[supermax]

Many of us have driven cars for a long time, but the number of times we've had to perform full-blown emergency style braking, where the intent is not to slow down the car, but to come to a complete stop in the quickest possible time, varies. Some of us might have had to do this multiple times, while others might never have been exposed to such situations. The speeds at which such emergency braking has been experienced would also significantly vary.

In Sweden, before one gets to take a driving test, one has to clear a theory test, which includes many questions which require us to calculate stopping distances. We also need to complete a mandatory risk training session on a special skid pad, where we practice emergency style braking, bringing a car to a complete stop, after reaching various target speeds. This ensures that we not only know the theory behind stopping distances, but also know what it feels like, and exactly how long stopping distances can be, in real world conditions. And oh, we carry out these emergency stopping tests in both dry and simulated icy conditions (soapy water), so we are able to realize just how different stopping distances can be, depending on the conditions.

The formula for calculating braking distance

There is a simple formula for calculation of braking distances, in ideal conditions (dry and perfect road, a car with perfect tires). This formula is thus:
1. Divide the speed by 10 (or take away a zero).
2. Square the result of 1. (original speed divided by 10 and multiplied by itself).
3. Multiply the result of 2 by 0.4.

If the speed of the car is 120 km/h, the braking distance under ideal conditions for this would be 12x12x0.4 which is 57.6 meters, or 189 feet.
For a car to stop from 70 km/h, the theoretical braking distance therefore is 7x7x0.4 which is 19.6 meters, or 64.3 feet

Stopping distance vs braking distance

Braking distance is the time taken by the car to come to a stop, after the brakes are hit. Stopping distance is the total distance a car rolls, before it comes to a stop, and this includes the reaction time to the incident that requires the braking.

Stopping distance = reaction distance + braking distance

For professional formula 1 drivers, the reaction speeds can be as less as a third of a second, but for normal individuals, this reaction time is estimated to be a full second.

If you are driving a car at 120 km, and see a cow, or a child that suddenly ran onto the road, it'll take a full second before you actually hit the brakes. During this one second, your car would have moved 36 meters, i.e. reaction distance is 36 meters. Then, when you hit the brakes fully, the car takes a further 57.6 meters (in ideal conditions) before coming to a stop, a whole 93.6 meters after you spotted the cow in the first place, making the stopping distance 93.6 meters, or 307 feet. Do you think you would have been able to stop in time?

Another fun fact is that the rate of deceleration is not constant; speed decays slower at higher values and faster as it drops, so the speed stays high pretty long, before eventually dropping to non-fatal levels.

Personal experience on the skid pad

When I did my risk training, I actually did a 70 to 0 stop, with a full emergency style braking, by putting all my weight onto the brakes. This was extremely violent, the car slowed down really hard, the seatbelts tugged really hard, and the actual stopping distance was measured to be 25 meters.

I was then asked to guess how long the stopping distance would be, on wet/icy conditions, if I needed to stop from 60 km/h to 0. My guess was 60 meters. In reality, when I actually performed the braking maneuver, it was 97 meters, if I remember correctly. Reaction times didn't play a part in our tests, as we braked on command; the instructor gave the order to brake, on a two-way radio from outside the car, and we braked immediately upon receiving the order.

Conclusion

1. Most of us grossly underestimate stopping distances, thinking that we can stop on a dime, while in reality, it takes a lot longer.
2. Many of us don't factor for the reaction time too, which can be the difference between something we thought would be a just miss, to an accident with a fatal outcome.
3. If you have the opportunity, practice at a skid pad or race track to see for yourself just how long braking distances can be, in real world conditions.
4. Prevailing road and weather conditions can cause your stopping distance to double or even triple, so adjust your driving style accordingly, to factor for altered conditions, where necessary.
5. Use the formula stated above, to calculate braking distances at various speeds, and add in the reaction distances so you know where you potentially stand, instead of relying on crude guesses.

Source/additional reading

https://trafiko.se/en/faktabank/stop...a-bromsstracka

[Blooming Flower]

Where is the formula for calculating braking distance? It varies with different cars and their relevant components of braking; hence, cannot be quantified with a single straight-forward formula. While the stopping distance formula is well understood the assumptions of braking distance are way too generic it seems.

[anb]

Originally Posted by Blooming Flower

Where is the formula for calculating braking distance? It varies with different cars and their relevant components of braking; hence, cannot be quantified with a single straight-forward formula. While the stopping distance formula is well understood the assumptions of braking distance are way too generic it seems.

Here a suitable deceleration is assumed. In the real case, deceleration will be different in different situations.

[Turbanator]

Originally Posted by supermax

In Sweden, before one gets to take a driving test, one has to clear a theory test, which includes many questions which require us to calculate stopping distances.
There is a simple formula for calculation of braking distances-
If the speed of the car is 120 km/h, the braking distance under ideal conditions for this would be 12x12x0.4 which is 57.6 meters, or 189 feet.

This will be, in theory only else what's the need for brake tests that most reviewers do. You cannot have the same braking distance driving a Maruti Alto vs a 911-Turbo S at 100km. Countless examples.

Stopping distance vs braking distance

Stopping distance = reaction distance + braking distance

Similar to above, good for theory only. I agree that the reaction time of the person is important, but the braking distance will play a role too. In the same example, a 911 driven by an amateur will stop at a much shorter distance than an Alto driven by a professional at 100 Km/hr.

Another fun fact is that the rate of deceleration is not constant; speed decays slower at higher values and faster as it drops, so the speed stays high pretty long, before eventually dropping to non-fatal levels.

Again, it will vary from car to car by a big margin.

Use the formula stated above to calculate braking distances at various speeds, and add in the reaction distances so you know where you potentially stand, instead of relying on crude guesses.

That's not going to help in practical situations. Take both cars in my example and tell me what one will do with the formula?

Most of us grossly underestimate stopping distances, thinking that we can stop on a dime, while in reality, it takes a lot longer.

This is the only point I agree with and probably the idea behind the test. A lot or most learners need to know these facts before they take cars on the road. So, it's good to have that in the test, but once you are experienced, the best is to know the limitations/ advantages of your car and then drive safely.

[supermax]

Originally Posted by Turbanator

This will be, in theory only else what's the need for brake tests that most reviewers do. You cannot have the same braking distance driving a Maruti Alto vs a 911-Turbo S at 100km. Countless examples.

The formula is indeed an oversimplication, but the logic is sound. Acceleration is very car specific, with different engine displacements, fuel types, number of cylinders etc, but deceleration is much simpler. Earlier, you had drum brakes vs disc brakes etc, but now braking systems on consumer grade cars are more standardized. Comparisons such as Alto vs any supercar would be pointless, and yes, you can clutch at them, but that is besides the point. The formula is used to computed theoretical stopping distances for cars. Indeed your mileage (or in this case, stopping distance) can vary. Also, the real world number can be much higher than this in a consumer grade car, but not much lower. Also, this post came about because another BHPian in a different thread mentioned how he'd slowed down from 122 km/h to 0 in a Slavia, within what he initially claimed was 10-20 feet. This formula will give you a high benchmark which is not ridiculous, but based on sound science. I have myself driven a consumer grade car and put it to the test, and the numbers were within the range. Can you drive a supercar with carbon fiber brakes and cooled rotors and have a much better stopping distance? Yes, but that's not the point.

My post only serves to remind people that apart from the braking distance which itself is grossly underestimated, they need to factor for the reaction distance too, which is what can well be the difference between an almost accident, to a fatal one.
The formula is a crude back of the envelop kind of calculation, which can be used to check your assumptions, and I have validated it on the track myself, with a Renault Zoe. It's possible that a Tesla or a Porsche might have better braking performance. Not everybody has the means or will to do a full emergency-style braking from high speed, knowing that the tire life is going to be affected. Driving license aspirants in Sweden enjoy this privilege, though we have to pay a rather steep fee for the skid pad session, but it allows us to actually put our assumptions to the test.

Regarding the point about brake performance tests conducted by experts, that is as much about the braking performance as is about the car's reliability itself, and this formula is definitely not a substitute for that, nor have I claimed that it is so.

Cheers!
-S

PS: and before you ask me who defines what a consumer grade car is, I just chose the term for want of something better, but let me point out that this formula and the textbook it is part of, is used by driving licence aspirants in Sweden, most of them who are going to be driving a standard car which can be bought new or used from a local car dealership, not an exotic supercar.

[Turbanator]

Originally Posted by supermax

My post only serves to remind people that apart from the braking distance which itself is grossly underestimated, they need to factor for the reaction distance too, which is what can well be the difference between an almost accident, to a fatal one.

Absolutely correct and valid to include in the test. But, why all the calculations

I am pretty sure, within consumer grade or whatever you term them, there can be a large differences too, say a Toyota Camry vs 5 series

[supermax]

Originally Posted by Turbanator

Absolutely correct and valid to include in the test. But, why all the calculations

I am pretty sure, within consumer grade or whatever you term them, there can be a large differences too, say a Toyota Camry vs 5 series

Right. Let me explain then. In India, nobody cares about educating license aspirants about the seriousness of maintaining at least 3 seconds of separation between cars on a highway, or why it is so important not to pass a bus at a high speed, when it is stopped at a bus stop. Here, it is taken very seriously, and since you can't obviously update the textbook with stopping distances of every car model and variant in the market and expect aspirants to know them all, there is a need to have a sensible formula to calculate braking distances. The purpose of doing the mandatory Risk 2 session on a skid pad is to put this formula to the test, in a real passenger car. Since I got to do both the theory and the actual drive, I could actually test the predicted numbers against what I really obtained. The calculation came up with 19.6 m for 70 to 0, and I managed 25m. The staff who run the tests also know what the best stopping distances are, for those cars and conditions, and they decide if I've performed as I should, or not. If I'd taken say 35 meters to stop it, I'm sure they would have told me that I didn't brake as hard as they'd told me to. So, the formula is a great way to guesstimate your stopping distance, if you are not going to take your car to the track to find out the actual numbers. And if you assume that your car is going to be some 10-20 percent worse than that, it'll ensure that you have a really good safety threshhold, instead of having a totally incorrect picture, like the gentleman who thought he'd stopped his Slavia in 15 feet, from 122 km/h.

Cheers!
-S

[GrammarNazi]

Human cognitive limitations considered, Speed kills, but bad braking kills more people.

Govts should set braking distance standards, instead of just speed limits. Car manufacturers should design brake components such that braking distances stay within parameters.

Govt should also mandate Traction Control System & Electronic Stability Program be made as standard for all large vehicles, especially cars above say 4 meters.

It'd be really good if this study is given the importance it deserves.

[aaggoswami]

After years of driving experience, I can safely say there's no safe formula considering multitude of factors. Braking on wet surface when discs are wet, it will take a longer distance in most of the cars sold there are not much ways to know how much discs are wet and how much it will impact braking distance.

Road and Tyre condition plus quality, braking system of the car, braking components, incline of the road, etc., lots of factors. Honda has some of the best braking performance, but last week I was in for a rude shock after a heavy shower.

Here the experience and skill of driver are of utmost importance apart from a well maintained vehicle. May be for lab tests, etc., there could be some formula and we may stipule conditions to measure all vehicles under same condition, sort of Standard Temperature and Pressure which is there for certain scientific tests and/or experiments.

ABS actually increases braking distance in wet and even in sand. So electronic aids are secondary, primary is the person driving vehicle. Electronic aids help but that should in case to avoid an accidental eventuality. While steps are taken to improve upon safety, its really surprising that there are bikes with only drum brakes. Around a decade and half ago, 130 mm drum brakes were an additional feature.

[supermax]

Originally Posted by GrammarNazi

Human cognitive limitations considered, Speed kills, but bad braking kills more people.

Govts should set braking distance standards, instead of just speed limits. Car manufacturers should design brake components such that braking distances stay within parameters.

Govt should also mandate Traction Control System & Electronic Stability Program be made as standard for all large vehicles, especially cars above say 4 meters.

It'd be really good if this study is given the importance it deserves.

Excellent suggestion, but that's only part of the issue. The real issue is that most drivers in India have never trained to do the most efficient braking, the thing that ensures that the car actually performs as effectively as its design limitations allow for it. Since most of us would not dream of wearing out parts or tires, we never do emergency-style braking, and that's not something that the driving school guys would like you to do either, with their cars, so the first time someone actually does a hard braking is when they really have a situation that calls for it. Knowing what it feels like can be a big help in how much in control you are of a critical situation, and the government should mandate training with all kinds of braking, so drivers know what to expect. In my own case, I had a deer that ran into my path on a 100 km road, just inside a segment where there had been a warning sign noting possible animal incidents. I reacted on instinct, did a hard braking which gave the deer the much needed time to pass my car, and then floored the acceleration, to ensure that I didn't stall out and stop in the middle of a 100 km road.

[supermax]

Originally Posted by aaggoswami

After years of driving experience, I can safely say there's no safe formula considering multitude of factors. Braking on wet surface when discs are wet, it will take a longer distance in most of the cars sold there are not much ways to know how much discs are wet and how much it will impact braking distance.

Road and Tyre condition plus quality, braking system of the car, braking components, incline of the road, etc., lots of factors. Honda has some of the best braking performance, but last week I was in for a rude shock after a heavy shower.

Here the experience and skill of driver are of utmost importance apart from a well maintained vehicle. May be for lab tests, etc., there could be some formula and we may stipule conditions to measure all vehicles under same condition, sort of Standard Temperature and Pressure which is there for certain scientific tests and/or experiments.

ABS actually increases braking distance in wet and even in sand. So electronic aids are secondary, primary is the person driving vehicle. Electronic aids help but that should in case to avoid an accidental eventuality. While steps are taken to improve upon safety, its really surprising that there are bikes with only drum brakes. Around a decade and half ago, 130 mm drum brakes were an additional feature.

Which doesn't mean that the formula isn't useful. It only means that the formula cannot alone be sufficient. Which is why we study the formula, which is supposed to give us an idea of what braking distance would be like, in ideal conditions, and we can apply our own additional approximations, for altered conditions. Driving license aspirants here in Sweden undergo a full range of braking exercises as a mandatory prerequisite to taking the driving test. In these exercises, we perform emergency style braking from a variety of speeds, both in wet and dry conditions. Even these tests are not meant to be absolutes, but meant to show us how different braking distances can be, in wet and dry conditions.
Here are my recorded numbers, from the braking exercises:
40 km to 0, in dry conditions: 12 meters.
40 km to 0, in wet/icy conditions: 35 meters.
70 km to 0, in dry conditions: 25 meters.
60 km to 0, in wet/icy conditions: 110 meters.

Going by the earlier tests, my guess prior to the 60-0 run had been that it might take 70 meters, but it was quite an eye opener that it took 110 meters. What this showed is that stopping distances change dramatically, and it can be much worse than what we'd think, or anticipate.

Cheers,
-S

[GrammarNazi]

Originally Posted by aaggoswami

After years of driving experience, I can safely say there's no safe formula considering multitude of factors...
Here the experience and skill of driver are of utmost importance apart from a well maintained vehicle... Around a decade and half ago, 130 mm drum brakes were an additional feature.

True. It's the nut behind the wheel that matters most.

Originally Posted by supermax

...The real issue is that most drivers in India have never trained to do the most efficient braking, the thing that ensures that the car actually performs as effectively as its design limitations allow for it. Since most of us would not dream of wearing out parts or tires, we never do emergency-style braking, and that's not something that the driving school guys would like you to do either, with their cars, so the first time someone actually does a hard braking is when they really have a situation that calls for it. Knowing what it feels like can be a big help in how much in control you are of a critical situation, and the government should mandate training with all kinds of braking, so drivers know what to expect. In my own case, I had a deer that ran into my path on a 100 km road...

While the world is truly filled with immature (sometimes downright foolish) people who manage to get their hands on a driving license. Even experienced careful folks may make mis-judgements.

Govt should be able to implement a mandate of training people into defensive driving. Maybe a scoring system that maps any individuals driving capability & is linked to car insurance - those performing well should get a small discount as an incentive.

[Poitive]

Originally Posted by supermax

The formula for calculating braking distance

There is a simple formula for calculation of braking distances, in ideal conditions (dry and perfect road, a car with perfect tires). This formula is thus:
1. Divide the speed by 10 (or take away a zero).
2. Square the result of 1. (original speed divided by 10 and multiplied by itself).
3. Multiply the result of 2 by 0.4.

If the speed of the car is 120 km/h, the braking distance under ideal conditions for this would be 12x12x0.4 which is 57.6 meters, or 189 feet.
For a car to stop from 70 km/h, the theoretical braking distance therefore is 7x7x0.4 which is 19.6 meters, or 64.3 feet

My understanding and takeaway from the above are:

• The idea for the formula isn't literal but conceptual. Somewhere the 'conceptual' part has been lost; it should not be.
• The formula can also be stated as Speed x Speed x 0.004, or simply (Speed Squared) x 0.004
• That the relationship between speed and braking distance is not linear but exponential
  (something I learnt in my early days of interest in automobiles, but that had nothing to do with the licencing process, as it should have been)
  
  Eg: If it takes distance A to brake at 50kmph, a newbie might assume the distance to be twice at 100kmph, whereas it actually would be exponential, i.e. 4 times the braking distance for 2 times the speed.
  
  Using this formula for the concept:
  Braking distance at 50 kmph = 50^2 x 0.004 = 10m
  Braking distance at 100kmph = 100^2 x 0.004 = 40m
  
  (Of course, this is with other things being equal, and the results only for comparison and not as a literal distance)
• It is important that a new driver has this relationship embedded in their minds, and it is appreciable that the authorities are going through such lengths for the applicant to really experience it all, than suddenly realize it while driving risking much.
• Simlarly, also appreciable that applicants are being sensitized to how traction varies. I learnt it the hard way (as a kid who was in a car which met with an accident on the highway in heavy rain).

Maybe the title of the thread should be changed to say "Correlation between Braking Distance and Speed"

[anb]

Originally Posted by Poitive

Maybe the title of the thread should be changed to say "Correlation between Braking Distance and Speed"

I think it is basically Newton's 3rd equation of motion. Something that we study in plus two.



where s is the braking distance and a is the deceleration. Here some value is assigned to deceleration and speed is converted into m/s from km/h.

[libranof1987]

Originally Posted by supermax

There is a simple formula for calculation of braking distances, in ideal conditions (dry and perfect road, a car with perfect tires). This formula is thus:

Shouldn't mass (weight) be a big part of the equation. After all, braking is a form of Force. And F = m * a.