Shape sensitivity analysis and design studies for CAD flume sections

Abstract

This paper presents shape design sensitivity analysis (DSA) and design studies for recreational waterslides represented in computer-aided design (CAD) environment. The mathematical representations of a number of commonly used flume sections that serve as the building blocks for waterslide configurations are created in CAD tools. Geometric dimensions of the individual sections that affect not only their geometric shape but also the overall configurations are identified as design variables. These design variables can be varied to search for better design alternatives, for example, safer waterslides. A set of coupled differential equations based on Lagrange’s equations of motion that describe the motion of the riding object are derived. The equations of motion incorporate friction forces between the riding object and the surface of the flume sections. These second-order differential equations are then solved using Mathematica. Based on the equations of motion and design variables identified, a set of differential equations are derived for calculating shape DSA coefficients. These equations are solved numerically again using Mathematica. The major contribution of the paper are (1) extending waterslide design parameterization and shape DSA computation to true CAD-based flume sections, which greatly alleviates the design for manufacturing issues previously encountered, (2) incorporating friction forces into shape DSA computation, and (3) developing a design scenario that includes sensitivity display and what-if studies for a compromised design that is safer and with a larger acceleration, therefore, higher excitement levels. Incorporating friction forces into the computation supports design for rider’s excitement levels, which are related to accelerations. Waterslide design will not be realistic without including friction forces.