Applet to carry out some of the calculations in the book "Mechanical Engineering Design: Theme - Automotive Engines", by David J Grieve

NB This applet requires the Java Run Time Environment (JRE) to enable the applet to run in a browser. This can be down loaded from You can either download just the JRE or the complete Java Development Kit (JDK). The JDK seems to install itself so that the browser can find it OK. The applet has so far been tested with Netscape, Flock and Microsoft IE.

The angular measurements are degrees after bdc from the start of the compression stroke. Velocities and accelerations of the piston away from bdc position are positive.

In the "Reciprocating mass" input field enter the mass of the piston, rings, gudgeon pin and a portion of the connecting rod mass (about one quarter is probably reasonable). The "Plot indicated torque" plot assumes the reciprocating mass is zero, neither torque plot makes any allowance for friction. Clicking the "Plot torque *2" button lists and plots the torque after allowance has been made for the force needed to accelerate and decelerate the piston.

NB Only integer values for "Ignition" (in degrees after bdc) can be entered, "Combustion duration" will accept integer and non integer values, as will most other input boxes.
For the Otto cycle (4th and 5th grey plot buttons) the heat release is assumed to be almost instantaneous (between 180o and 181o after bdc).
For the finite combustion process the heat release rate is assumed to follow a Weibe function with values of 'a'=5 and 'n'=3, see Chapter 8 and the results are listed and plotted with the 3rd, 6th, 7th, 8th and 9th grey plot buttons.

N.B: The calculations of torque, indicated work done and indicated power are based on the finite heat release model rather than the (much less realistic) Otto cycle.
As neither the Otto cycle nor the finite heat release model computations make any allowance for heat transfer out of the combustion chamber, cylinder walls or piston crown, the actual temperatures and pressures will be lower than those shown and consequently the calculations using these will be overestimates. This and friction are the two main causes of the computed results for torque, work and power being greater than those actually achieved.

The blank boxes adjacent to the pink labels do not need any entry, these will contain results after the yellow 'Calculate' button has been clicked. Click the other buttons to plot curves only after the calculate button has been clicked.
Plot values are at 10o intervals except for 181 degrees. after bdc.

Each time a grey plot button is clicked, the title and values of the variable at one degree intervals are added into the results listing area.

There are two options for specifying the total energy input per cycle:

1) Where a value in J is to be specified, enter the value into the input box by the label "Specified energy in" (the value must be greater than 1.0).

2) If the energy input is to be calculated from volumetric efficiency, the air density, the fuel energy and the air:fuel ratio, enter a value of 0 in the "Specified energy in" box and the appropriate values in the other boxes and the energy input will be calculated from these values and the computed V1 value.

Further improvements to this applet are planned.

Please send comments and suggestions to or

David J Grieve, Updated: 21st April 2013, Original: 23rd September 2008.