MadSci Network: Engineering

Re: In reference to 'how to calculate horsepower from acceleration rate and

Date: Sun May 1 12:40:30 2005
Posted By: Madhu Siddalingaiah, Physicist, author, consultant
Area of science: Engineering
ID: 1111163239.Eg


Many people are often confused about power and energy.

Let's start from the beginning, with some basic equations:

Energy = Force * distance

For a mass m moving at a speed v, the energy E is:

E = 0.5 * m * v * v

Energy can be measured in Joules (J) or British Thermal units (BTU). 1 BTU
is equal to roughly 1055 Joules. If a 2100 pound car is travelling at 60
miles/hour, the energy is about 342600 Joules or 325 BTUs. This is the same
amount of energy required to accelerate the car from 0 to 60 miles/hour on
level pavement. This is independent of acceleration, it doesn't matter if
it takes 6 seconds or 60 seconds, it's the same amount of energy.

Energy is always conserved, meaning it can't created or destroyed, it can
only change form.

Power = rate of energy

Power can be measured in Watts (W) or Horsepower (HP). 1 HP is the same as
746 Watts.

Power, unlike energy, is not always conserved. If we have a system where
energy is flowing at a constant rate, then power is conserved, meaning the
power in is equal to the power out. For standard cars, power from the
engine is delivered to the wheels through a transmission. There are some
losses due to the transmission, air conditioner, alternator, and other
systems, but this is not considered a significant loss. If the air
conditioner is turned off, your headlights are off, and you have a manual
transmission, the losses will be not more than a few percent. Automatic
transmissions only increase losses.

The gear ratio is a transmission does not change power output. Remember,
power is conserved in this case. There might be some slight change in power
loss for different gear ratios, but for the most part, it's insignificant.

Since we know power is the rate of energy, we can divide the energy
calculated above by the time required to produce the energy. If it takes
your car 6 seconds to go from 0 to 60 miles/hour, then the power is about
57000 Watts or 76.6 HP. Keep in mind, this is the average power, it doesn't
tell us the power at any time during the acceleration. We would need
detailed speed measurements from start to finish to calculate that.

Given these numbers, I would guess the engine is capable of producing 150
HP or more. How did I come up with that number? Internal combustion
engines, like gasoline, Diesel, and even turbines, do not have a flat power
curve. The power output is zero at zero RPM and increases more or less
linearly until some peak. In stock gasoline engines, the peak power is at
5000-6000 RPM or so. As a rule of thumb, the peak is generally 1000 RPM
below red line. So if you could run your engine at 1000 RPM below red line,
then you could achieve near peak performance. If watch your tachometer, I
would guess that the RPM averages much less than that, maybe even half.
That's why you are getting only half of the power the engine is capable of

RPM, power and torque are all related. Torque is simply power divided by
RPM. The power out of a transmission is the same as the power in (minus
small losses), but the RPM is different depending on the gear ratio. If the
output shaft spins at half the speed of the input, then the output torque
is double that of the input. RPM doesn't really matter in the end as far as
power is concerned, remember, power is conserved. Changing gear ratios does
not change the power, it only affects torque and RPM. It's easier to start
with calculate power and work out RPM and torque if you need it. You can do
it the other way, but it's easy to make mistakes.

The reason most cars have a transmission at all is because gasoline engines
cannot produce torque over a wide range of RPM, particularly at zero RPM.
Diesel electric locomotives and subways do not have transmissions with
variable gear ratios because they use electric traction motors instead of
transmissions. Electric motors can produce torque over a wide range, even
at zero RPM. This is known as the stall torque. Note that steam locomotives
don't have transmissions either. That's because piston driven steam engines
can also produce very high stall torque.

In summary, here is all you need to know:

Energy = 0.5 * mass * v * v
Power = Energy / time (if power is continuous)
Power = RPM * Torque

That's it. To use these equations with your car, all you need to know is
the mass, speed, and time. Be careful to use consistent units in your
calculations. I tend to start with MKS units and then convert to other
units if needed. That's why I use Watts instead of HP and kilograms instead
of pounds.

Good luck!

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