Teaching a Verification and Validation Course Using Simulations and Experiments With Paper Helicopters

In teaching a course on verification and validation (V&V) in scientific simulations, it is desirable for students to carry out repeated experiments on devices/systems that they can build and that can be easily repeated. This allows them to be exposed to the inherent aleatory uncertainty associated with building and testing when experiments are used to validate the scientific simulation tools. This paper reports on our experience in using paper helicopters for this purpose in a V&V graduate course. Paper helicopters have been used for various courses, from statistics in high school to graduate optimization courses. They are easily made from paper and paper clips and share the feature of autorotation with real helicopters when they are dropped from altitude. For the V&V course, the helicopters permitted comparison of two models of the drag produced by autorotation that slows their fall. A quadratic dependence of the drag on the speed is generally valid for high Reynolds numbers and a linear model appears for low Reynolds numbers. A gratifying result was that some of the helicopters fitted well the linear model and some fitted better the quadratic model, reflecting the fact that the Reynolds number is in an intermediate range. The paper provides details of how the experiments were conducted and analyzed, which would allow them to be used in similar courses. In addition, actual data are provided, which may be useful for teachers who need to cover the subject in a short time that would not allow the physical experiments. The project also allows a verification component of comparing an analytical solution to one obtained by numerical integration.