3.11.2.4Engineering PhysicsCore

Engine Cycles and Efficiencies

An engine’s indicator diagram measures work inside its cylinders. Brake power is smaller because friction and other mechanical loads consume part of that work. This lesson is part of the Engineering Physics option; study it if this is your centre’s chosen Paper 3 Section B topic.

40 min 3.11 Engineering Physics

What you'll be able to do

Explain petrol and diesel four-stroke operation
Compare idealised and measured indicator diagrams
Calculate indicated, brake and friction power and efficiencies

Four strokes and idealised cycles

A four-stroke petrol engine takes in a fuel–air mixture, compresses it, ignites it near the end of compression and expands during the power stroke, then expels the products. A diesel engine compresses air first; fuel injected into the hot compressed air ignites without a spark.

The idealised petrol cycle has adiabatic compression and expansion joined by constant-volume heating and cooling. The idealised diesel cycle replaces the heating stage with constant-pressure heating. Real pressure changes are rounded; combustion takes time, heat escapes and gas exchange adds a pumping loop. Construction details are not required, but the sequence and diagram interpretation are.

From one loop to indicated power

An indicator diagram records cylinder pressure against cylinder volume. Its net loop area gives work per cylinder per complete cycle, after allowing for any negative pumping contribution. Multiply by cycles per second and number of cylinders to find indicated power.

A four-stroke cylinder completes one full cycle in two crankshaft revolutions. Divide rpm by 120, not 60, for cycles per second. Brake power is useful shaft power, calculated from measured torque and angular speed. The difference between indicated and brake power is friction power in this model.

P_i=W_{\mathrm{cycle}}fn,\qquad P_b=T\omega,\qquad P_f=P_i-P_b

Here f is cycles per second per cylinder and n is the cylinder count.

Track each efficiency boundary

Input power is fuel mass-flow rate times calorific value. Thermal efficiency compares indicated power with fuel input; mechanical efficiency compares brake with indicated power; overall efficiency compares brake with fuel input.

Their product is a useful consistency check: thermal efficiency times mechanical efficiency equals overall efficiency. Use decimal fractions inside calculations, then convert to percentages. An unfamiliar cycle can still be analysed using its supplied diagram and the same energy accounting.

\eta_{\mathrm{th}}=\frac{P_i}{P_{\mathrm{in}}},\quad \eta_{\mathrm{mech}}=\frac{P_b}{P_i},\quad \eta_{\mathrm{overall}}=\frac{P_b}{P_{\mathrm{in}}}

Input power = calorific value × fuel mass-flow rate.

Work through the reasoning

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.

Example 1A four-cylinder four-stroke engine runs at 3000 rpm. Each cylinder produces 400 J per cycle. Find indicated power.

f=3000/120=25

cycles s⁻¹ per cylinder.

P_i=400(25)(4)=40000

Answer40 kW.

Example 2That engine delivers 30 kW brake power from 100 kW fuel input. Find friction power and all three efficiencies.

P_f=40-30=10

kW.

\eta_{th}=40/100=0.40

\eta_{mech}=30/40=0.75

and

\eta_{overall}=30/100=0.30

Answer10 kW; thermal 40%, mechanical 75%, overall 30%.

Equation recap

P_i=W_{\mathrm{cycle}}fn,\qquad P_b=T\omega,\qquad P_f=P_i-P_b

Here f is cycles per second per cylinder and n is the cylinder count.

\eta_{\mathrm{th}}=\frac{P_i}{P_{\mathrm{in}}},\quad \eta_{\mathrm{mech}}=\frac{P_b}{P_i},\quad \eta_{\mathrm{overall}}=\frac{P_b}{P_{\mathrm{in}}}

Input power = calorific value × fuel mass-flow rate.

Common mistakes to avoid

Using rpm/60 for four-stroke cycle frequency.

Each cylinder needs two revolutions per cycle.

Calling indicated power the useful shaft output.

Brake power is the shaft output after mechanical losses.

Key takeaways

Petrol and diesel cycles differ in ignition and idealised heat addition.
Indicator loop area gives work per cycle.
Separate fuel, indicated and brake power when calculating efficiency.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Engine Cycles and Efficiencies

40 min 3.11 Engineering Physics