# Working Principles of the Four-Stroke Gasoline Internal Combustion Engine > A first look inside a gasoline engine, built for beginning engineering students. One cylinder is drawn to scale and set in motion: the cylinder, piston, connecting rod, crankshaft, valves and spark plug, then the intake, compression, power and exhaust strokes that take two turns of the crank. The lecture then follows the energy, from the chemistry of burning fuel, to gas pressure, to work as the integral of p dV and the area of the Otto cycle loop, and ends with why the compression ratio sets the efficiency and why knock limits it. - Canonical watch page: [Working Principles of the Four-Stroke Gasoline Internal Combustion Engine](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine) - Publisher: [Academa, Inc.](https://academa.ai) - Subject: Engineering - Published: 2026-10-05T16:23:32.290Z - Updated: 2026-10-05T16:23:32.290Z - Duration: PT457S (7 minutes 37 seconds) - Chapters: 3 - Views: 4 - Language: en-US - Access: Free - Video stream: [HLS content](https://academa.ai/media/l/01M46CT1ZEF8KJE0SG50T7XMW7/0/dark/master.m3u8) - Embed: [Player](https://academa.ai/embed/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine) - Audiovisual record: [Semantic JSON](https://academa.ai/media/l/01M46CT1ZEF8KJE0SG50T7XMW7/0/semantic.json) - Thumbnail: [Image](https://academa.ai/media/l/01M46CT1ZEF8KJE0SG50T7XMW7/0/dark/poster.jpg) ## Description How a four-stroke gasoline engine works: the parts of one cylinder, the four strokes, and how burning fuel becomes work on the crankshaft. ## Chapters - [00:00–02:42.611 · One Cylinder, Four Strokes](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=0) - [02:42.611–05:20.023 · From Fuel to Work](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=162.61085416666663) - [05:20.023–07:37 · How Much of the Heat Becomes Work](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=320.0233333333333) ## Transcript ### [00:00 · One Cylinder, Four Strokes](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=0) 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. ### [02:42.611 · From Fuel to Work](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=162.61085416666663) 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. ### [05:20.023 · How Much of the Heat Becomes Work](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=320.0233333333333) 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. ## About Academa, Inc. Academa makes technical knowledge easier to understand through visual lectures and lets learners request new lecture videos on the topics they need. ## Complete audiovisual record Immutable source: [semantic.json](https://academa.ai/media/l/01M46CT1ZEF8KJE0SG50T7XMW7/0/semantic.json) Record version: 1. Render attempt: 0. ### How to read this timeline Each scene owns its object identifiers. A beat's board is the complete board when listed, empty when marked empty, and unchanged from the nearest earlier listed board in the same scene when marked unchanged. Action times are absolute positions in the published video. ### Scene 1: [One Cylinder, Four Strokes](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=0) Span: 00:00–02:42.611 (0s–162.61085416666663s). #### Objects - bdc: a Line \[gray\] labelled "upright("BDC")" drawn in engine (start=(-1.8, 2.9), end=(-1.1, 2.9), dashed=True) - card: a Title that says "Introduction to Thermal Engineering — Working Principles of the Four-Stroke Gasoline Internal Combustion Engine" - crank: a VariableNumber - crank\_arm: a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…) - crank\_path: a Circle \[gray\] drawn in engine (radius=1.2) - engine: a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)) - flow\_in: a Vector \[green\] drawn in engine (start=(-2.0, 6.9), end=(-0.8, 5.9)) - flow\_out: a Vector \[magenta\] drawn in engine (start=(0.8, 5.9), end=(2.0, 6.9)) - head: a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)) - heading: a Heading that says "Inside One Cylinder" - lift\_in: a VariableNumber - lift\_out: a VariableNumber - name\_cyl: a Point \[text\] labelled "upright("cylinder")" drawn in engine (location=(1.0, 2.3), show\_marker=False) - name\_in: a Point \[text\] labelled "upright("intake valve")" drawn in engine (location=(-0.55, 6.5), show\_marker=False) - name\_out: a Point \[text\] labelled "upright("exhaust valve")" drawn in engine (location=(0.55, 6.5), show\_marker=False) - name\_piston: a Point \[text\] labelled "upright("piston")" drawn in engine (location=(0.95, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.…, show\_marker=False) - name\_plug: a Point \[text\] labelled "upright("spark plug")" drawn in engine (location=(0.0, 6.8999999999999995), show\_marker=False) - name\_rod: a Point \[text\] labelled "upright("connecting rod")" drawn in engine (location=((((1.2 \* sin((crank \* 0.017453292519943295))) + 0.0) / 2.0), (…, show\_marker=False) - piston: a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6) - plug: a Line \[yellow\] drawn in engine (start=(0.0, 5.6), end=(0.0, 6.8999999999999995)) - point: a Point \[yellow\] drawn in engine (location=(0.0, 5.45)) - polygon: a Polygon \[green\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.35) - polygon\_2: a Polygon \[red\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.35) - polygon\_3: a Polygon \[gray\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.35) - promise: a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$" - rod: a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…) - shaft: a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine - spark: a Point \[yellow\] drawn in engine (location=(0.0, 5.4799999999999995), marker\_radius=0.14) - stem\_in: a Line \[green\] drawn in engine (start=(-0.55, (5.6 - lift\_in)), end=(-0.55, (6.5 - lift\_in))) - stem\_out: a Line \[magenta\] drawn in engine (start=(0.55, (5.6 - lift\_out)), end=(0.55, (6.5 - lift\_out))) - strokes: a Table \[text\] that says "Stroke Piston Valves Intake down intake open Compression up both closed Power down both closed Exhaust up exhaust open" (rows=(('Stroke', 'Piston', 'Valves'), ('Intake', 'down', 'intake ope…, header=True) - tdc: a Line \[gray\] labelled "upright("TDC")" drawn in engine (start=(-1.8, 5.3), end=(-1.1, 5.3), dashed=True) - valve\_in: a Line \[green\] drawn in engine (start=(-0.85, (5.6 - lift\_in)), end=(-0.25, (5.6 - lift\_in))) - valve\_out: a Line \[magenta\] drawn in engine (start=(0.25, (5.6 - lift\_out)), end=(0.85, (5.6 - lift\_out))) - wall\_l: a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)) - wall\_r: a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)) #### Beats ##### [00:00](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=0) Narration: 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. Board: Empty. Actions: - [00:00](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=0): card is shown on the screen, written out. - [00:1.52](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=1.520479156684236): card: enter:write-left-to-right. - [00:17.28](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=17.28): card is hidden from the screen — left the board. ##### [00:18.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=18.48) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [00:18.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=18.48): heading is shown on the screen, written out. - [00:20.6](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=20.6): promise is shown on the screen, written out. - [00:26.24](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=26.24): strokes is shown on the screen, written out. - [00:27.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=27.479999999999997): strokes is shown on the screen, written out. - [00:28.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=28.4): strokes is shown on the screen, written out. - [00:29.24](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=29.24): strokes is shown on the screen, written out. - [00:29.84](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=29.839999999999996): strokes is shown on the screen, written out. - [00:30.94](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=30.94): promise moves to a new place on the board. - [00:30.94](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=30.94): strokes moves to a new place on the board. ##### [00:31.54](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=31.54) Narration: Here is one cylinder, cut open. The cylinder itself is a smooth bore, closed at the top by the cylinder head. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder" Actions: - [00:31.54](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=31.54): engine is shown on the screen, written out. - [00:34.12](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=34.120000000000005): wall\_l is shown on the screen, written out. - [00:34.12](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=34.120000000000005): wall\_r is shown on the screen, written out. - [00:34.52](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=34.519999999999996): name\_cyl is shown on the screen, written out. - [00:37.72](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=37.72): head is shown on the screen, written out. ##### [00:38.98](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=38.98) Narration: Inside it slides the piston, sealed against the wall by rings. Everything happens in the small space above it. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); name\_cyl — a Point \[text\] labelled "upright("cylinder")" drawn in engine (location=(1.0, 2.3), show\_marker=False); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)) Actions: - [00:40.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=40.31999999999999): piston is shown on the screen, written out. - [00:41.08](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=41.07999999999999): name\_piston is shown on the screen, written out. - [00:44.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=44.47999999999999): point is shown on the screen, grown. ##### [00:46.44](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=46.44) Narration: Under the piston, a connecting rod links it to the crankshaft. The crank arm swings the bottom of the rod around a circle. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); name\_cyl — a Point \[text\] labelled "upright("cylinder")" drawn in engine (location=(1.0, 2.3), show\_marker=False); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); name\_piston — a Point \[text\] labelled "upright("piston")" drawn in engine (location=(0.95, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.…, show\_marker=False); point — a Point \[yellow\] drawn in engine (location=(0.0, 5.45)) Actions: - [00:46.853](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=46.8532269344843): point is hidden from the screen. - [00:47.8](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=47.8): rod is shown on the screen, written out. - [00:48.44](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=48.44): name\_rod is shown on the screen, written out. - [00:49](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=48.99999999999999): shaft is shown on the screen, written out. - [00:50.6](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=50.599999999999994): crank\_arm is shown on the screen, written out. - [00:52.6](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=52.59999999999999): crank\_path is shown on the screen, written out. ##### [00:53.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=53.919999999999995) Narration: 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. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); name\_cyl — a Point \[text\] labelled "upright("cylinder")" drawn in engine (location=(1.0, 2.3), show\_marker=False); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); name\_piston — a Point \[text\] labelled "upright("piston")" drawn in engine (location=(0.95, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.…, show\_marker=False); rod — a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…); name\_rod — a Point \[text\] labelled "upright("connecting rod")" drawn in engine (location=((((1.2 \* sin((crank \* 0.017453292519943295))) + 0.0) / 2.0), (…, show\_marker=False); shaft — a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine; crank\_arm — a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…); crank\_path — a Circle \[gray\] drawn in engine (radius=1.2) Actions: - [00:56.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=56.47999999999998): valve\_in is shown on the screen, written out. - [00:56.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=56.47999999999998): stem\_in is shown on the screen, written out. - [00:56.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=56.47999999999998): name\_in is shown on the screen, written out. - [00:59.6](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=59.59999999999998): valve\_out is shown on the screen, written out. - [00:59.6](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=59.59999999999998): stem\_out is shown on the screen, written out. - [00:59.6](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=59.59999999999998): name\_out is shown on the screen, written out. - [01:3.36](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=63.359999999999985): plug is shown on the screen, written out. - [01:3.36](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=63.359999999999985): name\_plug is shown on the screen, written out. ##### [01:4.84](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=64.83999999999999) Narration: 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. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); name\_cyl — a Point \[text\] labelled "upright("cylinder")" drawn in engine (location=(1.0, 2.3), show\_marker=False); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); name\_piston — a Point \[text\] labelled "upright("piston")" drawn in engine (location=(0.95, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.…, show\_marker=False); rod — a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…); name\_rod — a Point \[text\] labelled "upright("connecting rod")" drawn in engine (location=((((1.2 \* sin((crank \* 0.017453292519943295))) + 0.0) / 2.0), (…, show\_marker=False); shaft — a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine; crank\_arm — a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…); crank\_path — a Circle \[gray\] drawn in engine (radius=1.2); valve\_in — a Line \[green\] drawn in engine (start=(-0.85, (5.6 - lift\_in)), end=(-0.25, (5.6 - lift\_in))); stem\_in — a Line \[green\] drawn in engine (start=(-0.55, (5.6 - lift\_in)), end=(-0.55, (6.5 - lift\_in))); name\_in — a Point \[text\] labelled "upright("intake valve")" drawn in engine (location=(-0.55, 6.5), show\_marker=False); valve\_out — a Line \[magenta\] drawn in engine (start=(0.25, (5.6 - lift\_out)), end=(0.85, (5.6 - lift\_out))); stem\_out — a Line \[magenta\] drawn in engine (start=(0.55, (5.6 - lift\_out)), end=(0.55, (6.5 - lift\_out))); name\_out — a Point \[text\] labelled "upright("exhaust valve")" drawn in engine (location=(0.55, 6.5), show\_marker=False); plug — a Line \[yellow\] drawn in engine (start=(0.0, 5.6), end=(0.0, 6.8999999999999995)); name\_plug — a Point \[text\] labelled "upright("spark plug")" drawn in engine (location=(0.0, 6.8999999999999995), show\_marker=False) Actions: - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): piston is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): name\_piston is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): rod is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): name\_rod is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): crank\_arm is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): polygon is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): polygon\_2 is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): polygon\_3 is redrawn as the numbers it depends on change. - [01:5.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.55999999999997): crank ticks to 180.0. - [01:5.96](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.95999999999998): name\_cyl is hidden from the screen. - [01:5.96](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.95999999999998): name\_piston is hidden from the screen. - [01:5.96](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.95999999999998): name\_rod is hidden from the screen. - [01:5.96](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.95999999999998): name\_in is hidden from the screen. - [01:5.96](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.95999999999998): name\_out is hidden from the screen. - [01:5.96](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=65.95999999999998): name\_plug is hidden from the screen. - [01:10.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=70.03999999999998): piston is redrawn as the numbers it depends on change. - [01:10.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=70.03999999999998): rod is redrawn as the numbers it depends on change. - [01:10.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=70.03999999999998): crank\_arm is redrawn as the numbers it depends on change. - [01:10.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=70.03999999999998): polygon is redrawn as the numbers it depends on change. - [01:10.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=70.03999999999998): polygon\_2 is redrawn as the numbers it depends on change. - [01:10.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=70.03999999999998): polygon\_3 is redrawn as the numbers it depends on change. - [01:10.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=70.03999999999998): crank ticks to 360.0. ##### [01:14.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=74.32) Narration: 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. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); rod — a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…); shaft — a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine; crank\_arm — a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…); crank\_path — a Circle \[gray\] drawn in engine (radius=1.2); valve\_in — a Line \[green\] drawn in engine (start=(-0.85, (5.6 - lift\_in)), end=(-0.25, (5.6 - lift\_in))); stem\_in — a Line \[green\] drawn in engine (start=(-0.55, (5.6 - lift\_in)), end=(-0.55, (6.5 - lift\_in))); valve\_out — a Line \[magenta\] drawn in engine (start=(0.25, (5.6 - lift\_out)), end=(0.85, (5.6 - lift\_out))); stem\_out — a Line \[magenta\] drawn in engine (start=(0.55, (5.6 - lift\_out)), end=(0.55, (6.5 - lift\_out))); plug — a Line \[yellow\] drawn in engine (start=(0.0, 5.6), end=(0.0, 6.8999999999999995)) Actions: - [01:18.96](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=78.96): tdc is shown on the screen, written out. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): piston is redrawn as the numbers it depends on change. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): rod is redrawn as the numbers it depends on change. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): crank\_arm is redrawn as the numbers it depends on change. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): polygon is redrawn as the numbers it depends on change. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): polygon\_2 is redrawn as the numbers it depends on change. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): polygon\_3 is redrawn as the numbers it depends on change. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): bdc is shown on the screen, written out. - [01:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=81.03999999999999): crank ticks to 540.0. ##### [01:26.54](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.53999999999999) Narration: 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. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); rod — a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…); shaft — a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine; crank\_arm — a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…); crank\_path — a Circle \[gray\] drawn in engine (radius=1.2); valve\_in — a Line \[green\] drawn in engine (start=(-0.85, (5.6 - lift\_in)), end=(-0.25, (5.6 - lift\_in))); stem\_in — a Line \[green\] drawn in engine (start=(-0.55, (5.6 - lift\_in)), end=(-0.55, (6.5 - lift\_in))); valve\_out — a Line \[magenta\] drawn in engine (start=(0.25, (5.6 - lift\_out)), end=(0.85, (5.6 - lift\_out))); stem\_out — a Line \[magenta\] drawn in engine (start=(0.55, (5.6 - lift\_out)), end=(0.55, (6.5 - lift\_out))); plug — a Line \[yellow\] drawn in engine (start=(0.0, 5.6), end=(0.0, 6.8999999999999995)); tdc — a Line \[gray\] labelled "upright("TDC")" drawn in engine (start=(-1.8, 5.3), end=(-1.1, 5.3), dashed=True); bdc — a Line \[gray\] labelled "upright("BDC")" drawn in engine (start=(-1.8, 2.9), end=(-1.1, 2.9), dashed=True) Actions: - [01:26.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.67999999999999): piston is redrawn as the numbers it depends on change. - [01:26.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.67999999999999): rod is redrawn as the numbers it depends on change. - [01:26.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.67999999999999): crank\_arm is redrawn as the numbers it depends on change. - [01:26.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.67999999999999): polygon is redrawn as the numbers it depends on change. - [01:26.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.67999999999999): polygon\_2 is redrawn as the numbers it depends on change. - [01:26.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.67999999999999): polygon\_3 is redrawn as the numbers it depends on change. - [01:26.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=86.67999999999999): crank ticks to 720.0. - [01:33.84](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=93.83999999999999): strokes (the "row=4" part) is indicated — a transient flash. ##### [01:36.22](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=96.22) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [01:36.44](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=96.44): strokes (the "row=2" part) is emphasized. - [01:38.52](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=98.52): valve\_in is redrawn as the numbers it depends on change. - [01:38.52](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=98.52): stem\_in is redrawn as the numbers it depends on change. - [01:38.52](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=98.52): polygon is shown on the screen, written out. - [01:38.52](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=98.52): lift\_in ticks to 0.2. - [01:39.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=99.48): piston is redrawn as the numbers it depends on change. - [01:39.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=99.48): rod is redrawn as the numbers it depends on change. - [01:39.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=99.48): crank\_arm is redrawn as the numbers it depends on change. - [01:39.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=99.48): polygon is redrawn as the numbers it depends on change. - [01:39.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=99.48): polygon\_2 is redrawn as the numbers it depends on change. - [01:39.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=99.48): polygon\_3 is redrawn as the numbers it depends on change. - [01:39.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=99.48): crank ticks to 900.0. - [01:41.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=101.67999999999999): flow\_in is shown on the screen, written out. - [01:45.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=105.32): flow\_in is hidden from the screen. ##### [01:46.56](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=106.56) Narration: 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. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); rod — a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…); shaft — a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine; crank\_arm — a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…); crank\_path — a Circle \[gray\] drawn in engine (radius=1.2); valve\_in — a Line \[green\] drawn in engine (start=(-0.85, (5.6 - lift\_in)), end=(-0.25, (5.6 - lift\_in))); stem\_in — a Line \[green\] drawn in engine (start=(-0.55, (5.6 - lift\_in)), end=(-0.55, (6.5 - lift\_in))); valve\_out — a Line \[magenta\] drawn in engine (start=(0.25, (5.6 - lift\_out)), end=(0.85, (5.6 - lift\_out))); stem\_out — a Line \[magenta\] drawn in engine (start=(0.55, (5.6 - lift\_out)), end=(0.55, (6.5 - lift\_out))); plug — a Line \[yellow\] drawn in engine (start=(0.0, 5.6), end=(0.0, 6.8999999999999995)); tdc — a Line \[gray\] labelled "upright("TDC")" drawn in engine (start=(-1.8, 5.3), end=(-1.1, 5.3), dashed=True); bdc — a Line \[gray\] labelled "upright("BDC")" drawn in engine (start=(-1.8, 2.9), end=(-1.1, 2.9), dashed=True); polygon — a Polygon \[green\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.35) Actions: - [01:46.88](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=106.88): strokes (the "row=2" part) is no longer emphasized. - [01:46.88](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=106.88): strokes (the "row=3" part) is emphasized. - [01:48.88](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=108.88): valve\_in is redrawn as the numbers it depends on change. - [01:48.88](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=108.88): stem\_in is redrawn as the numbers it depends on change. - [01:48.88](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=108.88): lift\_in ticks to 0.0. - [01:49.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=109.92): piston is redrawn as the numbers it depends on change. - [01:49.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=109.92): rod is redrawn as the numbers it depends on change. - [01:49.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=109.92): crank\_arm is redrawn as the numbers it depends on change. - [01:49.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=109.92): polygon is redrawn as the numbers it depends on change. - [01:49.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=109.92): polygon\_2 is redrawn as the numbers it depends on change. - [01:49.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=109.92): polygon\_3 is redrawn as the numbers it depends on change. - [01:49.92](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=109.92): crank ticks to 1080.0. - [01:55.68](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=115.67999999999999): polygon is indicated — a transient flash. ##### [01:58.58](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=118.58) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [01:58.76](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=118.75999999999999): strokes (the "row=3" part) is no longer emphasized. - [01:58.76](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=118.75999999999999): strokes (the "row=4" part) is emphasized. - [02:1.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=121.39999999999999): spark is shown on the screen, written out. - [02:2.44](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=122.44): polygon is hidden from the screen. - [02:2.44](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=122.44): polygon\_2 is shown on the screen, faded in. - [02:2.84](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=122.83999999999999): spark is hidden from the screen. - [02:9.16](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=129.15999999999997): piston is redrawn as the numbers it depends on change. - [02:9.16](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=129.15999999999997): rod is redrawn as the numbers it depends on change. - [02:9.16](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=129.15999999999997): crank\_arm is redrawn as the numbers it depends on change. - [02:9.16](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=129.15999999999997): polygon\_2 is redrawn as the numbers it depends on change. - [02:9.16](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=129.15999999999997): polygon\_3 is redrawn as the numbers it depends on change. - [02:9.16](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=129.15999999999997): crank ticks to 1260.0. ##### [02:11.36](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=131.35999999999999) Narration: 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. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); rod — a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…); shaft — a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine; crank\_arm — a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…); crank\_path — a Circle \[gray\] drawn in engine (radius=1.2); valve\_in — a Line \[green\] drawn in engine (start=(-0.85, (5.6 - lift\_in)), end=(-0.25, (5.6 - lift\_in))); stem\_in — a Line \[green\] drawn in engine (start=(-0.55, (5.6 - lift\_in)), end=(-0.55, (6.5 - lift\_in))); valve\_out — a Line \[magenta\] drawn in engine (start=(0.25, (5.6 - lift\_out)), end=(0.85, (5.6 - lift\_out))); stem\_out — a Line \[magenta\] drawn in engine (start=(0.55, (5.6 - lift\_out)), end=(0.55, (6.5 - lift\_out))); plug — a Line \[yellow\] drawn in engine (start=(0.0, 5.6), end=(0.0, 6.8999999999999995)); tdc — a Line \[gray\] labelled "upright("TDC")" drawn in engine (start=(-1.8, 5.3), end=(-1.1, 5.3), dashed=True); bdc — a Line \[gray\] labelled "upright("BDC")" drawn in engine (start=(-1.8, 2.9), end=(-1.1, 2.9), dashed=True); polygon\_2 — a Polygon \[red\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.35) Actions: - [02:13.52](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=133.51999999999998): piston is indicated — a transient flash. - [02:16.24](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=136.23999999999998): shaft is indicated — a transient flash. ##### [02:21.04](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=141.04) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [02:21.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=141.4): strokes (the "row=4" part) is no longer emphasized. - [02:21.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=141.4): strokes (the "row=5" part) is emphasized. - [02:23.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=143.4): valve\_out is redrawn as the numbers it depends on change. - [02:23.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=143.4): stem\_out is redrawn as the numbers it depends on change. - [02:23.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=143.4): polygon\_2 is hidden from the screen. - [02:23.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=143.4): polygon\_3 is shown on the screen, written out. - [02:23.4](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=143.4): lift\_out ticks to 0.2. - [02:24.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=144.32): piston is redrawn as the numbers it depends on change. - [02:24.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=144.32): rod is redrawn as the numbers it depends on change. - [02:24.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=144.32): crank\_arm is redrawn as the numbers it depends on change. - [02:24.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=144.32): polygon\_3 is redrawn as the numbers it depends on change. - [02:24.32](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=144.32): crank ticks to 1440.0. - [02:25.08](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=145.07999999999998): flow\_out is shown on the screen, written out. - [02:28.2](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=148.2): valve\_out is redrawn as the numbers it depends on change. - [02:28.2](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=148.2): stem\_out is redrawn as the numbers it depends on change. - [02:28.2](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=148.2): flow\_out is hidden from the screen. - [02:28.2](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=148.2): polygon\_3 is hidden from the screen. - [02:28.2](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=148.2): lift\_out ticks to 0.0. - [02:30](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=149.99999999999997): valve\_in is redrawn as the numbers it depends on change. - [02:30](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=149.99999999999997): stem\_in is redrawn as the numbers it depends on change. - [02:30](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=149.99999999999997): lift\_in ticks to 0.2. - [02:31.88](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=151.88): strokes (the "row=5" part) is no longer emphasized. ##### [02:32.48](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=152.48) Narration: 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. Board: promise — a Math \[text\] that says "$upright("fuel") arrow.r upright("heat") arrow.r upright("pressure") arrow.r upright("work")$"; heading — a Heading that says "Inside One Cylinder"; engine — a Figure (x\_range=(-3.2, 3.2), y\_range=(-1.6, 7.6), aspect=(6.4, 9.2)); wall\_l — a Line \[gray\] drawn in engine (start=(-1.0, 1.9), end=(-1.0, 5.6)); wall\_r — a Line \[gray\] drawn in engine (start=(1.0, 1.9), end=(1.0, 5.6)); head — a Line \[gray\] drawn in engine (start=(-1.0, 5.6), end=(1.0, 5.6)); piston — a Polygon \[blue\] drawn in engine (vertices=((-0.95, (((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((…, fill\_opacity=0.6); rod — a Line \[blue\] drawn in engine (start=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…, end=(0.0, ((1.2 \* cos((crank \* 0.017453292519943295))) + sqrt((12.9…); shaft — a Point \[yellow\] labelled "upright("crankshaft")" drawn in engine; crank\_arm — a Line \[blue\] drawn in engine (end=((1.2 \* sin((crank \* 0.017453292519943295))), (1.2 \* cos((crank…); crank\_path — a Circle \[gray\] drawn in engine (radius=1.2); valve\_in — a Line \[green\] drawn in engine (start=(-0.85, (5.6 - lift\_in)), end=(-0.25, (5.6 - lift\_in))); stem\_in — a Line \[green\] drawn in engine (start=(-0.55, (5.6 - lift\_in)), end=(-0.55, (6.5 - lift\_in))); valve\_out — a Line \[magenta\] drawn in engine (start=(0.25, (5.6 - lift\_out)), end=(0.85, (5.6 - lift\_out))); stem\_out — a Line \[magenta\] drawn in engine (start=(0.55, (5.6 - lift\_out)), end=(0.55, (6.5 - lift\_out))); plug — a Line \[yellow\] drawn in engine (start=(0.0, 5.6), end=(0.0, 6.8999999999999995)); tdc — a Line \[gray\] labelled "upright("TDC")" drawn in engine (start=(-1.8, 5.3), end=(-1.1, 5.3), dashed=True); bdc — a Line \[gray\] labelled "upright("BDC")" drawn in engine (start=(-1.8, 2.9), end=(-1.1, 2.9), dashed=True) Actions: - [02:39.12](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=159.11999999999998): promise is indicated — a transient flash. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): engine is hidden from the screen — left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): wall\_l is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): wall\_r is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): head is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): piston is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): rod is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): shaft is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): crank\_arm is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): crank\_path is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): valve\_in is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): stem\_in is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): valve\_out is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): stem\_out is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): plug is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): tdc is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): bdc is hidden from the screen — engine left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): heading is hidden from the screen — left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): promise is hidden from the screen — left the board. - [02:41.569](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=161.5691875): strokes is hidden from the screen — left the board. ### Scene 2: [From Fuel to Work](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=162.61085416666663) Span: 02:42.611–05:20.023 (162.61085416666663s–320.0233333333333s). #### Objects - blow\_line: a Line \[gray\] drawn in pv (start=(1.0, 2.5), end=(1.0, 1.0)) - burn\_line: a Line \[yellow\] drawn in pv (start=(0.1, 25.118864315095795), end=(0.1, 62.797160787739486)) - compression: a ParametricCurve \[blue\] drawn in pv (function=\) - energy: a Math \[text\] that says "$Q = m\_f thin Q\_"LHV"$" - expansion: a ParametricCurve \[red\] drawn in pv (function=\) - gas\_law: a Math \[text\] that says "$p V = m R T$" - h\_fuel: a Heading that says "Where the Push Comes From" - h\_loop: a Heading that says "Work Is the Loop" - h\_work: a Heading that says "Pressure Does Work" - intake\_line: a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)) - lhv: a Math \[text\] that says "$Q\_"LHV" approx 44 thin upright("MJ/kg")$" - net: a Polygon \[yellow\] drawn in pv (vertices=((0.1, 62.797160787739486), (0.13, 43.49299505075181), (0.16, 3…, fill\_opacity=0.45) - point: a Point \[yellow\] drawn in pv (location=(0.1, 1.0)) - pv: an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25) - reaction: a Math \[text\] that says "$2 upright(C)\_8 upright(H)\_18 + 25 upright(O)\_2 arrow.r 16 upright(C O)\_2 + 18 upright(H)\_2 upright(O)$" - s1: a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)) - s2: a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)) - s3: a Point \[text\] labelled "3" drawn in pv (location=(0.1, 62.797160787739486)) - s4: a Point \[text\] labelled "4" drawn in pv (location=(1.0, 2.5)) - w\_in: a Math \[text\] that says "$W\_"in" = upright("area under") 1 arrow.r 2$" - w\_net: a Math \[text\] that says "$W\_"net" = W\_"out" - W\_"in" = upright("loop area")$" - w\_out: a Math \[text\] that says "$W\_"out" = upright("area under") 3 arrow.r 4$" - work: a Derivation \[text\] that says "$F &= p A \\ dif W &= F dif x = p A dif x \\ dif W &= p dif V \\ W &= integral p dif V$" - work\_in: a Polygon \[blue\] drawn in pv (vertices=((1.0, 1.0), (0.97, 1.0435651612459236), (0.94, 1.0904882865070…) - work\_out: a Polygon \[red\] drawn in pv (vertices=((0.1, 62.797160787739486), (0.13, 43.49299505075181), (0.16, 3…) #### Beats ##### [02:42.611](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=162.61085416666663) Narration: 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. Board: Empty. Actions: - [02:42.611](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=162.61085416666663): h\_fuel is shown on the screen, written out. - [02:47.571](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=167.57085416666663): reaction is shown on the screen, written out. - [02:49.931](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=169.93085416666662): reaction (the "2 upright(C)\_8 upright(H)\_18" part) is emphasized. - [02:50.371](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=170.37085416666662): reaction (the "2 upright(C)\_8 upright(H)\_18" part) is no longer emphasized. - [02:50.371](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=170.37085416666662): reaction (the "25 upright(O)\_2" part) is emphasized. - [02:51.811](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=171.81085416666662): reaction (the "16 upright(C O)\_2" part) is emphasized. - [02:51.811](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=171.81085416666662): reaction (the "25 upright(O)\_2" part) is no longer emphasized. - [02:52.771](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=172.77085416666662): reaction (the "16 upright(C O)\_2" part) is no longer emphasized. - [02:52.771](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=172.77085416666662): reaction (the "18 upright(H)\_2 upright(O)" part) is emphasized. - [02:53.331](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=173.33085416666663): reaction (the "18 upright(H)\_2 upright(O)" part) is no longer emphasized. ##### [02:55.051](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=175.05085416666662) Narration: 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. Board: reaction — a Math \[text\] that says "$2 upright(C)\_8 upright(H)\_18 + 25 upright(O)\_2 arrow.r 16 upright(C O)\_2 + 18 upright(H)\_2 upright(O)$"; h\_fuel — a Heading that says "Where the Push Comes From" Actions: - [03:0.811](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=180.81085416666662): lhv is shown on the screen, written out. - [03:2.571](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=182.57085416666663): lhv (the "44" part) is emphasized. - [03:4.411](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=184.41085416666664): lhv (the "44" part) is no longer emphasized. - [03:6.171](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=186.17085416666663): energy is shown on the screen, written out. ##### [03:8.631](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=188.63085416666664) Narration: 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. Board: reaction — a Math \[text\] that says "$2 upright(C)\_8 upright(H)\_18 + 25 upright(O)\_2 arrow.r 16 upright(C O)\_2 + 18 upright(H)\_2 upright(O)$"; lhv — a Math \[text\] that says "$Q\_"LHV" approx 44 thin upright("MJ/kg")$"; energy — a Math \[text\] that says "$Q = m\_f thin Q\_"LHV"$"; h\_fuel — a Heading that says "Where the Push Comes From" Actions: - [03:16.051](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=196.05085416666662): gas\_law is shown on the screen, written out. - [03:19.011](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=199.0108541666666): gas\_law (the "T" part) is emphasized. - [03:20.091](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=200.09085416666662): gas\_law (the "T" part) is no longer emphasized. - [03:20.091](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=200.09085416666662): gas\_law (the "p" part) is emphasized. - [03:22.211](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=202.21085416666662): gas\_law (the "p" part) is no longer emphasized. - [03:23.371](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=203.37085416666662): energy is hidden from the screen — left the board. - [03:23.371](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=203.37085416666662): gas\_law is hidden from the screen — left the board. - [03:23.371](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=203.37085416666662): h\_fuel is hidden from the screen — left the board. - [03:23.371](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=203.37085416666662): lhv is hidden from the screen — left the board. - [03:23.371](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=203.37085416666662): reaction is hidden from the screen — left the board. ##### [03:24.571](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=204.57085416666663) Narration: 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. Board: Empty. Actions: - [03:24.571](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=204.57085416666663): h\_work is shown on the screen, written out. - [03:29.731](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=209.73085416666663): work is shown on the screen, written out. - [03:32.451](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=212.4508541666666): pv is shown on the screen, written out. ##### [03:36.691](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=216.6908541666666) Narration: 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. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); h\_work — a Heading that says "Pressure Does Work" Actions: - [03:40.651](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=220.65085416666662): work is shown on the screen, written out. - [03:45.131](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=225.1308541666666): work is shown on the screen, written out. ##### [03:47.751](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=227.7508541666666) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [03:50.851](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=230.8508541666666): work is shown on the screen, written out. ##### [03:57.071](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=237.07085416666663) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [03:59.611](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=239.6108541666666): intake\_line is shown on the screen, drawn. - [04:4.331](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=244.3308541666666): point is shown on the screen, grown. - [04:5.731](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=245.7308541666666): s1 is shown on the screen, written out. - [04:6.037](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=246.03661174825896): point is hidden from the screen. ##### [04:7.291](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=247.29085416666663) Narration: 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. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); h\_work — a Heading that says "Pressure Does Work"; intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)) Actions: - [04:7.411](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=247.41085416666664): compression is shown on the screen, drawn. - [04:9.571](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=249.5708541666666): s2 is shown on the screen, written out. ##### [04:16.271](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=256.27085416666665) Narration: 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. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); h\_work — a Heading that says "Pressure Does Work"; intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)); compression — a ParametricCurve \[blue\] drawn in pv (function=\); s2 — a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)) Actions: - [04:24.491](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=264.4908541666666): burn\_line is shown on the screen, drawn. - [04:26.171](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=266.17085416666663): s3 is shown on the screen, written out. ##### [04:27.431](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=267.4308541666666) Narration: The power stroke is the expansion from three to four, the hot gas pushing the piston all the way down. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); h\_work — a Heading that says "Pressure Does Work"; intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)); compression — a ParametricCurve \[blue\] drawn in pv (function=\); s2 — a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)); burn\_line — a Line \[yellow\] drawn in pv (start=(0.1, 25.118864315095795), end=(0.1, 62.797160787739486)); s3 — a Point \[text\] labelled "3" drawn in pv (location=(0.1, 62.797160787739486)) Actions: - [04:28.611](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=268.6108541666666): expansion is shown on the screen, drawn. - [04:30.091](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=270.09085416666665): s4 is shown on the screen, written out. ##### [04:34.191](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=274.19085416666667) Narration: 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. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); h\_work — a Heading that says "Pressure Does Work"; intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)); compression — a ParametricCurve \[blue\] drawn in pv (function=\); s2 — a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)); burn\_line — a Line \[yellow\] drawn in pv (start=(0.1, 25.118864315095795), end=(0.1, 62.797160787739486)); s3 — a Point \[text\] labelled "3" drawn in pv (location=(0.1, 62.797160787739486)); expansion — a ParametricCurve \[red\] drawn in pv (function=\); s4 — a Point \[text\] labelled "4" drawn in pv (location=(1.0, 2.5)) Actions: - [04:36.971](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=276.97085416666664): blow\_line is shown on the screen, drawn. - [04:39.291](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=279.29085416666663): intake\_line is indicated — a transient flash. - [04:42.831](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=282.83085416666665): h\_work is hidden from the screen — left the board. - [04:42.831](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=282.83085416666665): work is hidden from the screen — left the board. ##### [04:44.031](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=284.03085416666664) Narration: 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. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)); compression — a ParametricCurve \[blue\] drawn in pv (function=\); s2 — a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)); burn\_line — a Line \[yellow\] drawn in pv (start=(0.1, 25.118864315095795), end=(0.1, 62.797160787739486)); s3 — a Point \[text\] labelled "3" drawn in pv (location=(0.1, 62.797160787739486)); expansion — a ParametricCurve \[red\] drawn in pv (function=\); s4 — a Point \[text\] labelled "4" drawn in pv (location=(1.0, 2.5)); blow\_line — a Line \[gray\] drawn in pv (start=(1.0, 2.5), end=(1.0, 1.0)) Actions: - [04:44.031](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=284.03085416666664): h\_loop is shown on the screen, written out. - [04:49.731](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=289.73085416666663): w\_out is shown on the screen, written out. - [04:50.571](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=290.57085416666666): work\_out is shown on the screen, faded in. ##### [04:52.771](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=292.77085416666665) Narration: During compression the piston does work on the gas instead: the area under the bottom curve, which has to be paid back. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)); compression — a ParametricCurve \[blue\] drawn in pv (function=\); s2 — a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)); burn\_line — a Line \[yellow\] drawn in pv (start=(0.1, 25.118864315095795), end=(0.1, 62.797160787739486)); s3 — a Point \[text\] labelled "3" drawn in pv (location=(0.1, 62.797160787739486)); expansion — a ParametricCurve \[red\] drawn in pv (function=\); s4 — a Point \[text\] labelled "4" drawn in pv (location=(1.0, 2.5)); blow\_line — a Line \[gray\] drawn in pv (start=(1.0, 2.5), end=(1.0, 1.0)); w\_out — a Math \[text\] that says "$W\_"out" = upright("area under") 3 arrow.r 4$"; h\_loop — a Heading that says "Work Is the Loop"; work\_out — a Polygon \[red\] drawn in pv (vertices=((0.1, 62.797160787739486), (0.13, 43.49299505075181), (0.16, 3…) Actions: - [04:56.691](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=296.69085416666667): work\_in is shown on the screen, faded in. - [04:57.411](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=297.41085416666664): w\_in is shown on the screen, written out. ##### [05:0.351](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=300.35085416666664) Narration: 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. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)); compression — a ParametricCurve \[blue\] drawn in pv (function=\); s2 — a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)); burn\_line — a Line \[yellow\] drawn in pv (start=(0.1, 25.118864315095795), end=(0.1, 62.797160787739486)); s3 — a Point \[text\] labelled "3" drawn in pv (location=(0.1, 62.797160787739486)); expansion — a ParametricCurve \[red\] drawn in pv (function=\); s4 — a Point \[text\] labelled "4" drawn in pv (location=(1.0, 2.5)); blow\_line — a Line \[gray\] drawn in pv (start=(1.0, 2.5), end=(1.0, 1.0)); w\_out — a Math \[text\] that says "$W\_"out" = upright("area under") 3 arrow.r 4$"; w\_in — a Math \[text\] that says "$W\_"in" = upright("area under") 1 arrow.r 2$"; h\_loop — a Heading that says "Work Is the Loop"; work\_out — a Polygon \[red\] drawn in pv (vertices=((0.1, 62.797160787739486), (0.13, 43.49299505075181), (0.16, 3…); work\_in — a Polygon \[blue\] drawn in pv (vertices=((1.0, 1.0), (0.97, 1.0435651612459236), (0.94, 1.0904882865070…) Actions: - [05:2.731](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=302.73085416666663): work\_out is hidden from the screen. - [05:2.731](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=302.73085416666663): work\_in is hidden from the screen. - [05:4.931](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=304.9308541666667): net is shown on the screen, faded in. - [05:6.411](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=306.41085416666664): w\_net is shown on the screen, written out. - [05:9.471](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=309.47085416666664): A box is drawn around w\_net. ##### [05:10.071](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=310.07085416666666) Narration: So the chain is complete. Fuel becomes heat, heat becomes pressure, and pressure acting through the swept volume becomes work on the crankshaft. Board: pv — an Axes (x\_range=(0.0, 1.15), y\_range=(0.0, 70.0), x\_ticks\_every=0.25); intake\_line — a Line \[green\] drawn in pv (start=(0.1, 1.0), end=(1.0, 1.0)); s1 — a Point \[text\] labelled "1" drawn in pv (location=(1.0, 1.0)); compression — a ParametricCurve \[blue\] drawn in pv (function=\); s2 — a Point \[text\] labelled "2" drawn in pv (location=(0.1, 25.118864315095795)); burn\_line — a Line \[yellow\] drawn in pv (start=(0.1, 25.118864315095795), end=(0.1, 62.797160787739486)); s3 — a Point \[text\] labelled "3" drawn in pv (location=(0.1, 62.797160787739486)); expansion — a ParametricCurve \[red\] drawn in pv (function=\); s4 — a Point \[text\] labelled "4" drawn in pv (location=(1.0, 2.5)); blow\_line — a Line \[gray\] drawn in pv (start=(1.0, 2.5), end=(1.0, 1.0)); w\_out — a Math \[text\] that says "$W\_"out" = upright("area under") 3 arrow.r 4$"; w\_in — a Math \[text\] that says "$W\_"in" = upright("area under") 1 arrow.r 2$"; w\_net — a Math \[text\] that says "$W\_"net" = W\_"out" - W\_"in" = upright("loop area")$"; h\_loop — a Heading that says "Work Is the Loop"; net — a Polygon \[yellow\] drawn in pv (vertices=((0.1, 62.797160787739486), (0.13, 43.49299505075181), (0.16, 3…, fill\_opacity=0.45) Actions: - [05:17.411](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=317.4108541666666): net is indicated — a transient flash. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): h\_loop is hidden from the screen — left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): pv is hidden from the screen — left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): intake\_line is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): s1 is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): compression is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): s2 is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): burn\_line is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): s3 is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): expansion is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): s4 is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): blow\_line is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): net is hidden from the screen — pv left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): w\_in is hidden from the screen — left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): w\_net is hidden from the screen — left the board. - [05:18.982](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=318.9816666666667): w\_out is hidden from the screen — left the board. ### Scene 3: [How Much of the Heat Becomes Work](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=320.0233333333333) Span: 05:20.023–07:36.749 (320.0233333333333s–456.7492916666667s). #### Objects - deriv: a Derivation \[text\] that says "$eta &= frac(W\_"net", Q\_"in") \\ &= 1 - frac(Q\_"out", Q\_"in") \\ &= 1 - frac(T\_4 - T\_1, T\_3 - T\_2) \\ frac(T\_2, T\_1) &= frac(T\_3, T\_4) = r^(gamma - 1) \\ eta &= 1 - frac(1, r^(gamma - 1))$" - eta\_axes: an Axes (x\_range=(1.0, 16.0), y\_range=(0.0, 0.8), x\_ticks\_every=2.0) - eta\_curve: a FunctionPlot \[blue\] drawn in eta\_axes (function=\, x\_range=(1.0, 16.0)) - h\_eff: a Heading that says "Efficiency of the Ideal Cycle" - h\_recap: a Heading that says "What to Carry Away" - knock: a Polygon \[red\] labelled "upright("knock")" drawn in eta\_axes (vertices=((13.0, 0.0), (16.0, 0.0), (16.0, 0.8), (13.0, 0.8)), fill\_opacity=0.2) - line: a Line \[yellow\] drawn in eta\_axes (start=(4.0, 0.42565082250148245), end=(0.0, 0.42565082250148245), dashed=True) - line\_2: a Line \[yellow\] drawn in eta\_axes (start=(4.0, 0.42565082250148245), end=(4.0, 0.0), dashed=True) - point: a Point \[yellow\] drawn in eta\_axes (location=(4.0, 0.42565082250148245)) - r\_live: a VariableNumber (initial\_value=4.0, format\_spec='.0f') - real: a Polygon \[gray\] labelled "upright("real engines")" drawn in eta\_axes (vertices=((8.0, 0.28), (13.0, 0.28), (13.0, 0.38), (8.0, 0.38)), fill\_opacity=0.4) - recap: a Block \[text\] that says "Four strokes take two crank turns, and only one of them delivers work. The valves time the gas exchange; the spark times the burn. Burning fuel raises gas pressure, and work is the integral of $p dif V$. Efficiency rises with compression r…" - rider: a PlotPoint \[yellow\] labelled "r = 4" drawn in eta\_axes (target='eta\_curve', x=\) #### Beats ##### [05:20.023](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=320.0233333333333) Narration: We have the work. Now, what did it cost? Efficiency is the net work out, divided by the heat the fuel put in. Board: Empty. Actions: - [05:20.023](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=320.0233333333333): h\_eff is shown on the screen, written out. - [05:23.463](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=323.4633333333333): deriv is shown on the screen, written out. ##### [05:28.723](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=328.7233333333333) Narration: Net work is the heat in minus the heat thrown away with the exhaust, so efficiency is one minus heat out over heat in. Board: h\_eff — a Heading that says "Efficiency of the Ideal Cycle" Actions: - [05:33.423](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=333.4233333333333): deriv is shown on the screen, written out. ##### [05:37.743](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=337.74333333333334) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [05:43.063](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=343.06333333333333): deriv is shown on the screen, written out. - [05:45.263](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=345.2633333333333): deriv (the "T\_3 - T\_2" part) is emphasized. - [05:47.303](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=347.3033333333333): deriv (the "T\_3 - T\_2" part) is no longer emphasized. - [05:47.303](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=347.3033333333333): deriv (the "T\_4 - T\_1" part) is emphasized. - [05:49.503](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=349.50333333333333): deriv (the "T\_4 - T\_1" part) is no longer emphasized. ##### [05:50.103](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=350.1033333333333) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [05:50.943](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=350.9433333333333): deriv is shown on the screen, written out. - [05:58.063](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=358.06333333333333): deriv (the "r^(gamma - 1)" part) is emphasized. - [05:59.023](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=359.0233333333333): deriv (the "r^(gamma - 1)" part) is no longer emphasized. ##### [06:3.643](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=363.6433333333333) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [06:7.703](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=367.7033333333333): deriv is shown on the screen, written out. - [06:12.343](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=372.3433333333333): deriv is indicated — a transient flash. - [06:15.403](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=375.4033333333333): deriv moves to a new place on the board. ##### [06:16.003](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=376.00333333333333) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [06:16.003](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=376.00333333333333): eta\_axes is shown on the screen, written out. - [06:18.783](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=378.7833333333333): eta\_curve is shown on the screen, drawn. - [06:21.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=381.6633333333333): rider is shown on the screen, written out. - [06:23.823](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=383.8233333333333): point is shown on the screen, grown. - [06:23.823](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=383.8233333333333): line is shown on the screen, drawn. - [06:23.823](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=383.8233333333333): line\_2 is shown on the screen, drawn. - [06:25.464](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=385.463898989899): point is hidden from the screen. - [06:25.464](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=385.463898989899): line is hidden from the screen. - [06:25.464](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=385.463898989899): line\_2 is hidden from the screen. ##### [06:26.863](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=386.86333333333334) Narration: At eight, fifty six percent. At ten, sixty. Squeeze harder still and it keeps climbing, but ever more slowly. Board: h\_eff — a Heading that says "Efficiency of the Ideal Cycle"; eta\_axes — an Axes (x\_range=(1.0, 16.0), y\_range=(0.0, 0.8), x\_ticks\_every=2.0); eta\_curve — a FunctionPlot \[blue\] drawn in eta\_axes (function=\, x\_range=(1.0, 16.0)); rider — a PlotPoint \[yellow\] labelled "r = 4" drawn in eta\_axes (target='eta\_curve', x=\) Actions: - [06:27.223](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=387.22333333333336): rider is redrawn as the numbers it depends on change. - [06:27.223](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=387.22333333333336): r\_live ticks to 8.0. - [06:29.303](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=389.3033333333333): rider is redrawn as the numbers it depends on change. - [06:29.303](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=389.3033333333333): r\_live ticks to 10.0. - [06:30.943](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=390.9433333333333): rider is redrawn as the numbers it depends on change. - [06:30.943](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=390.9433333333333): r\_live ticks to 13.0. ##### [06:35.583](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=395.5833333333333) Narration: 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. Board: Unchanged from the preceding beat in this scene. Actions: - [06:45.423](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=405.4233333333333): knock is shown on the screen, faded in. ##### [06:51.563](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=411.56333333333333) Narration: 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. Board: h\_eff — a Heading that says "Efficiency of the Ideal Cycle"; eta\_axes — an Axes (x\_range=(1.0, 16.0), y\_range=(0.0, 0.8), x\_ticks\_every=2.0); eta\_curve — a FunctionPlot \[blue\] drawn in eta\_axes (function=\, x\_range=(1.0, 16.0)); rider — a PlotPoint \[yellow\] labelled "r = 4" drawn in eta\_axes (target='eta\_curve', x=\); knock — a Polygon \[red\] labelled "upright("knock")" drawn in eta\_axes (vertices=((13.0, 0.0), (16.0, 0.0), (16.0, 0.8), (13.0, 0.8)), fill\_opacity=0.2) Actions: - [06:53.623](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=413.62333333333333): eta\_curve is indicated — a transient flash. - [07:2.903](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=422.9033333333333): real is shown on the screen, faded in. - [07:6.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=426.6633333333333): deriv is hidden from the screen — left the board. - [07:6.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=426.6633333333333): eta\_axes is hidden from the screen — left the board. - [07:6.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=426.6633333333333): eta\_curve is hidden from the screen — eta\_axes left the board. - [07:6.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=426.6633333333333): rider is hidden from the screen — eta\_axes left the board. - [07:6.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=426.6633333333333): knock is hidden from the screen — eta\_axes left the board. - [07:6.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=426.6633333333333): real is hidden from the screen — eta\_axes left the board. - [07:6.663](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=426.6633333333333): h\_eff is hidden from the screen — left the board. ##### [07:7.863](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=427.86333333333334) Narration: Let's gather it up. Four strokes take two turns of the crank, and only one of them delivers work. Board: Empty. Actions: - [07:7.863](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=427.86333333333334): h\_recap is shown on the screen, written out. - [07:7.863](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=427.86333333333334): recap is shown on the screen, written out. - [07:12.063](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=432.06333333333333): recap (the "only one of them delivers work" part) is emphasized. ##### [07:14.423](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=434.4233333333333) Narration: The valves time the flow of gas in and out, and the spark times the burn. Board: recap — a Block \[text\] that says "Four strokes take two crank turns, and only one of them delivers work. The valves time the gas exchange; the spark times the burn. Burning fuel raises gas pressure, and work is the integral of $p dif V$. Efficiency rises with compression r…"; h\_recap — a Heading that says "What to Carry Away" Actions: - [07:14.783](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=434.78333333333336): recap (the "The valves time the gas exchange" part) is emphasized. - [07:14.783](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=434.78333333333336): recap (the "only one of them delivers work" part) is no longer emphasized. ##### [07:19.783](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=439.7833333333333) Narration: Burning fuel raises the gas pressure, and the work it does is the integral of p d V, the area of the loop. Board: Unchanged from the preceding beat in this scene. Actions: - [07:20.023](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=440.0233333333333): recap (the "Burning fuel raises gas pressure" part) is emphasized. - [07:20.023](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=440.0233333333333): recap (the "The valves time the gas exchange" part) is no longer emphasized. ##### [07:27.143](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=447.1433333333333) Narration: And efficiency climbs with compression ratio, until knock sets the limit. That, in one cylinder, is how a gasoline engine works. Board: Unchanged from the preceding beat in this scene. Actions: - [07:30.223](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=450.22333333333336): recap (the "Burning fuel raises gas pressure" part) is no longer emphasized. - [07:30.223](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=450.22333333333336): recap (the "until knock sets the limit" part) is emphasized. - [07:35.458](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=455.457625): recap (the "until knock sets the limit" part) is no longer emphasized. - [07:35.708](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=455.707625): h\_recap is hidden from the screen — left the board. - [07:35.708](https://academa.ai/@yanclanpops/lectures/working-principles-of-the-four-stroke-gasoline-internal-combustion-engine?t=455.707625): recap is hidden from the screen — left the board.