{"version":1,"lectureId":"01M50YV9KAREAMYX0CPJTDF7QG","attempt":0,"publication":{"slug":"the-physics-of-downforce-in-formula-1-racing","title":"The Physics of Downforce in Formula 1 Racing","subject":"physics","summary":"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.","metaDescription":"How Formula 1 downforce works: inverted wings, Bernoulli and ground effect, grip without extra mass, and the drag trade-off behind lap times.","transcript":"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. 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. 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. 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.","watch":{"version":1,"scenes":[{"title":"Grip in a Corner","start":0,"end":101.17737499999998,"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=(<VariableNumber grip_tip = 0.6>, 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, <VariableNumber push = 5.6>))","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":[{"start":0,"say":"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.","live":[],"does":[[0,"card is shown on the screen, written out."],[1.3763631411711306,"card: enter:write-left-to-right."],[17.775,"card is hidden from the screen — left the board."]]},{"start":18.974999999999998,"say":"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.","live":null,"does":[[18.974999999999998,"heading is shown on the screen, written out."],[18.974999999999998,"view is shown on the screen, written out."],[23.28,"body is shown on the screen, written out."],[24.919999999999998,"ground is shown on the screen, written out."],[25.599999999999998,"left_tyre is shown on the screen, written out."],[25.852727918388428,"right_tyre is shown on the screen, written out."]]},{"start":26.967499999999998,"say":"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.","live":["view","heading","body","ground","left_tyre","right_tyre"],"does":[[36.599999999999994,"friction is shown on the screen, written out."]]},{"start":39.724999999999994,"say":"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.","live":["view","heading","body","ground","left_tyre","right_tyre","friction"],"does":[[39.724999999999994,"view moves to a new place on the board."],[39.724999999999994,"need is shown on the screen, written out."],[43.239999999999995,"need (the \"frac(m v^2, r)\" part) is emphasized."],[47.75999999999999,"need (the \"frac(m v^2, r)\" part) is no longer emphasized."]]},{"start":51.269999999999996,"say":"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.","live":["need","view","heading","body","ground","left_tyre","right_tyre","friction"],"does":[[52.599999999999994,"grip is shown on the screen, written out."],[58.04,"normal is shown on the screen, written out."],[59.879999999999995,"grip (the \"N\" part) is emphasized."],[61.724999999999994,"grip (the \"N\" part) is no longer emphasized."]]},{"start":62.324999999999996,"say":"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.","live":["need","grip","view","heading","body","ground","left_tyre","right_tyre","friction","normal"],"does":[[64.96000000000001,"load is shown on the screen, written out."],[65.44,"weight is shown on the screen, written out."],[72.28000000000002,"grip (the \"mu N\" part) is indicated — a transient flash."],[73.52000000000001,"need (the \"frac(m v^2, r)\" part) is indicated — a transient flash."]]},{"start":76.79249999999999,"say":"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.","live":["need","grip","load","view","heading","body","ground","left_tyre","right_tyre","friction","normal","weight"],"does":[[80.60000000000001,"downforce is shown on the screen, written out."],[82.04,"normal is redrawn as the numbers it depends on change."],[82.04,"push ticks to 5.6."],[86.68000000000002,"load becomes \"$N = m g + D$\"."]]},{"start":88.01999999999998,"say":"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.","live":["need","grip","load","view","heading","body","ground","left_tyre","right_tyre","friction","normal","weight","downforce"],"does":[[90.96000000000001,"friction is redrawn as the numbers it depends on change."],[90.96000000000001,"grip_tip ticks to 0.6."],[96.72000000000001,"A box is drawn around load."],[100.1357083333333,"grip is hidden from the screen — left the board."],[100.1357083333333,"heading is hidden from the screen — left the board."],[100.1357083333333,"load is hidden from the screen — left the board."],[100.1357083333333,"need is hidden from the screen — left the board."],[100.1357083333333,"view is hidden from the screen — left the board."],[100.1357083333333,"body is hidden from the screen — view left the board."],[100.1357083333333,"ground is hidden from the screen — view left the board."],[100.1357083333333,"left_tyre is hidden from the screen — view left the board."],[100.1357083333333,"right_tyre is hidden from the screen — view left the board."],[100.1357083333333,"friction is hidden from the screen — view left the board."],[100.1357083333333,"normal is hidden from the screen — view left the board."],[100.1357083333333,"weight is hidden from the screen — view left the board."],[100.1357083333333,"downforce is hidden from the screen — view left the board."]]}]},{"title":"The Upside-Down Wing","start":101.17737499999998,"end":230.09516666666667,"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, <VariableNumber ride = 0.5>), (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":[{"start":101.17737499999998,"say":"An aeroplane wing is shaped to lift. 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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.","live":[],"does":[[230.09516666666667,"heading is shown on the screen, written out."],[230.09516666666667,"axes is shown on the screen, written out."]]},{"start":245.66516666666666,"say":"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.","live":["axes","heading"],"does":[[245.97516666666667,"need_curve is shown on the screen, written out."],[251.85516666666666,"flat_grip is shown on the screen, written out."]]},{"start":258.78516666666667,"say":"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.","live":["axes","heading","need_curve","flat_grip"],"does":[[258.97516666666667,"probe is shown on the screen, written out."],[262.81516666666664,"probe is redrawn as the numbers it depends on change."],[262.81516666666664,"speed ticks to 30.0."],[264.09516666666667,"probe is redrawn as the numbers it depends on change."],[264.09516666666667,"speed ticks to 44.0."],[267.61516666666665,"probe is redrawn as the numbers it depends on change."],[267.61516666666665,"speed ticks to 38.3."],[268.3351666666667,"plain_limit is shown on the screen, written out."],[272.4601666666667,"probe is hidden from the screen."]]},{"start":273.06016666666665,"say":"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.","live":["axes","heading","need_curve","flat_grip","plain_limit"],"does":[[273.06016666666665,"axes moves to a new place on the board."],[273.06016666666665,"work is shown on the screen, written out."],[275.6551666666667,"work (the \"frac(m v^2, r)\" part) is emphasized."],[278.6551666666667,"work (the \"frac(m v^2, r)\" part) is no longer emphasized."],[278.6551666666667,"work (the \"mu (m g + D)\" part) is emphasized."],[282.97766666666666,"work (the \"mu (m g + D)\" part) is no longer emphasized."]]},{"start":283.5776666666667,"say":"From the last section, downforce is a constant k times speed squared. Put that in, and gather every v squared term on the left.","live":null,"does":[[288.3351666666666,"work is shown on the screen, written out."],[289.29516666666666,"work is shown on the screen, written out."]]},{"start":292.28266666666667,"say":"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.","live":null,"does":[[293.0151666666667,"work is shown on the screen, written out."],[303.1351666666667,"work (the \"1 - frac(mu k r, m)\" part) is emphasized."],[306.48516666666666,"work (the \"1 - frac(mu k r, m)\" part) is no longer emphasized."]]},{"start":307.0851666666667,"say":"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.","live":null,"does":[[308.8951666666667,"aero_grip is shown on the screen, written out."],[315.7751666666667,"aero_limit is shown on the screen, written out."],[318.4951666666667,"result is shown on the screen, written out."]]},{"start":322.3376666666667,"say":"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.","live":["result","axes","heading","need_curve","flat_grip","plain_limit","aero_grip","aero_limit"],"does":[[325.09516666666667,"work (the \"frac(mu k r, m)\" part) is indicated — a transient flash."],[332.0551666666667,"A box is drawn around result."],[336.2659791666666,"axes is hidden from the screen — left the board."],[336.2659791666666,"need_curve is hidden from the screen — axes left the board."],[336.2659791666666,"flat_grip is hidden from the screen — axes left the board."],[336.2659791666666,"plain_limit is hidden from the screen — axes left the board."],[336.2659791666666,"aero_grip is hidden from the screen — axes left the board."],[336.2659791666666,"aero_limit is hidden from the screen — axes left the board."],[336.2659791666666,"heading is hidden from the screen — left the board."],[336.2659791666666,"result is hidden from the screen — left the board."],[336.2659791666666,"work is hidden from the screen — left the board."]]}]},{"title":"The Price and the Payoff","start":337.30764583333337,"end":477.92502083333335,"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=<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=<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=<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":[{"start":337.30764583333337,"say":"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.","live":[],"does":[[337.30764583333337,"h_drag is shown on the screen, written out."],[337.30764583333337,"power_axes is shown on the screen, written out."],[344.3476458333334,"power_axes moves to a new place on the board."],[344.3476458333334,"drag is shown on the screen, written out."],[347.30764583333337,"drag (the \"v^2\" part) is emphasized."],[348.6026458333334,"drag (the \"v^2\" part) is no longer emphasized."]]},{"start":349.20264583333335,"say":"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.","live":["drag","power_axes","h_drag"],"does":[[349.4276458333334,"power is shown on the screen, written out."]]},{"start":362.32264583333335,"say":"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.","live":["drag","power","power_axes","h_drag"],"does":[[362.7876458333334,"lean is shown on the screen, written out."],[365.9076458333334,"engine is shown on the screen, written out."],[370.74764583333337,"lean_top is shown on the screen, written out."]]},{"start":373.0476458333334,"say":"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.","live":["drag","power","power_axes","h_drag","lean","engine","lean_top"],"does":[[374.38764583333335,"heavy is shown on the screen, written out."],[382.1476458333334,"heavy_top is shown on the screen, written out."],[386.30514583333337,"drag is hidden from the screen — left the board."],[386.30514583333337,"h_drag is hidden from the screen — left the board."],[386.30514583333337,"power is hidden from the screen — left the board."],[386.30514583333337,"power_axes is hidden from the screen — left the board."],[386.30514583333337,"lean is hidden from the screen — power_axes left the board."],[386.30514583333337,"engine is hidden from the screen — power_axes left the board."],[386.30514583333337,"lean_top is hidden from the screen — power_axes left the board."],[386.30514583333337,"heavy is hidden from the screen — power_axes left the board."],[386.30514583333337,"heavy_top is hidden from the screen — power_axes left the board."]]},{"start":387.50514583333336,"say":"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.","live":[],"does":[[387.50514583333336,"h_setup is shown on the screen, written out."],[387.50514583333336,"table is shown on the screen, written out."],[392.06764583333336,"table is shown on the screen, written out."]]},{"start":397.62764583333336,"say":"At Monza the straights are long, so the wings are cut almost flat to save drag. Most circuits sit somewhere in between.","live":["h_setup"],"does":[[398.1076458333334,"table is shown on the screen, written out."],[403.1476458333334,"table is shown on the screen, written out."]]},{"start":405.81514583333336,"say":"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.","live":null,"does":[[408.70764583333334,"lap is shown on the screen, written out."],[409.6676458333334,"lap (the \"t_(upright(\"corners\"))\" part) is indicated — a transient flash."],[411.1076458333334,"lap (the \"t_(upright(\"straights\"))\" part) is indicated — a transient flash."],[418.19764583333335,"h_setup is hidden from the screen — left the board."],[418.19764583333335,"lap is hidden from the screen — left the board."],[418.19764583333335,"table is hidden from the screen — left the board."]]},{"start":419.3976458333334,"say":"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.","live":[],"does":[[419.3976458333334,"h_stable is shown on the screen, written out."],[422.94764583333335,"brake is shown on the screen, written out."],[428.62764583333336,"brake (the \"frac(D, m)\" part) is emphasized."],[432.06764583333336,"stable is shown on the screen, written out."],[432.06764583333336,"brake (the \"frac(D, m)\" part) is no longer emphasized."]]},{"start":434.01014583333335,"say":"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.","live":["brake","stable","h_stable"],"does":[[440.2676458333334,"stable (the \"Steadier over bumps and kerbs\" part) is emphasized."],[442.5876458333334,"stable (the \"Balance\" part) is emphasized."],[442.5876458333334,"stable (the \"Steadier over bumps and kerbs\" part) is no longer emphasized."],[445.86764583333337,"stable (the \"Balance\" part) is no longer emphasized."],[446.9651458333334,"brake is hidden from the screen — left the board."],[446.9651458333334,"h_stable is hidden from the screen — left the board."],[446.9651458333334,"stable is hidden from the screen — left the board."]]},{"start":448.1651458333334,"say":"So, from the top. Upside-down wings, and a floor that makes the air rush underneath, lower the pressure beneath the car.","live":[],"does":[[448.1651458333334,"h_sum is shown on the screen, written out."],[448.1651458333334,"summary is shown on the screen, written out."],[451.9476458333334,"summary (the \"Inverted wings and the floor\" part) is emphasized."]]},{"start":456.5451458333334,"say":"That pressure pushes the tyres into the road without adding a single kilogram, so the car grips harder in every corner and under braking.","live":["summary","h_sum"],"does":[[460.8676458333334,"summary (the \"Inverted wings and the floor\" part) is no longer emphasized."],[460.8676458333334,"summary (the \"adds to the normal force, but not to the mass\" part) is emphasized."],[462.1476458333334,"summary (the \"More normal force means more grip\" part) is emphasized."],[462.1476458333334,"summary (the \"adds to the normal force, but not to the mass\" part) is no longer emphasized."]]},{"start":465.53014583333334,"say":"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.","live":null,"does":[[466.5076458333334,"summary (the \"More normal force means more grip\" part) is no longer emphasized."],[466.5076458333334,"summary (the \"The price is drag\" part) is emphasized."],[473.5876458333334,"summary (the \"The price is drag\" part) is no longer emphasized."],[476.8833541666667,"h_sum is hidden from the screen — left the board."],[476.8833541666667,"summary is hidden from the screen — left the board."]]}]}]},"durationSeconds":478,"chapters":[{"title":"Grip in a Corner","startSeconds":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. 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."},{"title":"The Upside-Down Wing","startSeconds":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. 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."},{"title":"How Much Faster?","startSeconds":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. 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."},{"title":"The Price and the Payoff","startSeconds":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. 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."}]}}