Measurement of friction power by Willans line method

We will discuss the measurement of friction power by Willans line method and its limitations. Let’s dive into it.


The difference between Indicated Power (IP) and Brake Power (BO) is called frictional power which includes friction losses in the flywheel, governor, oil pump, water pump, and other moving parts. Therefore you can calculate frictional power (FP) by using the formula:
F.P = I.P – B.P

Read: Derivation of continuity equation in cartesian coordinates

There are different methods of measurement of friction power(F.P) as follows:

  • Measuring I.P and B.P
  • Morse test
  • Willans line method
  • Motoring test.

Measurement of friction power by Willans line method:

friction power by Willans line method
Willan’s line method
  • In this article, we are going to know more about the measurement of friction power by Willan’s line method. Willan’s line method is also known as the fuel rate extrapolation method. In this method, we draw a graph where we take brake power (B.P)(kW) on X-axis and fuel flow rate (kg/hr) on Y-axis on a condition that the engine is running at a constant speed.
  • As shown in the figure, the graph is anticipated back to zero fuel flow rate of zero fuel where it cuts at point A on the negative X-axis.
  • Point A on the negative X-axis shows the friction power at the same speed on the engine. When break power becomes zero, then fuel consumption at the same power represents the fuel consumed to overcome the friction loss of the engine.
  • As per the graph, variation in the fuel flow rate and brake power is linear.  It results in the anticipation of the straight part of the main curve as a negative crossing on the X-axis at zero fuel flow rate will represent the friction power (F.P).

Limitations of Willans line method:

  • Willan’s line method is only used in the compression ignition (C.I) engine. It is not applicable to S.I engine.
  • The friction power given by this method is approximate.
  • Friction power changes while an increase in engine speed. That’s why the engine should run at a constant speed throughout the Willan’s line test


We have discussed about willans line method for the measurement of the friction power. We also learned about difference between indicated power and brake power. do you have any queries about willans line method? then elaborate it in the comment box.

2 thoughts on “Measurement of friction power by Willans line method”

Comments are closed.