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Re: Impact force
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Helmut F. Microys Ph. D.
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Nov 01, 2004 12:39 PST
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By the way, the static/frictionless system mathematics has been worked out by Arnold Wexler over 50 years ago (The Theory of Belaying, American Alpine Journal, Vol. VII, No.4, 1950) . The impact force depends only on the mass of the climber, the fall factor (which includes the amount of rope out and the distance fallen) and the elastic modulus of the rope (the stretch factor). The last is not a linear quantity (the rope is not a perfectly elastic material), and thus leads to an approximation, but a pretty good one. From this follows that the maximum impact force is independent of the absolute height of fall.
The problem of the selfbelay, and its high force leading to possible failure, is the fact that the fall factor is two.
I do recall that the case where rope slip is included in the equation (once the maximum force in the belay device is exceeded) has also been solved, but I do not know where this was published.
Helmut.
----- Original Message -----
From: Mark Misselhorn
To: sabol-@topica.com
Sent: Tuesday, October 26, 2004 1:43 AM
Subject: Re: [BOLTS] Impact force
PS: also assuming a static belayer who does not move to absorb some of the impact
----- Original Message -----
From: Mark Misselhorn
To: sabol-@topica.com
Cc: Andy Davies
Sent: Tuesday, October 26, 2004 9:21 AM
Subject: [BOLTS] Impact force
Dear all
Can anyone please assist with some data and formula for impact force as follows?
a.. A formula for impact force experienced on the gear (as opposed to on the belayer of falling climber) which takes into account the following variables: mass of falling climber, fall factor, distance fallen, amount of rope out, and stretch in the rope (which varies with such factors as rope diameter) (any I'm missing). The assumption is a perfect system (ie: no rope drag up to the effective protection). This would be a formula into which one could put data for different scenarios to determine how much force is actually exerted on a piece of protection. I am assuming that impact force is the maximum effective force / energy experienced in the system during a fall.
b.. Any pre-calculated information for different types of falls and climber masses to give us an idea of the actual forces involved.
c.. Any measured figures for such forces?
Thanks
Mark Misselhorn
MCSA KZN
Bolt Safe or Bolt Not!
Bolt Safe or Bolt Not!
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<DIV>By the way, the static/frictionless system mathematics has been worked
out by Arnold Wexler over 50 years ago (The Theory of
Belaying, <EM>American Alpine Journal</EM>, Vol. VII, No.4,
1950) <EM>.</EM> The impact force depends only on the mass of the climber,
the fall factor (which includes the amount of rope out and the distance fallen)
and the elastic modulus of the rope (the stretch factor). The last is not a
linear quantity (the rope is not a perfectly elastic material), and thus leads
to an approximation, but a pretty good one. From this follows that the maximum
impact force is independent of the absolute height of fall.</DIV>
<DIV> </DIV>
<DIV>The problem of the selfbelay, and its high force leading to possible
failure, is the fact that the fall factor is two.</DIV>
<DIV> </DIV>
<DIV>I do recall that the case where rope slip is included in the equation
(once the maximum force in the belay device is exceeded) has also been solved,
but I do not know where this was published.</DIV>
<DIV> </DIV>
<DIV>Helmut.</DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=-@icon.co.za href="mailto:mis-@icon.co.za">Mark Misselhorn</A>
</DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=sa-@topica.com
href="mailto:sabol-@topica.com">sabol-@topica.com</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, October 26, 2004 1:43
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> Re: [BOLTS] Impact force</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>PS: also assuming a static belayer who does not
move to absorb some of the impact</FONT></DIV>
<BLOCKQUOTE dir=ltr
style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px">
<DIV style="FONT: 10pt arial">----- Original Message ----- </DIV>
<DIV
style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B>
<A title=-@icon.co.za href="mailto:mis-@icon.co.za">Mark
Misselhorn</A> </DIV>
<DIV style="FONT: 10pt arial"><B>To:</B> <A title=sa-@topica.com
href="mailto:sabol-@topica.com">sabol-@topica.com</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Cc:</B> <A title=And-@eskom.co.za
href="mailto:Andy.D-@eskom.co.za">Andy Davies</A> </DIV>
<DIV style="FONT: 10pt arial"><B>Sent:</B> Tuesday, October 26, 2004 9:21
AM</DIV>
<DIV style="FONT: 10pt arial"><B>Subject:</B> [BOLTS] Impact force</DIV>
<DIV><BR></DIV>
<DIV><FONT face=Arial size=2>Dear all</FONT></DIV>
<DIV><FONT face=Arial size=2></FONT> </DIV>
<DIV><FONT face=Arial size=2>Can anyone please assist with some data and
formula for impact force as follows?</FONT></DIV>
<UL>
<LI><FONT face=Arial size=2>A formula for impact force experienced on the
gear (as opposed to on the belayer of falling climber) which takes into
account the following variables: mass of falling climber, fall
factor, distance fallen, amount of rope out, and stretch in the rope
(which varies with such factors as rope diameter) (any I'm missing).
The assumption is a perfect system (ie: no rope drag up to the
effective protection). This would be a formula into which one could
put data for different scenarios to determine how much force is
actually exerted on a piece of protection. I am assuming that impact
force is the maximum effective force / energy experienced in the system
during a fall.</FONT>
<LI><FONT face=Arial size=2>Any pre-calculated information for
different types of falls and climber masses to give us an idea of the
actual forces involved.</FONT>
<LI><FONT face=Arial size=2>Any measured figures for such
forces?</FONT></LI></UL>
<DIV><FONT face=Arial size=2>Thanks</FONT></DIV><FONT face=Arial size=2>
<DIV><BR>Mark Misselhorn</DIV>
<DIV>MCSA KZN</FONT></DIV><PRE>Bolt Safe or Bolt Not!
</PRE></BLOCKQUOTE><PRE>Bolt Safe or Bolt Not!
</PRE></BLOCKQUOTE></BODY></HTML>
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