Research Papers

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

[+] Author and Article Information
Chanyoung Park

Department of Mechanical
and Aerospace Engineering,
University of Florida,
PO Box 116250,
Gainesville, FL 32611-6250
e-mail: cy.park@ufl.edu

Joo-Ho Choi

School of Aerospace and
Mechanical Engineering,
Korea Aerospace University,
Goyang-City 412-791, Gyeonggi-Do, Korea
e-mail: jhchoi@kau.ac.kr

Raphael T. Haftka

Distinguished Professor
Department of Mechanical and
Aerospace Engineering,
University of Florida,
PO Box 116250,
Gainesville, FL 32611-6250
e-mail: haftka@ufl.edu

1Corresponding Author.

Manuscript received November 25, 2014; final manuscript received May 28, 2016; published online July 15, 2016. Editor: Ashley F. Emery.

J. Verif. Valid. Uncert 1(3), 031002 (Jul 15, 2016) (11 pages) Paper No: VVUQ-14-1004; doi: 10.1115/1.4033889 History: Received November 25, 2014; Revised May 28, 2016

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.

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Grahic Jump Location
Fig. 1

Paper helicopter dimensions in meters: Rr = 0.1143, Rw = 0.0508, B1 = 0.0381, TI = 0.0508, Tw = 0.0254 (dimensions in inches: Rr = 4.5, Rw = 2, B1 = 1.5, TI = 2, Tw = 1)

Grahic Jump Location
Fig. 2

Area metrics (shaded in gray) of the same data (helicopter 1 and condition 1 of student A in Appendix B) for different epistemic uncertainty models: a predictive distribution and a p-box of 2.5 and 97.5 percentiles (left and right dashed lines) using N of 10,000 samples: (a) validation area metric of a predictive distribution (0.032) and (b) validation area metric of a p-box (0.001)

Grahic Jump Location
Fig. 3

Process of updating posterior distributions of the mean and standard deviation of CD of helicopter 1, for student A data (see Table 1): (a) after 2nd update and (b) after 10th update

Grahic Jump Location
Fig. 4

Velocity (v) and falling distance (d) using numerical schemes with time-steps n = 10 and n = 20 and exact solutions

Grahic Jump Location
Fig. 5

Normal probability plots of pooled drag coefficient data for the quadratic and linear drag models



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