Overtaking with speed

[7db]

Please!

I can't find it, but I can reproduce it.

* * * *

The example was an overtake on a car travelling at 50mph. Everyone has 1g braking and 1s reaction times. The overtaking car can accelerate at 0.2g (that's 0-60 in about 14s) at 50mph. Cars are 3m long.

The danger zone is defined so that a car is in the danger zone when it cannot stop behind the target car when it exerts maximum braking, until the time when it is clear of the nose of the target car.

In each example we calculate time in danger.

Momentum overtake
Approach at 70mph and clean pass.

i) How far behind does danger start?
50mph car stops in (v^2=2as)
70mph car stops in (vT + v^2/2a)
So danger starts 56m behind target.

Relative to first car, danger zone extends 62m and is travelled at 20mph so
TED = 6.9s

More generally - http://tinyurl.com/2q57wz


Triangle overtake
Safe offside following position is at 50mph thinking distance = 22.3m

So distance to clear is 28.3m, covered relative to target at a starting speed of 0 and with acceleration of 0.2g. (s=1/2 at^2)

TED = 5.4s

More generally - http://tinyurl.com/yulumz


Edited to correct braking value in Momentum example and html formatting.

[jont]

I can't find it, but I can reproduce it.

<maths>

That makes for very interesting reading, even with the large assumptions about acceleration/reaction times etc. Given that, is there an optimum speed differential to use for a momentum overtake, or is minimum TED always starting from 0 initial differential speeds? (sorry, I'm feeling lazy although I probably could do the maths myself). And how does that speed vary with different accelerations available? (for instance a quicker car with maybe 0-60 in around 7s).

[7db]

Just factorise the difference of the two energies in the banana example and you'll be able to extract and cancel a factor of speed differential throughout.

You'll have the answer to your question staring you in the face then and no need to figure out the partial differentials.

You might also spot the weakness in the underlying assumptions. You might not.

[7db]

PS - the numbers I've posted are wrong. I'll correct them later.

Done.

[7db]

Given that, is there an optimum speed differential to use for a momentum overtake

Yes. I think it's some sort of bastardised hyperbola with a linear component. I'm not differentiating it for you.

But it's 102.7mph in this example.

[Luke]

Overtaking...102.7mph...

Sometimes we can overanalyse things. Its actually quite simple, as long as you overtake at the right place.

[TripleS]

Overtaking...102.7mph...

Yes, I know, hilarious isn't it; but what's wrong with it?

Sometimes we can overanalyse things. Its actually quite simple, as long as you overtake at the right place.

I think you sometimes end up with a worse result if you try too hard. That may not appear to be logical, but it sometimes seems to work out like that. Maybe it's due to too much concentration on a detail that really doesn't matter that much, and consequently neglecting more important aspects.

Best wishes all,
Dave.

[martine]

...Just factorise the difference of the two energies in the banana...

Damm, I'd love to be able to say that in a conversation...sounds like something from a Star Trek convention.

[VinnyP!]

Both obviously have their place IMHO. One of the best momentum techniques is on the long open single carriageway one lane in each direction. As you close on the car in front by observing traffic towards and adjusting your speed you can time it so that you can safely overtake in a much smaller oncoming gap by having a much higher differential but as has been said you are committed earlier so your planning has to be right and to be honest without using exemptions I think it will seldom appear in day to day driving.

[7db]

Sometimes we can overanalyse things.

The maths is easy and available. Why discard anything that aids understanding?

Unless you are scared of numbers.

[James]

[Luke]

Not scared of numbers but I just think that you can't teach someone how to do a safe overtake by figure crunching.

Its just an observation on my part, no need for anyone to take the wee-wee.

[Gromit37]

I don't wish to upset our engineering/scientific brethren, but I agree with Luke. You don't learn to drive a car by figuring out all the maths behind it. An overtake is a matter of judgement and spatial awareness. If it were all down to numbers, why aren't all the best racing drivers, bowls, snooker and darts players engineers?

And YES, I hate numbers. My brain works very well with words, but numbers just do not flow smoothly. It's like trying to write with the other hand... possible but messy. Something to do with being left handed and the right side of the brain perhaps?

[VinnyP!]

I don't wish to upset our engineering/scientific brethren, but I agree with Luke. You don't learn to drive a car by figuring out all the maths behind it. An overtake is a matter of judgement and spatial awareness. If it were all down to numbers, why aren't all the best racing drivers, bowls, snooker and darts players engineers?

And YES, I hate numbers. My brain works very well with words, but numbers just do not flow smoothly. It's like trying to write with the other hand... possible but messy. Something to do with being left handed and the right side of the brain perhaps?

I'm with you but you would be astonished how many race drivers who otherwise appear to have axle grease instead of brain tissue are happy around slip angles, dynamic COG calculations suspension geometry etc.

[Gromit37]

I don't wish to upset our engineering/scientific brethren, but I agree with Luke. You don't learn to drive a car by figuring out all the maths behind it. An overtake is a matter of judgement and spatial awareness. If it were all down to numbers, why aren't all the best racing drivers, bowls, snooker and darts players engineers?

And YES, I hate numbers. My brain works very well with words, but numbers just do not flow smoothly. It's like trying to write with the other hand... possible but messy. Something to do with being left handed and the right side of the brain perhaps?

I'm with you but you would be astonished how many race drivers who otherwise appear to have axle grease instead of brain tissue are happy around slip angles, dynamic COG calculations suspension geometry etc.

I wouldn't be surprised, but the qualities that make them 'good' racing drivers don't generally come from an understanding of the maths. Unfortunatley, I can't drive well or do the maths!