Overtaking Distance

[lyndon]

I want to calculate how much road I need to overtake another vehicle. I've got someone elses spreadsheet that purports to do this, but want to check it out myself, so I know all the assumptions that I am using.

At the moment, I am assuming that
1. the 'overtaking' position is 1 second behind the vehicle that I want to pass,
2. I can cut back in when I can leave a gap equivalent to that given by the two second rule.
3. that I cut back with a clearance of at least 5 second between me and an approaching vehicle.

Given these assumptions, or some variation on them, and knowing the length of my vehicle, the length of the vehicle I'm overtaking, the acceleration capability of my vehicle, my current speed and the speed limit, and can calculate how much road I need. I realise I can't do the sums while driving, but it will be interesting to compare the numbers with my intuitive guesses.

Can anyone help me come up with realistic figures for the above three?

[jont]

Don't forget to factor in whether the road is uphill or downhill, weight of any luggage/passengers and what the wind is doing

(I think you can overcalculate these things too much - better to have a good understanding and feel for what "looks" right than overly worry about calculations)

[lyndon]

Well, as I said I'm really not planning to enter the figures into my laptop before overtaking. I want to run a check on whether my instincts are reasonably accurate. Once I've checked myself out, I'll be happy to get back to using my instinct, or not.

I just need to know whether what "looks" right "is" right.

You could say the same thing about stopping distances, but my guess is that a lot of people 'out there' can't tell when it looks right.

[jont]

Well, as I said I'm really not planning to enter the figures into my laptop before overtaking. I want to run a check on whether my instincts are reasonably accurate. Once I've checked myself out, I'll be happy to get back to using my instinct, or not.

I just need to know whether what "looks" right "is" right.

Are you getting back in before half the distance you can see to be clear at the point you commit? Most people I've come across seem to think this a reasonable metric for a "safe" overtake.

[Horse]

Well, as I said I'm really not planning to enter the figures into my laptop before overtaking. I want to run a check on whether my instincts are reasonably accurate. Once I've checked myself out, I'll be happy to get back to using my instinct, or not.

I just need to know whether what "looks" right "is" right.

Are you getting back in before half the distance you can see to be clear at the point you commit? Most people I've come across seem to think this a reasonable metric for a "safe" overtake.

With a fall-back plan in case the driver you're overtaking puts his foot down . . .


Someone posted some figures a while back, comparing the 'traditional' and 'elastic' overtakes, which might fit the bill.

[lyndon]

Are you getting back in before half the distance you can see to be clear at the point you commit? Most people I've come across seem to think this a reasonable metric for a "safe" overtake.

According to my sums that will mean that sometimes a vehicle coming towards you will have to brake quite hard to avoid a head on collision!

[GJD]

Are you getting back in before half the distance you can see to be clear at the point you commit? Most people I've come across seem to think this a reasonable metric for a "safe" overtake.

According to my sums that will mean that sometimes a vehicle coming towards you will have to brake quite hard to avoid a head on collision!

Getting back in before half the distance will conflict with oncoming traffic only if it is going faster than you. That's certainly possible of course, but I just wanted to check you'd understood what I believe jont was saying.

[TiJay]

Are you getting back in before half the distance you can see to be clear at the point you commit? Most people I've come across seem to think this a reasonable metric for a "safe" overtake.

I believe this is to be used when there is no oncoming traffic visible, so you should be in by the time you're halfway to the loss of vision? Although I heard somewhere two-thirds is sometimes applied.

With oncoming traffic then the original poster's rule seems most sensible - back in with 5 seconds between you and the oncoming vehicle.

[GJD]

Are you getting back in before half the distance you can see to be clear at the point you commit? Most people I've come across seem to think this a reasonable metric for a "safe" overtake.

I believe this is to be used when there is no oncoming traffic visible, so you should be in by the time you're halfway to the loss of vision?

It's the same. The distance you can see to be clear is either the loss of vision or the oncoming traffic. After all, the moment after you commit, an oncoming vehicle could appear. To use a different 'rule' when there is no oncoming at the point you commit would imply assuming that there still won't be oncoming traffic a moment later - and that's not a valid assumption.

Although I heard somewhere two-thirds is sometimes applied.

Not heard that before. In this highly simplified analysis, you could bank on two thirds if you could bank on the oncoming traffic doing no more than half your speed.

With oncoming traffic then the original poster's rule seems most sensible - back in with 5 seconds between you and the oncoming vehicle.

I thought about that when I read Lyndon's first post. You certainly want some margin in hand, but I wondered whether 5 seconds could be a little on the conservative side - not that there's anything wrong with conservative when it comes to overtaking safety. If you're both doing 60mph (so closing at 120), 5 seconds is just under 300 yards (293.3). If I remember, I'll have a look at the distance to go to the exit when I pass a 300 yard marker on the motorway tomorrow and see if I think I'd be happy being any closer to an oncoming vehicle as I moved back in after an overtake.

[lyndon]

Getting back in before half the distance will conflict with oncoming traffic only if it is going faster than you. That's certainly possible of course, but I just wanted to check you'd understood what I believe jont was saying.

That's what I thought you meant. My worry is twofold:
1. The chances are high that approaching traffic has an average speed greater than yours. They may be travelling at the speed limit. You accelerated to the speed limit from a lower speed. This gives you a negative margin for error.

2. If the approaching traffic is doing the same as you - overtaking, and planning to get back in before half the distance they can see to be clear, I believe you have a recipe for a disaster.

[7db]

Anyone who wants to run the numbers as an additional check is fine by me.

Indeed, a quick search on this forum will show my working from when this came up last time.

Definitions:-
1. Your overtake starts when you can no longer stop behind the car in front if it brakes with maximum force.
2. Your overtake finishes when - should you brake with maximum force and the car behind start to brake with maximum force 2s later you do not collide.

Then make the mother of all assumptions:-
- target is constant speed
- braking force available -- g is often acceptable
- accelerative force available -- g/2 is pretty good
- length of vehicles - 3m works for me

Then run the sums. I would use an inertial frame moving with the target, taking the front of the target as the zero point.

[7db]

I simplified my assumptions to ending the overtake at the point where there is a 2s gap between vehicles. This is conservative given the speed differential, but removes the need for braking force calculation which makes the whole thing unnecessarily complex for little benefit in accuracy.

I also assumed nice linear acceleration with no regard to the higher limit. Nice and realistic.

This gave me this calculation:-
http://tinyurl.com/3xcth92

You can clearly see the assumptions in there (target speed, acceleration, vehicle length).


I think there are two interesting outcomes:-
1) That's about right for judgement (and I would be a lot more conservative than this in the real world)
2) If this calculation helps people to realise that you are committed to the overtake when you can't stop behind the car in front when it emergency brakes, that's useful.

[GJD]

If I remember, I'll have a look at the distance to go to the exit when I pass a 300 yard marker on the motorway tomorrow and see if I think I'd be happy being any closer to an oncoming vehicle as I moved back in after an overtake.

Well I remembered to have a look, but it was pretty inconclusive. Very difficult to judge on a motorway whether 300 yards felt conservative. Moving back in after overtaking obviously takes some time. I *think* I decided that I'd probably want to have started to move back in with 300 yards to go, rather than necessarily wanting to have finished moving back in with 300 yards to go. But mainly I decided that a motorway with 300 yard signs is not very representative of oncoming traffic on a single carriageway.

If I'm still feeling unscientific next time I overtake someone, I might try counting 5 seconds in my head and see where it gets me.

[lyndon]

Well I remembered to have a look, but it was pretty inconclusive. Very difficult to judge on a motorway whether 300 yards felt conservative. Moving back in after overtaking obviously takes some time. I *think* I decided that I'd probably want to have started to move back in with 300 yards to go, rather than necessarily wanting to have finished moving back in with 300 yards to go. But mainly I decided that a motorway with 300 yard signs is not very representative of oncoming traffic on a single carriageway.

If I'm still feeling unscientific next time I overtake someone, I might try counting 5 seconds in my head and see where it gets me.

Thanks GJ. Would it be more conclusive if we turned the problem around. If a car was approaching you with a closing speed of say 120 mph. How far away would you like to be when it cut back in?

[GJD]

Thanks GJ. Would it be more conclusive if we turned the problem around. If a car was approaching you with a closing speed of say 120 mph. How far away would you like to be when it cut back in?

I'm not sure that would be much more conclusive since it's still a case of imagining while I'm sat at my computer . The answer is, I'd like the oncoming car you describe to be "not so close that I feel uncomfortable" when it moves back in, but unfortunately I don't think I could decide without seeing it for real whether 5 seconds or 300 yards made me feel uncomfortable.

My initial pondering was based on my impression (which may not be correct) that in these sort of situations, the actual passing of time and one's perception of the passing of time are different - one second is longer than you think it is. Which lead me to wonder whether 5 seconds might be more conservative than it sounds.

Just to come out of the abstract and back to reality for a moment: it's worth reiterating that if you don't feel comfortable that an overtake is on, then don't do it - no matter what anyone else might say.