This article presents an integrated modeling, analysis, and design method for the safety of recreational water slides. Safety and excitement levels of riding on the water slide are the two common criteria for water slide design. Between the two, safety is far more critical than excitement. The safety aspect of the water slide design is ensured by restricting the riding object to stay within the physical boundary of the slide. The safety constraints must be imposed on the object for the entire time domain. A geometric modeling method was first developed. The modeling method converts a given set of discrete points that represent the geometric shape of the water slide into a smooth and parametric B-spline surface in which the control point positions are defined as design variables. A set of differential equations, based on the Lagrange equation of motion, that describes the motion of the riding object is derived. These ordinary differential equations are solved using Mathematica. An analytical shape design sensitivity analysis (DSA) method was developed and employed to support the design of the water slide. A what if study method that supports interactive design of the water slide using the shape DSA information was developed and proved effective for designing safe water slides. A real-world water slide configuration is presented to demonstrate the proposed design method.
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