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Engine Assessment

Indicator Diagrams: Powercards



The Power Card or Indicator Diagram is a graphical representation of pressure and volume within the engine cylinder. From the diagram the Indicated Power or IP for the cylinder can be calculated.

To explain what actually happens let's first look at a simple example:


If a gas is expanded in a cylinder at a constant pressure of say 20 bar (2000000N/m2) and the volume in the cylinder increases from 0.075m3 to 0.525m3, then the work done by the expanding gas is represented by the coloured area of the graph which in this case is pressure change in volume or p(V2-V1)

pressure (N/m2) change in volume (m3) = Nm3/m2 which cancels down to Nm or Joules (the basic unit of work)

inserting values: 20 105(0.525 - 0.075) = 9 105 J or 900kJ

Similarly, if the piston was pushed up the cylinder and the pressure remained constant at 20 bar then the work input would be 900kJ (if we used the formula p(V2-V1) then the answer would be 20 105(0.075 - 0.525) = -9 105 J or -900kJ:- the negative figure indicates work input)


When a piston is moving downwards on the power stroke in a diesel engine, the pressure does not remain constant. However this does not change the principle that the work done is represented by the area under the expansion curve as shown on the diagram


When the piston moves up the cylinder compressing the charge of air, this takes work. Again this is represented by the area under the compression curve, but this time remember that this is work that is having to be put into the engine.


It should be evident therefore that the actual work obtained per revolution of the two stroke engine is represented by the area under the expansion curve minus the area under the compression curve.


Ok, this is all very well, you may say, but how do we draw this diagram, let alone measure the area under the curves and calculate the work output?

First things first...


To measure the pressure in the cylinder at any time during the cycle, use is made of a tapping in the cylinder head, terminating in a valve known as an indicator cock. The indicator cock is fitted with a male screw thread on its outlet, and using this thread the piece of equipment shown, known as the engine indicator is mounted.

When the indicator cock is opened, the gas pressure in the cylinder acts on the under side of a piston moving it upwards against a spring.

As the piston moves upwards, so a marker, connected through a parallel link motion will move up a drum, tracing a vertical line on a piece of paper wound around the drum. The height of the line is proportional to the maximum pressure in the cylinder.

The manufacturer of the equipment gives the relationship between the pressure rise and the vertical distance the marker will move. This is known as the spring constant.


The drum is spring loaded and free to rotate backwards and forwards by pulling and releasing a cord which is wrapped round the drum.

The end of this cord is fixed to a cam operated linkage so that the drum rotates forwards and backwards as the piston moves up and down the cylinder.

This means that as the marker is moving up and down, the drum is rotating backwards and forwards in time with the engine. The indicator diagram or power card is traced out on the paper as shown.






The next thing to do is measure the area of the diagram. This could be done mathematically using the mid-ordinate rule, or by using a piece of kit known as a planimeter (shown below). The outline of the powercard is traced using the planimeter and the  area read off the scale.

The length of the diagram is also measured.


If the total area of the diagram is divided by the length, the average or mean height of the diagram will be obtained. Looking at it another way, we now have an indicator diagram of a rectangular form with the same area and length as the original power card.


Because the mean height of the diagram can be converted into a pressure by multiplying by the spring constant, a pressure known as the mean indicated pressure or MIP can be obtained.

The length of the diagram is representative of the swept volume of the cylinder. This volume can be obtained by multiplying the cross sectional area of the cylinder by the stroke.

If the MIP is multiplied by the swept volume, the work done per cycle will be obtained.


Area of diagram = 840mm2

Length of diagram = 105mm

Mean height of diagram = 8mm

Spring constant = 200kN/m2 per mm.

MIP = 8 200 = 1600N/m2

Diameter of cylinder = 960mm (radius 0.48m)

Stroke of piston = 2.5m

Work per cycle (or revolution) = 1600 p 0.482 2.5 = 2895 kNm or kJ

If this figure is now multiplied by the number of power strokes/sec, the power output of the cylinder will be obtained. (work done per second)

E.G. 90RPM = 1.5revs/sec.

2895 1.5 = 4343kW

This process is repeated for each cylinder on the engine. The total indicated power for the engine can therefore be calculated, and individual power outputs for respective cylinders compared to each other.

The formula to remember is


where IP = indicated power

MIP = mean indicated pressure

L = length of stroke

A = cross sectional area of cylinder

n = number of power strokes/second

NOTE: The number of power strokes/second is the same as the revs/second for a 2 stroke engine, and revs/second 2 for a 4 stroke engine.


The powercard for a 4 stroke engine is exactly the same as for a 2 stroke engine except that on the exhaust and inlet strokes, a horizontal line is traced.


Although the pressure in the cylinder is different for the inlet and exhaust strokes, the difference is to small to be shown on the scale of the diagram.


Modern engines use pressure transducers to measure the pressure in the cylinder. The position of the piston is obtained from a pick up mounted to read the position of the crankshaft. This information is relayed back to the engine computer which will then draw the power card, and calculate the indicated power for you. However, the principle is the same, and it is this principle that marine engineers have to understand.


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