What is the difference in distance that you need to be able to see clearly between overtaking someone at 10 mph and overtaking the same person going at 15 mph?
That's a how long is a piece of string question. Depends entirely on how fast the car can accelerate. Its going to be a completely different answer for a Nissan Micra and a Porche 911.
Quite a lot of the highway rules have been the same for decades which is interesting given that the average family car now accelerates faster, has a higher top speed, handles better and brakes quicker than most sports cars at the time the rules were formulated. You could argue that the 10mph rules should be changed to 15mph. The counter argument is that although the cars are much better traffic is heavier so its more likely that something is coming the other way much more rapidly than it would have done in the past.
According to my sums, the performance of your car makes surprisingly little difference. Of course 0-60 times aren't really relevant here, because we're in a speed range where all ordinary cars show more or less constant acceleration. A quick google for "car acceleration curve" finds graphs suggesting that a Ferrari can accelerate at about 10mph / s, or 4.4ms
-2; a 1970 Ford Capri at 5mph/s, or 2.2ms
-2.
The manoeuvre needs to get you from 2s behind the cyclist, 9m at 10mph, (13.5m at 15mph) to 2s in front (ditto, as the bike speed is constant), and let's add 5m for the length of the bike and of your car. So a total of 23m (32m) relative to the bike.
You're starting the manoeuvre at the speed of the bicycle, so in its frame for the Ferrari we take s = 23 (32) u=0, a = 4.4, and calculate
- s = ut + 1/2 a t2
- t = 3.2 s (3.8 s)
For the Capri we get t = 4.6s (5.4s). Twice the performance of the car gets you only 30% less time, because of the square root. The faster bike costs the Capri 0.8s; the Ferrari 0.6s.
Now let's use s =ut + 1/2a t^2 in the frame of an oncoming vehicle doing 60, i.e. 26.4 ms
-1. So now u = 30.8 (33), t = 3.2(3.8
). We conclude that for the Ferrari, with a = 4.4, s = 121m (157m). For the Capri, a = 2.2, s = 165m (210m)
So your instinct is right: using a Ferrari to overtake a 15mph cyclist you need to see a clear road for a distance about the same as, or slightly than, when using a Capri for a 10mph one. Twice the acceleration saves you about 25% of the distance.
But this model is grossly oversimplified. I would prefer to have completed it with 2s to spare before meeting that oncoming lorry. This starts to reduce the Ferrari's advantage, unless you can stop accelerating very accurately. What's more, the time you take to clear the opposite lane is determined by how fast you are happy to move laterally across the road, which is at best constant no matter how fast your car lengthwise along it---in reality I think it diminishes with speed, as the consequences of misjudging your steering become more severe. By hypothesis we're on a twisty road, too. Allow another 2s for this and the Ferrari's advantage has been almost completely eliminated, down to 11m (15m).
(And he's driving like a cunt, too. Suddenly opening up next to a cyclist and gunning for the speed limit: yes, that's friendly.)
