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squeaks
Big Wall climber
Denver
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Topic Author's Original Post - Nov 24, 2005 - 05:35pm PT
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I know there are a bunch of engineers here, so I thought I might be able to get some help on a school asignment.
Using VBA and excel I need to create a fall force callculator that will have more than one user interface.
The user will be able to choose the rope thickness, the length of the fall and the type of the top most piece.
For the calculation of the fall force I am still a bit unsure how to go about it.
Order of calculations
1.Calculate the speed of the climber when he hits the rope.
d=1/2*A*T^2
v(f)=V(i)+A*T
2.If I know how fast the climber is going and how quickly they stop I can calculate the force on the top piece.
v(f)^2=v(i)^2+(2*A*D)
f=m*A
Yet where can I get a value for the stretch of the rope?
Is there a better way to go about calculating the fall force?
This is a freshmen engineering computing class so I am looking for more of a general model.
Thanks for any help.
-Eric
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Eric Chisholm
Trad climber
Sebastopol, CA
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Nov 24, 2005 - 10:41pm PT
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WOW! That link made my head hurt.
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squeaks
Big Wall climber
Denver
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Topic Author's Reply - Nov 26, 2005 - 04:25am PT
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The first equation fails to show up when I load up the page. Does anyone know what this equation is?
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TradIsGood
Trad climber
Gunks end of country
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Nov 26, 2005 - 09:55am PT
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Probably something like eqn. 1 or 2 here.
Obviously, you are going to need more than just the limited inputs mentioned in your original post. MtnTools.com has information on elasticity of a number of typical modern ropes.
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rgold
Trad climber
Poughkeepsie, NY
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Nov 26, 2005 - 02:50pm PT
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The climbtennessee site is ok, although I'd say the mathematics could have been presented more clearly. The failure to mention Hooke's Law, which is the theoretical underpinning of the calculation, is a matter of concern.
There is one portion of the calculator on that site that may lead to errors: the calculation of the rope modulus from the static elongation. This works if the rope is ideally elastic, but engineers have worked hard to reduce elongation below the theoretical value at low loads so that jugging and upper-belayed falls are subject to less stretching. Using the static elongation load as the input to impact force calculations may produce answers that are far off.
A much better source for the basic theory in the elastic case is the paper, "Rope System Analysis" by Stephen W. Attaway, available as .pdf from www.losalamos.org/climb/xRopes.pdf. (This is the "here" link posted by TradIsGood.)
Squeaks, your step 2 isn't going to work. The problem is that you want to calculate the peak force on the protection, and you can't get at this via F=ma with a taken to be the average deceleration (presumably computed from "how fast he stops," although it isn't clear where you will get this time from).
You have two choices: (1) Begin with the differential equation for simple harmonic motion, convert it to an equivalent one with velocity as the dependent variable, and use your step (1) to provide an initial condition. (2) Attaway's account (which is by no means original with him) uses an elementary conservation of energy approach to calculate the maximum elongation in the rope and from that the peak load on protection. This approach is mathematically a little less sophisticated, replacing the solution of a differential equation with a very elementary integration and the solution of a quadratic equation.
Both approaches end up with the same formula for impact load, given the weight of the falling climbiner, the "spring constant" for the rope, and the fall factor for the fall.
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Yah00
Trad climber
CA
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Nov 26, 2005 - 03:03pm PT
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Ok, I know nothing about physics. I was playing around with the calculator linked above and am wondering why G-factor is inversely proportional to weight; whereas the force on the climber is proportional to their weight. Many thanks to anyone who can explain this in simple terms.
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