waremark wrote:I would want to gain more than 2 seconds, and to reach a peak speed of less than 90. If your maths is right, my judgement that I would have taken the overtake may have been wrong. Are you sure it is? Empirical experience suggests that if I have 16 seconds to where the view disappears I would have enough space for an overtake with a differential of not more than about 20 mph.
I will repeat an exercise I have tried in the past of using an overtake of an LGV on a multilane road to simulate a single carriageway overtake and trying to note time and distance.
Couple of things
- Peak theoretically required speed won't need to be reached in 99% of actual overtakes. Every second you continue into the overtake without a fastest-reasonable oncoming car appearing gives you more time to complete the overtake than you had at the start, so in practice you'd be slower almost all the time to avoid looking like too much of a hooligan (the +20mph you suggest sounds reasonable). This might partly be why it sounds high.
- The main issue with assessing this overtake based on the video timeline is that the video car starts out fast (mid 50s) and ends up slow (falling to ~40 thanks to the hill). An oncoming vehicle could reasonably cover ground much faster down the hill. The timeline if you went for the overtake (what matters) would look quite different. The bend after the overtake could be exited quite fast.
None of the above allows for a plan B of 'hit the brakes and tuck back in behind if something appears in the first second'. To what extent to people find themselves doing this / think it's acceptable to rely on?
I agree with playtent that starting as early as possible makes a huge difference; and is the only way to complete that safely.
Personally I would never do it in those conditions, and I doubt I would in the dry either. Having said that I do miss a lot of overtakes.
Painful details of my original calculation follow. Probably nobody cares, but I did it so hey.
Average Dave speed = 48mph (I guessed) gives the distance of 386m (~48mph * 18s). Target vehicle speed during the part where you'd actually pass ~=54mph = 24m/s (this appears alot later).
To avoid needing to consider complex acceleration profiles; I've simply took the overtake as jumping a certain amount forward from the target's perspective (2s is probably about as tight as this reasonably gets).
The overtake time (6s) could be estimated by matching a lorry from 2s back, accelerating to alongside and changing lane. It needs to be padded to include all reaction times and moving back in time. You can approximate an acceleration from this if you like: gaining 2s in 5s (leave 1s lane change time) means you need to gain 48m (2s * 54mph). 48m = 0.5At^2 = 12.5A, so A = 2.84ms^-2 (and therefore top speed of 5*2.84+24 -> 85mph - note that this depends on many factors not modelled here).
This means distance used until you're back in is 8 seconds of the target's speed. 24*8 = 192m.
That leaves 194m for the oncoming car. It it can cover that in 5 seconds, you crash (or abort), if not you're clear. 194m/6s = 72mph. This seems borderline for declaring 'safe' to me.
54-85 in ~5 seconds is pretty fast - my RX-8 won't do that anyway. As such I don't believe it could complete that overtake safely in any conditions. A quicker car would be able to, subject to the above (you might have to get quite close before and after).
(Am I just being annoying here? I'm genuinely unsure.)