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Engines.

A car engine turns thousands of times a minute, pushed by burning fuel. How does a small fire in a metal cylinder become a turning wheel?

Explore the scene Interactive article

01 / The experiment

Four strokes, one loop.

Change the engine speed and the throttle, then switch on Draw the P–V loop to watch the pressure and volume trace out each cycle's work.

Still of the Engines 3D scene, which explores: Why does squeezing the fuel and air before they burn get more work out of the same fuel?
Interactive scene

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One cylinder of a typical two-litre petrol engine (86 mm bore, 86 mm stroke), shown 60 times slower than it runs. Pressures follow an ideal Otto cycle in which the fuel burns the instant the spark fires.The cycle is idealised. No heat leaks into the metal, nothing rubs, the gas flows only in its own stroke, and the burning takes no time. The cams are drawn as real ones, so each valve opens a little before its stroke and shuts a little after it. A real petrol engine turns about a third of its fuel's energy into work, not the 50 to 65 % this ideal gives.

02 / Three loads

Same cylinder, three loops.

The throttle sets how big each loop is; the engine speed sets how many loops a second.

Waiting at the lights01
pressurechamber, 55 cm³600 cm³volume

Idle

The throttle is nearly shut. Thin air makes a small loop, and the piston wastes a fifth of it pulling against the partial vacuum.

Throttle (intake)
30 kPa
Work per cycle
159 J
Power strokes
6.7 a second
Power, one cylinder
1.1 kW
Steady on a main road02
pressurechamber, 55 cm³600 cm³volume

Cruising

Half-open, the loop is twice as big, and the engine turns faster too. Power is the work in each loop times the loops per second.

Throttle (intake)
60 kPa
Work per cycle
370 J
Power strokes
21 a second
Power, one cylinder
7.7 kW
Overtaking uphill03
pressurechamber, 55 cm³600 cm³volume

Full power

Wide open, a full charge burns in every cycle and almost nothing goes on breathing. Fifty-four big loops a second.

Throttle (intake)
100 kPa
Work per cycle
652 J
Power strokes
54 a second
Power, one cylinder
35 kW
The big idea

The area of the pressure–volume loop is the work done in one cycle. Power is that work times the number of cycles each second, one for every two turns of the crank.

P = W × rpm ÷ 120

Suck, squeeze, bang, blow

Inside a car’s engine, a metal plug called a piston slides up and down in a closed tube, the cylinder, many times a second. A connecting rod joins it to a crankshaft, whose offset crank turns the up-and-down motion into rotation, as your leg turns a bicycle pedal. A counterweight on the far side of the crank balances the swing.

A petrol engine repeats four steps, called strokes, each lasting half a turn of the crank:

  1. Intake. The piston moves down with the intake valve open, drawing in air with a fine mist of petrol.
  2. Compression. Both valves close and the rising piston squeezes the mixture into a small space at the top.
  3. Power. A spark plug fires. The mixture burns in a flash, its pressure leaps, and it drives the piston down hard.
  4. Exhaust. The exhaust valve opens and the rising piston pushes the burnt gas out.

That is two turns of the crank for every power stroke. Egg-shaped cams press on cup-shaped bucket followers to push the valves open against their springs; the camshafts turn at half the crank’s speed, so each valve opens once every two turns.

A cutaway engine

The Scene is cut through the middle, like the sectioned engines in museums and workshops, with the cut faces painted red. The cylinder is bored into a cast-iron block, round which a water jacket carries coolant to take heat away. An aluminium cylinder head closes the top. Its curved ports lead the mixture in and the exhaust out, and each is sealed by a valve on a hard ring, its seat. Piston rings in grooves round the piston seal it against the cylinder wall, and a hollow gudgeon pin joins it to the rod. The spark plug’s white ceramic insulator keeps its high voltage from leaking into the metal round it. Switch on Labels to name the parts.

Pressure times volume is work

When gas pushes a piston, the work it does is its pressure times the change in volume it sweeps out. Plot the gas pressure against the cylinder volume through all four strokes and you get a closed loop. The area inside it is the work the gas did on the piston in one cycle.

During compression the piston does work on the gas; after the spark, the hot gas at much higher pressure gives back far more on the way down. The difference, the shaded area, is what turns the wheels. Below it sits a thin, flat loop running the other way: the work the piston spends breathing, drawing fresh charge in and pushing exhaust out.

Try it: choose On under Draw the P–V loop, then slide Throttle (intake pressure) from 30 kPa up to 100 kPa. The tall loop grows and the pumping loop in the corner shrinks.

Back to the experiment

Each cycle does about the same work whatever the speed, so power, the work done each second, goes up in step with engine speed. Half-open at 2,000 revolutions a minute, this cylinder does about 370 joules per cycle and completes about 17 cycles a second, roughly 6 kilowatts. A four-cylinder engine has four of them.

How the throttle works

The accelerator pedal opens a flap, the throttle, in the air intake. Nearly closed, it lets air in slowly, so the pressure in the intake falls well below the air outside. Each intake stroke then fills the cylinder with thinner air, the injector adds fuel to match, and the whole loop shrinks. The piston must also pull against that partial vacuum, which is why an engine wastes a bigger share of its fuel when ticking over than when working hard.

Why squeeze first?

The compression ratio is how many times smaller the gas volume is at the top of the stroke than at the bottom. The more the mixture is squeezed, the more it expands after burning, and the more of its heat becomes work before the exhaust valve opens. For the ideal cycle the share of heat turned into work is

1 − r^(1−γ),

where r is the compression ratio and γ, about 1.4 for air, describes how gas heats as it is compressed. A ratio of 10 gives 60 %; 6 gives 51 %; 14 gives 65 %. Petrol engines stop at about 10 to 13, because squeezing harder heats the mixture enough to explode on its own before the spark, a damaging knock. Diesel engines use that effect deliberately: they squeeze plain air 15 to 20 times, then spray in fuel that ignites in the heat.

What this model leaves out

This is the ideal Otto cycle, a textbook model, not a measured engine. Real burning takes a few thousandths of a second, so the pressure peak is lower and rounder; heat leaks into the cooling water; friction and the pumps for oil and water take their share; and real valves open early and close late to help the gas flow, as the drawn cams do, though the pressures here ignore it. Together these bring a real engine’s efficiency down to about 30 to 40 % at best. The model also adds a fixed amount of heat per kilogram of charge, about two thirds of what the fuel holds, as a rough allowance for those losses. The motion is shown 60 times slower than real, the gas colours are a guide rather than what you would see, and only one cylinder is drawn.

04 / Learn this in a course

Practise it, step by step.

This lesson teaches the topic with checked questions.

  1. Engines Physics · Machines at work