Applied Physics Tutorial 5 - Internal Combustion Engines


Internal Combustion Engines

The internal combustion engine does away with the need for an external heat source.  Fuel is burned within the engine to provide the heat that does the useful work.  Generally these engines use fossil fuels which are particularly concentrated forms of energy.  We will look at the two most common types:


The Otto Cycle

The four-stroke Otto cycle is shown in the diagram:




The indicator diagram for the Otto cycle is like this:





Let's look at the cycle and link it to the indicator diagram:

  1. The induction stroke takes place at A.  Although in theory the pressure should be the same as atmospheric, in practice it's rather lower.  The amount of petrol air mixture taken in can be increased by use of a supercharger.

  2. A to B is the compression stroke.  Both valves are closed.  The compression is adiabatic, and no heat enters or leaves the cylinder. 

  3. Ignition occurs at C.  The gases resulting from the ignition expand adiabatically, leading to the power stroke.

  4. D to A the gas is cooled instantaneously.  

  5. At A the exhaust stroke occurs and the the gases are removed at constant pressure to the atmosphere.

  6. Strange as it may seem, the piston does half a revolution at A.  Actually it's slightly more in practice, as the the valve timing is more complex.


In practice the thermodynamics of a petrol engine are more complex:


The picture shows a large petrol engine that was used in a war-time transport aeroplane.  Each engine had a capacity of 29 litres, with a power output of 750 kW (1000 PS).



The efficiency of a petrol engine can be increased by increasing the compression ratio.  However the heating of the gases can ignite the petrol prematurely.  This pre-ignition is known as knocking or pinking.  It can do a lot of damage to the engine.



Diesel Cycle:

The Diesel cycle differs from the Otto cycle in that the induction stroke takes in only air.  The air is compressed quite a lot so that it gets hot.  The fuel is injected into the hot air, and ignites.  This produces the power stroke.




The indicator diagram is quite different to that of a petrol engine:



Let's now look what happens in the indicator diagram:

  1. The induction stroke takes air in ideally at constant volume, pressure and temperature.

  2. The compression stroke takes place from A to B.  The air is compressed adiabatically to about 1/20 of its original volume.  It gets hot.

  3. From B to C fuel is injected in atomised form.  It burns steadily so that the pressure on the piston is constant.

  4. From C to D the power stroke moves the piston down as adiabatic expansion takes place.

  5. D to A cooling and exhaust occurs.


The diesel engine has a higher thermal efficiency than the petrol engine.  However it does have the disadvantage in that it is heavier.  Also the size of engine for a given power tends to be bigger.  They also tend to be noisier and incomplete combustion makes for considerable pollution.  Complex exhaust systems have been developed to tackle this problem.  However they are expensive if they go wrong.


Several European countries have pledged to ban diesel cars by the year 2040.


However diesels have been made lighter and more refined for luxury cars.  Experiments with diesels for aircraft have been hugely successful.  Jet A1 fuel (paraffin) costs 80 p a litre compared with Avgas (aviation petrol) at £2.00 a litre.




This aircraft (a Diamond Twinstar) uses two 2.0 litre diesels (of the same type as found in Mercedes cars, but with higher quality components).  It can fly at 360 km/h, and flying at 150 km/h burns about 3 litres of fuel per hour.  Rather more economical than a family saloon, but at 300 000 euros not exactly a snip. 



For either kind of engine, we can predict the power that the engine can give out by using a simple formula:


Power output = area of p-V loop × no of cylinders × number of cycles per second



A common bear trap is to forget that a single cylinder four stroke engine goes through each cycle once every two revolutions


We can also work out the maximum energy that can be put into an engine by this formula:


Input Power = calorific value of fuel × flow rate of the fuel


The fuel for any engine has a calorific value which is the energy that can be got out of the fuel per unit mass.  It is measured in joules per kilogram. 



In engineering articles, watch out for fuel flows in kg min-1 which need to be converted to kg s-1.  You do know how to do that, don't you?


Question 1

Test-bed measurements made on a single-cylinder 4-stroke petrol engine produced the following data:

  • mean temperature of gases in cylinder during combustion stroke 820 °C

  • mean temperature of exhaust gases 77 °C

  • area enclosed by indicator diagram loop 380 J

  • rotational speed of output shaft 1800 rev min-1

  • power developed by engine at output shaft 4.7 kW

  • calorific value of fuel 45 MJ kg-1

  • flow rate of fuel 2.1 × 10-2 kg min-1

(a) The rate at which energy is supplied to the engine;

(b) The indicated power of the engine;

(c) The thermal efficiency of the engine.  (AQA Question, adapted)





Larger aeroplanes use gas turbines.  Turbines work on the same principle as piston engines (suck, squeeze, bang, blow), but they are rotary engines rather than reciprocating engines.  Therefore they tend to be lighter than piston engines of equivalent power.  Here is an example (incomplete) on an old commercial aeroplane.



The engine (a Rolls-Royce Dart) could produce 1100 kW, (1500 PS).


The picture below shows the general layout of a gas turbine engine.


It works on the same general principle of a diesel piston engine in the way that air is sucked in, compressed, fuel is ignited, and heated air rushes out of the back.  In a turbojet, the heated air drives a turbine, which drives a compressor.  In a ramjet, you don't have a turbine or a compressor, just a hollow tube.  However the aircraft has to be moving fast through the air for the engine to work.


The turbojet is less efficient than the turbofan, which is nowadays used widely in jet aircraft of all kinds.


The jet engine drives a large fan in a duct, and large amounts of cold air are moved backwards without being heated.  In the largest turbofans, the hot gases from the exhaust only contribute about 25 % of the total thrust.  The fan at the front may run at a lower speed (3000 rpm) to the rest of the turbine (33 000 rpm), so there would be a reduction gearbox.


In a turboprop, the power is extracted from the hot air stream to drive a propeller.  The hot gases from the back contribute about 5 % or less to the thrust.


The turbine drives both the compressor and a propeller through a reduction gearbox.  Typically the propeller will turn at 2000 rpm, while the turbine spins at 30 000 rpm.  Turbines like this can also be used to drive generators.



The advantage of a a turbine like this is that it is more efficient at high power than a piston engine.  If you are driving at 50 km/h, the engine in your car may be turning at 1000 rpm.  If you speed up to 100 km/h, the engine will be turning at 2000 rpm.  However, in an aeroplane, it's rather different.  The propeller develops full thrust at 2500 rpm.  At 1250 rpm it develops hardly any thrust at all.  So aircraft engines have to give all or nothing. 


A turbine is very inefficient at low revs (which is why you don't find them in cars).  It will gobble 50 kg of Jet A1 every hour when idling.  At full power, it uses 150 kg every hour.  Turbines also lose power at high altitudes where the air is thin.  A turbo-charged piston engine retains its power.


The main disadvantage with turbines is that they are eye-wateringly expensive to buy and maintain.  Machines that spin at 30 000 rpm have to be made to a high precision, requiring skilled craftsmen to make them.  Any imbalance would shake the engine to pieces within seconds.  A blade coming loose would smash every other blade off - the engineers call this "having a haircut".  Another problem can be a "surge" or a compressor stall.  The compressor stops compressing momentarily and the flame goes to the front of the engine with a loud bang, with a loss of thrust.  A surging engine often leads to an emergency landing.



Wankel Rotary Engines

For smaller turbine aircraft, some engineers are suggesting the use of a Wankel rotary engine, designed by the German engineer Felix Wankel (1902 - 1988), which acts in a similar way to a piston petrol engine.  These have the advantage of being more efficient than a piston engine, as well as being much lighter, but are a lot less expensive than a turbine.  They are less prone to being over-revved, which can do catastrophic damage to a piston engine.


Photo by J Lyon, Wikimedia Commons


The picture shows the rotor of a Mazda 1.3 litre Wankel engine that is found in some of their sports cars.  Some aircraft manufacturers are planning to use these in light aircraft.  In larger aircraft, a Mazda engine of capacity 2.6 litres is being considered, as these can safely produce 525 kW (700 PS).


The limiting factor with Wankel Rotary engines is the seal at the tip of each rotor, which tends to wear.  Also the engines discussed here run on petrol, which is expensive.  The "holy grail" is to get a Wankel engine that runs on Jet A1.  This is more difficult as diesel engines need a high compression, although there has been some success with diesel Wankel engines.



Testing Engines

Before any engine is put on the market, it has to be thoroughly tested.  Nobody wants an engine that is going to fail in use.  Nor do they want one that gobbles the fuel. There is nothing more useless than a broken-down car.  In an aeroplane, you cannot pull off and stop behind a cloud; there is only one way - down.  So various tests are done on engines, of which we will look at a few.


Useful Power

You will have seen that many engines have their power quoted as brake horsepower (bhp).  This has been used by engineers for at least two hundred years.  At its crudest, it is a comparison with the power you can get out of a horse, which had been the common form of motive power for many centuries.  However a more scientific test was needed, and the diagram below shows the kind of set up, called a dynanometer.



The mass and strap act as a brake because they provide a frictional couple, t (= mgr) against the rotation of the engine.  The power produced by the engine is given by the formula:


P = tw


[P - power (W); t - torque (N m); w - angular velocity (rad s-1)]


Originally 1 brake horsepower worked out at 746 W; now it is considered as 750 W.  It is often given the shorthand PS ("Pferdstärke", German for "horsepower").


Question 2

An engine gives out a torque of 250 N m at 3300 rpm.  What is its power in watts and PS?




The method above, although simple, has a disadvantage in that a lot of heat is generated.  Although the principle is much the same, the test beds for engines are much more sophisticated.  They can be:

The picture below shows an engine test bed:


Photo Aniketdp.mech, Wikimedia Commons


This picture shows a water pump that an aircraft engine manufacturer uses to test engines before they are reinstalled into aircraft.  It mimics the loads experienced by the engines in flight.



The useful power that can be got from an engine is always less that the power worked out from an indicator diagram.  This is because there is friction within the engine.  The power needed to overcome friction is the friction power:

friction power = indicated power - brake power



Question 3

In Question 1 you worked out that the indicated power of an engine was 5700 W.  The power available at the output shaft is 4.7 kW.  What is the power dissipated in overcoming frictional losses in the engine?  What fraction is this of the indicated power?



The answer you worked out in the previous question shows that a lot of power is used to overcome friction.  It is dissipated as heat.  Oil lubrication is essential in such an engine:

Without lubrication the engine would rapidly seize up.


Aircraft engines are subject to rigorous testing, as catastrophic failure can be disastrous.  On aerodromes, flocks of birds can be a nuisance, since an aeroplane running into a flock will cause serious damage, and not just to the birds.  Recently an airliner climbing from a New York airport ingested birds into both engines, which stalled and failed completely.  The pilot glided his 56 tonne aeroplane to a successful landing in the Hudson River.  Thanks to his skill and training, everybody got off safely.  The aeroplane was fished out of the river, and is now in a museum.


Sometimes engineers test the engines to destruction, including firing (dead) chickens at them, or deliberately shearing a blade at high speed (see link).  Such tests are very expensive, so good results are essential.



Engine Efficiency

The indicated or thermal efficiency is given by:


thermal efficiency = indicated power ÷ power input from the fuel


As we have seen there are mechanical losses in an engine.  The mechanical efficiency of an engine can be defined as the ratio of the output power to the indicated power or workable power.  The output power is the power we can get from a dynamometer.


mechanical efficiency = output power ÷ indicated power



Question 4

What is the mechanical efficiency of the engine in Question 3?



As the engine runs faster, the power absorbed in overcoming friction increases, so the mechanical efficiency falls away.  We can see this in the graph below:



The frictional power increase almost mirrors the decrease in mechanical efficiency.


The overall efficiency is the fraction of the input power of the fuel that is delivered as useful power:


Overall efficiency = output power ÷ input power of the fuel.




Question 5

In Question 1 you worked out that the power gained from the fuel of the engine was 15.8 kW.  If the power output is 4.7 kW, what is the overall efficiency? 



The overall efficiency of internal combustion engines is not very good, with even the best being about 40 %.