lunduniversity.lu.se

# Mechanica

Mechanica  opened at Liseberg on 25 april 2015.

It is a Zierer Star Shape ride which moves around three axes: The star with 6 gondola, each 4 m, are mounted at the end of a long (12 m) arm, which can rotate around a horizontal axis  (X). (Data are taken from the drawing.) The star rotates around the long arm (z axis) and the gondola can rotate freely. (See also Liseberg's playlist for Mechanica.)

What forces act on a rider during different parts of the ride? Physics is sometimes said to be the "art of systematic oversimplification", so let us first consider the different motions separately.

## Main rotation

• The main arm moves a full turn in about 8 seconds, with relatively constant angular velocity (see video). What is the acceleration of the centre of the star due to this motion? What forces are required this motion - and in what direction?
• The forces acting on the rider are the force of gravity and the force from the gondola. Draw a free-body diagram of these forces in the photo of the star.
• How do the forces due to the main rotation change if you sit at the end of a gondola, about 4m from the center of the star?

See comments together with accelerometer graphs.

## Highest point: Rotating star and swinging gondolas

After a few full turns, the star stops in the highest position and the star rotates around the z axis (coinciding with the Z axis at this point. Upper case denotes axes in a stationary coordinate system, whereas lower case denotes axis in the coordinate system of the star - see the top figure for a definition of the axes).

As the star reaches the top and the main rotation stops, the gondolas are swinging back to front, with smaller and smaller motion - a textbook example of a damped oscillating, clearly visible in the accelerometer data. This gondola oscillations are analysed in more detail on a separate page.

During the time in the highest point, the direction of rotation changes, from moving backward to moving forwards. The direction of the rotation of the start may be worth some consideration: The initial rotation of the star made riders move forward - when (or why) did the direction change?

From the movie we can measure the rotational speed, and see that the star makes a full turn in about 10s. Assuming that you sit at the end of one of the gondolas - around 4 m from the center of the star - what are the forces from the ride acting on a rider during this part of the ride?

## Combined rotations

What forces act on a rider while the arm is horizontal, as in the photo, and we consider both the main rotation and the rotation of the star itself? Both rotations lead to centripetal accelerations:

The rotation of the star leads to an acceleration towards the center of the star, and the main rotation contributes an acceleration towards the diameter of the star that is parallel to the main axis of rotation.

The rotation of the coordinate axes of the star lead to an additional change of velocity (the "Coriolis effect"), proportional to both angular velocities involved and to the distance from the centre of the star.

## A more detailed analysis

On a separate page the forces are analysed in more detail, and compared to experimental data and a computer simulation.

In comparing theoretical and experimental results, a few additional effects may need consideration.

• The gondolas rotate invididually and the swinging motion affects the orientation of the axes of the sensor, and could possibly add a centripetal acceleration due to the motion around the gondola axis.
• If the main rotation (see video) is not completely even, but faster when the star is closer to the ground, the "vertical" component would increase during this part of the ride, due to the increased angular velocity (and decrease correspondingly at the top).
• movie from the opening day shows the motion of Mechanica together with accelerometer graphs.

## A more detailed analysis

On a separate page the forces are analysed in more detail, and compared to experimental data and a computer simulation.

In comparing theoretical and experimental results, a few additional effects may need consideration.

• The gondolas rotate invididually and the swinging motion affects the orientation of the axes of the sensor, and could possibly add a centripetal acceleration due to the motion around the gondola axis.
• If the main rotation (see video) is not completely even, but faster when the star is closer to the ground, the "vertical" component would increase during this part of the ride, due to the increased angular velocity (and decrease correspondingly at the top).
• movie from the opening day shows the motion of Mechanica together with accelerometer graphs.