in message <
[email protected]>, Mark
Thompson ('
[email protected]') wrote:
>> This suggests to me that there are people (I don't know if BHIT see it
>> this way) who regard the 14mph+ situation as essentially beyond
>> solution, so they turn to what can be done about other situations. If
>> they're right about that then I can see why they think the best that
>> can be done is eliminating all those cuts and bruises,
>
> No no no. What they see about the Xmph situation is with a helmet it's
> X-
> 12mph. So they think a crash with helmet at 20mph becomes a crash at
> 8mph.
>
> Could somone post some physics?
KE = (m * v^2) / 2
The energy of an impact varies with the square of the closing speed.
Which is quite simple and straightforward until you start throwing
soft-bodied objects (such as, for example, people) into the mix.
To quote
<URL:http://www.pacts.org.uk/parliament/briefings/ianneilsonpaper.htm>
"A number of studies have estimated the probability of a fatality
occurring at different speeds. These have produced varying results,
but Andersson and Nilsson (1) estimated that the probability varied by
the fourth power of the speed..."
Assume mass is 1. Then KE at 12 velocity units is (144/2); KE at 20
velocity units is (400/2); and we can in practice ignore the '/2' term
since it's a constant. The actual velocity units don't matter either,
since we're simply compating values. The 'energy equivalent speed', if
BHIT's assumptions that
(i) that a helmet protects against all injuries in collisions up
to 12 mph
(ii) that helmets respond linearly as energy increases
(iii) that injuries to unprotected parts of the body are negligible
are correct is (sqrt (400 - 144)), or 16 mph, and indeed the table goes
like this[1]
collision speed energy-equivalent
with helmet speed without helmet
12 0
20 16
30 27.49
40 38.15
50 48.53
60 58.78
But, as discussed above, injury appears to vary by a higher power. Let's
assume the Andersson and Nilsson value of the fourth power. Then the
injury equivalent speeds are[2]
collision speed injury-equivalent
with helmet speed without helmet
12 0
20 19.31
30 29.80
40 39.91
50 49.95
60 59.97
So in reality, assuming all the most generous assumptions to BHITs case
and in particular that there is no critical impact force at which the
helmet simply fails, and that there are no injuries to other parts of
the body, then an impact of 30mph wearing a helmet has the same
probability of death as a 29.8mph impact not wearing a helmet, and a
60mph impact wearing a helmet has the same probability of death as a
59.97mph impact not wearing a helmet.
[1] computed with
(defun energy-equivt-speed (speed)
(sqrt (- (expt speed 2) 144)))
[2] computed with
(defun injury-equivt-speed (speed)
(expt (- (expt speed 4)(expt 12 4)) .25))
--
[email protected] (Simon Brooke)
http://www.jasmine.org.uk/~simon/
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