# The Physics of Downforce in Formula 1 Racing > Why can a Formula One car corner at speeds that would throw a road car off the track? This lecture builds the answer from the forces on a car in a turn: friction must supply the pull a corner demands, and friction is capped by the normal force. Downforce raises that cap without adding mass. We see where it comes from, through inverted wings, Bernoulli's principle and ground effect under the floor, then work a numerical example showing how much faster a corner can be taken. Finally we weigh the price, drag and lost top speed, and see why teams tune downforce track by track and why it matters for braking and stability. - Canonical watch page: [The Physics of Downforce in Formula 1 Racing](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing) - Publisher: [Academa, Inc.](https://academa.ai) - Subject: Physics - Published: 2026-10-15T23:50:02.244Z - Updated: 2026-10-15T23:50:02.244Z - Duration: PT478S (7 minutes 58 seconds) - Chapters: 4 - Views: 0 - Language: en-US - Access: Free - Video stream: [HLS content](https://academa.ai/media/l/01M50YV9KAREAMYX0CPJTDF7QG/0/dark/master.m3u8) - Embed: [Player](https://academa.ai/embed/@sina/lectures/the-physics-of-downforce-in-formula-1-racing) - Audiovisual record: [Semantic JSON](https://academa.ai/media/l/01M50YV9KAREAMYX0CPJTDF7QG/0/semantic.json) - Thumbnail: [Image](https://academa.ai/media/l/01M50YV9KAREAMYX0CPJTDF7QG/0/dark/poster.jpg) ## Description How Formula 1 downforce works: inverted wings, Bernoulli and ground effect, grip without extra mass, and the drag trade-off behind lap times. ## Chapters - [00:00–01:41.177 · Grip in a Corner](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=0) - [01:41.177–03:50.095 · The Upside-Down Wing](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=101.17737499999998) - [03:50.095–05:37.308 · How Much Faster?](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=230.09516666666667) - [05:37.308–07:58 · The Price and the Payoff](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=337.30764583333337) ## Transcript ### [00:00 · Grip in a Corner](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=0) A Formula One car can take a fast corner at a speed that would throw an ordinary road car straight off the track. The reason is a force you cannot see, pressing the car into the ground. It is called downforce, and in the next few minutes we will see where it comes from, why it helps, and what it costs. Let's start with a car going round a corner, seen from behind. Here is the car, and here is the track under its tyres. To follow a curve, something has to keep pulling the car toward the inside of the turn, which here is off to the left. For a car, the only thing that can do that is friction, between the tyres and the road. How much pull does the corner demand? The car's mass, times its speed squared, divided by the radius of the turn. Go twice as fast, and you need four times the force. But friction has a ceiling. The most grip a tyre can give is the friction coefficient, mu, times the normal force N, the force pressing the tyre into the road. For an ordinary car, that normal force is simply its weight, m g. Now notice something. Mass shows up on both sides. More mass gives more grip, but it also demands more force, and the two cancel. So here is the question this lecture answers. What if we could press the car into the road harder, without making it any heavier? That extra push is called downforce. Downforce adds to N, so the tyres can grip harder, yet it adds nothing to the mass the car must swing round the corner. That is the whole trick. Before we use it, let's see where it comes from. ### [01:41.177 · The Upside-Down Wing](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=101.17737499999998) An aeroplane wing is shaped to lift. Turn that same shape upside down, flat on top and curved underneath, and it pushes down instead. Formula One cars carry wings like this at the front and at the back. Air meeting the wing splits in two. The air sweeping under the curved side is forced to speed up, while the air over the flat top moves more slowly. Bernoulli's principle links speed and pressure along a stream of air. Pressure plus one half of density times speed squared stays the same. So where the air is faster, its pressure must be lower. Underneath the wing the pressure drops. Above it, the slower air keeps a higher pressure. The wing has more pressure on top than below, and that difference, spread over its area, is a force pointing down. There is a second way to see the same force. The wing turns the passing air upward, and by Newton's third law, the air pushes the wing down. Both pictures describe one flow. How big is it? Downforce grows with air density, with the wing's area, with a shape factor called the lift coefficient, and with the square of the speed. Double the speed and you get four times the downforce. The biggest wing on a modern Formula One car is not a wing at all. It is the floor. Seen from the side, the floor and the track make a channel, and the air rushes through it. The channel narrows in the middle. The same air has to squeeze through a smaller gap, so it must move faster. Faster air means lower pressure, so the car is sucked toward the track. Now lower the car. The gap shrinks, the air under the floor speeds up even more, and the downforce grows. This is ground effect. It supplies a large share of a modern car's downforce, and for less drag than a wing would cost. That is why the cars run so close to the road, and why teams fight over every millimetre of ride height. Too low, and the flow under the floor can stall. So downforce comes from two places: upside-down wings, and a floor shaped to make the air rush underneath. ### [03:50.095 · How Much Faster?](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=230.09516666666667) Let's put numbers on it. Take a car of eight hundred kilograms, on tyres with a friction coefficient of one point five, in a corner of radius one hundred metres. Across the bottom is speed, in metres per second, and up the side is force, in kilonewtons. The red curve is the sideways force the corner demands. It grows with the square of the speed. The gray line is the grip of a car with no downforce at all. It is flat, because the weight does not change with speed. Below the crossing, the grip is more than the corner asks for, and the car holds its line. Push past it, and the tyres let go. For this car, the limit is about thirty eight metres per second, roughly one hundred and forty kilometres per hour. We can see why on paper. The corner demands m v squared over r. The grip available is mu times the normal force, which is the weight plus the downforce. From the last section, downforce is a constant k times speed squared. Put that in, and gather every v squared term on the left. Now solve for the speed. Without downforce, k is zero and the mass cancels completely: the limit depends only on grip and radius. With downforce, the bottom of this fraction shrinks, and the limit speed rises. Here is the same car with downforce. Its grip curve now climbs with speed, because faster air presses harder. The crossing moves out to about forty seven metres per second, close to one hundred and seventy kilometres per hour, on the very same tyres. And notice where the mass sits in that fraction: underneath k. The same downforce helps a light car more than a heavy one. Downforce is grip that the car never has to accelerate, which is exactly why it is so valuable. ### [05:37.308 · The Price and the Payoff](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=337.30764583333337) Downforce is not free. The air that presses the car down also holds it back, and that backward force is drag. Like downforce, it grows with the square of the speed. Pushing against drag takes power, and power is force times speed, so the power needed grows with the cube of the speed. On this graph, speed runs across and power runs up, in kilowatts. The blue curve is a car with small, flat wings. The yellow line is everything the engine can give. Where they meet is the top speed, about ninety five metres per second. Now bolt on bigger wings for more downforce. The red curve climbs faster, because there is more drag, and it meets the engine's limit sooner, at about eighty five. More grip in the corners has cost speed on the straight. So every team faces the same question at every circuit. At Monaco, the corners are slow and tight, so the cars run as much wing as they can. At Monza the straights are long, so the wings are cut almost flat to save drag. Most circuits sit somewhere in between. The rule behind the choice is simple. A lap is time in the corners plus time on the straights, and downforce moves time from one to the other. Teams set the wings wherever the total comes out smallest. Downforce pays off in two more ways. Braking is also limited by grip, so the same rule applies: with downforce, the car can slow far harder than its weight alone would allow, and brake later into every corner. And it makes the car stable. Tyres pressed firmly into the road are slower to break loose over a bump or a kerb, and with downforce balanced between front and rear, both ends of the car stay planted at high speed. So, from the top. Upside-down wings, and a floor that makes the air rush underneath, lower the pressure beneath the car. That pressure pushes the tyres into the road without adding a single kilogram, so the car grips harder in every corner and under braking. The price is drag, and that is why the wings change from track to track. Downforce is not about going faster in a straight line. It is about carrying speed everywhere else. ## 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/01M50YV9KAREAMYX0CPJTDF7QG/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: [Grip in a Corner](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=0) Span: 00:00–01:41.177 (0s–101.17737499999998s). #### Objects - body: a Polygon \[gray\] drawn in view (vertices=((3.0, 1.2), (7.0, 1.2), (7.0, 2.6), (3.0, 2.6)), fill\_opacity=0.5) - card: a Title that says "Physics of Motorsport — The Physics of Downforce in Formula 1 Racing" - downforce: a Vector \[yellow\] labelled "D" drawn in view (start=(5.0, 6.1), end=(5.0, 2.7)) - friction: a Vector \[green\] labelled "F" drawn in view (start=(5.0, 0.5), end=(\, 0.5)) - grip: a Math \[text\] that says "$F\_(upright("max")) = mu N$" - grip\_tip: a VariableNumber (initial\_value=2.0) - ground: a Line \[gray\] drawn in view (start=(0.3, 0.5), end=(9.7, 0.5)) - heading: a Heading that says "What Holds a Car in a Corner" - left\_tyre: a Polygon \[text\] drawn in view (vertices=((2.6, 0.5), (3.4, 0.5), (3.4, 1.9), (2.6, 1.9)), fill\_opacity=0.6) - load: a Math \[text\] that says "$N = m g$" - need: a Math \[text\] that says "$F\_(upright("need")) = frac(m v^2, r)$" - normal: a Vector \[blue\] labelled "N" drawn in view (start=(4.2, 0.5), end=(4.2, \)) - push: a VariableNumber (initial\_value=3.6) - right\_tyre: a Polygon \[text\] drawn in view (vertices=((6.6, 0.5), (7.4, 0.5), (7.4, 1.9), (6.6, 1.9)), fill\_opacity=0.6) - view: a Figure (x\_range=(0.0, 10.0), y\_range=(-1.0, 6.5), aspect=(10.0, 7.5)) - weight: a Vector \[red\] labelled "m g" drawn in view (start=(5.8, 1.9), end=(5.8, -0.6)) #### Beats ##### [00:00](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=0) Narration: A Formula One car can take a fast corner at a speed that would throw an ordinary road car straight off the track. The reason is a force you cannot see, pressing the car into the ground. It is called downforce, and in the next few minutes we will see where it comes from, why it helps, and what it costs. Board: Empty. Actions: - [00:00](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=0): card is shown on the screen, written out. - [00:1.376](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=1.3763631411711306): card: enter:write-left-to-right. - [00:17.775](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=17.775): card is hidden from the screen — left the board. ##### [00:18.975](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=18.974999999999998) Narration: Let's start with a car going round a corner, seen from behind. Here is the car, and here is the track under its tyres. Board: Unchanged from the preceding beat in this scene. Actions: - [00:18.975](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=18.974999999999998): heading is shown on the screen, written out. - [00:18.975](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=18.974999999999998): view is shown on the screen, written out. - [00:23.28](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=23.28): body is shown on the screen, written out. - [00:24.92](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=24.919999999999998): ground is shown on the screen, written out. - [00:25.6](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=25.599999999999998): left\_tyre is shown on the screen, written out. - [00:25.853](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=25.852727918388428): right\_tyre is shown on the screen, written out. ##### [00:26.967](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=26.967499999999998) Narration: To follow a curve, something has to keep pulling the car toward the inside of the turn, which here is off to the left. For a car, the only thing that can do that is friction, between the tyres and the road. Board: view — a Figure (x\_range=(0.0, 10.0), y\_range=(-1.0, 6.5), aspect=(10.0, 7.5)); heading — a Heading that says "What Holds a Car in a Corner"; body — a Polygon \[gray\] drawn in view (vertices=((3.0, 1.2), (7.0, 1.2), (7.0, 2.6), (3.0, 2.6)), fill\_opacity=0.5); ground — a Line \[gray\] drawn in view (start=(0.3, 0.5), end=(9.7, 0.5)); left\_tyre — a Polygon \[text\] drawn in view (vertices=((2.6, 0.5), (3.4, 0.5), (3.4, 1.9), (2.6, 1.9)), fill\_opacity=0.6); right\_tyre — a Polygon \[text\] drawn in view (vertices=((6.6, 0.5), (7.4, 0.5), (7.4, 1.9), (6.6, 1.9)), fill\_opacity=0.6) Actions: - [00:36.6](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=36.599999999999994): friction is shown on the screen, written out. ##### [00:39.725](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=39.724999999999994) Narration: How much pull does the corner demand? The car's mass, times its speed squared, divided by the radius of the turn. Go twice as fast, and you need four times the force. Board: view — a Figure (x\_range=(0.0, 10.0), y\_range=(-1.0, 6.5), aspect=(10.0, 7.5)); heading — a Heading that says "What Holds a Car in a Corner"; body — a Polygon \[gray\] drawn in view (vertices=((3.0, 1.2), (7.0, 1.2), (7.0, 2.6), (3.0, 2.6)), fill\_opacity=0.5); ground — a Line \[gray\] drawn in view (start=(0.3, 0.5), end=(9.7, 0.5)); left\_tyre — a Polygon \[text\] drawn in view (vertices=((2.6, 0.5), (3.4, 0.5), (3.4, 1.9), (2.6, 1.9)), fill\_opacity=0.6); right\_tyre — a Polygon \[text\] drawn in view (vertices=((6.6, 0.5), (7.4, 0.5), (7.4, 1.9), (6.6, 1.9)), fill\_opacity=0.6); friction — a Vector \[green\] labelled "F" drawn in view (start=(5.0, 0.5), end=(\, 0.5)) Actions: - [00:39.725](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=39.724999999999994): view moves to a new place on the board. - [00:39.725](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=39.724999999999994): need is shown on the screen, written out. - [00:43.24](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=43.239999999999995): need (the "frac(m v^2, r)" part) is emphasized. - [00:47.76](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=47.75999999999999): need (the "frac(m v^2, r)" part) is no longer emphasized. ##### [00:51.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=51.269999999999996) Narration: But friction has a ceiling. The most grip a tyre can give is the friction coefficient, mu, times the normal force N, the force pressing the tyre into the road. Board: need — a Math \[text\] that says "$F\_(upright("need")) = frac(m v^2, r)$"; view — a Figure (x\_range=(0.0, 10.0), y\_range=(-1.0, 6.5), aspect=(10.0, 7.5)); heading — a Heading that says "What Holds a Car in a Corner"; body — a Polygon \[gray\] drawn in view (vertices=((3.0, 1.2), (7.0, 1.2), (7.0, 2.6), (3.0, 2.6)), fill\_opacity=0.5); ground — a Line \[gray\] drawn in view (start=(0.3, 0.5), end=(9.7, 0.5)); left\_tyre — a Polygon \[text\] drawn in view (vertices=((2.6, 0.5), (3.4, 0.5), (3.4, 1.9), (2.6, 1.9)), fill\_opacity=0.6); right\_tyre — a Polygon \[text\] drawn in view (vertices=((6.6, 0.5), (7.4, 0.5), (7.4, 1.9), (6.6, 1.9)), fill\_opacity=0.6); friction — a Vector \[green\] labelled "F" drawn in view (start=(5.0, 0.5), end=(\, 0.5)) Actions: - [00:52.6](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=52.599999999999994): grip is shown on the screen, written out. - [00:58.04](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=58.04): normal is shown on the screen, written out. - [00:59.88](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=59.879999999999995): grip (the "N" part) is emphasized. - [01:1.725](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=61.724999999999994): grip (the "N" part) is no longer emphasized. ##### [01:2.325](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=62.324999999999996) Narration: For an ordinary car, that normal force is simply its weight, m g. Now notice something. Mass shows up on both sides. More mass gives more grip, but it also demands more force, and the two cancel. Board: need — a Math \[text\] that says "$F\_(upright("need")) = frac(m v^2, r)$"; grip — a Math \[text\] that says "$F\_(upright("max")) = mu N$"; view — a Figure (x\_range=(0.0, 10.0), y\_range=(-1.0, 6.5), aspect=(10.0, 7.5)); heading — a Heading that says "What Holds a Car in a Corner"; body — a Polygon \[gray\] drawn in view (vertices=((3.0, 1.2), (7.0, 1.2), (7.0, 2.6), (3.0, 2.6)), fill\_opacity=0.5); ground — a Line \[gray\] drawn in view (start=(0.3, 0.5), end=(9.7, 0.5)); left\_tyre — a Polygon \[text\] drawn in view (vertices=((2.6, 0.5), (3.4, 0.5), (3.4, 1.9), (2.6, 1.9)), fill\_opacity=0.6); right\_tyre — a Polygon \[text\] drawn in view (vertices=((6.6, 0.5), (7.4, 0.5), (7.4, 1.9), (6.6, 1.9)), fill\_opacity=0.6); friction — a Vector \[green\] labelled "F" drawn in view (start=(5.0, 0.5), end=(\, 0.5)); normal — a Vector \[blue\] labelled "N" drawn in view (start=(4.2, 0.5), end=(4.2, \)) Actions: - [01:4.96](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=64.96000000000001): load is shown on the screen, written out. - [01:5.44](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=65.44): weight is shown on the screen, written out. - [01:12.28](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=72.28000000000002): grip (the "mu N" part) is indicated — a transient flash. - [01:13.52](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=73.52000000000001): need (the "frac(m v^2, r)" part) is indicated — a transient flash. ##### [01:16.792](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=76.79249999999999) Narration: So here is the question this lecture answers. What if we could press the car into the road harder, without making it any heavier? That extra push is called downforce. Board: need — a Math \[text\] that says "$F\_(upright("need")) = frac(m v^2, r)$"; grip — a Math \[text\] that says "$F\_(upright("max")) = mu N$"; load — a Math \[text\] that says "$N = m g$"; view — a Figure (x\_range=(0.0, 10.0), y\_range=(-1.0, 6.5), aspect=(10.0, 7.5)); heading — a Heading that says "What Holds a Car in a Corner"; body — a Polygon \[gray\] drawn in view (vertices=((3.0, 1.2), (7.0, 1.2), (7.0, 2.6), (3.0, 2.6)), fill\_opacity=0.5); ground — a Line \[gray\] drawn in view (start=(0.3, 0.5), end=(9.7, 0.5)); left\_tyre — a Polygon \[text\] drawn in view (vertices=((2.6, 0.5), (3.4, 0.5), (3.4, 1.9), (2.6, 1.9)), fill\_opacity=0.6); right\_tyre — a Polygon \[text\] drawn in view (vertices=((6.6, 0.5), (7.4, 0.5), (7.4, 1.9), (6.6, 1.9)), fill\_opacity=0.6); friction — a Vector \[green\] labelled "F" drawn in view (start=(5.0, 0.5), end=(\, 0.5)); normal — a Vector \[blue\] labelled "N" drawn in view (start=(4.2, 0.5), end=(4.2, \)); weight — a Vector \[red\] labelled "m g" drawn in view (start=(5.8, 1.9), end=(5.8, -0.6)) Actions: - [01:20.6](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=80.60000000000001): downforce is shown on the screen, written out. - [01:22.04](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=82.04): normal is redrawn as the numbers it depends on change. - [01:22.04](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=82.04): push ticks to 5.6. - [01:26.68](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=86.68000000000002): load becomes "$N = m g + D$". ##### [01:28.02](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=88.01999999999998) Narration: Downforce adds to N, so the tyres can grip harder, yet it adds nothing to the mass the car must swing round the corner. That is the whole trick. Before we use it, let's see where it comes from. Board: need — a Math \[text\] that says "$F\_(upright("need")) = frac(m v^2, r)$"; grip — a Math \[text\] that says "$F\_(upright("max")) = mu N$"; load — a Math \[text\] that says "$N = m g$"; view — a Figure (x\_range=(0.0, 10.0), y\_range=(-1.0, 6.5), aspect=(10.0, 7.5)); heading — a Heading that says "What Holds a Car in a Corner"; body — a Polygon \[gray\] drawn in view (vertices=((3.0, 1.2), (7.0, 1.2), (7.0, 2.6), (3.0, 2.6)), fill\_opacity=0.5); ground — a Line \[gray\] drawn in view (start=(0.3, 0.5), end=(9.7, 0.5)); left\_tyre — a Polygon \[text\] drawn in view (vertices=((2.6, 0.5), (3.4, 0.5), (3.4, 1.9), (2.6, 1.9)), fill\_opacity=0.6); right\_tyre — a Polygon \[text\] drawn in view (vertices=((6.6, 0.5), (7.4, 0.5), (7.4, 1.9), (6.6, 1.9)), fill\_opacity=0.6); friction — a Vector \[green\] labelled "F" drawn in view (start=(5.0, 0.5), end=(\, 0.5)); normal — a Vector \[blue\] labelled "N" drawn in view (start=(4.2, 0.5), end=(4.2, \)); weight — a Vector \[red\] labelled "m g" drawn in view (start=(5.8, 1.9), end=(5.8, -0.6)); downforce — a Vector \[yellow\] labelled "D" drawn in view (start=(5.0, 6.1), end=(5.0, 2.7)) Actions: - [01:30.96](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=90.96000000000001): friction is redrawn as the numbers it depends on change. - [01:30.96](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=90.96000000000001): grip\_tip ticks to 0.6. - [01:36.72](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=96.72000000000001): A box is drawn around load. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): grip is hidden from the screen — left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): heading is hidden from the screen — left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): load is hidden from the screen — left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): need is hidden from the screen — left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): view is hidden from the screen — left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): body is hidden from the screen — view left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): ground is hidden from the screen — view left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): left\_tyre is hidden from the screen — view left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): right\_tyre is hidden from the screen — view left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): friction is hidden from the screen — view left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): normal is hidden from the screen — view left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): weight is hidden from the screen — view left the board. - [01:40.136](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=100.1357083333333): downforce is hidden from the screen — view left the board. ### Scene 2: [The Upside-Down Wing](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=101.17737499999998) Span: 01:41.177–03:50.095 (101.17737499999998s–230.09516666666667s). #### Objects - bern: a Math \[text\] that says "$p + frac(1, 2) rho v^2 = upright("constant")$" - chain: a Math \[text\] that says "$h arrow.b quad arrow.r.double quad v arrow.t quad arrow.r.double quad p arrow.b$" - compare: a Math \[text\] that says "$p\_(upright("below")) \< p\_(upright("above"))$" - cont: a Math \[text\] that says "$A\_1 v\_1 = A\_2 v\_2$" - down: a Vector \[yellow\] labelled "D" drawn in wing\_view (start=(5.0, 2.3), end=(5.0, 0.0)) - fast\_air: a Vector \[green\] labelled "upright("faster")" drawn in wing\_view (start=(2.0, 1.3), end=(8.5, 1.3)) - floor: a Polygon \[magenta\] drawn in floor\_view (vertices=((1.0, (ride + 0.8)), (3.5, \), (6.5,…, fill\_opacity=0.4) - floor\_view: a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 4.5), aspect=(10.0, 5.0)) - force: a Math \[text\] that says "$D = Delta p dot.op A$" - h\_ground: a Heading that says "Ground Effect: The Floor as a Wing" - h\_wing: a Heading that says "An Aeroplane Wing, Turned Over" - high\_p: a Math \[red\] that says "$p\_(upright("high"))$" drawn in wing\_view - low\_p: a Math \[blue\] that says "$p\_(upright("low"))$" drawn in wing\_view - over\_air: a Vector \[gray\] drawn in floor\_view (start=(2.5, 3.9), end=(4.5, 3.9)) - ride: a VariableNumber (initial\_value=1.2) - slow\_air: a Vector \[gray\] labelled "upright("slower")" drawn in wing\_view (start=(2.0, 4.4), end=(5.0, 4.4)) - suction: a Vector \[yellow\] labelled "D" drawn in floor\_view (start=(7.5, ((ride \* -0.5) + 4.35)), end=(7.5, (ride + 1.65))) - track: a Line \[gray\] drawn in floor\_view (start=(0.3, 0.0), end=(9.7, 0.0)) - turned\_air: a Vector \[gray\] drawn in wing\_view (start=(8.2, 3.0), end=(9.6, 3.9)) - under\_air: a Vector \[green\] labelled "v" drawn in floor\_view (start=(2.5, (ride \* 0.5)), end=(((ride \* -4.0) + 9.3), (ride \* 0.5))) - wing: a Polygon \[magenta\] drawn in wing\_view (vertices=((2.0, 3.0), (2.6, 3.0309016994374947), (3.2, 3.058778525229247…, fill\_opacity=0.4) - wing\_view: a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 6.0), aspect=(10.0, 6.5)) #### Beats ##### [01:41.177](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=101.17737499999998) Narration: An aeroplane wing is shaped to lift. Turn that same shape upside down, flat on top and curved underneath, and it pushes down instead. Formula One cars carry wings like this at the front and at the back. Board: Empty. Actions: - [01:41.177](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=101.17737499999998): h\_wing is shown on the screen, written out. - [01:41.177](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=101.17737499999998): wing\_view is shown on the screen, written out. - [01:45.257](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=105.25737499999998): wing is shown on the screen, written out. ##### [01:55](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=114.99987499999999) Narration: Air meeting the wing splits in two. The air sweeping under the curved side is forced to speed up, while the air over the flat top moves more slowly. Board: wing\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 6.0), aspect=(10.0, 6.5)); h\_wing — a Heading that says "An Aeroplane Wing, Turned Over"; wing — a Polygon \[magenta\] drawn in wing\_view (vertices=((2.0, 3.0), (2.6, 3.0309016994374947), (3.2, 3.058778525229247…, fill\_opacity=0.4) Actions: - [02:0.177](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=120.17737499999998): fast\_air is shown on the screen, written out. - [02:3.217](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=123.21737499999998): slow\_air is shown on the screen, written out. ##### [02:4.532](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=124.53237499999997) Narration: Bernoulli's principle links speed and pressure along a stream of air. Pressure plus one half of density times speed squared stays the same. So where the air is faster, its pressure must be lower. Board: wing\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 6.0), aspect=(10.0, 6.5)); h\_wing — a Heading that says "An Aeroplane Wing, Turned Over"; wing — a Polygon \[magenta\] drawn in wing\_view (vertices=((2.0, 3.0), (2.6, 3.0309016994374947), (3.2, 3.058778525229247…, fill\_opacity=0.4); fast\_air — a Vector \[green\] labelled "upright("faster")" drawn in wing\_view (start=(2.0, 1.3), end=(8.5, 1.3)); slow\_air — a Vector \[gray\] labelled "upright("slower")" drawn in wing\_view (start=(2.0, 4.4), end=(5.0, 4.4)) Actions: - [02:5.817](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=125.81737499999998): wing\_view moves to a new place on the board. - [02:5.817](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=125.81737499999998): bern is shown on the screen, written out. - [02:6.777](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=126.77737499999998): bern (the "p" part) is emphasized. - [02:9.897](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=129.89737499999998): bern (the "frac(1, 2) rho v^2" part) is emphasized. - [02:9.897](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=129.89737499999998): bern (the "p" part) is no longer emphasized. - [02:13.297](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=133.297375): bern (the "frac(1, 2) rho v^2" part) is no longer emphasized. ##### [02:17.255](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=137.25487499999997) Narration: Underneath the wing the pressure drops. Above it, the slower air keeps a higher pressure. The wing has more pressure on top than below, and that difference, spread over its area, is a force pointing down. Board: bern — a Math \[text\] that says "$p + frac(1, 2) rho v^2 = upright("constant")$"; wing\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 6.0), aspect=(10.0, 6.5)); h\_wing — a Heading that says "An Aeroplane Wing, Turned Over"; wing — a Polygon \[magenta\] drawn in wing\_view (vertices=((2.0, 3.0), (2.6, 3.0309016994374947), (3.2, 3.058778525229247…, fill\_opacity=0.4); fast\_air — a Vector \[green\] labelled "upright("faster")" drawn in wing\_view (start=(2.0, 1.3), end=(8.5, 1.3)); slow\_air — a Vector \[gray\] labelled "upright("slower")" drawn in wing\_view (start=(2.0, 4.4), end=(5.0, 4.4)) Actions: - [02:18.897](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=138.89737499999998): low\_p is shown on the screen, written out. - [02:21.617](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=141.61737499999998): high\_p is shown on the screen, written out. - [02:23.377](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=143.37737499999997): compare is shown on the screen, written out. - [02:26.337](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=146.33737499999998): fast\_air is hidden from the screen. - [02:26.337](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=146.33737499999998): slow\_air is hidden from the screen. - [02:27.057](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=147.05737499999998): force is shown on the screen, written out. - [02:29.017](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=149.01737499999996): down is shown on the screen, written out. ##### [02:30.072](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=150.07237499999997) Narration: There is a second way to see the same force. The wing turns the passing air upward, and by Newton's third law, the air pushes the wing down. Both pictures describe one flow. Board: bern — a Math \[text\] that says "$p + frac(1, 2) rho v^2 = upright("constant")$"; compare — a Math \[text\] that says "$p\_(upright("below")) \< p\_(upright("above"))$"; force — a Math \[text\] that says "$D = Delta p dot.op A$"; wing\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 6.0), aspect=(10.0, 6.5)); h\_wing — a Heading that says "An Aeroplane Wing, Turned Over"; wing — a Polygon \[magenta\] drawn in wing\_view (vertices=((2.0, 3.0), (2.6, 3.0309016994374947), (3.2, 3.058778525229247…, fill\_opacity=0.4); low\_p — a Math \[blue\] that says "$p\_(upright("low"))$" drawn in wing\_view; high\_p — a Math \[red\] that says "$p\_(upright("high"))$" drawn in wing\_view; down — a Vector \[yellow\] labelled "D" drawn in wing\_view (start=(5.0, 2.3), end=(5.0, 0.0)) Actions: - [02:34.457](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=154.45737499999998): turned\_air is shown on the screen, written out. - [02:37.177](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=157.17737499999998): down is indicated — a transient flash. ##### [02:41.57](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=161.56987499999997) Narration: How big is it? Downforce grows with air density, with the wing's area, with a shape factor called the lift coefficient, and with the square of the speed. Double the speed and you get four times the downforce. Board: bern — a Math \[text\] that says "$p + frac(1, 2) rho v^2 = upright("constant")$"; compare — a Math \[text\] that says "$p\_(upright("below")) \< p\_(upright("above"))$"; force — a Math \[text\] that says "$D = Delta p dot.op A$"; wing\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 6.0), aspect=(10.0, 6.5)); h\_wing — a Heading that says "An Aeroplane Wing, Turned Over"; wing — a Polygon \[magenta\] drawn in wing\_view (vertices=((2.0, 3.0), (2.6, 3.0309016994374947), (3.2, 3.058778525229247…, fill\_opacity=0.4); low\_p — a Math \[blue\] that says "$p\_(upright("low"))$" drawn in wing\_view; high\_p — a Math \[red\] that says "$p\_(upright("high"))$" drawn in wing\_view; down — a Vector \[yellow\] labelled "D" drawn in wing\_view (start=(5.0, 2.3), end=(5.0, 0.0)); turned\_air — a Vector \[gray\] drawn in wing\_view (start=(8.2, 3.0), end=(9.6, 3.9)) Actions: - [02:43.617](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=163.61737499999998): force becomes "$D = frac(1, 2) rho C\_L A v^2$". - [02:49.537](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=169.537375): force (the "v^2" part) is emphasized. - [02:52.497](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=172.49737499999998): force (the "v^2" part) is no longer emphasized. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): bern is hidden from the screen — left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): compare is hidden from the screen — left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): force is hidden from the screen — left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): h\_wing is hidden from the screen — left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): wing\_view is hidden from the screen — left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): wing is hidden from the screen — wing\_view left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): low\_p is hidden from the screen — wing\_view left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): high\_p is hidden from the screen — wing\_view left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): down is hidden from the screen — wing\_view left the board. - [02:54.27](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=174.26987499999998): turned\_air is hidden from the screen — wing\_view left the board. ##### [02:55.47](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=175.46987499999997) Narration: The biggest wing on a modern Formula One car is not a wing at all. It is the floor. Seen from the side, the floor and the track make a channel, and the air rushes through it. Board: Empty. Actions: - [02:55.47](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=175.46987499999997): h\_ground is shown on the screen, written out. - [02:55.47](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=175.46987499999997): floor\_view is shown on the screen, written out. - [03:0.097](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=180.097375): floor is shown on the screen, written out. - [03:2.817](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=182.81737499999997): track is shown on the screen, written out. - [03:4.577](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=184.577375): under\_air is shown on the screen, written out. - [03:4.814](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=184.81401471603232): over\_air is shown on the screen, written out. ##### [03:6.18](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=186.17987499999998) Narration: The channel narrows in the middle. The same air has to squeeze through a smaller gap, so it must move faster. Faster air means lower pressure, so the car is sucked toward the track. Board: floor\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 4.5), aspect=(10.0, 5.0)); h\_ground — a Heading that says "Ground Effect: The Floor as a Wing"; floor — a Polygon \[magenta\] drawn in floor\_view (vertices=((1.0, (ride + 0.8)), (3.5, \), (6.5,…, fill\_opacity=0.4); track — a Line \[gray\] drawn in floor\_view (start=(0.3, 0.0), end=(9.7, 0.0)); under\_air — a Vector \[green\] labelled "v" drawn in floor\_view (start=(2.5, (ride \* 0.5)), end=(((ride \* -4.0) + 9.3), (ride \* 0.5))); over\_air — a Vector \[gray\] drawn in floor\_view (start=(2.5, 3.9), end=(4.5, 3.9)) Actions: - [03:6.937](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=186.93737499999997): floor\_view moves to a new place on the board. - [03:6.937](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=186.93737499999997): cont is shown on the screen, written out. - [03:10.177](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=190.17737499999998): cont (the "A\_2" part) is emphasized. - [03:12.137](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=192.137375): cont (the "A\_2" part) is no longer emphasized. - [03:12.137](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=192.137375): cont (the "v\_2" part) is emphasized. - [03:15.817](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=195.81737499999997): suction is shown on the screen, written out. - [03:15.817](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=195.81737499999997): cont (the "v\_2" part) is no longer emphasized. ##### [03:17.807](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=197.80737499999998) Narration: Now lower the car. The gap shrinks, the air under the floor speeds up even more, and the downforce grows. This is ground effect. It supplies a large share of a modern car's downforce, and for less drag than a wing would cost. Board: cont — a Math \[text\] that says "$A\_1 v\_1 = A\_2 v\_2$"; floor\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 4.5), aspect=(10.0, 5.0)); h\_ground — a Heading that says "Ground Effect: The Floor as a Wing"; floor — a Polygon \[magenta\] drawn in floor\_view (vertices=((1.0, (ride + 0.8)), (3.5, \), (6.5,…, fill\_opacity=0.4); track — a Line \[gray\] drawn in floor\_view (start=(0.3, 0.0), end=(9.7, 0.0)); under\_air — a Vector \[green\] labelled "v" drawn in floor\_view (start=(2.5, (ride \* 0.5)), end=(((ride \* -4.0) + 9.3), (ride \* 0.5))); over\_air — a Vector \[gray\] drawn in floor\_view (start=(2.5, 3.9), end=(4.5, 3.9)); suction — a Vector \[yellow\] labelled "D" drawn in floor\_view (start=(7.5, ((ride \* -0.5) + 4.35)), end=(7.5, (ride + 1.65))) Actions: - [03:18.577](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=198.57737499999996): floor is redrawn as the numbers it depends on change. - [03:18.577](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=198.57737499999996): under\_air is redrawn as the numbers it depends on change. - [03:18.577](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=198.57737499999996): suction is redrawn as the numbers it depends on change. - [03:18.577](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=198.57737499999996): ride ticks to 0.5. - [03:19.897](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=199.89737499999998): chain is shown on the screen, written out. - [03:25.857](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=205.857375): suction is indicated — a transient flash. ##### [03:32.96](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=212.95987499999995) Narration: That is why the cars run so close to the road, and why teams fight over every millimetre of ride height. Too low, and the flow under the floor can stall. So downforce comes from two places: upside-down wings, and a floor shaped to make the air rush underneath. Board: cont — a Math \[text\] that says "$A\_1 v\_1 = A\_2 v\_2$"; chain — a Math \[text\] that says "$h arrow.b quad arrow.r.double quad v arrow.t quad arrow.r.double quad p arrow.b$"; floor\_view — a Figure (x\_range=(0.0, 10.0), y\_range=(-0.5, 4.5), aspect=(10.0, 5.0)); h\_ground — a Heading that says "Ground Effect: The Floor as a Wing"; floor — a Polygon \[magenta\] drawn in floor\_view (vertices=((1.0, (ride + 0.8)), (3.5, \), (6.5,…, fill\_opacity=0.4); track — a Line \[gray\] drawn in floor\_view (start=(0.3, 0.0), end=(9.7, 0.0)); under\_air — a Vector \[green\] labelled "v" drawn in floor\_view (start=(2.5, (ride \* 0.5)), end=(((ride \* -4.0) + 9.3), (ride \* 0.5))); over\_air — a Vector \[gray\] drawn in floor\_view (start=(2.5, 3.9), end=(4.5, 3.9)); suction — a Vector \[yellow\] labelled "D" drawn in floor\_view (start=(7.5, ((ride \* -0.5) + 4.35)), end=(7.5, (ride + 1.65))) Actions: - [03:40.617](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=220.61737499999998): floor is indicated — a transient flash. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): chain is hidden from the screen — left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): cont is hidden from the screen — left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): floor\_view is hidden from the screen — left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): floor is hidden from the screen — floor\_view left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): track is hidden from the screen — floor\_view left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): under\_air is hidden from the screen — floor\_view left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): over\_air is hidden from the screen — floor\_view left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): suction is hidden from the screen — floor\_view left the board. - [03:49.053](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=229.05349999999999): h\_ground is hidden from the screen — left the board. ### Scene 3: [How Much Faster?](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=230.09516666666667) Span: 03:50.095–05:37.308 (230.09516666666667s–337.30764583333337s). #### Objects - aero\_grip: a FunctionPlot \[green\] labelled "mu (m g + D)" drawn in axes (function=\) - aero\_limit: a PlotPoint \[green\] labelled "47 thin upright("m/s")" drawn in axes (target='need\_curve', x=46.8) - axes: an Axes (x\_range=(0.0, 80.0), y\_range=(0.0, 60.0), x\_ticks\_every=20.0) - flat\_grip: a FunctionPlot \[gray\] labelled "mu m g" drawn in axes (function=\) - heading: a Heading that says "How Much Faster?" - need\_curve: a FunctionPlot \[red\] labelled "F\_(upright("need"))" drawn in axes (function=\) - plain\_limit: a PlotPoint \[text\] labelled "38 thin upright("m/s")" drawn in axes (target='need\_curve', x=38.3) - probe: a PlotPoint \[yellow\] labelled "20" drawn in axes (target='need\_curve', x=\) - result: a Math \[text\] that says "$v\_(upright("max")) approx 47 thin upright("m/s") approx 168 thin upright("km/h")$" - speed: a VariableNumber (initial\_value=20.0, format\_spec='.0f') - work: a Derivation \[text\] that says "$frac(m v^2, r) &= mu (m g + D) \\ &= mu m g + mu k v^2 \\ v^2 (frac(m, r) - mu k) &= mu m g \\ v\_(upright("max"))^2 &= frac(mu g r, 1 - frac(mu k r, m))$" #### Beats ##### [03:50.095](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=230.09516666666667) Narration: Let's put numbers on it. Take a car of eight hundred kilograms, on tyres with a friction coefficient of one point five, in a corner of radius one hundred metres. Across the bottom is speed, in metres per second, and up the side is force, in kilonewtons. Board: Empty. Actions: - [03:50.095](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=230.09516666666667): heading is shown on the screen, written out. - [03:50.095](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=230.09516666666667): axes is shown on the screen, written out. ##### [04:5.665](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=245.66516666666666) Narration: The red curve is the sideways force the corner demands. It grows with the square of the speed. The gray line is the grip of a car with no downforce at all. It is flat, because the weight does not change with speed. Board: axes — an Axes (x\_range=(0.0, 80.0), y\_range=(0.0, 60.0), x\_ticks\_every=20.0); heading — a Heading that says "How Much Faster?" Actions: - [04:5.975](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=245.97516666666667): need\_curve is shown on the screen, written out. - [04:11.855](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=251.85516666666666): flat\_grip is shown on the screen, written out. ##### [04:18.785](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=258.78516666666667) Narration: Below the crossing, the grip is more than the corner asks for, and the car holds its line. Push past it, and the tyres let go. For this car, the limit is about thirty eight metres per second, roughly one hundred and forty kilometres per hour. Board: axes — an Axes (x\_range=(0.0, 80.0), y\_range=(0.0, 60.0), x\_ticks\_every=20.0); heading — a Heading that says "How Much Faster?"; need\_curve — a FunctionPlot \[red\] labelled "F\_(upright("need"))" drawn in axes (function=\); flat\_grip — a FunctionPlot \[gray\] labelled "mu m g" drawn in axes (function=\) Actions: - [04:18.975](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=258.97516666666667): probe is shown on the screen, written out. - [04:22.815](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=262.81516666666664): probe is redrawn as the numbers it depends on change. - [04:22.815](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=262.81516666666664): speed ticks to 30.0. - [04:24.095](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=264.09516666666667): probe is redrawn as the numbers it depends on change. - [04:24.095](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=264.09516666666667): speed ticks to 44.0. - [04:27.615](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=267.61516666666665): probe is redrawn as the numbers it depends on change. - [04:27.615](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=267.61516666666665): speed ticks to 38.3. - [04:28.335](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=268.3351666666667): plain\_limit is shown on the screen, written out. - [04:32.46](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=272.4601666666667): probe is hidden from the screen. ##### [04:33.06](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=273.06016666666665) Narration: We can see why on paper. The corner demands m v squared over r. The grip available is mu times the normal force, which is the weight plus the downforce. Board: axes — an Axes (x\_range=(0.0, 80.0), y\_range=(0.0, 60.0), x\_ticks\_every=20.0); heading — a Heading that says "How Much Faster?"; need\_curve — a FunctionPlot \[red\] labelled "F\_(upright("need"))" drawn in axes (function=\); flat\_grip — a FunctionPlot \[gray\] labelled "mu m g" drawn in axes (function=\); plain\_limit — a PlotPoint \[text\] labelled "38 thin upright("m/s")" drawn in axes (target='need\_curve', x=38.3) Actions: - [04:33.06](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=273.06016666666665): axes moves to a new place on the board. - [04:33.06](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=273.06016666666665): work is shown on the screen, written out. - [04:35.655](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=275.6551666666667): work (the "frac(m v^2, r)" part) is emphasized. - [04:38.655](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=278.6551666666667): work (the "frac(m v^2, r)" part) is no longer emphasized. - [04:38.655](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=278.6551666666667): work (the "mu (m g + D)" part) is emphasized. - [04:42.978](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=282.97766666666666): work (the "mu (m g + D)" part) is no longer emphasized. ##### [04:43.578](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=283.5776666666667) Narration: From the last section, downforce is a constant k times speed squared. Put that in, and gather every v squared term on the left. Board: Unchanged from the preceding beat in this scene. Actions: - [04:48.335](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=288.3351666666666): work is shown on the screen, written out. - [04:49.295](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=289.29516666666666): work is shown on the screen, written out. ##### [04:52.283](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=292.28266666666667) Narration: Now solve for the speed. Without downforce, k is zero and the mass cancels completely: the limit depends only on grip and radius. With downforce, the bottom of this fraction shrinks, and the limit speed rises. Board: Unchanged from the preceding beat in this scene. Actions: - [04:53.015](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=293.0151666666667): work is shown on the screen, written out. - [05:3.135](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=303.1351666666667): work (the "1 - frac(mu k r, m)" part) is emphasized. - [05:6.485](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=306.48516666666666): work (the "1 - frac(mu k r, m)" part) is no longer emphasized. ##### [05:7.085](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=307.0851666666667) Narration: Here is the same car with downforce. Its grip curve now climbs with speed, because faster air presses harder. The crossing moves out to about forty seven metres per second, close to one hundred and seventy kilometres per hour, on the very same tyres. Board: Unchanged from the preceding beat in this scene. Actions: - [05:8.895](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=308.8951666666667): aero\_grip is shown on the screen, written out. - [05:15.775](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=315.7751666666667): aero\_limit is shown on the screen, written out. - [05:18.495](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=318.4951666666667): result is shown on the screen, written out. ##### [05:22.338](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=322.3376666666667) Narration: And notice where the mass sits in that fraction: underneath k. The same downforce helps a light car more than a heavy one. Downforce is grip that the car never has to accelerate, which is exactly why it is so valuable. Board: result — a Math \[text\] that says "$v\_(upright("max")) approx 47 thin upright("m/s") approx 168 thin upright("km/h")$"; axes — an Axes (x\_range=(0.0, 80.0), y\_range=(0.0, 60.0), x\_ticks\_every=20.0); heading — a Heading that says "How Much Faster?"; need\_curve — a FunctionPlot \[red\] labelled "F\_(upright("need"))" drawn in axes (function=\); flat\_grip — a FunctionPlot \[gray\] labelled "mu m g" drawn in axes (function=\); plain\_limit — a PlotPoint \[text\] labelled "38 thin upright("m/s")" drawn in axes (target='need\_curve', x=38.3); aero\_grip — a FunctionPlot \[green\] labelled "mu (m g + D)" drawn in axes (function=\); aero\_limit — a PlotPoint \[green\] labelled "47 thin upright("m/s")" drawn in axes (target='need\_curve', x=46.8) Actions: - [05:25.095](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=325.09516666666667): work (the "frac(mu k r, m)" part) is indicated — a transient flash. - [05:32.055](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=332.0551666666667): A box is drawn around result. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): axes is hidden from the screen — left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): need\_curve is hidden from the screen — axes left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): flat\_grip is hidden from the screen — axes left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): plain\_limit is hidden from the screen — axes left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): aero\_grip is hidden from the screen — axes left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): aero\_limit is hidden from the screen — axes left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): heading is hidden from the screen — left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): result is hidden from the screen — left the board. - [05:36.266](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=336.2659791666666): work is hidden from the screen — left the board. ### Scene 4: [The Price and the Payoff](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=337.30764583333337) Span: 05:37.308–07:57.925 (337.30764583333337s–477.92502083333335s). #### Objects - brake: a Math \[text\] that says "$a\_(upright("brake")) = mu (g + frac(D, m))$" - drag: a Math \[text\] that says "$F\_(upright("drag")) = frac(1, 2) rho C\_D A v^2$" - engine: a FunctionPlot \[yellow\] labelled "P\_(upright("engine"))" drawn in power\_axes (function=\) - h\_drag: a Heading that says "The Price: Drag" - h\_setup: a Heading that says "Choosing the Compromise" - h\_stable: a Heading that says "Braking and Stability" - h\_sum: a Heading that says "What Downforce Does" - heavy: a FunctionPlot \[red\] labelled "upright("high wing")" drawn in power\_axes (function=\, x\_range=(0.0, 95.0)) - heavy\_top: a PlotPoint \[red\] labelled "85 thin upright("m/s")" drawn in power\_axes (target='heavy', x=85.0) - lap: a Math \[text\] that says "$t\_(upright("lap")) = t\_(upright("corners")) + t\_(upright("straights"))$" - lean: a FunctionPlot \[blue\] labelled "upright("low wing")" drawn in power\_axes (function=\, x\_range=(0.0, 100.0)) - lean\_top: a PlotPoint \[blue\] labelled "95 thin upright("m/s")" drawn in power\_axes (target='lean', x=95.0) - power: a Math \[text\] that says "$P = F\_(upright("drag")) v prop v^3$" - power\_axes: an Axes (x\_range=(0.0, 110.0), y\_range=(0.0, 1200.0), x\_ticks\_every=20.0) - stable: a Block \[text\] that says "Later braking: the same grip rule stops the car harder. Steadier over bumps and kerbs: loaded tyres slide less. Balance: front and rear downforce keep both ends planted." - summary: a Block \[text\] that says "Inverted wings and the floor make low pressure under the car. That pressure adds to the normal force, but not to the mass. More normal force means more grip: faster corners, harder braking. The price is drag, so every circuit gets its own …" - table: a Table \[text\] that says "Circuit Character Wing level Monaco slow, tight corners maximum Monza long straights minimum Most circuits a mix of both in between" (rows=(('Circuit', 'Character', 'Wing level'), ('Monaco', 'slow, tigh…, header=True) #### Beats ##### [05:37.308](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=337.30764583333337) Narration: Downforce is not free. The air that presses the car down also holds it back, and that backward force is drag. Like downforce, it grows with the square of the speed. Board: Empty. Actions: - [05:37.308](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=337.30764583333337): h\_drag is shown on the screen, written out. - [05:37.308](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=337.30764583333337): power\_axes is shown on the screen, written out. - [05:44.348](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=344.3476458333334): power\_axes moves to a new place on the board. - [05:44.348](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=344.3476458333334): drag is shown on the screen, written out. - [05:47.308](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=347.30764583333337): drag (the "v^2" part) is emphasized. - [05:48.603](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=348.6026458333334): drag (the "v^2" part) is no longer emphasized. ##### [05:49.203](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=349.20264583333335) Narration: Pushing against drag takes power, and power is force times speed, so the power needed grows with the cube of the speed. On this graph, speed runs across and power runs up, in kilowatts. Board: drag — a Math \[text\] that says "$F\_(upright("drag")) = frac(1, 2) rho C\_D A v^2$"; power\_axes — an Axes (x\_range=(0.0, 110.0), y\_range=(0.0, 1200.0), x\_ticks\_every=20.0); h\_drag — a Heading that says "The Price: Drag" Actions: - [05:49.428](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=349.4276458333334): power is shown on the screen, written out. ##### [06:2.323](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=362.32264583333335) Narration: The blue curve is a car with small, flat wings. The yellow line is everything the engine can give. Where they meet is the top speed, about ninety five metres per second. Board: drag — a Math \[text\] that says "$F\_(upright("drag")) = frac(1, 2) rho C\_D A v^2$"; power — a Math \[text\] that says "$P = F\_(upright("drag")) v prop v^3$"; power\_axes — an Axes (x\_range=(0.0, 110.0), y\_range=(0.0, 1200.0), x\_ticks\_every=20.0); h\_drag — a Heading that says "The Price: Drag" Actions: - [06:2.788](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=362.7876458333334): lean is shown on the screen, written out. - [06:5.908](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=365.9076458333334): engine is shown on the screen, written out. - [06:10.748](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=370.74764583333337): lean\_top is shown on the screen, written out. ##### [06:13.048](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=373.0476458333334) Narration: Now bolt on bigger wings for more downforce. The red curve climbs faster, because there is more drag, and it meets the engine's limit sooner, at about eighty five. More grip in the corners has cost speed on the straight. Board: drag — a Math \[text\] that says "$F\_(upright("drag")) = frac(1, 2) rho C\_D A v^2$"; power — a Math \[text\] that says "$P = F\_(upright("drag")) v prop v^3$"; power\_axes — an Axes (x\_range=(0.0, 110.0), y\_range=(0.0, 1200.0), x\_ticks\_every=20.0); h\_drag — a Heading that says "The Price: Drag"; lean — a FunctionPlot \[blue\] labelled "upright("low wing")" drawn in power\_axes (function=\, x\_range=(0.0, 100.0)); engine — a FunctionPlot \[yellow\] labelled "P\_(upright("engine"))" drawn in power\_axes (function=\); lean\_top — a PlotPoint \[blue\] labelled "95 thin upright("m/s")" drawn in power\_axes (target='lean', x=95.0) Actions: - [06:14.388](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=374.38764583333335): heavy is shown on the screen, written out. - [06:22.148](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=382.1476458333334): heavy\_top is shown on the screen, written out. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): drag is hidden from the screen — left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): h\_drag is hidden from the screen — left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): power is hidden from the screen — left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): power\_axes is hidden from the screen — left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): lean is hidden from the screen — power\_axes left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): engine is hidden from the screen — power\_axes left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): lean\_top is hidden from the screen — power\_axes left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): heavy is hidden from the screen — power\_axes left the board. - [06:26.305](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=386.30514583333337): heavy\_top is hidden from the screen — power\_axes left the board. ##### [06:27.505](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=387.50514583333336) Narration: So every team faces the same question at every circuit. At Monaco, the corners are slow and tight, so the cars run as much wing as they can. Board: Empty. Actions: - [06:27.505](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=387.50514583333336): h\_setup is shown on the screen, written out. - [06:27.505](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=387.50514583333336): table is shown on the screen, written out. - [06:32.068](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=392.06764583333336): table is shown on the screen, written out. ##### [06:37.628](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=397.62764583333336) Narration: At Monza the straights are long, so the wings are cut almost flat to save drag. Most circuits sit somewhere in between. Board: h\_setup — a Heading that says "Choosing the Compromise" Actions: - [06:38.108](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=398.1076458333334): table is shown on the screen, written out. - [06:43.148](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=403.1476458333334): table is shown on the screen, written out. ##### [06:45.815](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=405.81514583333336) Narration: The rule behind the choice is simple. A lap is time in the corners plus time on the straights, and downforce moves time from one to the other. Teams set the wings wherever the total comes out smallest. Board: Unchanged from the preceding beat in this scene. Actions: - [06:48.708](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=408.70764583333334): lap is shown on the screen, written out. - [06:49.668](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=409.6676458333334): lap (the "t\_(upright("corners"))" part) is indicated — a transient flash. - [06:51.108](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=411.1076458333334): lap (the "t\_(upright("straights"))" part) is indicated — a transient flash. - [06:58.198](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=418.19764583333335): h\_setup is hidden from the screen — left the board. - [06:58.198](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=418.19764583333335): lap is hidden from the screen — left the board. - [06:58.198](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=418.19764583333335): table is hidden from the screen — left the board. ##### [06:59.398](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=419.3976458333334) Narration: Downforce pays off in two more ways. Braking is also limited by grip, so the same rule applies: with downforce, the car can slow far harder than its weight alone would allow, and brake later into every corner. Board: Empty. Actions: - [06:59.398](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=419.3976458333334): h\_stable is shown on the screen, written out. - [07:2.948](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=422.94764583333335): brake is shown on the screen, written out. - [07:8.628](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=428.62764583333336): brake (the "frac(D, m)" part) is emphasized. - [07:12.068](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=432.06764583333336): stable is shown on the screen, written out. - [07:12.068](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=432.06764583333336): brake (the "frac(D, m)" part) is no longer emphasized. ##### [07:14.01](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=434.01014583333335) Narration: And it makes the car stable. Tyres pressed firmly into the road are slower to break loose over a bump or a kerb, and with downforce balanced between front and rear, both ends of the car stay planted at high speed. Board: brake — a Math \[text\] that says "$a\_(upright("brake")) = mu (g + frac(D, m))$"; stable — a Block \[text\] that says "Later braking: the same grip rule stops the car harder. Steadier over bumps and kerbs: loaded tyres slide less. Balance: front and rear downforce keep both ends planted."; h\_stable — a Heading that says "Braking and Stability" Actions: - [07:20.268](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=440.2676458333334): stable (the "Steadier over bumps and kerbs" part) is emphasized. - [07:22.588](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=442.5876458333334): stable (the "Balance" part) is emphasized. - [07:22.588](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=442.5876458333334): stable (the "Steadier over bumps and kerbs" part) is no longer emphasized. - [07:25.868](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=445.86764583333337): stable (the "Balance" part) is no longer emphasized. - [07:26.965](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=446.9651458333334): brake is hidden from the screen — left the board. - [07:26.965](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=446.9651458333334): h\_stable is hidden from the screen — left the board. - [07:26.965](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=446.9651458333334): stable is hidden from the screen — left the board. ##### [07:28.165](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=448.1651458333334) Narration: So, from the top. Upside-down wings, and a floor that makes the air rush underneath, lower the pressure beneath the car. Board: Empty. Actions: - [07:28.165](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=448.1651458333334): h\_sum is shown on the screen, written out. - [07:28.165](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=448.1651458333334): summary is shown on the screen, written out. - [07:31.948](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=451.9476458333334): summary (the "Inverted wings and the floor" part) is emphasized. ##### [07:36.545](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=456.5451458333334) Narration: That pressure pushes the tyres into the road without adding a single kilogram, so the car grips harder in every corner and under braking. Board: summary — a Block \[text\] that says "Inverted wings and the floor make low pressure under the car. That pressure adds to the normal force, but not to the mass. More normal force means more grip: faster corners, harder braking. The price is drag, so every circuit gets its own …"; h\_sum — a Heading that says "What Downforce Does" Actions: - [07:40.868](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=460.8676458333334): summary (the "Inverted wings and the floor" part) is no longer emphasized. - [07:40.868](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=460.8676458333334): summary (the "adds to the normal force, but not to the mass" part) is emphasized. - [07:42.148](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=462.1476458333334): summary (the "More normal force means more grip" part) is emphasized. - [07:42.148](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=462.1476458333334): summary (the "adds to the normal force, but not to the mass" part) is no longer emphasized. ##### [07:45.53](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=465.53014583333334) Narration: The price is drag, and that is why the wings change from track to track. Downforce is not about going faster in a straight line. It is about carrying speed everywhere else. Board: Unchanged from the preceding beat in this scene. Actions: - [07:46.508](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=466.5076458333334): summary (the "More normal force means more grip" part) is no longer emphasized. - [07:46.508](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=466.5076458333334): summary (the "The price is drag" part) is emphasized. - [07:53.588](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=473.5876458333334): summary (the "The price is drag" part) is no longer emphasized. - [07:56.883](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=476.8833541666667): h\_sum is hidden from the screen — left the board. - [07:56.883](https://academa.ai/@sina/lectures/the-physics-of-downforce-in-formula-1-racing?t=476.8833541666667): summary is hidden from the screen — left the board.