side to side
- TheSpiceIsLife 7y agoIn motorsports it’s known as the racing line. You’re right, the gains are small for the average road user :) Wikipedia article https://en.wikipedia.org/wiki/Racing_line https://en.wikipedia.org/wiki/Racing_line
- GhostVII 7y agoThe real gains come not from decreasing the distance travelled (sometimes the racing line does the opposite), they come from limiting the radius of the turn so you can carry more speed through. At least thats what I've learned from playing Grid 2 for far to many hours.
- TheSpiceIsLife 7y agoYep, that Wikipedia article talks about that, and one it suggests are further too https://en.m.wikipedia.org/wiki/Trail_braking https://en.m.wikipedia.org/wiki/Trail_braking
- lonelappde 7y agoI think that's the whole point of Grid 2, just to tech people about racing lines.