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Engine Performance, Background

In a piston engine, chemical energy is converted into heat energy by the combustion of fuel and then transformed into mechanical energy by the pistons to rotate the crankshaft. The expansion of the gases caused by the heat produced from the combustion process result in an increase in cylinder pressure and this force moves the piston down and thereby finally rotating the propeller.

This process is more than one hundredth years old and generating mechanical power this way has not changed very much, the efficiency of the piston engine has improved by a small amounts in the same time period. It is safe to say that the original design was quite good.

The power of an engine is a way of measuring the rate at which it is doing work during a certain time period.
On this page we are going to dive into how force, work and power are developed and show you some insights into engine efficiency (as nothing in this world is perfect)

Of course this will involve a refresher of some basic physics as we all used to learn at school.

Some background

For a bit of understanding on how engines create power we need to revisit physics we once learned but may have forgotten and or not used in years gone by.

Force, Work & Power

To get an object to change its speed or direction we need to act on that object with a force. The formula is: F = m × a, where m is mass and a is acceleration. This force is expressed in Newtons or kgm/s2. This effect is also known as Newton's 2nd law.

Work is done when a force (or torque) on a object causes it to move. So force over a distance equals work. In a formula: W = F × d, where F is force and d is distance. The amount of work is expressed in Newton × meters, Nm. It is the same as Joule and used to be called foot-pound or ft-lb.

Power is simply the rate of doing work. Thus the amount of work in a certain period or time. Its formula: P = W / t, where W is work and t is time. Power is expressed in watts (W) and is the equivalent of 1 Joule per second (J/s). Engine power is nowadays expressed in kW and as HP (horsepower) in the old system.

Engines

With rotating objects like our propeller we must use the RPM (rotational speed) or angular velocity instead of distance when using work. The work formula for torque (work) then becomes t = F × r, where F is force and r is radius. Rewritten to force the formula then becomes: F = t / r.

By definition, we know that linear distance is linear speed × time = radius × angular speed × time.
Power then results in: (force × linear distance) / time or after some conversions into torque × angular speed where angular (or rotational) speed is 2 π RPM with power in watts (W), torque in Nm and RPM in revolutions per minute.

After applying the conversion factor for imperial units (33,000 ft·lbf/min per horsepower) power (HP) finally becomes (torque × RPM) / 5252 because 33000 / 2π = 5252.11 or thereabouts.

Energy

Energy is the capacity to do work over time and it is expressed in Joules. For example: one kg of gasoline or JET both contains about 44 MJ, but as JET is denser it has more energy per liter. This explains the longer range a diesel engine powered aircraft has compared to an AVgas model with the same contents in the fuel tanks.

Measuring engine power

To determine the power an engine can deliver it is installed on a test bank and its torque is measured at severals RPMs and then converted to power using its RPM. This method obtains brake horsepower, BHP. The engine itself produces somewhat more power as it must overcome internal friction, and using oil specified by the engine manufacturer will minimize this effect.

Internal friction is obtained by connecting an electric motor to the engine (at specified operating temperatures) and measuring the power required to rotate the engine. The viscosity of the engine oil, design of the engine, its RPM and the accessories all determine how much power lost to internal friction. With good engine design this can be minimized.

Rated power

This is normally expressed in a form like: 160 BHP at 2700 RPM. Rated altitude is the altitude where rated power is developed with full throttle, which will be at mean sea level (MSL) for a normally aspirated engine and at a higher altitude if the engine is super- or turbocharged.

Engine efficiency

Efficiency is rate of energy in the fuel used and useful work done by the engine. Thus Brake Thermal Efficiency = Brake Power (Joules/sec) / Fuel Consumption (Joules/sec), or put differently: Brake Specific Fuel Consumption = Fuel Flow / Brake Power in kg/hr per watt, or lb/hr per BHP. AVgas (or gasoline) engines have efficiencies of about 20 - 30 % where as diesels can run from 30 % for light weight four stroke diesels and up to 50 % for large two stroke marine diesels.

Volumetric efficiency

Another type of efficiency important to engines is volumetric efficiency. This relates to the volume of fuel/air the engine breathes in at the intake stroke. A normal aspirated engine pumps the mixture in by opening the intake valve combined with the downward motion of the piston. The design of the intake manifold and inertia of the mixture results in less mixture taken in than there is room for when the piston is at bottom dead center.

It can be defined as: volume of the charge / piston displacement and the highest volumetric efficiency is obtained with a full open throttle and open intake valve, good manifold design and cool inlet air (highest density). You will notice that this will coincide at the point where the engine creates its maximum torque.

Of course using a super- or turbocharger will help too as these devices will pump in more air/mixture into the combustion chamber overcoming some of the losses and increase the power.

We can conclude that for an engine to achieve the best BSFC it must be run at high MAP, low RPM, be at full throttle height, mixture leaned and carburetor heat set to cold.