Computer-Aided Modeling and Simulation for Recreational Waterslides^#

Abstract

This paper presents a computer-aided modeling and simulation method for analyzing position, velocity, and acceleration of sliding objects on recreational waterslides. Safety and excitement levels of the object sliding down the waterslide are the two common criteria for waterslide design. Between the two, safety is far more critical than excitement level. Safety aspects of the waterslide design can be reasonably ensured; by restricting the sliding object, which stays within the physical boundary of the flume sections. In this paper, mathematical representations of a number of common flume sections are first created in parametric surfaces. These basic building blocks have also been implemented in Computer-Aided Design (CAD) tools, such as SolidWorks. A set of coupled differential equations based on Lagrange's equations of motion that describe the motion of the sliding object are derived, in which friction forces are included. These second order differential equations are then solved using Mathematica. Initial position and velocity are specified for the entire waterslide, which is composed of basic flume sections. A different set of differential equations is solved for each section. The position and velocity of the sliding object at the entrance of the following section are obtained from those at the exit of the previous neighboring section. The solutions are then brought back to CAD for visualization. A real-world waterslide configuration is presented to demonstrate the feasibility of the modeling and simulation method. The major contribution of the paper is extending waterslide simulation to true CAD-based flume sections, and bringing friction forces into the formulations that make the simulations more realistic.

Keywords:

• Computer-aided design
• Differential equations
• Waterslides

Notes

^#Communicated by S. Velinsky.