I am just curious about the methodology.
How does the height of a jump calculated? Based on competition?
Rotation I believe can be measured with recorded videos more accurately, but height...
Briefly, the calculations are based on the kinematic equations. More specifically on their simple form that we learn even in school physics. The results are quite good and close the real values.
So you consider the body to be a point mass (the center of mass of the skater). When the skater jumps his center of mass is doing a parabolic trajectory. This comes from the kinematics laws. In this trajectory the skater at some point is reaching his maximum height, let's call it H.
In kinematics, there is the law of the independent component of movement. So if the body is moving in the horizontal direction (the distance that is covered on the ice in his jump direction) and vertical the (the vertical move to reach his higher point of jump). You can consider the jump as a composition of this two movements.
Since this two movements can be considered independently we consider that the skater is just doing a straight vertical jump.
When the skater is in his higher point (H cm above the ice) he starts to fall. This fall we approximate it as free fall. The free fall equation is:
H = g x (t^2)/2 where is g is the gravity acceleration 980 cm/sec^2 , t is the time that is takes for the fall.
Because of the symmetry of the parabolic trajectory, we also consider that the time that it takes to skater to reach his higher point is the same as the time for the fall from the heighest piont to ice.
So we can calculate this time. You go by frame by frame and you check when the skater leaves the ice and when he is reaching the ice again, lets that time be T. Half of this time is for the fall (T/2). Now you use the formula above and you have
H = g x ((T/2)^2)/2 = g x (T^2)/8
and you find the desired height of the jump
.
It's very simplistic approximation of the body movement but it works relatively good.
