Optimal landing ramp profile for downhill bike drops

[erobz]

I think some videos of your riding group are needed here...

I don't have youtube for videos, but maybe I can get some still frames.

 

[erobz]

Professional cyclists achieve astonishing acceleration but don’t flip over backwards. It would seem perverse to try to do the lift entirely by pedal power when it would be so much easier to get a start using the body’s inertia. No doubt pedal power comes into play thereafter.

To me personally it feels like you are initiating pedaling (in a high gear), while leaning back simultaneously. It puts a "smooth" tension in your arms.

 

[A.T.]

Does that mean they push down on the handlebars while the front wheel is still grounded, throwing the body up and back, so that they can then pull up on the handlebars when the front wheel leaves the ground?

Things you could do:

- Start with your CoM as high as possible.
- Once the front wheel looses support, drop your body down, so the CoM of bike+rider accelerates downwards.

This reduces the ground support force on the back wheel during the single wheel support phase (it becomes less than m*g), and thus the torque that this support force creates on bike+rider around their CoM.

If you additionally drop body backwards, then the CoM also moves back, which reduces the lever arm of that support force on the back wheel around the CoM.

This seems to be what the riders in the videos are doing.

 

[erobz]

@berkeman I'm in the grey shirt. This is Mt. Creek Bike Park in New Jersey.

This is me coming off of a pretty nice sized drop.

And landing!

We are all in our 40's and 50's. I only get out to do this 1 to 2 times annually. Otherwise we prefer to ride technical XC (Enduro).

 

[A.T.]

@erobz Another numerical solution approach:
- Define a vector field, by assigning each point in space the orientation of the bike during a jump from a given launch point.
- Use a streamline algorithm on that vector field, to compute the landing ramp profile that is always parallel to the local bike orientation vector.

@erobz I have experimented with the approach above a bit. I'm getting the impression that the inverse relationship of $\omega$ and $v$ can make it difficult to find a landing zone profile that results in a two wheel landing for a wide range of $v$.

What range of $v$ can be covered, is highly sensitive to the relationship $\omega(v)$, which is affected by the active measures the rider takes to avoid front wheel drop. In the two examples below I changed $I$ to demonstrate this. The values of $I$ are unrealistic, I just use them to reduce $\omega$ which could also be achieved by rider actions.

arrows: bike orientations
red lines: example trajectories for $v=1 \dots 10 m/s$
black line: example landing zone profile with 2 wheel landing for the trajectories which intersect it.

 

[erobz]

View attachment 370686
View attachment 370687

So the drop height (minimum the rider drops) here is like a third of a meter here in these graphs? If the moment of inertia is low the profile is convex, and if high it becomes "mostly" concave. All interesting things.

Given that most bikes and riders are similarly sized; in a passive drop (one that lets physics control the rotational dynamics as opposed to the rider input) there could be a "most" reasonable profile for the most averagely sized rider on a given drop it seems.

 

[A.T.]

So the drop height (minimum the rider drops) here is like a third of a meter here in these graphs?

If you want to allow very slow passive going over the edge, then you cannot have a high initial drop. The bike will just flip over forward.

If the moment of inertia is low the profile is convex, and if high it becomes "mostly" concave. All interesting things.

Yeah, but the $I$ required for the concave profile (2nd plot) assuming passive rider is unrealistically high. In real life, making $\omega$ that low, would require an active rider.

Given that most bikes and riders are similarly sized; in a passive drop (one that lets physics control the rotational dynamics as opposed to the rider input) there could be a "most" reasonable profile for the most averagely sized rider on a given drop it seems.

Passive drop with somewhat realistic $I$ results in those convex profiles (1st plot), which cover only a small range of $v$, and even in the valid range of $v$ you never fly very high above the ground. That's because the orientation of the bike is very close to its motion direction (see red arrows along the trajectories).

But to be honest, I don't really know the actual $I$ of a passive rider. Just that the optimal profile is highly sensitive to $\omega$, which makes it rather difficult to find one that works for all riders. I think that at very low speeds, even novice riders will intuitively try to counter the front wheel drop.

 

[berkeman]

Another fun video about dropoffs (well, and some other stuff)...