The pyramid shape is the natural consequence of removing all sheer drops from a traditional half-pipe. Even a talented cyclist can become a Christopher Reeves if they inadvertently fall on their heads from a sheer 9 foot drop. It is all too hip to sacrifice oneself only to find out you can't come back the next day and have fun. Also every surface and path should form a ridable loop. Bikes should flow through the pipe, and not simply begin and end at one end or the other. The variables on the back and side face slopes are: 1) If the slope is too steep, it becomes unridable and dangerous for the inexperienced. 2) If the slope is too shallow, the rampodium becomes very large for a given ramp height and therefore excessively expensive.
The shape of the half pipe itself is important and reflects the transform by which the horizontal kinetic energy of rider approach speed is converted to the vertical potential energy of height, or as riders like to call it, "air". An elliptical pipe of continuous curvature softens the gee load compared to a traditional ramp that goes from flat to circular instantaneously.
Surface Issues:
The pyramid surface characteristics are derived from the physics of impact. When a rider falls down, and all riders do, we would like to minimize the injury that results. Obviously helmets and pads are helpfull here. Not so obvious are how the riding surface itself can be tailored to reduce the injury from impact. There are two competing design goals here. The first goal is to make the surface itself springy or elastic. The second goal is to decrease the apparent mass of the ramp so that the entire ramp can deflect to cushion or catch the rider. The problem with making the ramp surface springy is that this slows the ramp down. The ramp must appear locally rigid to the tire footprint, but must deform when the rider impacts. The problem with reducing the apparent mass of the ramp is that it becomes very thin and can be penetrated by the rider.
Art Attack:
There are 6000 square feet (558 square meters) of surface = 188 plywood panel murals. These murals serve artistic function and spectator entertainment .