## Monday, February 20, 2012

### The relationship between Power, Torque, RPM

In the specification of the vehicle engine, it has power written in horsepower units or kilowatts at a certain engine speed, and torque with of kg-m or lbf-ft at certain engine speed. What is the relationship between the torque and power and engine speed?

In the
internal combustion engine, the combustion gas will push the piston which is connected to the crankshaft by connecting rod. Gas pressure provides torque on the crankshaft and rotates the crankshaft.

Read also: RPM meter (tachometer) functions on the vehicle, how to install a tachometer.

Power is torque multiplied by the rotation (angular velocity)
:

P = τ x ω

Units of measurement for System International (SI)
are:

Power P units is watt
Torque τ units is Nm (newton meters)
Angular velocity ω units is radians per second.

The formula for the other units are:

P = τ x ω x 2 p / 60 000

W
ith units of measurement are:

Power P units is kilowatts (kW)
Torque τ units is newton meters (Nm)
Angular velocity ω in
Revolution Per Minutes (RPM)

Example calculations:
Torque = τ = 145 Nm
Angular velocity = ω = 4800 RPM

The
refore power = P = 145 x 4800 x 2 x 22/7 / 60,000 = 72.91 kW

For internal combustion engine, maximum torque is not produced at exactly the same engine speed as maximum power obtained.

Read also: calculation of acceleration, speed, and power on a vehicle, with examples of calculations on a Toyota Corolla car and a Honda CBR1000RR motorcycle.

On vehicles
that used to pull heavy loads such as truck, the maximum engine power is at a low RPM so that maximum torque is also at low rpm.

On vehicles
that used for high speed with light load such as sedan and motorbike, the maximum power generated at high engine speed, so that maximum torque is also at high RPM.

Here is a sample of power and torque chart that show maximum torque is produced at about 3900 RPM engine speed, while maximum power is obtained at about 5800 RPM engine speed, this example is from a V8 engine:

Formula below is using American
units:
P = τ x ω x 2
p / 33,000

Where units
of measurement are:

Power P in horsepower (hp)
Torque τ  in pound feet (lbf.ft)
Angular velocity ω in
Revolution Per Minutes (RPM)