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 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.
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:
If you want more details about the acceleration of things moving in circles, check this post out.
If I call up the y-direction, then I can write the following for the y-components of forces on the car:
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:
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:
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:
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.
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:
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:
But the angle is difficult to measure there because of perspective issues.
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.