Back to School
Well, here we are again, in front of that black board. But today's reminder is about the very acceleration you get when falling down to some dodgy impact destiny, and how you can cope with it on a bike.
This is the only in-depth physics lecture you'll get on the web, regarding the landing theory of bicycles. And I reckon it's quite clear.
Subjects
Gravity rules: the speed of impact when launching a drop off
Graphical analysis: a physical explanation of why you can jump from higher on a bike than on your bare feet



Gravity rules
At what speed will you smash your rear wheel on the rocky bit that you didn't see when dropping off?
Here is the theory. Although this is stricly right in vacuum, we'll consider that for the heights we're dealing with, air resistance does not play a major role.
When falling freely, a body undergoes the gravity acceleration (a=9.8) in m*s-2, that increases the body's speed proportionally to the fall duration (dT) in s. Hence
(1): dS=a*dT
where dS is the increase of speed in m/s.

But the speed is also defined as the distance dH (in our case the height of fall) divided by the time slot (dT) it took the body to fall from dH. Hence
(2): dS=dH/dT

Of course, expression (1) = expression (2), hence we get
(3): dS=dH/dT = a*dT

By integrating the expression (3) on the actual time T it takes to fall from the total height H, we obtain
(4): T*T=2H/a

wich is equivalent to say:
(5): T=square root(2H/a)

where T is the time of fall in seconds, from an height H in metres.
Replacing T by its expression (5) in the expression (1) gives the speed of impact
=========================================================================== (6): S = square root (2aH) = square root (19.6*H)
=========================================================================== The speed of impact on landing S, is in metres per second and H, the height of the wall is in metres.
On Earth a=9.8m*s-2

To get the resulting speed in kilometres per hour, multiply by 3.6

To get the resulting speed in miles per hour, multiply by 2.237

As an example, a drop off from an height of 3 metres (about 10 feet), gives a landing vertical speed of 7.6 metres per second.

In kilometres per second, that gives 7.6*3.6= 27.4 kilometres/hour.
In miles per second, that gives 7.67*2.237= 17 miles/hour.

You wouldn't ride into a wall for fun at that speed!