Dot Physics

Mercedes Roll

Here is a commercial for some Mercedes car. The first part is quite boring, but check out the stunt at around 2:00 minutes into the video.

I haven’t bothered to check if this is officially fake or not. Instead, I will do what I do – see if this is even feasible.

The common question people ask when they see something like this is: “how does the car defy gravity?” Well, it doesn’t. Why doesn’t it fall? In a sense it does. This is essentially the same as spinning a bucket of water over your head. Maybe a diagram of the car at the top of the tunnel will help.

i-e2d84cf4265f3ed5d5738acf74c6c84d-2010-07-13_untitled_1.jpg

I tried to make the car stand out a little more in this image, but it doesn’t look too great. The point is that this is a car coming out of the screen and there are essentially only two forces acting on it. There is the gravitational force (down) and there is also the wall (or ceiling) pushing down. There is no force pushing it up.

I know what you are thinking – but if there is no force pushing it up, wouldn’t it move down? Remember that forces don’t make things move, forces change the momentum (or change the velocity – which ever way you like to think about it). So, if the car’s velocity is changing, then that is ok. The velocity, not the speed. If the direction of the velocity changes, that will work. Let me re-draw the diagram showing the velocity.

i-36126d4194347c548b2c6acdcad11226-2010-07-13_untitled_2.jpg

As long as this acceleration is greater than the acceleration of a free falling object, then the wall must still exert a force on the car (and thus the car will still be on the wall). The relationship between speed, radius and acceleration is:

i-922e95abc1af9b57e5e5f5affd2454c0-2010-07-13_la_te_xi_t_1_1.jpg

If you want more details about the acceleration of things moving in circles, check this post out.

Some Calculations

If I call up the y-direction, then I can write the following for the y-components of forces on the car:

i-cd1e1b4f19c3debccb7851fa9aabda44-2010-07-13_la_te_xi_t_1_6.jpg

I guess I should make something clear here. This car is not moving in a simple circle. It is really moving in a spiral. I am just going to look at the motion in the plane perpendicular to the road. The v in the above equation is not what the speedometer reads in the car, but rather the speed the car moves tangent to the road or the speed of the car going around the circle.

Let me find the minimum speed a car could go and not “fall”. At this minimum speed, there will be no force between the car and the wall, N will be zero Newtons. This means:

i-00a38c5a85fc27b4f87ed254bed3970a-2010-07-13_la_te_xi_t_1_13.jpg

Now I just need the radius of this circle. Using the person standing there (dumb thing to do really) as 1.8 meters, the diameter of the tunnel is about 8.5 meters. This means the tangential velocity of the car must be at a minimum:

i-3306cdae8073ac825575d84e583b9181-2010-07-13_la_te_xi_t_1_14.jpg

6.5 m/s is about 14.5 mph. How fast is the car actually going? From the video, I get that the car rotates through about 180 degrees in .44 seconds. Using the same value of r from above, this would give a tangential velocity of:

i-d294a6fa35bb929bf1d772e31eb9964c-2010-07-13_la_te_xi_t_1_15.jpg

30.3 m/s is greater than the minimum 6.5 m/s. How does this compare to the total speed of the car? Well, I don’t know why they did it, but the video shows these distance markers.

i-282ec621959bfa0a30723f31d3999e01-2010-07-13_av_mercedes_slsrollwmv_3.jpg

Using those markers (that appear to be 25 meters apart), I find that it takes the car 1.28 seconds to go 150 meters. This gives a speed of 117 m/s or 260 mph? Really? Can that be right? Even 200 mph seems too fast.

Maybe I can get an estimate on that speed another way. I already calculated a tangential velocity of 30 m/s. If I can estimate the angle the car is traveling with respect to the road, I should be able to get the tangential velocity as a component of the total velocity. Using the numbers I already have, this would be:

i-b9e780b9c698fac91f376fdcfee8cc69-2010-07-13_la_te_xi_t_1_16.jpg

That doesn’t seem unreasonable for an angle. Also, there is no real good evidence from the video for this angle. The best shot I have is this:

i-5f3a905ccd0703b5a603700c0053f96f-2010-07-13_av_mercedes_slsrollwmv_5.jpg

But the angle is difficult to measure there because of perspective issues.

Conclusion

Real or fake? Well, remember I was going to look at if it was even possible. It is obviously possible. There has to be some other videos out there that show a car doing this (I briefly searched, but didn’t find anything good). I am pretty sure I have seen a stunt like this before (there is the similar “loop the loop” stunt – 5th Gear did this). Physics-wise, this is possible.

As for this stunt, I don’t see anything that says it HAS TO BE fake. I find it unlikely that a car would go 260 mph in a tunnel while turning and trying to line up the ramp. Just seems a little fast to me. Maybe I messed up that part of the calculation.

UPDATE: Thanks to Dale (in the comments) for pointing out that the distance markers don’t seem to 25 meters apart – that would give me the wrong speed. Also, double bonus to commenter hillby for finding another tunnel roll video. This was done by Top Gear.

Comments

  1. #1 Daniel Pineda
    July 13, 2010

    Does this car have a diffuser/effective spoiler? If so, it might provide additional downforce to keep it close to the wall.

  2. #2 hillby
    July 14, 2010

    Top Gear did the same thing – running a compact car through a sewer tunnel. It’s a lot funnier, and clearly not fake. He just barely makes it without a flip.
    http://www.youtube.com/watch?v=-TbpgZ2Dt0A

  3. #3 Dale
    July 14, 2010

    I don’t think the markers are a real 25m apart. If you look at the car near the markers the size just doesn’t seem right. Unless it is a huge car.

  4. #4 lordaxil
    July 14, 2010

    You assumed constant (linear) velocity during the approach: perhaps the car is accelerating? You could check the intermediate velocities between each marker point.

    Also – your minimum tangential speed is too low. N = 0 would mean the car wheels are spinning. Setting it equal to, say, half the car’s weight might be more reasonable.

  5. #5 Rhett Allain
    July 14, 2010

    @hillby,

    YES! That is where I saw it – thanks for the link.

  6. #6 Rhett Allain
    July 14, 2010

    @Dale,

    I think you may be right. I just assumed the signs where what they said they were. Silly me.

  7. #7 mcjhn
    July 14, 2010

    not vertical, but pretty impressive at the end!

    http://www.youtube.com/watch?v=Oq1QnZPRp20

  8. #8 mark
    July 14, 2010

    not vertical, but pretty impressive at the end!

    http://www.youtube.com/watch?v=Oq1QnZPRp20

  9. #9 Curmudgeon
    July 14, 2010

    I have to echo the “It’s not 25m comment.” If you look at the distance between the two yellow lines, you can get a sense of the distance to various parts of the turn.

    Additionally, pausing the video when the car is abreast of the long light bulbs (and looking down from drivers side – camera mounted on opposite wall near the ceiling) show that those bulbs are about the length of the car on center.

    I almost think those signs were included post filming.

    Still it’s really cool. And, I think, legit.

  10. #10 fkat
    July 18, 2010

    most definitely a fake; scenes are all cut up. angle of entry does not seem to be great enough to produce the centripetal force to overcome the gravitational force. If SLS was even going 180 mph it would fall most certainly fall to the ground. But it’s fun to watch. Thanks for the analysis.

  11. #11 Justin Case
    July 24, 2010

    The Mercedes commercial is certainly within the realm of possibility; one thing that makes me think it’s real is that there are ramps to curve where the tunnel meets the pavement – which NEED to be there.

    HOWEVER, there are people and vehicles standing all over the roadway; if anything went wrong, many would be killed. This makes me think the actual video is fake.

  12. #12 Mr. Practical
    August 30, 2010

    There is a curb on each side of the road bed. Also there appears to be a conduit box that sticks out that the lights are set into running the full length of the tunnel at the top of the wall. The walls also appear to be fairly straight vertical, not curved. So… driving over a curb at high speed at a 15° angle (without peeling your tires off), losing all of your horizontal momentum on contact with the base of the wall and somehow managing to climb up the rest of the way, plowing through or over the light conduit, and then doing the same thing on the way down again. Not likely. It is fun to think these things through though.

  13. #13 Matt Clare
    September 14, 2010

    The funny fake part is when the Mercedes signed Michael Schumacher they re-cut the last scene to make it look like he driving http://www.youtube.com/watch?v=izrNv4nMxAg&feature=fvsr

    You can see their commitment to integrity in this project.

  14. #14 Trolly Mcgeek
    September 26, 2010

    Lady Di tried the same thing…

  15. #15 John Becker
    November 10, 2010

    The physics of a roll are good, amusement park roller coasters do it all the time. However, I don’t think this was done exactly as depicted.
    1. Firemen, onlookers and vehicles in the roadway were probably photoshopped post-production.
    2. The film was sped up to make the car appear to be going faster, so velocity calculations based on the time between markers are invalid. Likewise the tangential velocity calculations.
    3. Distance markers probably were 25 meters apart, but the apparent spacing was foreshortened by using a long lens. You can tell they used a long lens by looking at the screen shot of the side wall with the ramp: if the camera was as close to the ramp as it appeared, it would have been run over. Plus, you can’t see it in the long shot. Related to this,
    4. You can see additional foreshortening in the long shot where the car is at the top of the tunnel. The lighting rack was removed in the section at the transition from side wall to ceiling, the foreshortening makes it appear to be right at the ramp.

  16. #16 Dev Null
    January 11, 2011

    Good logic, but keep running with it:

    You’re worried about 260 mph being too ridiculous a speed (and I think you’re right – you’d have to hit that apparently fairly small ramp at exactly the right angle or you’d simply shoot down the middle of the tunnel upside-down in mid-air. At that speed I don’t like your chances of hitting the angle just right.)

    Fair enough; but if you were going slower, then your 15 degree angle would have to get much sharper in order to maintain your 30 m/s tangential velocity. At half that speed – and 130mph is still bloody fast to be hurtling down a tunnel, muchtheless up its walls – you’d have to have an angle of ~31 degrees, which is a moderately sharp turn to take at 130mph, in the width of a tunnel, and hit a ramp dead on.

    On the other hand, assume the video were sped up – you calculated only 6.5 m/s tangential was necessary. Give it a healthy safety margin and call it 10, use an angle of 30, and you’d theoretically only have to be going 45 mph.

    Now that doesn’t sound right. Come to think of it, neither does 6.5 m/s. So if they parked the car perpendicular to the tunnel, pointing at the ramp, and got it up to 15 mph before it hit the ramp, it could safely loop-the-loop at 15 mph? Don’t think I believe that.

  17. #17 rob hill
    January 27, 2011

    The neat thing about this problem is that way too slow and you fall off the top, slightly too slow and you don’t have a ramp, and too fast and you overshoot the ramp. Your speed needs to be relatively constant, provided the helix slope is also constant.

  18. #18 ETM
    February 7, 2011

    There are people standing too close, and even under the car, the car does not even have a cage in it and both lanes of the roadway are blocked off so the driver could not abort if necessary. The Mercedes commercial is a fake. The transition from the flat wall to the curved ceiling and back to the flat walls as too abrupt and would bounce the car out of control at the speeds necessary. Fake.

    The TG clip proves that you can flip a car, not that it can be driven in a spiral. They could remove the roof from that tunnel without effecting the stunt.

  19. #19 John
    July 8, 2011

    People ignorant of film production and lenses often make many of the same mistakes and say “obviously fake”.
    Yes there was lots of post production (BTW photoshop is for STILLS not movies) but the stunt itself was pretty much as you see it. While the car was moving fast it was not 260 mph (though I’m not sure how fast exactly it was about 145 as best as an ex-racer (me) could estimate it).

    I know. I was there. and no one was standing in it’s path – long-lens effect and tight editing take the credit (along with some minor CGI -such as subbing Schumacher for the real driver in later versions).

    Yes folks – there really are people this crazy – though Clarkson in the sewers of Belfast was way crazier IMHO -and for those still doubting I remind you that Clarkson barrel rolled at 37MPH in a subcompact – a far reach from Mercedes.

  20. #20 Tinpusher
    April 10, 2012

    I have driven through that tunnel British Columbia many times. The sides are vertical and 14-15 feet high. Clever commercial but very fake. As a marketing ploy the results are in the math. Google the commercial and you will find it being discussed everywhere. I even found a Hyundai forum dedicated to it. Fake or not it did it’s job……