The physics of Webber’s Valencia crash

Have a look at the current issue of Red Bulletin for an interesting perspective on Mark Webber’s terrifying crash with Heikki Kovalainen in Valencia.

Professor Thomas Schrefl does the maths on Webber’s aerial flip and comes up with some fascinating figures:

Doing the maths we see that the potential energy and the rotational energy take up about one to two per cent of the kinetic energy. After hitting the ground, Webber?s car slides towards the tyre barrier. Sliding means friction. The frictional force is FR = ??mg, whereby ?? is the friction coefficient between the car and the ground. The work, FRs, done by the frictional force is calculated simply: force times distance to the barrier. Friction reduces the kinetic energy by roughly 10 per cent.

From the reduced kinetic energy we find the velocity at which Webber hits the barrier to be around 280kph (174mph, 4, 5).
Professor Thomas Schrefl

He reached a height of two metres during his brief flight seen in the video below:

Find the full article in the current issue of Red Bulletin.

Read more: Webber hits Kovalainen and flips

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83 comments on The physics of Webber’s Valencia crash

  1. David Sherwood said on 5th August 2010, 9:07

    The speed with which the Red Bull moves across the run off area is incredible, with no retardation at all.

    I have heard a few people, e.g. Martin Brundle, say that a return to gravel traps would help with racing as too many people are getting away with mistakes that would previously have cost them a finish.

    Would a gravel trap have slowed the RB down safely here? If so, they should be brought back quickly.

    • RobR (@robr) said on 5th August 2010, 9:14

      I’m not sure if it would have made that much difference at that speed. He probably would have just skidded over the top of the gravel.

      I would like to see gravel traps come back though.

      • Patrickl said on 5th August 2010, 9:21

        Or the airbox might have dug in and started him spinning.

      • synapseza said on 5th August 2010, 9:37

        Probably would have just skimmed it at that speed – but the friction coefficient is probably still higher than plain concrete. And kinetic energy squares with velocity, so every little bit of speed that can be dissipated through friction will reduce the energy at impact.

        And yes, bring back gravel traps. If we can argue that they save money they will be back in flash…

        • Does anyone know why the high-friction asphalt used at Paul Ricard has not been considered at any other circuits? It isn’t the most television friendly set up, with blue lines and swirls off the track, but it would eliminate any advantage gained by running wide such as at turn 1 of Spa and the Hungaroring, and I believe could have taken off more energy in Webber’s crash.

          • KlBD said on 5th August 2010, 17:26

            Well…Paul Ricard has absolutely huge runoff areas to implement those, so it might be a space concern? Most corners requiring runoff on modern F1 tracks probably don’t have enough space to accomodate both the blue and red asphalt the HTTT has.

          • Vince said on 16th August 2010, 13:58

            Maybe high-friction run offs aren’t used because the tracks are also used to host motorbike events. Gravel is best option in that situation.

    • Mark Blundell hit a concrete wall at 185 mph + in Rio in 1996 and broke nothing (122 g’s at impact)but his internals were all re-arranged.

    • Bullfrog said on 5th August 2010, 10:52

      I don’t want to see drivers having to retire from the race – an F1 car stuck in gravel, wheels spinning, looks pathetic, and the marshals are in danger for a long time while they recover it.

      But if somehow drivers could lose more time and positions if they run wide, that would be better. More abrasive run-off area surfaces? Or some gravel, dirt or bumps at the point where the driver rejoins the track from the run-off area.

      • hawkfist said on 5th August 2010, 12:59

        Just make sure there’s enough oil/debris that drivers will probably have to pit for new tyres and they’ll soon stop using so much runoff. Bernie will probably like it to, he can advertise the specific type of oil!

  2. Same, bring back gravel traps, though of course if his car had dug in the accident could have been a lot worse. Somewhere like Valencia you are probably unlikely to get gravel traps even if they were brought back.

  3. spawinte said on 5th August 2010, 9:38

    I don’t believe for a second that he hit the barriers at 174. He’d have serious injuries if that was the case. Air resistance as the car flew broadside through the air would have immediately had the car well below 174.

    • f1yankee said on 5th August 2010, 9:48

      professor thomas schrefl has shown his math, please show yours.

      • Mike said on 5th August 2010, 10:56

        My Year 12 physics last year tells me, that this is riddle with problems, Keith I know I wasn’t nice recently but, I really would like to know where you got this from, pretty please?

        “Doing the maths we see that the potential energy and the rotational energy take up about one to two per cent of the kinetic energy”
        Ok I don’t like this, First, Newtons 3rd law of motion means that this, Can’t be correct, Assuming the Vehicle is travelling in a straight line towards the barrier, and it only travels directly up and down, (which is what my understand of physics necessitates we do), there is now reason ignoring air resistance, that the vehicle once airborne should slow down.

        This is because for it to slow down a force must act on it to slow it down, the only forces that can affect it while airborne are gravity and air resistance, of which gravity will not affect it’s speed in a perpendicular direction to the gravitational pull of the earth, and air resistance is being ignored.

        “After hitting the ground, Webber’s car slides towards the tyre barrier.”
        A lot of the cars velocity would already have been bled of by air resistance, (MUCH! more than 1 or 2%.
        ” Sliding means friction.”
        Correct

        “The frictional force is FR = µmg, whereby µ is the friction coefficient between the car and the ground.”

        I’d like to know how he knows the friction coefficient, most ideally this could be estimated by working out the contact patch of the tyres, (and each tyres friction coefficient from that) but that assumes all four wheels were touching the ground constantly from when Webber landed, not only that, but it assume that Webber has the brakes on and the wheels can’t rotate. in which case, the rolling friction would be significantly less than the sliding based friction (bad terminology I know!)

        “The work, FRs, done by the frictional force is calculated simply: force times distance to the barrier.
        Friction reduces the kinetic energy by roughly 10 per cent.

        “This would require me to get my physics book, I never fully understood work.
        So I’ll accept 10%.

        “From the reduced kinetic energy we find the velocity at which Webber hits the barrier to be around 280kph (174mph, 4, 5).”

        That’s wrong, 1) He has ignore Air resistance, put your hand out of a car window to see if it’s important, and then pretend the car was going over 200km/h and your hand was the size of an F1 car. (I think i made my point)

        Also, When the car hit the ground it would have been travelling in a diagonal direction (or there abouts) which means a equal force would exert itself on the car, slowing it down as part of that force (once broken down into parallel and perpendicular to the gravitation force using Vectors) would be opposite the direction of the cars velocity, ergo slowing it down.

        I am quite proud of myself!

        • Keith Collantine (@keithcollantine) said on 5th August 2010, 10:57

          I really would like to know where you got this from

          Red Bulletin – it says in the article.

        • Mike said on 5th August 2010, 11:07

          there is now reason ignoring air resistance, that the vehicle once airborne should slow down.

          Should read

          There is no reason it should slow down, if you ignore air resistance.

          • Mike said on 5th August 2010, 11:20

            The Professor is right to simplify it, otherwise it would be impossible, but the negation of air resistance means the reults, as they were would be way off,

            I think rather than a demonstration of the physics of the crash his working could demonstrat it once the car has hit the ground, but, he has that bit about “one to two per cent of the kinetic energy” which, I can’t see how that could happen, if no forces are acting against the car. (ignoring air resistance as he did.)

    • Kris said on 5th August 2010, 9:57

      Exactly! this is not taken into account in calculations at all. Drag at 170 on its own gives deacceleration grater than road car at full brakes. On the top of that when he spins surface are of whole floor acts as huge air brake.

      • Swampie said on 5th August 2010, 11:04

        After reading the document, air resistance is definitely not included. He only considers conversion to potential energy (energy required to raise the car the into the air), rotational engergy (energy required to rotate the car) and friction on the ground.

        He claims it was 2m in the air, but the car hits the sign (14 seconds into above video) and is upside down at the height of the sign. Judging by the height of rear wing (1m), the blue barriers are slightly higher than the car, wire fencing appears 2x height of blue barriers, and the sign itself appears to be about 1m high. That means the car was raised 3-4m, up to double that which he suggested.

        Failing to include the drag is a big flaw in the calculation. Airbrakes make a huge difference to deceleration. The equation for drag is Fd = (pv^2CdA)/2 (Fd = force of drag, p = density of fluid, v = speed relative to fluid, A is the area and Cd drag coefficient). High speed creates high drag (it’s squared), the larger the area A, the higher the drag (and the area of a F1 car’s floor is large). Whilst I don’t have the figures to plug into the equation, having a high velocity and high area is going to create a high drag force. To leave this out of the equation is a significant omission.

        I would therefore suggest that the actual impact speed was much less than 174mph. How much less, I don’t know.

        • graham228221 said on 5th August 2010, 11:15

          Agreed, it doesn’t include air resistance.

          Most dynamics equations don’t include this as it’s incredibly hard to factor in. For this problem you’d need to model the changing drag as the car rotates through the air; possibly doable if you had the might of RBR’s CFD at your disposable, but probably not possible if you’re working it out on the back of an envelope.

          The weirdest thing is that a physicist would let an article bearing his name to be quite obviously wrong!

          • graham228221 said on 5th August 2010, 11:17

            “Most dynamics equations don’t include this as it’s incredibly hard to factor in.”

            Most dynamics equations in undergrad and below level physics, that should be. That’s why most exam questions include the disclaimer: “Not accounting for air resistance”.

          • Mike said on 5th August 2010, 12:20

            It’s quite an important point for what his subject is, also, He talks about loss of kinetic energy due to rotation and potential energy, which is height, but, and this is what I can’t understand, The height only occurred because of the collision of the cars, yet, he’s ignored the actual collision’s effect, Which means the initial speed when it took off, is wrong.

            So it can’t be demonstrating the collision in my mind, on the other hand it could be used as an example of a physics principle, as if used in a classroom environment.

    • Keith Collantine (@keithcollantine) said on 5th August 2010, 10:08

      If anyone can come up with a better mathematical model for the crash than the professor’s that’s a Comment of the Day right there.

  4. Jeff said on 5th August 2010, 9:51

    Yes no way he hit the barrier at 174mph, it only took 70mph at Silverstone to break Schumis leg…cars have come on since then but no way 174mph…

    • The_Pope said on 5th August 2010, 12:59

      Actually, I believe the regulations beefed up the nose-cone structure as a result of that crash to better protect drivers from intrusions like suspension components.

      Also, am I remembering rightly that Schumi was very unlucky and somehow managed to crash right between the tyres or something? Also resulting in a rethink on barriers…

  5. LewisC said on 5th August 2010, 10:10

    I haven’t read the document yet, but are they seriously telling me they don’t have an accelerometer in that car to know exactly how hard it hit?

    Or, I don’t know… maybe look at the video and do distance/time?

  6. Alex Andronov said on 5th August 2010, 10:23

    This gives me a chance to pull out my favourite physics joke… Why did the cat fall off the roof? Because it lost it’s µ (pronounced Mu).

  7. Nixon (@nixon) said on 5th August 2010, 10:25

    It looks really slow, and instead of bringing gravel traps i think sand traps are better because it won’t damage the car.

  8. Swampie said on 5th August 2010, 10:38

    Surely the easiest way of checking it is to know the distance he travelled on the ground and measure the time. Estimating number of car lengths may help. It doesn’t appear that he decelerated much once skidding on the runoff, so it’s probably a fair estimate of his impact speed.

  9. get rid of tarmac in the run of area, when there was gravel no driver could make a mistake, now they just pushing but there is no real limit … white line ? No thats not a limit…

    Lets pick just few tracks with gravel traps, Spa – Sepang – Melbourne – when there is gravel the races are much better.

    If drivers makes a mistake or is over the limit he is stuck in gravel but on tarmac, they just cut the road

    • yes but (a) tarmac run off = more cars left in race as opposed to (b) gravel traps – less cars left in race (a) = better for spectators

    • Robert McKay said on 5th August 2010, 10:52

      “Lets pick just few tracks with gravel traps, Spa – Sepang – Melbourne – when there is gravel the races are much better.”

      Surely you’re not suggesting gravel traps are the primary decider of where races are good.

    • Joey-Poey said on 5th August 2010, 15:31

      I would normally agree that I’d like to see a return to gravel traps to better punish mistakes. HOWEVER, in this case, a gravel trap could have been majorly disastrous. If his car had caught any crest in the gravel, it could have started it rolling. And rolling at that speed heading into the barrier doesn’t bear to think about. We might not have our 5 championship contender right now.

  10. FIA need to look at over track signage, if the sign webber hit was stronger the accident would have been horrific

  11. Robert McKay said on 5th August 2010, 10:47

    If you reverse engineer the calculation as the Professor gives it then he only lost about 10-15 mph through the whole thing, which I find difficult to believe.

  12. Chris Powell said on 5th August 2010, 10:56

    How about “stingers” instead of run off/gravel? that would make things interesting.

  13. John H said on 5th August 2010, 10:56

    We probably have a high Reynolds number meaning quadratic drag.

    drag equation: F = (p*u^2*C*A)

    p = density of air at 35 degrees 1.15 kg/m3.
    A = area exposed = about 10 m2
    C = average drag coefficient (of such a rotating body) 0.5
    u = speed relative to air = 85m/s (190 mph, this is Valencia)

    So, F = about 20000 Newtons

    Using Newton’s second law:
    (F*dt)/m = dv

    Car is about 650kg. Time through the air about 2 seconds.

    so dv = -30 m/s (approx)

    Hence before the friction comes into play, we have scrubbed about 35% of the speed, although this is a bit exaggerated because as the car slows, so the drag decreases.

    So before the friction came into play, Webber was doing about 120mph. He probably hit the wall at about 100-110 mph I reckon, although this is all approximate of course!

    • Robert McKay said on 5th August 2010, 10:58

      I’ll nominate this one for post of the day, for both the physics and getting the numbers to look sensible :-D

    • I tried to copy your drag arguments but I think you might have missed a factor of 2 in Newton’s equation (2 seconds), which would make dv a massive -60m/s.

      As you said, the answer is exaggerated as the drag depends on the velocity (pretty strongly too).

      F = (pCAv^2)/2 (I think you forgot the 1/2 here but given that you found F=20.000 you must have taken it into account) i.e. F = 2.875*v^2

      Then, F = -m*dv/dt, i.e. dv/dt = -0.0044*v^2

      Integrating, we find 1/v = 0.0044*t + 1/85 (the 1/85 comes from the initial condition), i.e. after 2 seconds we have v = 49 m/s or 180kph.

      The velocity affects the drag pretty heavily, hence if you calculate the drag for the total “journey” (I took this to be 5 seconds, from memory) you find v = 30 m/s or 108kph.

      Friction would reduce the speed even further.

      I am not sure about the A parameter – is it really as much as 10 m^2? A reduced A would change the calculations quite a bit so if someone has a suggestion please correct me.

      • John H said on 5th August 2010, 13:20

        Thanks for correcting my sloppiness, and integrating for a changing velocity.

        The area is obviously dependent on the time due to the rotation of the car in quite complex way, so the 10m^2 would not be exposed for the full 5 seconds, that’s why I only took the time flying through the air.

        And in this period, you’re right that 10m^2 is a bit over the top (it’s probably about half that – especially as the angle of the floor is always changing to the direction of travel).

        Plus there are the impact forces when he hits the ground that probably slow the thing down too… and the bridge contact… etc!!

        • Well done John H and Ino! The only interesting point I can add to that is that single seater racing cars typically have a Cd of around 1, even when they’re facing in the right direction. It’s a surprisingly high number (most road cars are in the range of 0.2 to 0.4) but that’s where they get all the downforce. But then, as you note, 10m^2 is too high so it probably balances out.

          Prof. Schrefl – whose main field of interest appears to be micromagnetism and simulation of other micro- and small-scale material properties, rather than anything directly related to this subject – additionally neglected to take into account the external force applied by Heikki’s rotating rear wheel. He also assumed that the rotational kinetic energy of Mark’s rolling car had been converted from straight-line speed (whereas in fact it was purely down to aerodynamics and the external force I just mentioned), and forgets that the rotational kinetic energy in at least two axes, like the potential energy term, was absorbed by the car & suspension when it landed back on its wheels.

          • Thanks for the Cd reference, I didn’t know what that was but it clearly depends on the car orientation. The area is also hard to calculate.

            Basically, the final speed depends so much on the drag that it almost doesn’t make sense to try and calculate it. For example, if we take half the drag (say A=5m^2) then the speed after the full 5 seconds is about v=45m/s (or thereabouts- I did the calculations earlier and threw that piece of paper away!)- much higher!

            And there’s extra complications: the friction, the impact with Heikki’s car, the impact when it landed on the ground again, etc.

            What is “for sure”, is that Professor Thomas Schrefl doesn’t make much sense…

    • I loved physics in scholl and all but right now, my head is melting! :P

  14. Johnny86 said on 5th August 2010, 11:13

    I think in physics we normally ignore the air resistance. But in reality its relevent.and the fact that the car’s front is upside provides more surface area for resistance.and when webber’s car lands a lot of kinetic energy will be converted to pot energy on the basis of Mgh we may find out the exact loss of k.e. So the total k. energy of the car at the time of crash= k.e before the crash – loss of k.e at the time of contact-air resistance-loss due to the car rotation(given)- loss of k.e. At the time of landing-loss of k.e due to kinetic friction. Which will result in quite less then the predicted 175mph impact velocity. I m guessing only Bcoz i’m a 17 yrs old student only.

  15. Good morning everybody. I have to say that’s my main job is to assess risks involved in these kind of accidents, especially for riders but not only, and I investigate daily the physics law and the tarmac friction/gravel bed run-off areas pro/cons.

    Said this…all F1 cars have an ADR onboard (Accident Data Recorder) that record like a black box all speed and forces generated in an impact. So RedBull know perfectly the speeds. I don’t know about Prof Schrefl knowledge about these accident data, but his formulae and result are correct (IF the starting speed is right and if the friction coefficient assumed is too).

    What I suggest is that I don’t think that the speed was so high in impact because in that point, if I’m not wrong, there was a conveyor belt with three layers of tyre barriers behind a concrete temporary block. FIA knows for sure (because they tested it), that these kind of barriers don’t resist to a F1 penetration at over 150/180 kph. Obviously here the Webber’s car was not hitting in straight, but I think that 280 Kph could be too high.

    On the friction side, I would say that the tarmac reduces his friction while increasing the speed, so the coefficient to use at 300 Kph is less than the one you need to use at 200 kph. Is anyway absolutely believable that the decreasing of speed was so less, because the friction between carbon fiber and tarmac is very low, and the speed decay curve give reason to this.

    Once again, despite formulae are good, we need to know that starting data are good too. Reversing the video could for sure check the result.

    Last but not least: the Paul Ricard run-offs are painted only for graphical reasons. The friction is made with the tarmac compound, not with the color, so it could be (but it cost too much) deployed in any tarmac run-off.

    • BasCB said on 5th August 2010, 17:31

      Thanks very much for this post Jarno! Although you don’t have the auto COTD for the right formula you shed a lot of light onto what is going on here.

      Thumbs up.

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