Content Alert: Newtonian physics, manholes and bikes
The other day on the road, a group of friends rode past a manhole without cover. We easily avoided it but it got us thinking that it would hurt pretty bad to hit it straight on without seeing it first.
So we asked ourselves how fast we would need to go to not crash riding over an uncovered manhole on the street.
The problem is that we can’t agree on the math and the simple math gives an answer that is hard to believe.
The simple math would have you fall into the hole by simple gravity only, for the duration you ride over the hole. The faster you go, the less time you have for your wheel to fall into the hole. So by the time you hit the end of the hole (the far lip) with your horizontal travel, if you travel fast enough, your front wheel won’t go down enough to cause you to endo.
So what is that speed you need to go to to avoid an endo?
Here is the simple math computation:
Assumptions: cannot fall more than 3cm into whole otherwise crash. manhole is 1 meter across. Assumes rider is unaware of hole, so no dynamic forces to try to unweight the front wheel or bunny hope.
How much time an object needs to fall 3cm:
t=square root(2D/g)
t =Â 0.0782195453699Â seconds
Speed needed to cross 1 meter under that t time
s = d/t
s = 1m/0.0782195453699s
s= 12.78 m/s
s = 28.6mph
So in ideal conditions, ignoring friction and dynamic moves, you should survive if you go faster than 28.6 mph.
With 2cm max assumption, that is ~35mph minimum speed.
Feels like we would need to go faster to not crash or I screwed up my math.
Is my math correct?
Is it much more complicated than this? My friend feels you fall faster into the hole because the rider has his weight on the front wheel. And than the wheel rotation and pivot with back wheel may cause front wheel to fall faster into the hole.
Thoughts?
Thanks.
The other day on the road, a group of friends rode past a manhole without cover. We easily avoided it but it got us thinking that it would hurt pretty bad to hit it straight on without seeing it first.
So we asked ourselves how fast we would need to go to not crash riding over an uncovered manhole on the street.
The problem is that we can’t agree on the math and the simple math gives an answer that is hard to believe.
The simple math would have you fall into the hole by simple gravity only, for the duration you ride over the hole. The faster you go, the less time you have for your wheel to fall into the hole. So by the time you hit the end of the hole (the far lip) with your horizontal travel, if you travel fast enough, your front wheel won’t go down enough to cause you to endo.
So what is that speed you need to go to to avoid an endo?
Here is the simple math computation:
Assumptions: cannot fall more than 3cm into whole otherwise crash. manhole is 1 meter across. Assumes rider is unaware of hole, so no dynamic forces to try to unweight the front wheel or bunny hope.
How much time an object needs to fall 3cm:
t=square root(2D/g)
t =Â 0.0782195453699Â seconds
Speed needed to cross 1 meter under that t time
s = d/t
s = 1m/0.0782195453699s
s= 12.78 m/s
s = 28.6mph
So in ideal conditions, ignoring friction and dynamic moves, you should survive if you go faster than 28.6 mph.
With 2cm max assumption, that is ~35mph minimum speed.
Feels like we would need to go faster to not crash or I screwed up my math.
Is my math correct?
Is it much more complicated than this? My friend feels you fall faster into the hole because the rider has his weight on the front wheel. And than the wheel rotation and pivot with back wheel may cause front wheel to fall faster into the hole.
Thoughts?
Thanks.