Safe Stopping Distances

[Jamie123]

I have lots of important work to do, and consequently I am wasting my precious time writing letters to politicians which I know are going to go straight into the bin. (The letters that is - not the politicians. (Though who knows?))

Anyway, I thought this lunchtime's effort might be of more than passing interest to some of you:

The Right Honourable Louise Haigh MP,

Secretary of State for Transport,

33 Horseferry Road,

London SW1P 4DR

Dear Ms. Haigh,

Safe Stopping Distances: Proposed New System

I am writing to you as Secretary of State for Transport, to express concerns I have had for many years about safe stopping distances, and to propose a possible solution. I am a chartered physicist, have been an examiner for A-level mathematics and mechanics for many years, and therefore feel I am qualified to express an opinion on this matter.

My father (who is in his 80s) is fond of saying that you should leave “five car lengths” between yourself and the car in front. This was probably the advice everyone was given in the 1950s when he learned to drive, and I expect many older drivers still hold to it. However, it is not very useful because (i) “five care lengths” is almost impossible to gauge accurately from a driver’s low-lying view, and (ii) it takes no account of vehicle speed.

Another commonly quoted rule is to leave a two second gap between yourself and the car in front. (A TV advert in the 1980s told us to recite “only a fool ignores the two second rule” which takes almost exactly two seconds to say.) This does appear in the Highway Code in Rule 126, and is an improvement because (i) it is easily implemented by means of a fixed point on the road, (ii) it eliminates the mental trigonometry of converting oblique perception to “car lengths” and (iii) it increases the distance automatically with speed.

However, the distance associated with 2 seconds scales proportionally with speed, and this is not a good model of stopping distance, especially when the speed is high. If braking force is constant then the energy absorbed in coming to a halt must equal this force times the stopping distance, which must in turn equal the initial kinetic energy one half mass times velocity squared. The distance is therefore proportional not to speed, but speed squared. We must also add to this the “thinking distance” (the distance the car travels between the driver perceiving the need to brake and when he/she actually begins braking), and this distance is indeed proportional to speed.

To its merit, Rule 126 does include a table of data consistent with this model. I can remember having to learn this table (or one very similar) as a teenager, and being examined on it in my test. However, it is completely useless unless you can judge exactly what “24 car lengths” looks like from a driver’s low-lying perspective.

However, if you do the algebra you will find that the time associated with the “true” stopping distance is a linear function of speed: specifically, if you start with 0.65s and add 0.35s for each 10mph you are travelling, you will get almost the exact stopping distances quoted in the Highway Code. For example, if you are travelling 60mph, that is 0.65+6*0.35=2.75s, during which the car travels 73m – exactly what Rule 126 states. It takes about 0.65 seconds to say “stop time” and 3.5 seconds to count briskly from 1 to 10. Therefore, if you’re travelling at 60mph, quickly say “stop time one two three four five six” and you will just about have covered the required stopping distance.

I have performed this experiment, timing how long it takes me to say this phrase for each speed. Further research would be needed on how long different people take to say the phrase, but I think you will agree the Highway Code stopping distances are reproduced quite accurately:

Stopping distances do of course depend on road conditions: drivers could be recommended to say the phrase twice when driving on wet or icy roads.

Thank you very much for your attention.

Yours sincerely,

etc.

Edited September 6, 2024 by Jamie123
Spelling (wrong kind of "braking" - Louise Haigh will no doubt think I'm an illiterate, but so long as the science is right!)

[Carborendum]

54 minutes ago, Jamie123 said:

Safe Stopping Distances: Proposed New System

[Jamie123]

27 minutes ago, Carborendum said:

This is the table from the Highway Code I was referring to:

I just bunged your numbers and ours into Excel:

Your stopping distances are more than twice ours. Maybe yours are a worst case scenario (assuming flood, ice and snow all together).

I'm not sure what I'm supposed to get from the diagram of the car and the dog (except that it does illustrate what I said about low-lying perspective). Maybe the accompanying text would have explained it.

 

Edited September 6, 2024 by Jamie123

[zil2]

1 hour ago, Jamie123 said:

I have lots of important work to do, and consequently I am wasting my precious time writing letters to politicians which I know are going to go straight into the bin.

Quote

"Anyone can do any amount of work, provided it isn't the work he is supposed to be doing at that moment."
-- Robert Benchley

1 hour ago, Jamie123 said:

Secretary of State for Transport,

33 Horseferry Road,

How fitting.

1 hour ago, Jamie123 said:

A TV advert in the 1980s told us to recite “only a fool ignores the two second rule” which takes almost exactly two seconds to say.)

For someone from New York City, or someone from rural Alabama?  Cuz I'm thinkin' there's a significant difference there.

Meanwhile, my eyes started to glaze over when you started getting all equation-like.  You might should have included some diagrams and a funny story about someone getting rear-ended.

1 hour ago, Jamie123 said:

you can judge exactly what “24 car lengths” looks like

In Utah, it looks like 22 cars cutting in front of you...

1 hour ago, Jamie123 said:

Further research would be needed on how long different people take to say the phrase,

Actually, just create the rule for the fastest speakers (maybe excepting autioneers) and then everyone else will leave even more room, which is generally a good idea, unless you dislike people cutting in front of you.

1 hour ago, Jamie123 said:

Pretty sure you need to extend that chart up to at least 100mph, and maybe better 120mph (though I suppose in the UK if one is going east or west, by the time one reaches 120mph and then slows to a stop, one will have reached the other coast, so maybe not...).

Quote

...driver's eye height... ...thinking distance...

What if I'm really tall, or really short, but a very fast thinker?   (Fighter pilots will be applying for exceptions, as their reaction times are exceptional...)

Finally, what's with the dude from the UK using miles + meters, and what's with the dude from the US using all metric?  It's like the world is backwards.  I'm going to go read about liveships, dragons, and sea serpents now.

Edited September 6, 2024 by zil2

[Jamie123]

3 minutes ago, zil2 said:

Finally, what's with the dude from the UK using miles + meters, and what's with the dude from the US using all metric?  It's like the world is backwards.  I'm going to go read about lifeships, dragons, and sea serpents now.

Since the early 1970s, the UK has had the most ghastly mish-mash of metric and imperial units. Temperature is always in centigrade, but for people's heights some people use feet and others use metres. Distances on road signs are always in miles and speed limits are always in miles per hour. Beer and milk are nearly always sold in pints. On the other hand, petrol (gasoline) is usually sold in litres, though fuel efficiency is always quoted in "miles per gallon". To make things easier still, a UK gallon is not the same as a US gallon.

Thankfully a mile is the same in both countries.

[Carborendum]

4 hours ago, Jamie123 said:

Your stopping distances are more than twice ours. Maybe yours are a worst case scenario (assuming flood, ice and snow all together).

I'm not sure what I'm supposed to get from the diagram of the car and the dog (except that it does illustrate what I said about low-lying perspective). Maybe the accompanying text would have explained it.

There are two situations we're talking about.

• The 2-second rule is about "following distance."  i.e. the potential impact is a moving target.  It is moving at roughly the same speed that you are moving.  Thus, when they hit their brakes, they require some stopping/braking distance as well.  This is in addition to the 2-second distance you've allowed for already.
• AASHTO SSD is about visibility of a stationary object (like a rock or log) or an animal (which is what the dog in the diagram is about) that will not perceive the danger to run away.

The first allows for a closer following distance.  The second is what AASHTO addresses.

I don't know which one your UK Highway code was addressing.

Edited September 6, 2024 by Carborendum

[Jamie123]

1 hour ago, Carborendum said:

There are two situations we're talking about.

• The 2-second rule is about "following distance."  i.e. the potential impact is a moving target.  It is moving at roughly the same speed that you are moving.
• AASHTO SSD is about visibility of a stationary object (like a rock or log) or an animal that will not perceive the danger to run away.

The first allows for a closer following distance.  The second is what AASHTO addresses.

I don't know which one your UK Highway code was addressing.

Quote from the Highway Code:

Quote

Drive at a speed that will allow you to stop well within the distance you can see to be clear. You should leave enough space between you and the vehicle in front so that you can pull up safely if it suddenly slows down or stops. The safe rule is never to get closer than the overall stopping distance (see Typical Stopping Distances diagram, shown above).

All this is fine. However, it then goes on to introduce the "two second rule", which totally contradicts the first paragraph. (You cannot say that this is a "following rule" whereas the first is a "stationary object rule" because the first paragraph already made it clear that that was a following rule.) The whole thing needs to be tidied up by someone with a basic knowledge of kinematics.

https://highwaycode.org.uk/stopping-distances-rule-126/

Edited September 6, 2024 by Jamie123

[mikbone]

My patients always ask me when they can start driving again.  I always give the same schpiel.

1) This is a legal question not a medical question.

2) We know from studies that with significant extremity injuries, reaction time is doubled to tripled.

3) If you get into an accident and the opposing attorney is any good, you will be hosed.

4) My wife and children live in the community and I love them.

5) I know what I would be doing if I was in your situation, and I won’t tell you.

[Jamie123]

47 minutes ago, mikbone said:

My patients always ask me when they can start driving again.  I always give the same schpiel.

1) This is a legal question not a medical question.

2) We know from studies that with significant extremity injuries, reaction time is doubled to tripled.

3) If you get into an accident and the opposing attorney is any good, you will be hosed.

4) My wife and children live in the community and I love them.

5) I know what I would be doing if I was in your situation, and I won’t tell you.

I think you're quite right. If they did have an accident they could always point to you and say "He said it would be OK! Blame him!" Make them aware of the facts and let them decide.

[Jamie123]

I've been mulling over the "following rule". Suppose you have car A following car B at an initial distance D, both travelling at velocity v. If B starts to decelerate at time zero, and A a time T seconds later, then assuming their decelerations are equal both will come to rest a distance D-vT apart. (Do the algebra if you don't believe me.) To avoid a collision D-vT>0, so the safe stopping distance does scale linearly with speed and if the time gap is greater than T (the time needed to notice the car ahead is braking, move your foot to the brake pedal and press it) then in theory you'll be OK. However if the decelerations are different then the expression becomes a three term quadratic in v - which is a can of worms best left unopened. I still think the safe stopping distance method is best.

P.S. I am coming over somewhat to Carborendum's view - the Highway Code does conflate two quite separate issues: following distance and visible road ahead (as in the case of a bending road or fog/rain). The wording does need to be clarified.

Edited September 7, 2024 by Jamie123

[JohnsonJones]

I normally go by instinct on how far I should be behind the car in front of me.

By that, I mean, a kind of second hand ingrained idea of how long and how far I need to be behind the car.

This is normally far greater than other cars on the highway feel I should be.  Many cars cut in front of me while I drive because I'm too slow (old person syndrome I suppose they may think) and following too far behind the car in front of me.

I think people in general tend to follow too closely to stop in time of an emergency, rather than giving enough distance to safely stop in case a vehicle in front of them need to stop suddenly.

Last wreck I was in was due to my suddenly stopping to avoid an object in the road.  I was going around 30 miles per hour. 

Not a big deal, you would think...yet the concrete truck behind me apparently didn't get the memo.  It rammed into the back of my vehicle.  Luckily the Lord was watching over me and my wife at the time and no one was hurt, and the damage was covered by the concrete company.  In that instance though, I'd think the truck driver was following too closely for a load of concrete and the size of his truck which is why I got hit (edit:  When I say I got hit, I mean the vehicle I was in was hit). 

Edited September 7, 2024 by JohnsonJones
Clarity

[Jamie123]

45 minutes ago, JohnsonJones said:

(edit:  When I say I got hit, I mean the vehicle I was in was hit). 

LOL a pity: you might have got more money out of the concrete company if the guy had punched you! 👊 

[Carborendum]

14 hours ago, Jamie123 said:

Quote from the Highway Code:

All this is fine. However, it then goes on to introduce the "two second rule", which totally contradicts the first paragraph. (You cannot say that this is a "following rule" whereas the first is a "stationary object rule" because the first paragraph already made it clear that that was a following rule.) The whole thing needs to be tidied up by someone with a basic knowledge of kinematics.

https://highwaycode.org.uk/stopping-distances-rule-126/

Yes, that one sentence seems to have an ambiguous meaning which lends itself to your reading more than the intended meaning.  So, yes, poor wording.