# Chain flyer - Wave Swinger

The photos from Gröna Lund and Liseberg both show the Zierer 48 seat wave swinger. See also a movie of the motion from start.

The wave swinger is among the classical amusement rides found in many parks, smaller or larger, with different decorative designs to fit the local park environment. The patent classification, A63G1/28 ”Roundabouts ... with centrifugally-swingable suspended seats” includes 394 items, the first of which seems to be the ”Flying horse machine” from 1869 by Newhall and Cummings. A more recent version is the StarFlyer ride, where the swings move up while moving around a high tower. (See e.g. the description of Himmelskibet in Tivoli Gardens)

Chain flyers involve beautiful physics, often surprising, but easily observed, when brought to attention. An introductory observation is to consider possible differences between empty and loaded swings.

Wave swingers can be used for a number of student assignments of different degrees of difficulty, across a number of math and physics topics. Theoretical investigations for the classroom can be based on ride data, photographs, movies or accelerometer datasets. Physical model experiments can be used to develop a deeper understanding of the physics involved. Worksheets during park visits may scaffold measurements for the actual amusement park ride, as well as the follow-up calculations. Through variations in the task formulations and in the choice of data provided, the degree of difficulty can be adapted, as well as the physics or math in focus. Which physics or math topics can you identify as relevant in connection with these rides? Which questions can you ask and what tasks can be identified, using these photos? What investigations can be performed on-site or on the ride? What assignments would you like to include in a worksheet?

## Accelerometer data for a Wave Swinger ride.

The graph shows accelerometer data for a swing in the outer ring of the Slänggungan wave swinger at Liseberg, where a tilt of the roof leads to a wave motion. The blue graph shows the angular velocity calculated for the time for each full turn, measured by shaking the accelerometer every time the swing passes a well-defined point on the ground. The stars mark the center of each of these time intervals.

## Wave motion due to the tilt of the roof

The graph shows the accelerometer data together with elevation data. The lower graphs show in detail the effect of the tilt of the roof.

## Forces on the rider

The free-body diagrams show the forces (divided by the mass) on the rider when the roof is horizontal, and in the upper and lower positions of the wave motion (as in the lower photo on the top of this page), taking the vertical acceleration into account.

## Work sheet questions

What questions would you like to include in worksheets for your students? Below follows a number of possible questions of different degrees of difficulty.

Geometry

- How large is the circumference of the circle of swings when the carousel is at rest? There are 16 swings, hanging at at distance of 2 m.
- How large is the diameter of the circle of the swings when the carousel is at rest?
- How large is the diameter when the carousel is in motion? Use the photo to compare the diameters of the suspension points in the roof and of the swings at the end of the chain?

### Velocity and acceleration

- How far does a swing move during a full turn of the carousel?
- What is the time (T) required for a full turn if the carousel makes 11 turns in a minute for the wave swinger?
- How fast does a swing move?
- Insert your values into the expression for the centripetal acceleration.
- What angle between the chains and the vertical do you expect for this acceleration?

Older students may be asked to calculate the angular velocity. For students who have taken trigonometry, additional questions can be asked concerning the geometry, e.g.

- Use the diameter of the motion of the swings to estimate the angle between the chains and the vertical? Use an estimated of L=5.5 m for the the chain length.

The angle can then be used to obtain a value for the centripetal acceleration

### Challenge:

Can you use the photos to estimate the time required for the carousel to move a full circle if you know that the 16 swings in the outer circle hang at a distance of 2m? Sufficient information, is, in principle, available, but only by making estimates from the photo and invoking previous knowledge in both math and physics, along the lines indicated above.

### Choosing questions for worksheets

Some of the questions above can be described as "inserting numbers" / "fill in the blanks", whereas others are more challenging for the conceptual understanding. What preparation and follow-up is needed for different questions? What concepts are familiar to your students - and what concepts do you want them to learn?

## Read more about field trips, worksheets and physics

- Bagge Sand Pendrill A-M (2002) Classical physics experiments in the amusement park, Physics Education 27, 507-511
- Pendrill et al (2014) The equivalence principle comes to school- falling objects and other middle school investigations, Physics Education, 49, 425
- Pendrill A-M (2015) Rotating Swings - a Theme with variations (submitted to Physics education)
- Behrendt and Franklin (2014) A Review of Research on School Field Trips and Their Value in Education Int. J. Env. Sci. Ed., 9 235-245 available at www.ijese.com/ijese.2014.213a.pdf
- Anderson and Nashon (2007) Predators of knowledge construction: Interpreting students' metacognition in an amusement park physics program, Science Education, 91, 298
- Kisiel (2003) Teachers, museums, and worksheets: A closer look at learning experience, Journal of Science Teacher Education, 14, 3–21