Using solver, I discovered that airborne time was maximised when = 67.8045, whereas maximum value for height in the air is achieved when = 72, which is the maximum value of with a non-negative value for 𝜃 (the maximum value for height in the air while taking all real values of 𝜃 into account is when = 85.38 ). Since both variables contribute to score, I decided to optimise around a new variable, Hmax + t , aiming to achieve a more accurate
Airborne time versus alpha
3.564 3.5645 3.565 3.5655 3.566 3.5665 3.567 3.5675 3.568 3.5685 3.569
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71
Alpha
optimum value for , yet the output from solver was still 72 o . I deduced that the weighting was unfair, since a 4 o decrease in to 68 o produced a 0.5m change in height but only 0.01s increase in airborne time. In addition, I noted that snowboard halfpipe commentators continually mention the difficulty of the tricks, and how a fraction of a second could make all the difference, whilst ignoring the factor of height in the air completely. Consequently, I decided to use a weighted average, with 95% based on the skills, and therefore airborne time, and only 5% on height reached in the air. Maximum height reached was divided by time airborne to provide a more similar change in values for each degree increase of , providing me with a value for alpha of 69.64 o , and thus a value for theta of 2.36 o . To validate my result, I analysed some images of halfpipe snowboarders taking off, as shown below, the measured angle of take-off was around 69 o .
71 o
To conclude, professional snowboarders have adopted an angle of take-off in line with the result which I derived using mathematical optimisation, empirical evidence therefore supports my solution.
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