How do you work out the amount of braking power (or force?) to stop a
vehicle?
I know the Nm exerted by the braking system, and the weight(Kg) and
velocity(m/s) of the vehicle; I need the equation.

Dear rob1981,

There are two most common ways to calculate the amount of power that
is necessary for stopping an automobile.

The first way is to calculate the constant work of the brakes in
Kilojoule (kJ). Do to so, use this formula:
 
W = ( F * ( v * v ) ) : 2000

W = Work of brakes in kJ
F = Braking system output in Newton
v = Velocity in m/s

The second way is to calculate the average brakepower in Kilowatts
(kW):

P = ( F * v ) : 2000

P = Average brakepower in kW
F = Braking systems output in Newton
v = Velocity in m/s

Both formulas refer to stopping a car on flat road under ideal
circumstances and don't take into account the countless possible
concomitants.

Source:

Tabellenbuch Fahrzeugtechnik (Reference Chart Book Automotive
Engineering), published by Gehlen Verlag, 1999. ISBN 3-441-92255-7

Hope this helps!
Regards,
Scriptor

---

Request for Answer Clarification by rob1981-ga on 26 Jan 2003 14:22 PST

Hi,
how can these equations be used to work out the Kj or Kw needed to
stop a vehicle from a given speed, e.g if you have a car that weighs
1000kg travellimg at 20m/s?

Rob

---

Clarification of Answer by scriptor-ga on 26 Jan 2003 16:18 PST

Dear rob1981,

Here are examples how to use the formulas.

Let us assume that we have the following values:
Braking system output - 150 Newton ("F")
Vehicle velocity - 5 m/s ("v")
The value "2000" represents the mass of the vehicle in kilograms.

We calculate the constant work of brakes in kJ ("W") step by step:
W = ( 150 * ( 5 * 5 ) ) : 2000
W = ( 150 * 25 ) : 2000
W = 3750 : 2000
W = 1.875 kJ

We calculate the average brakepower in kW ("P") step by step:
P = ( 150 * 5 ) : 2000
P = 750 : 2000
P = 0.375 kW

Hope this answers your question.
Regards,
Scriptor

Exactly what I was looking for, thanks.

This answer is utter nonsense. 

The amount of work required to stop an automobile is negative since
the force is in the opposite direction of the motion, and its
magnitude is equal to the kinetic energy of the car:  m v^2 /2, where
m is the mass of the automobile and v is the velocity.  So in the
'work' part of the answer, the F (force) should be an m (mass).  The
2000 is there rather than just a 2 so the work comes out in KJ rather
than J.

The instantaneous power is also negative, and its magnitude is Fv,
where F is the braking force.  Assuming a constant breaking force, the
average braking power is Fv/2.  So the average power part of the
answer is actually right.  But then the 'clarification of answer' is
crap again.  The '2000' certainly does not have anything to do with
the mass of the vehicle.

One other thing: it seems the Nm referred to in the question might
mean torque (newton-meters).  If this is the case, then you must
divide the torque by the radius of the wheel to get the braking force,
F.