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 produces a torque on the crankshaft and rotates the crankshaft.

Power is torque multiplied by the rotation (angular velocity)

P = τ x ω

In the System International (SI)
units of measurement 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

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

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 the same engine speed as maximum power obtained.

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 sampe chart power and torque on the V8 engine:

For America
as the units are different then use the following formula:
          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)

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