Quoted message said:On Sun, 08 Jul 2007 01:23:09 -0500, Tim McNamara
<[email hidden]> wrote:
[snip]
Quoted message said:I haven't got a bowling ball. Maybe we can get Fogel Labs to give it a
try and video the results. Anybody got an old undamaged helmet or two
to send to Carl?
[snip]
Dear Tim,
Fogel Labs has no bowling equipment, but the experiment probably isn't
worth pursuing.
A head inside a helmet is practically guaranteed to fit without
putting spreading pressure on the sides of the helmet.
Heads are longer than they are wide--look at any reasonably
well-fitting stiff hat. (Soft caps simply bend to fit the noggin.)
In contrast, a bowling ball is round. If large enough, it should
easily crack a typical bicycle helmet against the floor by acting as a
blunt wedge.
Most bicycle helmet manufacturers recommend replacing any helmet
dropped on the ground, since they crack easily. Fewer and fewer
bicycle helmets pass even the watered-down recent tests, none of which
ever matched the force of a six-foot rider toppling over sideways
after forgetting to unclip at a stop light.
Curiously, toppling over sideways (as opposed to a free fall drop)
produces a greater acceleration and impact for the end (or head) of
the thing toppling.
(This is why tall chimneys break as they fall. They're not stiff
enough to accelerate the upper part without breaking. Think of a
felexible rod--the end lags behind if you wave it.)
As others have calculated in earlier threads, the far end of a
toppling board hits the ground at 3/2 or 150% of the speed it would
strike if dropped in free fall from the same height.
Since kinetic energy for the same mass increases with the square of
the velocity, this means 9/4 or 225% of the original impact energy of
100%.
An object (such as a severed head in a helmet) dropping free for the 5
feet often mentioned will hit the ground at 17.93 feet per second, or
12.2 mph.
The same object falling over sideways on a pole (closer to how heads
actually hit the ground when bike frames are between legs) will land
at 3/2 that speed, about 27 feet per second, or 18.4 mph.
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html
Given the flexibility of the human body, actual impacts should be
somewhat less than the rigid-pole example, but still noticeably
greater than free fall.
Cheers,
Carl Fogel
Aargh!
I goofed free-fall versus topping. My careless mistake exaggerated the
increased speed and force.
A toppling column strikes the ground at the same speed as if it had
been dropped in free-fall from 3/2 the height of the column.
(That's 3/2 the height, not 3/2 as fast--my mistake.)
This in turn works out to a 50% increase in kinetic energy.
(That's 150% of the original, not 225% of the original--my mistake.)
For example, a severed head in a helmet dropped in free fall from 5
feet lands at 17.9 feet per second, but the end of toppling 5-foot
column lands as if it had been dropped from 7.5 feet, 21.96 feet per
second.
The kinetic energy increases 50% (the speed increases by the square
root of 1.5, 1.225 times as fast):
speed ke
5.0 feet of free-fall = 17.93 fps 17.93^2 = 321.5 X
7.5 feet of free-fall = 21.96 fps 21.96^2 = 482.3 X
(same as 5.0 topple) (x sqrt 1.5) (50% more whomp)
The free-fall speeds can be checked here:
http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html
And here's where Joe Riel explained that "To achieve the same velocity
as the toppling rod, the horizontal rod must start at a height of
3/2*l":
http://groups.google.com/group/rec.bicycles.tech/msg/564aad73e9e0cb44
Cheers,
Carl Fogel
