Adds height attribute to the skier and adjust simulations based on new mass center location.
Jan van der Schot suggested that not accounting for the height of the mass center of the jumper can cause significant differences in EFH values when analyzing jumps. The merge requests adds a mass center height to the simulations to investigate this claim. This approach ignores rotational dynamics and sticks with a point mass simulation and simple kinematics to manage the mass center height. The point mass moves along a parallel surface when sliding, such that the point mass is a constant normal distance from the surface (see https://en.wikipedia.org/wiki/Parallel_curve). When the point mass is in flight, the "foot point" moves along a parallel trajectory below the flight curve. Instead of assessing when the point mass intersects a landing surface, the foot point's intersection is used. The surface normal velocity of the point mass at the moment of foot impact is used to calculate EFH. This approach ignores that the fact foot point velocity is different than the mass center velocity (to calculate friction force or impact force, for example). As mass center height goes to zero, the results tend to the same results as we've had before when not accounting for mass center height. If the mass center height is small relative to the size of the jump, there is likely little effect to resulting EFH values.
The following figure shows the construction of an offset constant EFH jump. The solid (sliding) and dotted (flight) green lines is the mass center motion trajectory. The green dash-dotted line is the constant EFH landing surface for the mass center. The blue lines are parallel curves to the green ones and represent the actual jump surface and foot point trajectory.
The next figures show the comparisons of this example: https://skijumpdesign.readthedocs.io/en/stable/analyze-jump.html using a skier with no mass center height and a height of 1 meter.
No height:
1 meter height:
And then the EFH analysis.
No height:
1 meter height:
You can see that there are differences in the plots, but they are relatively minor. The no height takeoff speed is 15 m/s and the 1 meter height takeoff speed is 16 m/s. So the tall skier goes a bit faster down that particular slope.
The following plot shows the landing surface generated from the point mass simulation with no skier height (blue) and the one generated from the 1 meter height mass center point mass (orange):
My current conclusion is that adding in skier height (in this way) has negligible effects to any EFH results.
Other notes:
- It isn't necessary to create offset surfaces in Skier.fly_to() and Skier.slide_on() to design a jump, so maybe do not do that. Although it may be necessary for Surface.calculate_efh() to work.