DH Mt Bike - Optimizing Drop Landing Ramp Profile

[erobz]

I do downhill Mt Biking - and this question popped into my head; Is there a kind of "optimal" landing profile mathematically for a drop feature that is not obvious in the sense that it is not what we "intuitively design" for landings on these features?

My idea is that the bike leaves the top of the drop with a certain velocity $v$, and angular velocity $\omega$ that are related through Newtons Laws and the bike geometry. Ignoring drag, these parameters remain constant throughout the remaining projectile motion(s).

I "feel" as though I would like the landing profile $f(x)$ slope at any point of landing (at particular set of initial conditions on $v$ and $\omega$) to coincide with the angle through which the bike will rotate until that point is achieved.

This is not what is done in practice. The idea in the field is that the feature builder would want you to get the speed "right enough" to land somewhere around "here", and put some slope on it (estimated from past experience) in that region and let the shocks do the rest... hopefully well enough.

For reference the typical landing looks similar to this:

we don't anticipate the rider basically "falling off" from riding in real slow which would be a very large angle of rotation for the short trajectory, but also we don't expect the overshoot; a large rotation from excessive hang time on a typical landing profile. Both of these scenarios happen from time to time, even with experienced riders.

This mathematical problem seems challenging to me, I don't know if I'm really rusty, or if I've ever solved one quite like it. I'm expecting some differential equation to describe it.

Any thoughts/opinions appreciated.

Also, for the sake of simplification ignore the bike geometry w.r.t. the landing profile, I certainly don't want to get that in depth.