Considerations
for Stopping Your Tractor/Trailer
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 60MPH in 60 seconds, then the same vehicle will
also take 100 horsepower to decelerate to a stop from 60MPH in
60 seconds. If you wanted that same vehicle to stop from 60MPH
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 20MPH, it is also traveling at
30feet per second. Measurement of deceleration, measures how
much the vehicles slow down each second. If your vehicle is traveling
at 30feet per second and 1second later it is traveling at 20feet
per second, then the deceleration is measured as 10feet per second
per second. What this means is that your vehicle has slowed 10feet
per second for each second of time lapse while the brakes are
applied.
At
the end of the first second, the vehicle slows to 20feet per
second, at the end of the 2nd second, the vehicle slows to 10feet
per second, and at the end of the 3rd second, the vehicle is stopped.
So the deceleration of your vehicle was 10feet/sec/sec, which
looks a little strange, but is an accurate measurement just the
same.
When
a fast vehicle travels at 60MPH, how long would it take for this
fast vehicle to stop if the deceleration remained at 10feet/sec?
This is three times faster than 20MPH, so the speed would be
90feet/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
30feet/sec down to 20feet/sec. This averages out to 25 feet/sec,
so the vehicle traveled 25 feet. During the 2nd second, the vehicle
speed varied from 20feet/sec down to 10feet/sec, so the average
speed was 15feet/sec, so the vehicle traveled 15 feet. And during
the final second, the vehicle speed varied from 10feet/sec down
to 0feet/sec, so the average speed was 5feet/sec, so the vehicle
traveled 5feet. 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 60MPH. It is traveling at 90feet/sec:
During the first second, the vehicle slows to 80feet/sec, and
covers 85feet.
During the next second, the vehicle slows to 70feet/sec, and
covers 75feet. During the third second, the vehicle slows to
60feet/sec, and covers 65feet. During the fourth second, the
vehicle slows to 50feet/sec, and covers 55 feet. During the fifth
second, the vehicle slows to 40feet/sec, and covers 45 feet.
During the sixth second, the vehicle slows to 30feet/sec, and
travels 35feet. During the seventh second, the vehicle slows
to 20feet/sec, and travels 25feet. During the eighth second,
the vehicle slows to 10feet/sec, and travels 15feet. During
the ninth second, the vehicle comes to a stop and travels 5feet.
The total distance traveled by the vehicle is 85+75+65+55+45+35+25+15+5
= 405feet
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 2seconds:
Speed/Stopping
Distance for 10feet/sec/sec Braking
40MPH
= 180feet stopping distance + 120feet reaction = 300feet
60MPH = 405feet stopping distance + 180feet reaction = 585feet
80MPH = 720feet stopping distance + 240feet reaction = 960feet
100MPH = 1125feet stopping distance + 300feet reaction = 1425feet
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 20MPH, 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 11/2 seconds to get
your foot on the brake for an unexpected panic stop. At 60MPH,
you travel 135feet, nearly 21/2 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 1.55seconds 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 60MPH (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 60MPH? 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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