Everything looks very easy on the devil’s wheel. Everyone sits on the disc raised in the middle, it begins to rotate, it accelerates to 23 revolutions per minute, and whoever stays seated the longest wins. But what determines success and failure? What is important? Ludwig Kugler, the commander, says: especially on the clothing. It doesn’t matter how fat or thin one is. If you want to win, you should simply wear lederhosen and not a dirndl. Haferl shoes or tights are also bad, they are “like black ice”. The chances would be better with sneakers or completely barefoot.
Is that correct? This question is perfect for Georg Eggers. The physicist teaches at the Faculty of Applied Natural Sciences and Mechatronics at the Munich University of Applied Sciences, and in his series “Physics of Failure” he repeatedly explains in experiments in front of an audience why ambitious inventions didn’t work so well in practice – from the ones he built himself Low-cost airlines from the Ikarus to the supposedly unsinkable Titanic to the space telephone.
So is Ludwig Kugler right? In the physicist’s eyes, the devil’s wheel is a flat cone that rotates, meaning that centrifugal forces act on it. Unfortunately, the slope of the cone makes the formulas confusing. That’s why Eggers first explains everything using the example of a flat disk. The connections are the same.
The first thing that is important here is the centrifugal force FZ, because it pulls the guests away from the window. The force results from the mass m of the guest multiplied by the angular velocity w at which the disk rotates, squared and the radius r, i.e. the distance of the guest from the center: FZ = m · w² · r. The faster the disc rotates and the further out one sits, the stronger the centrifugal force. In the middle the radius is zero, and with it the centrifugal force. So that’s always the best place.
In order to cause a guest to slide, centrifugal force must overcome friction
But the formula also says: the heavier you are, the stronger the centrifugal force is. So does weight play a role? No, says Eggers. In order to cause a guest to slide, the centrifugal force must first overcome the friction, i.e. it must be greater than the so-called static friction force: FZ > FR.
This friction force, in turn, is calculated from the coefficient of friction µ, which depends on the materials rubbing against each other, and from the normal force FN; This is the force with which a body presses vertically onto the surface. For a horizontal surface, FN is identical to the weight FG. And you get that if you multiply its mass by the acceleration due to gravity g. So the formula is: FR = FN · µ = m · g · µ. This means that the mass m is on both sides of the inequality FZ > FR. As the mass increases, the centrifugal force and the frictional force increase equally. And that means: On the devil’s bike it doesn’t really matter how much you weigh.
Now the slope comes into play
This explains the basic principle. Now the slope comes into play and things get more complicated. Bodies sitting on a rotating disk are only pulled by centrifugal force. But on a rotating cone, i.e. the inclined devil’s wheel, the weight also pushes you towards the edge. In addition, part of the centrifugal force lifts you off the surface and thus reduces friction. So it’s twice as difficult to stay seated on the cone.
In order to clarify this physically, both the centrifugal force and the weight force must be broken down into partial forces that act parallel or perpendicular to the disk surface. How strong these partial forces are depends on the angle of inclination alpha of the cone. The ride is over when the total force pulling you to the edge is greater than the friction force on the slope. At the end there is this inequality: w² · r · (µ · sin Alpha + cos Alpha)>g · (µ · cos Alpha – sin Alpha).
Georg Eggers is known for his live experiments with the “physics of failure”.
(Photo: Alessandra Schellnegger)
The rest is calculation. The angle of inclination of the devil’s wheel is clear: the disc measures five meters in diameter and is raised by two decimeters in the middle, resulting in an angle of 4.6 degrees. The remaining variables are the rotation speed, the radius and the ominous coefficient of friction. It’s difficult to describe, because every lederhosen is different – and also different in fat. In addition, the coefficient changes when the surface becomes wet. If you sweat, you slip. Beer, on the other hand, can initially act like a lubricant, but later becomes sticky when it dries, says Eggers. This in turn increases the coefficient of friction.
For women in dirndls, on the other hand, it would stop at 3.8 revolutions per minute in the same place
Approximations should therefore suffice for a few example calculations. Assume that leather trousers on wood have a coefficient of friction of 1 (which is slightly more than the value of rubber on asphalt), but a silk dirndl only has 0.1. A person wearing leather suspenders could then easily sit down halfway up the devil’s wheel, i.e. at a radius of 1.25 meters. From there it would only slip at a speed of 24.7 revolutions per minute. In normal operation, the devil’s wheel only rotates at 23 revolutions per minute. No wonder that the operators regularly have to help with medicine balls and ropes to get people off the devil’s wheel.
For women in dirndls, on the other hand, it would stop at 3.8 revolutions per minute in the same place. Experienced dirndl wearers therefore gather the material on the devil’s wheel and sit on their bare skin. If someone really wanted to sit on the dress and stay on the pane until the end, she would have to sit exactly in the middle, very precisely. At 23 revolutions per minute, its center of gravity should be a maximum of 3.4 centimeters from the center. A millimeter more and it slips.
At least in theory. Eggers doesn’t want to commit to millimeter precision. His discipline is engineering, he says. In an emergency, he would help with a vacuum cleaner, a cyanoacrylate adhesive, a jet engine or even a wood screw. Unfortunately, this is all strictly forbidden on the Devil’s Wheel.
In the series “The Physics of the Oktoberfest” the SZ analyzes various components of the Oktoberfest according to scientific criteria.
Good Oktoberfest stories stay good. This text was first published on September 24, 2018 published.