Hi there, I've spent some hours on trying to make a simulator (in Excel) for calculating the forces involved in a climbers fall. I've found the following link (http://toad.stack.nl/~stilgar/calc.php) but can't figure it out - Maybe because my grades back in high-school were terrible :uhh: Could anyone please help me making the formulas? The following variables will be available: - Lenght of rope (in meters) - Fall factor / Height of fall - Dynamics of rope (in percent @ 80kg) - Weight of climber (in kg) Thanks in advance
You weren't clear as to what you were asking. I assume that you're asking what force a rope would exert on a person when the person, who has the rope tied around his waist falls and is prevented from falling all the way to the ground by the rope. That force is F = dp/dt where p is the momentum of the person who is falling and dt is the time inteval during which the person's momenum changes by the amount dp. I also don't know what you mean by "Dynamics of rope (in percent @ 80kg)". you need to know the properties of the rope such as Young's modulus for the rope. Pete
Hi Pete, When I look at Your answer I can see that what I'm missing is the Young's modulus for the rope. So lets start with that. I've found this formula: E = (L*F)/(l*A) E: Young's Modulus L: Length of the rope l: Change in lenght F: Force A: Area of the rope I donĀ“t know what units to use, please correct me in this example: L = 100 meters l = 7 meters (dynamics = 7%) F = 784,8 newtons (80 kg x 9.81) A = 314,29 mm^2 (10mm x 10mm x pi) E = 35,67 (100*784,8 / 7*314,29)
doesnt the rope act as a spring, it decelerates the faller. Dont you need the ropes spring coefficient?
well, you need to know the spring constant (k). This is in N/m. Then you can use the equation E = 1/2kx^2, where k is the spring constant, and x is the amount of strech from the resting possition of the rope. The force exerted on the object being stopped by the rope would be F = -kx. You can play around with there equations and find the right constant so the g-force on the person is not too high.