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Project Goal:
This project's goal is to determine the most probable and dangerous risks of the swing installation, design a safe swing addressing as many risks as possible, and validate the design using mathematical simulations that will accurately predict swing dynamics. This project will also focus on implementing methods of dampening or energy resistance on the swing to limit the heights reached by the users.
Functional Requirements:
1. Safety
a. The design should limit the swing height to 8ft
b. The swing should be able to untwist by itself
2. Maintenance
a. The swing should require minimal maintenance
3. Fun
a. The swing should be intuitive, similar to a playground swing
b. Any dampening factors should not make the swing difficult to move
4. Aesthetic
a. The swing should have minimal visible hardware and visually resemble a playground swing.
Background:
This project, sponsored by the Stuart Art Collection, is aimed to assist the development of Ann Hamilton’s vision of a sensory environment art piece that will be installed at the upcoming Pepper Canyon Station of the new MTS Trolley extension at UCSD. 19 large swings will be installed underneath the trolley tracks structure. These swing will range from 37.3 feet to 61.8 feet in height and be capable of supporting two adults.
To design a safe and fun swing, the swing dynamics must be examined. Ideally, a swing can be simplified to a 2D pendulum, but modeling a swing this way does not account for many other factors, such as air drag.
The most important differentiation between a pendulum and a swing is the user. For swing dynamics, the user can actively pump to generate a torque and increase the amplitude of the swing. Swing users may also be pushed by other park users with variable force, which is difficult to model. The final design was therefore very dependent on qualitative data obtained from full scale tests.
Figure 1: Illustration of swing components
1. Cable:
The cable are able support their own weight, the seat, and the user(s), a predicted load capacity of 400 lbs. (Total weight with user: 465 lbs) The cables are 3/8" braided stainless steel cables for rated for strength and durability.
Figure 2: Image of braided stainless steel cable
2. Seat:
The seat is able to support two adults or one adult and two children. It is also durable enough to withstand weather and decay. The seat is a 3’10” x 9” x 1.5” block of Eucalyptus wood. Using Solidworks Finite Element Analysis, the average factor of safety was determined to be around 10.
Figure 3: Image of eucalyptus seat
3. Seat Assembly:
The seat is attached to the cable through a through bolt connection consisting of a stiff 1" rod. Two jam nuts are placed at the cable to rod connection to prevent the cable from threading back out. To increase the stiffness of the seat to cable assembly, a stainless steel plate is mounted to the bottom of the seat to increase the lateral rigidity and overall stiffness of the seat assembly.
Seat Assembly Analysis:
The seat assembly was analyzed using Solidworks Finite Element Analysis. For a 400 lb load case, the lower value for the factor of safety range was determined to be 1.34 around the junction between the seat and through-bolt and averaged 10+ elsewhere, shown in Figure _ below. The factor of safety is likely an underestimation, but the connection points between the through-bolt to the seat and to the cable will most likely be the failure points. The seat assembly is not expected to fail but fatigue analysis is recommended to determine the predicted life cycle of a single seat assembly.
The following results were from the full scale test on May 24th, 2019.
As seen in Figure 5, the 33 foot swing with a threaded through-bolt connection (pink) was able to gain amplitude through standing pumping while the Y connection (black) was only able to maintain amplitude at best. This is consistent with the prediction that the Y connection pivot point absorbs momentum change that would otherwise increase swing amplitude. Standing pumping with a spreader bar, shown as the blue line in Figure 5, had a smaller amplitude gain as compared to without the bar, but the difference was too small to make a definitive conclusion. The tests showed that the 33 foot swing could be effectively pumped to potentially dangerous heights (seen in the video below).
Figure 5: Matlab simulation predictions compared to experimental data for standing pumping
Conclusion
After rigorous testing, it was concluded that swings under the length of 45 ft have potential to attain unsafe heights by self-pumping methods and are therefore not recommended to be included in this installation. Swings over 45 ft were determined to be much less likely to reach unsafe heights by self-pumping methods and the 47ft swing was not observed to reach unsafe heights during testing, however under certain circumstances a person (or persons) could reasonably push with enough force to exceed the safe height.
Because this project is freely accessible to the public, it is not possible to test for every scenario a user may encounter. It is not feasible to engineer the swings in such a way as to completely guarantee their safe operation no matter the swing length, especially when such weight is given to aesthetic appearance. The risk factors tested throughout the duration of this project are important, but by no means all inclusive of the possible events that may occur if the swings are installed.
If the University chooses to take on such liability, it should be clearly understood that the swings were designed for a limited use case that a user operating outside of those conditions could violate.
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