The cylinders of a four-cylinder in-line 4-stroke normally aspirated petrol engine are
equally spaced and numbered consecutively from one end. The angles of the cranks of
cylinders nos. 2, 3 and 4 relative to the crank of cylinder no. 1 are 180º, 180º and 0º
respectively. The engine develops 36 kW at 3000 rpm when tested on a brake
dynamometer. An indicator diagram test on any one cylinder reveals that the work done
on the gases during the compression stroke is around 0.25 times the work done by the
gases during the power stroke.
If

(radians) is the angle made by the crank of cylinder no.1 from its top dead centre
position, the cyclic variation of its contribution to the crankshaft torque (i.e. the
individual torque due to cylinder no. 1 only vs

) is given by the following expression:
( )





 
 
 
=
   
  
  

sin for 3 4
0 for 3
sin for 0
.1
B
A
T cylindern o
where A, B are positive constants.
Sketch the variation of the individual torque
( )cylinderno.1
T
over one four-stroke cycle and
calculate the values of A and B. Label your sketch to show the greatest values of the
individual torque during the power and compression strokes, and its mean value