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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
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
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.
INDICATOR MOUNTED ON ENGINE
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
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
Area of diagram =
diagram = 105mm
Mean height of diagram =
Spring constant =
200kN/m2 per mm.
8 × 200 = 1600N/m2
cylinder = 960mm (radius 0.48m)
Stroke of piston = 2.5m
per cycle (or revolution) = 1600 × p × 0.482
× 2.5 = 2895 kNm or kJ
If this figure is now multiplied by the number of
the power output of the cylinder will be obtained. (work done per
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
IP = MIPLAn
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.