impact upon loss of velocity between V b , but it does impact upon the trajectory angle, , which determines the maximum height reached by the snowboarder, therefore, 𝜃 is significant. From the diagram above, + + 𝜃 = 90 , hence = 90 − − 𝜃 , I will investigate the impact of . and V o
H max .
V v
V o
C
The diagram above illustrates the trajectory from the top of the half pipe, at point C.
Accordingly, I set up the problem as follows:
Superpipes are standard for all major competitions and have walls built of snow which are 6.7 metres high, therefore d = 6.7m, the pitch angle is typically 18 o , therefore = 18 o and gravitational field strength, g = 9.8 m/s 2 . We are also assuming that Shaun’s mass is 75kg. The law of conservation of energy states that energy can neither be created nor destroyed, rather it can only be transformed from one form to another. Therefore, as Shaun gains height, he gains gravitational potential energy, but loses kinetic energy, hence:
1 2
1 2
𝑉 2 =
𝑉 2 + ∆ℎ
Therefore, in terms of Vb, we can find Vo as :
𝑉 = √𝑉 2 − 2∆ℎ
The optimal take off velocity, Vo, is driven by the factors that the judges consider in their scores: height reached, technical difficulty, performance and overall control. The objective is not, like slalom, to achieve a maximum initial speed, but rather one which optimises the total score. In Pyeongchang, Shaun White attempting to beat Hirano, came out with energy and speed, but fell midway through to gain only 55 points. His more controlled final run, however, earned 97.75 points and the gold medal. Vb is therefore assumed to be in the range of 15-20 m/s. From the chart below, we see that initial speed is almost directly proportional to time airborne, and also maximum height achieved. The equations which I input into excel and their derivation are lengthy, and therefore they are not included in my main essay but added in the appendix . I then looked at the values of Hmax and t while changing Vo from 15 to 20 m/s, as shown in the graphs below.
Maximum height reached versus velocity
14
12
10
8
6
4
2
0
15
16
17
18
19
20
Velocity at the base of the pipe
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