Braking retardation..MathsGraph Help needed
Discussion
Having a big barney with my lad at the moment on what is a safe travelling distance, esp at higher speeds 60-70mph
I use the 2 sec rule, he drives under that
When i point out to him about the reaction time/braking distance etc, he poo poos it by saying that cars in front do not 'stop dead' at 70... but thats another discussion.
I am trying to point out to him that, and i hope this scenario makes sense
He is travelling at 60mph and he is leaving a 1 sec gap. Assuming that both cars have the same braking characteristics, there is a better thaan even chance he will shunt the guy, he says no ..see he reasons above.
What i am trying to get/draw is a graph that shows the retardation of car 1 against his,from the first application of car 1 braking
So from 60mph (88 feet per sec) car 1 brakes and immeadiately his fps is reducing. given the HC 'reaction distance' my lad will have travelled 60ft before his retardation kicks in, by which time he is going at 60 and car 1 is doing 50, and so on until car 1 comes to a halt.
Question is does he stop in time, and if not, what is the highest speed he could do with that separation distance before he is in a safe zone, or does the correlation appply to all speeds
Hope this makes some sense!!
I use the 2 sec rule, he drives under that
When i point out to him about the reaction time/braking distance etc, he poo poos it by saying that cars in front do not 'stop dead' at 70... but thats another discussion.
I am trying to point out to him that, and i hope this scenario makes sense
He is travelling at 60mph and he is leaving a 1 sec gap. Assuming that both cars have the same braking characteristics, there is a better thaan even chance he will shunt the guy, he says no ..see he reasons above.
What i am trying to get/draw is a graph that shows the retardation of car 1 against his,from the first application of car 1 braking
So from 60mph (88 feet per sec) car 1 brakes and immeadiately his fps is reducing. given the HC 'reaction distance' my lad will have travelled 60ft before his retardation kicks in, by which time he is going at 60 and car 1 is doing 50, and so on until car 1 comes to a halt.
Question is does he stop in time, and if not, what is the highest speed he could do with that separation distance before he is in a safe zone, or does the correlation appply to all speeds
Hope this makes some sense!!
I agree with the minimum recommendation is just enough for comfortable driving , but yes, i leave a bit more, and horrors, if i get someone up my chuff becaue he doesnt like my gap, i leaves a bit more for his braking distance
I am hoping that a graph where his line crosses the other guys at about 20mph might make him see a bit of sense, esp as he is carrying my grandson around, and there will be a granddaughter in Feb
NB there are NO child on board stickers at all!! nor 'proud granparents' on mine
bloody awful things ( the signs, not the kids)
I am hoping that a graph where his line crosses the other guys at about 20mph might make him see a bit of sense, esp as he is carrying my grandson around, and there will be a granddaughter in Feb
NB there are NO child on board stickers at all!! nor 'proud granparents' on mine
bloody awful things ( the signs, not the kids)
In pure mathematical terms, and assuming both cars decelerate in exactly the same way (decel profile vs time), then the "safe time seperation" is just a tiny tiny amount larger than your reaction time. For example, assuming it takes 0.5s to react (spot the brake lamps come on, take foot off accel pedal, apply fully braking force to brake pedal) then you need to be 0.5s behind the car ahead in time. Speed actually cancels out and this is true of all speeds.
However, the issue is one of telling that you need to do a "full" emergency stop. Generally speaking, unless every time you immediately assume the car ahead is doing a full emergency stop and do the same, you will hit the car ahead if you delay your max braking whatsoever.
It becomes somewhat annoying to have to start a full emergency stop every time the car ahead shows it's brake lamps!! Not to mention pretty annoying for your passengers!
Then there is the fact that differences in cars/drivers/braking systems/tyres etc means you are unlikely to be able to exactly match the car aheads decceleraton profile!
The "2 second rule" gives a happy medium, for the average driver.
However, the issue is one of telling that you need to do a "full" emergency stop. Generally speaking, unless every time you immediately assume the car ahead is doing a full emergency stop and do the same, you will hit the car ahead if you delay your max braking whatsoever.
It becomes somewhat annoying to have to start a full emergency stop every time the car ahead shows it's brake lamps!! Not to mention pretty annoying for your passengers!
Then there is the fact that differences in cars/drivers/braking systems/tyres etc means you are unlikely to be able to exactly match the car aheads decceleraton profile!
The "2 second rule" gives a happy medium, for the average driver.
Max Torque beat me to it 
By physics (and therefore what a teenage lad will think he's capable of, trust me), you need a gap no larger than your reaction time, which even at 70mph isn't very much at all.
But in reality, and as something that comes only from experience, you will never go full ABS stop the moment you see a brake light come on in front. It takes you far far longer to compute how much pedal force might be needed, and in reality it will almost always take you two seconds to get from brake lights on, through looking at the closing speed, looking ahead for a reason, then working your way down the pedal travel to actually get into the required braking. So two seconds is really a fairly fine margin, but one we accept for practicality and the unlikeliness of an unpredictable emergency stop right in front of you.
Perhaps your lad might find it easier to hear this coming from a 22-year-old engineer who enjoys driving hard, but has witnessed plenty accidents too!
By physics (and therefore what a teenage lad will think he's capable of, trust me), you need a gap no larger than your reaction time, which even at 70mph isn't very much at all.
But in reality, and as something that comes only from experience, you will never go full ABS stop the moment you see a brake light come on in front. It takes you far far longer to compute how much pedal force might be needed, and in reality it will almost always take you two seconds to get from brake lights on, through looking at the closing speed, looking ahead for a reason, then working your way down the pedal travel to actually get into the required braking. So two seconds is really a fairly fine margin, but one we accept for practicality and the unlikeliness of an unpredictable emergency stop right in front of you.
Perhaps your lad might find it easier to hear this coming from a 22-year-old engineer who enjoys driving hard, but has witnessed plenty accidents too!
cptsideways said:
Explain about visibility & seeing further ahead
Yeah. From 2 seconds back you can see things that might make the driver ahead brake before they do, and be braking before them. In theory you might have about 3 seconds of actual reaction time for some certain hazards, even with just 2 seconds between cars.You're always going to be going faster than the car infront during a braking event because they get on the brakes first. If you get on the brakes 1 second after the car infront then you will be traveling 1 seconds worth of braking faster (that makes very little sense written down!) So the gap between cars will continue to shrink even when you are at maximum braking.
Ian thats exactly what i mean
As in the original enquiry, if the two cars were doing 60 and 1 sec apart (88 ft) he starts to brake, therefor his 88ft per ec starts to reduce as his speed does, BUT in that reaction time my lad is still doing 88fps and therefore is nowq 44ft behind him but at 88fps. (They brake at the same rate no ABS EPS CDM or whatever the braking rate is exactly the same) So he MUST be gaining on the one in frontas the one in front is scrubbing his FPS off 0.5sec in advance of my lad so bearing in mind there are milliseconds involved car 1 is say 60 fps my lad might be 70ft per sec (being 0.5sec behind) and so on until car 1 has stops and my lad has another 0.5sec worth of travelling to do
As in the original enquiry, if the two cars were doing 60 and 1 sec apart (88 ft) he starts to brake, therefor his 88ft per ec starts to reduce as his speed does, BUT in that reaction time my lad is still doing 88fps and therefore is nowq 44ft behind him but at 88fps. (They brake at the same rate no ABS EPS CDM or whatever the braking rate is exactly the same) So he MUST be gaining on the one in frontas the one in front is scrubbing his FPS off 0.5sec in advance of my lad so bearing in mind there are milliseconds involved car 1 is say 60 fps my lad might be 70ft per sec (being 0.5sec behind) and so on until car 1 has stops and my lad has another 0.5sec worth of travelling to do
The thing is by the time he has reacted to the car in front braking hard at 60mph it has already shed around 15mph and is doing 45mph slowing quicker than a car at 60mph will.
Average reaction time is 0.7 seconds however advanced drivers tend to have reaction times of between 0.45-0.55 seconds. Newer drivers and those less alert tend to have reaction times of between 0.7 to 1.2 seconds.
Quite simply your son, as you know, is talking rubbish and driving 1 second off the car in front at 60mph is nothing short of a recipe for disaster. He will only learn that though when he shunts a car in front but judging by the attitude you suggest he has even then it won't be his fault.
Average reaction time is 0.7 seconds however advanced drivers tend to have reaction times of between 0.45-0.55 seconds. Newer drivers and those less alert tend to have reaction times of between 0.7 to 1.2 seconds.
Quite simply your son, as you know, is talking rubbish and driving 1 second off the car in front at 60mph is nothing short of a recipe for disaster. He will only learn that though when he shunts a car in front but judging by the attitude you suggest he has even then it won't be his fault.
Ian_sUK said:
You're always going to be going faster than the car infront during a braking event because they get on the brakes first. If you get on the brakes 1 second after the car infront then you will be traveling 1 seconds worth of braking faster (that makes very little sense written down!) So the gap between cars will continue to shrink even when you are at maximum braking.
The distance between the cars will shrink, but the time between them won't. MaxTorque was right;Imagine you're 1s behind an identical car travelling at the same speed and they apply full braking at a given point. If you react 1s later, then you'll start braking at the exact same point they did, from the same speed, but 1s later. Both cars will slow at the same rate, but yours will do everything 1s later.
Every point they pass, you'll pass at the same speed they did but 1s later. Eventually you'll both stop at exactly the same point, but you 1s later. Clearly if you've stopped at the same point, you've hit them.
Now imagine the same, but you react in very slightly under 1s, so the point you start braking is 1 car length before they did. Now everything is identical between the cars except yours does the same thing as theirs did just under 1s later, and 1 car length up the road. They'll stop, and just under 1s later you'll stop 1 car length behind, ie bumpers just touching.
So, theoretically as long as you hit your brakes over 1 car length before the point at which they hit theirs you'll be fine. That means you need to be just a tiny bit more than your reaction time behind them.
In reality, as others have said, we don't react fast, don't press the brake as hard as we could, etc, and 2s is a good rule of thumb.
What your son's saying works on a motorway, but imagine a vehicle coming round a corner on an A road - that'll actually be coming towards him, so he needs to lengthen the 2 second rule distance, not shorten it.
There's also a significant benefit to having time to not just react, but time to think about what to do. There's absolutely no point in driving closer to the vehicle in front; as soon as you slow for a junction you can make up all the time you want - why not travel with a 4 second gap? A 6 second gap? You lose no time on your journey but gain a whole load of thinking time.
There's also a significant benefit to having time to not just react, but time to think about what to do. There's absolutely no point in driving closer to the vehicle in front; as soon as you slow for a junction you can make up all the time you want - why not travel with a 4 second gap? A 6 second gap? You lose no time on your journey but gain a whole load of thinking time.
RobM77 said:
... - why not travel with a 4 second gap? A 6 second gap? ...
Now I like a 4s gap, but I find that 6s is too much. Two reasons:6s is long enough for someone waiting to emerge from a side road to think 'I can just make that gap', and pull into your safe space.
As you get further away from the car in front, you get less information about the road ahead from their position / movements / braking.
S. Gonzales Esq. said:
RobM77 said:
... - why not travel with a 4 second gap? A 6 second gap? ...
Now I like a 4s gap, but I find that 6s is too much. Two reasons:6s is long enough for someone waiting to emerge from a side road to think 'I can just make that gap', and pull into your safe space.
As you get further away from the car in front, you get less information about the road ahead from their position / movements / braking.
That's fair enough. The key thing here that the OP needs to get across to his son is that there is no advantage at all in being 1 sec from the car in front compared with 4 sec, because as soon as traffic slows for a junction, that advantage, albeit tiny, is lost.60mph = 27m/s.
1 second gap = 27m between cars
2 second gap = 54m between cars
Braking at 1G = 9.8m/s^2.
0.7s thinking time.
Car ahead brakes at 1G. After 0.7 seconds it is travelling at 20m/s. Car behind is still travelling at 27m/s. Gap closes to 20m with a 1 second gap, or 47m with a 2 second gap. A 26% or 13% reduction, respectively.
After a further 0.7 seconds with both cars braking at 1G, the first car is at 13m/s, the second car is at 20m/s. The distance between them closes to 13m at 1 second or 40m at 2 second gap, a 48% or 26% reduction respectively.
After another 0.7 seconds, the first car is at 7m/s, the second at 13m/s. Gap closes to 7m at one second or 33m at 2 seconds.
After another 0.7 seconds, the first car has stopped, the second car is still travelling at 7m/s and hits the car in front.
Putting it another way, a car can stop from 60mph in about 40m with no thinking time allowance, that's what the car in front is doing. With thinking and reaction time, that increases to to nearly 60m. So you need at least a 20m gap to make that up, and frankly 7m is nowhere near a reasonable safety margin.
Add in the fact that no two car/driver unit perform the same, and a one second gap is clearly retarded. Give you son a slap, he's talking feckin' s
te.
1 second gap = 27m between cars
2 second gap = 54m between cars
Braking at 1G = 9.8m/s^2.
0.7s thinking time.
Car ahead brakes at 1G. After 0.7 seconds it is travelling at 20m/s. Car behind is still travelling at 27m/s. Gap closes to 20m with a 1 second gap, or 47m with a 2 second gap. A 26% or 13% reduction, respectively.
After a further 0.7 seconds with both cars braking at 1G, the first car is at 13m/s, the second car is at 20m/s. The distance between them closes to 13m at 1 second or 40m at 2 second gap, a 48% or 26% reduction respectively.
After another 0.7 seconds, the first car is at 7m/s, the second at 13m/s. Gap closes to 7m at one second or 33m at 2 seconds.
After another 0.7 seconds, the first car has stopped, the second car is still travelling at 7m/s and hits the car in front.
Putting it another way, a car can stop from 60mph in about 40m with no thinking time allowance, that's what the car in front is doing. With thinking and reaction time, that increases to to nearly 60m. So you need at least a 20m gap to make that up, and frankly 7m is nowhere near a reasonable safety margin.
Add in the fact that no two car/driver unit perform the same, and a one second gap is clearly retarded. Give you son a slap, he's talking feckin' s
te.Edited by Kozy on Friday 29th November 09:51
Kozy said:
60mph = 27m/s.
1 second gap = 27m between cars
2 second gap = 54m between cars
Braking at 1G = 9.8m/s^2.
0.7s thinking time.
Car ahead brakes at 1G. After 0.7 seconds it is travelling at 20m/s. Car behind is still travelling at 27m/s. Gap closes to 20m with a 1 second gap, or 47m with a 2 second gap. A 26% or 13% reduction, respectively.
After a further 0.7 seconds with both cars braking at 1G, the first car is at 13m/s, the second car is at 20m/s. The distance between them closes to 13m at 1 second or 40m at 2 second gap, a 48% or 26% reduction respectively.
After another 0.7 seconds, the first car is at 7m/s, the second at 13m/s. Gap closes to 7m at one second or 33m at 2 seconds.
After another 0.7 seconds, the first car has stopped, the second car is still travelling at 7m/s and hits the car in front.
Don't think this is true. 1s gap = 27m. If 0.7s thinking time, 2nd car starts braking 0.3s further up the road. 0.3s = 8m. Both cars do exactly the same thing, but with the second one 8m further back and 0.3s later. I think the second car will stop 8m behind the first one, 0.3s after it does.1 second gap = 27m between cars
2 second gap = 54m between cars
Braking at 1G = 9.8m/s^2.
0.7s thinking time.
Car ahead brakes at 1G. After 0.7 seconds it is travelling at 20m/s. Car behind is still travelling at 27m/s. Gap closes to 20m with a 1 second gap, or 47m with a 2 second gap. A 26% or 13% reduction, respectively.
After a further 0.7 seconds with both cars braking at 1G, the first car is at 13m/s, the second car is at 20m/s. The distance between them closes to 13m at 1 second or 40m at 2 second gap, a 48% or 26% reduction respectively.
After another 0.7 seconds, the first car is at 7m/s, the second at 13m/s. Gap closes to 7m at one second or 33m at 2 seconds.
After another 0.7 seconds, the first car has stopped, the second car is still travelling at 7m/s and hits the car in front.
Kozy said:
Add in the fact that no two car/driver unit perform the same, and a one second gap is clearly retarded. Give you son a slap, he's talking feckin' ste.
This, however, is very true.te.Edit: Just realised I mean 0.7s after, not 0.3s after
Edited by AJB on Friday 29th November 11:04
AJB said:
Don't think this is true. 1s gap = 27m. If 0.7s thinking time, 2nd car starts braking 0.3s further up the road. 0.3s = 8m. Both cars do exactly the same thing, but with the second one 8m further back and 0.3s later. I think the second car will stop 8m behind the first one, 0.3s after it does.
There is no thinking time for the front car if the following car is simply reacting the brake lights.Every 0.7s, both cars drop 7m/s off their speed. With the following car starting earlier, the gap will close.
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