This topic will provide the detailed physics and human reaction time for getting your rig stopped. Understanding this topic could very well change your driving habits which could save your life.

The one theme which flows throughout this topic is that speed seriously limits your options, and that speed is the most significant factor contributing to accidents where stopping in time was unsuccessful.

The Physics of Braking
Speed & Deceleration
Braking Deceleration & Distance
Human Reaction Time

The Physics of Braking

All types of brake systems are mechanical devices for retarding the motion of a vehicle. This retarding action is achieved through friction, and the braking friction energy is dissipated as heat. Friction is the resistance to relative motion between any two bodies in contact, and it varies with the materials and with the condition of the materials.

The friction between two surfaces changes with any variation of either surface. For example, oil or grease place on either of the two surfaces greatly decreases the frictional coefficient between them. The coefficient of friction is simply a ratio of the braking force relative to the mass force of the object being braked. For example, if a 100 pound object was sliding on a floor, and it took 50 pounds of force to keep it sliding, then the coefficient of friction for that floor surface against the bottom of that object is 50/100 or 0.5. Remember, this is a measure of the friction between two surfaces. If you dragged the object through grease on the floor, then the pulling force would be reduced, and the coefficient of friction would be reduced.

Heat is always being generated where friction is taking place. Heated temperature of the two friction surfaces also effects the coefficient of friction. Adding heat to brake parts reduces their coefficient of friction, and this is commonly referred to as brake fade. All truckers have had the occasion to smell hot brake parts.

Speed & Deceleration

If a vehicle requires 100 horsepower to start at a dead stop and accelerate to 60-MPH in 60 seconds, then the same vehicle will also take 100 horsepower to decelerate to a stop from 60-MPH in 60 seconds. If you wanted that same vehicle to stop from 60-MPH in 6 seconds, then you would require 1000 horsepower of braking action.

If you doubled the weight of the vehicle, then the stopping horsepower would also double. If you double the speed of the vehicle, the stopping horsepower would quadruple! Therefore, the increase of speed is much more pronounced in stopping force requirements than increases in vehicle weight.

When describing braking action, the term deceleration is often used to describe the actual rate at which a vehicle looses speed. When a slow vehicle is traveling at 20-MPH, it is also traveling at 30-feet per second. Measurement of deceleration, measures how much the vehicles slow down each second. If your vehicle is traveling at 30-feet per second and 1-second later it is traveling at 20-feet per second, then the deceleration is measured as 10-feet per second per second. What this means is that your vehicle has slowed 10-feet per second for each second of time lapse while the brakes are applied.

At the end of the first second, the vehicle slows to 20-feet per second, at the end of the 2nd second, the vehicle slows to 10-feet per second, and at the end of the 3rd second, the vehicle is stopped. So the deceleration of your vehicle was 10-feet/sec/sec, which looks a little strange, but is an accurate measurement just the same.

When a fast vehicle travels at 60-MPH, how long would it take for this fast vehicle to stop if the deceleration remained at 10-feet/sec? This is three times faster than 20-MPH, so the speed would be 90-feet/sec. Therefore, it would take 9 seconds to stop this vehicle.

Braking Deceleration & Distance

For the same slow vehicle described above, although the deceleration was uniform for 3 seconds, the distance traveled each second is different. For the first second, the vehicle speed varied from 30-feet/sec down to 20-feet/sec. This averages out to 25 feet/sec, so the vehicle traveled 25 feet. During the 2nd second, the vehicle speed varied from 20-feet/sec down to 10-feet/sec, so the average speed was 15-feet/sec, so the vehicle traveled 15 feet. And during the final second, the vehicle speed varied from 10-feet/sec down to 0-feet/sec, so the average speed was 5-feet/sec, so the vehicle traveled 5-feet. Therefore, the total distance traveled by the slowing vehicle while braking is 25+15+5 = 45 feet.

The following numbers may be a little tedious, but understanding them could very well save your life someday. Let us consider a fast vehicle, which is traveling at 60-MPH. It is traveling at 90-feet/sec:

During the first second, the vehicle slows to 80-feet/sec, and covers 85-feet.
During the next second, the vehicle slows to 70-feet/sec, and covers 75-feet. During the third second, the vehicle slows to 60-feet/sec, and covers 65-feet. During the fourth second, the vehicle slows to 50-feet/sec, and covers 55 feet. During the fifth second, the vehicle slows to 40-feet/sec, and covers 45 feet. During the sixth second, the vehicle slows to 30-feet/sec, and travels 35-feet. During the seventh second, the vehicle slows to 20-feet/sec, and travels 25-feet. During the eighth second, the vehicle slows to 10-feet/sec, and travels 15-feet. During the ninth second, the vehicle comes to a stop and travels 5-feet.

The total distance traveled by the vehicle is 85+75+65+55+45+35+25+15+5 = 405-feet

Take special notice that the vehicle took 405/45 = 9 times the stopping distance for 3 times the speed. The relationship here is a square function. Therefore the stopping distance has the following relationship with speed increases:

2X speed increase = 4X stopping distance
3X speed increase = 9X stopping distance
4X speed increase = 16X stopping distance
5X speed increase = 25X stopping distance

Check out the following table, because your life could very well depend upon these numbers some day. Reaction time is fully explained below and totals 2-seconds:

Speed/Stopping Distance for 10-feet/sec/sec Braking

40-MPH = 180-feet stopping distance + 120-feet reaction = 300-feet
60-MPH = 405-feet stopping distance + 180-feet reaction = 585-feet
80-MPH = 720-feet stopping distance + 240-feet reaction = 960-feet
100-MPH = 1125-feet stopping distance + 300-feet reaction = 1425-feet

Ok, these numbers are real cute, but how do they relate to your rig? Here's what you can do. Find a location where you can safely take your loaded rig up to 20-MPH, and then kick in the clutch and make a panic stop on dry pavement. Accurately time, down to the nearest 1/10 second, how many seconds it takes for your loaded rig to come to a full stop. Only perform this test once, and only after you know that your brakes have cooled down completely from previous use.

Now select a speed on the speed table above, and write down the stopping distance listed on the table. Now multiply that stopping distance by the number of seconds that it took your rig to stop. Now divide this answer by 3. This will provide the approximate & underestimated stopping distance of your rig at that speed, on dry pavement, and with no brake fade.

Your stopping distance will actually be somewhat longer than this calculated distance during a real panic stop for two reasons. The first reason has to do with brake fade. As you step on the brake pedal, friction is generated. Once the friction is generated, the braking friction increases the brake lining temperature, the coefficient of friction will decrease, and the braking effect will decrease. The longer it takes to stop, the hotter the brakes get, and the less stopping power they have. Therefore, your stopping distance will be extended accordingly.

Human Reaction Time

The other reason your stopping distance will be greater than the chart above shows is based upon two delay factors. The first delay factor is the amount of time it takes your brain to realize that you need to make a panic stop, and the additional time it takes for your body to move your foot to the brake pedal and start pushing on the brake. It is reasonable to consider 1-1/2 seconds to get your foot on the brake for an unexpected panic stop. At 60-MPH, you travel 135-feet, nearly 2-1/2 times the length of your rig, before you can even get your foot on the brake pedal. Refer to the Oklahoma City High School experiment at http://oas.okstate.edu/ojas/hopper.htm for their conclusions about brake application reaction times. Although their test was to determine what effect music volume level had upon brake delays, they proved convincingly that the average person requires 1.55-seconds to apply the brakes for an unexpected situation. If the above website link fails, we will mirror a portion of their web page experiment data which can be viewed here.

The second delay factor is the time that it actually takes your brake system to start generating the stopping friction. This includes the time it takes the air pressure from your brake pedal to start charging the brake chambers, and the amount of time it takes for your slack adjusters to take the slack out of the brake chamber linkage, and to start generating brake friction. This whole process can easily exceed 1/2 second, so now your rig has traveled 2 seconds or 180 feet at 60-MPH (nearly 4 rig lengths) before the first braking action actually takes place.

What happens if a car or truck suddenly pulls out 150 feet in front of you while you are going 60-MPH? You will probably hit that car or truck before your brakes ever get a chance to engage. Just some food for thought. The whole purpose of this section is to get you to realize just how big of a factor speed plays when dealing with an unexpected and sudden braking situation.

This concludes the physics of braking. We hope you have benefited from the experience and will see speed in a different way than you used to.

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