Working Principles of the Four-Stroke Gasoline Internal Combustion Engine

Turn the key in a car, and drops of gasoline begin burning inside metal cylinders, each one shoving a piston about twenty five times a second. This lecture follows one cylinder through its four stroke cycle, and tracks how the chemical energy in the fuel becomes work on a turning shaft. Here is where we are going. Energy changes form, from fuel, to heat, to pressure, to work, and the engine does it in four strokes: intake, compression, power, and exhaust. Here is one cylinder, cut open. The cylinder itself is a smooth bore, closed at the top by the cylinder head. Inside it slides the piston, sealed against the wall by rings. Everything happens in the small space above it. Under the piston, a connecting rod links it to the crankshaft. The crank arm swings the bottom of the rod around a circle. In the head sit two valves. The intake valve lets in the mixture of air and fuel, and the exhaust valve lets burned gas out. Between them stands the spark plug. Now turn the crank. The rod changes the crank's rotation into straight up and down sliding of the piston, and it works just as well in reverse. Notice the two places where the piston stops and turns around. The top is top dead center, the bottom is bottom dead center, and one trip between them is a stroke, half a turn of the crank. Bring it back to the top, and we are ready. One full cycle takes four strokes, so the crank turns twice for every single power stroke. Intake. The intake valve opens and the piston slides down. The falling pressure draws a fresh charge of air, with a fine mist of fuel, in through the port. Compression. Both valves are shut, and the piston rises, squeezing the charge to about one ninth of its starting volume. Squeezed that hard, the gas heats up and its pressure climbs. Power. Near the top the spark plug fires. A flame races through the mixture in a few thousandths of a second, and the hot gas, now at many times its earlier pressure, drives the piston down. That is the only stroke that delivers work. The other three are carried through by the spinning crankshaft and its heavy flywheel, or by the other cylinders of the engine. Exhaust. The exhaust valve opens, and the rising piston pushes the spent gas out. Then the exhaust valve closes, the intake valve opens again, and the cycle starts over. Four strokes, two turns of the crank, one push. Next we look inside that push, and follow the energy from the fuel to the crankshaft.

So where does the push come from? Gasoline is a blend of hydrocarbons, and octane is a good representative. It burns with oxygen from the air to make carbon dioxide and water, releasing heat. The products hold less chemical energy than the reactants did. The difference comes out as heat, about forty four megajoules for every kilogram of gasoline, so burning a mass m f of fuel releases m f times that. Set free inside a closed cylinder, that heat drives the gas past two thousand kelvin. For a gas, p V equals m R T, so at fixed volume a hotter gas means a higher pressure. And pressure is what pushes the piston. Pressure is force per unit area. On a piston crown of area A, the gas pushes with a force p times A. On the right, I will draw that pressure against the volume above the piston. Let the piston move a small distance d x. The force does work p A d x, and A times d x is exactly the small volume swept, d V. Add those pieces over a whole stroke, and the work is the integral of p d V. Work is the area under a curve of pressure against volume. Now trace one ideal cycle. Intake fills the cylinder at about atmospheric pressure, while the volume grows from the small clearance volume up to the whole cylinder. Compression runs from state one to state two. It is too quick for much heat to leak away, so the pressure climbs steeply as the volume shrinks. Then the spark. The burn is so fast that the piston hardly moves, so the heat arrives at nearly constant volume, and the pressure jumps from state two to state three. The power stroke is the expansion from three to four, the hot gas pushing the piston all the way down. At the bottom the exhaust valve opens and the pressure drops. Then the exhaust stroke sweeps the rest out along the bottom line, back to where we began. Now read the work straight off the picture. During expansion the gas does work on the piston, equal to all the area under the top curve. During compression the piston does work on the gas instead: the area under the bottom curve, which has to be paid back. Take one from the other. The shared part cancels, and what is left is the area enclosed by the loop, the net work one cylinder delivers every cycle. So the chain is complete. Fuel becomes heat, heat becomes pressure, and pressure acting through the swept volume becomes work on the crankshaft.

We have the work. Now, what did it cost? Efficiency is the net work out, divided by the heat the fuel put in. Net work is the heat in minus the heat thrown away with the exhaust, so efficiency is one minus heat out over heat in. In the ideal cycle both heats are added and removed at constant volume, so each is proportional to a temperature change: heat in from state two to three, heat out from four back to one. Along the two adiabats, the temperature ratio depends only on the compression ratio r, the full volume over the clearance volume, raised to the power gamma minus one. Gamma is about one point four for air. Those equal ratios make the temperatures cancel, and we are left with the Otto efficiency: one minus one over r to the gamma minus one. It depends only on how hard the engine compresses. Now put in numbers. Here is that formula plotted against r. At a compression ratio of four, the ideal engine turns about forty three percent of the heat into work. At eight, fifty six percent. At ten, sixty. Squeeze harder still and it keeps climbing, but ever more slowly. So why do gasoline engines stop near ten to thirteen? Squeezing heats the mixture, and too much heat makes it ignite on its own before the spark. That is knock, and it can wreck a piston. A fuel's octane rating measures how well it resists. Real engines also fall below the ideal curve. Heat leaks into the cylinder walls, friction drags on the moving parts, and the burn takes time. A good gasoline engine turns roughly a third of its fuel energy into work, and the rest leaves as heat. Let's gather it up. Four strokes take two turns of the crank, and only one of them delivers work. The valves time the flow of gas in and out, and the spark times the burn. Burning fuel raises the gas pressure, and the work it does is the integral of p d V, the area of the loop. And efficiency climbs with compression ratio, until knock sets the limit. That, in one cylinder, is how a gasoline engine works.