Formula for Stopping Distances

cinneide

Hello all,

I'm taking my driving test soon and was frustrated with all the memorization that has to be done for various bit and pieces. The stopping distances especially annoyed me, so I worked out a formula for calculating them.

Afterwards, I realise that the maths are actually quite complicated making it pretty much useless for most - I'm afraid there's no avoiding it. It may be simpler just to memorise the numbers given in the book!

The distances are worked out in two parts: the thinking time and the braking time. The thinking time is always the same: 2/3 of a second. The braking time depends of course on how much deceleration can be applied - obviously in wet weather, this is going to be less than in dry weather.

The actual formula (derived using some applied maths formulas that I haven't used since my leaving cert) is this:

s = 5*v*(100*v/a + 1/27)

where s = stopping distance, v = velocity and a = deceleration.

The value of a depends on the weather conditions. For dry weather, a is 84240; for wet weather, it is 47952.

As a quick example, I'll work out the stopping distance for a vehicle travelling at 60 km/h in wet conditions.

wet => a = 47952.
s = 5*60*(100*60/47952 + 1/27) = 48.6 metres req'd to stop.
The actual value given in the Rules of the Road book is 48.5 metres. The difference is due to rounding errors.

In an effort to make this formula more realistically usable, rounding the a values to 84000 and 48000 might make things a little easier. As would changing the 1/27th to 1/25th.

Revisiting the previous example with the new values:
s = 5*60*(100*60/48000 + 1/25) = 300*(1/8+1/25) = 300*(33/200) = 99/2 = 49.5

We're off by a meter, but the examiner would probably forgive that and it's much easier to work out on the spot - marginally anyway.

I hope that someone gets some benefit out of this!

Stark

You preparing for the theory test or practical test? I don't think you get asked stopping distances on the oral portion of the practical test (open to correction).

Alanstrainor

I haven't heard of people being asked stopping distances on the oral part of your Driving test, they are asked on the theory test however. I wouldn't recommend, if asked stopping distances, taking out your calculator:pac:.

Wishbone Ash

cinneide wrote: »

s = 5*v*(100*v/a + 1/27)

where s = stopping distance, v = velocity and a = deceleration.

The value of a depends on the weather conditions. For dry weather, a is 84240; for wet weather, it is 47952.

As a quick example, I'll work out the stopping distance for a vehicle travelling at 60 km/h in wet conditions.

wet => a = 47952.
s = 5*60*(100*60/47952 + 1/27) = 48.6 metres req'd to stop.
The actual value given in the Rules of the Road book is 48.5 metres. The difference is due to rounding errors.

In an effort to make this formula more realistically usable, rounding the a values to 84000 and 48000 might make things a little easier. As would changing the 1/27th to 1/25th.

Revisiting the previous example with the new values:
s = 5*60*(100*60/48000 + 1/25) = 300*(1/8+1/25) = 300*(33/200) = 99/2 = 49.5

:eek: :eek: :eek: My head hurts!

cinneide - don't waste too much time and energy on one question to the detriment of others!

SheroN

I think they ask this at the practical test, it's very very rare though. They don't expect the exact figure either, they're happy with approxamations. Just multiply the regular dry stopping distances by two to get their wet equivalents.

Wishbone Ash

Just out of interest, and I'm very much open to correction on this but I have heard several times that the general 'given' stopping distances were determined in the early 1960s using cars such as the Ford Anglia and Mk I Cortina.

These cars probably had drum brakes all round and would have much longer stopping distances than a modern car with disc brakes and ABS.

sd123

Wishbone Ash wrote: »

Just out of interest, and I'm very much open to correction on this but I have heard several times that the general 'given' stopping distances were determined in the early 1960s using cars such as the Ford Anglia and Mk I Cortina.

These cars probably had drum brakes all round and would have much longer stopping distances than a modern car with disc brakes and ABS.

When they say stopping distances, I was of the opinion that they meant getting to the speed mentioned, and putting the car in neutral, allowing it to free wheel to a halt, otherwise, how could they get accurate figures, ie, exactly how much braking was used, etc. But, open to correction also!!

Wishbone Ash

sd123 wrote: »

When they say stopping distances, I was of the opinion that they meant getting to the speed mentioned, and putting the car in neutral, allowing it to free wheel to a halt

:eek: No - they mean under excessive braking force!

Putting it into neutral and freewheeling wouldnt give a 'braking' distance!

John Mason

er.... i think you are looking a little tweeney weeney to deep into this.

Its not rocket science just a driving test.

i really have no idea what was going on in the formula thing and i passed

so relax

sd123

Wishbone Ash wrote: »

:eek: No - they mean under excessive braking force!

Putting it into neutral and freewheeling wouldnt give a 'braking' distance!

Alright, like I said, open to correction, just I thought it said stopping distance, as opposed to braking distance. :pac:

Wishbone Ash

sd123 wrote: »

Alright, like I said, open to correction, just I thought it said stopping distance, as opposed to braking distance. :pac:

Yes, you are correct - it's 'stopping distance' but they mean when braking including reaction time!

SheroN

It's not an exact science. For example, the stopping distance for a mini copper and the stopping distance for a Ford Scorpio are going to be completely different.

DaveyGem

Why don't you just learn off the stopping distances like everyone else....