Harking back to Episodes 1 (Minimum Speed Equation) and 4 (Ballistic flight / Vault Equation),
we can sometimes use them together to find a takeoff speed for a pedestrian or rider in cases where we don’t have the data to solve either of them directly.
Imagine a motorcycle rider who goes over the hood of a car that turns left in front of him. He will leave his bike and the car at a shallow angle, fly some distance, land on the ground and bounce and tumble to rest (assuming his path doesn’t coincide with a pole or another car).

We can use the basic vault formula if we assume a takeoff angle and know where he landed.

We can use the Minimum Speed Equation if we estimate his drag factor and know his tumble distance.

But if we don’t get his point of landing, we can’t use either of these.

But if we know the total distance he traveled by both, we know that his speed at takeoff and landing are about the same (neglecting wind drag during flight is a reasonable assumption) so we can estimate the landing spot, calculate the speed from vault analysis, and then use the remainder of his travel distance to estimate the speed from slide...they should be the same.

If not, we need to estimate a different landing location and try again.

At our 2008 McHenry Training seminar while discussing launch/occupant trajectories/etc the late Chuck Moffatt (brilliant man, passed in 2013) had a suggestion for improvement in the relationships.

That we should consider the vertical impulse of the landing based on height of travel path (for launch angle/speed) and then the corresponding horizontal impulse due to the assumed friction coefficient.

Guess another things for me to dig out and work on!

This is a summary of analytical relationships for Occupant Trajectory:

Table 13 from McHenry Book.jpg (72.69 KiB) Viewed 78 times