Hi,

I am working on a small project and am hoping to get some outside insight from anyone who has the time or intrest...

One of my hobbies is rock climbing and because I am quite fanatic about it I train for it quite regularly. One of the methods commonly used for training is called 'dead hanging' which is used to improve finger strength. It involves hanging from a wooden on plastic edge, of various sizes (grip types), for various lengths of time. See pic...

http://www.urbanclimbermag.com/themag/workshop/workshop_-_26_-_hang_time/ [Broken]

I always keep track of my training including the grip type and hang times and am now trying to put my (elementary) physics knowledge to work and represent all the factors going into the dead hang into one value by forming or using a equation or set of equations so that it will be easier to track my progress.

As you can see the 3 factors are weight, area of contact, and hang time.

I first thought that I could use a torque equation (r1*F1=r2*F2) to measure the opposing forces using my finger joint as the axes point but quickly realized that I could not include the area factor if I used this reasoning (i.e. if I hang by 4 fingers or two fingers the resulting number would be the same).

Then I thought that I could use a pressure equation (m*g/area=P) which includes the area and weight (mg) but then couldn't figure out how to incorporate the time of the hang. I tried (mg)/area/time but that didn't really seem right.

In the end I ended up making my own equation mass*g*time/area which gives me a number value that represents the difficulty of a hang in relation with the difficulty of another hang but I am not really satisfied with that for several reasons. I want to be able to compare the difficulty of a hang with other things as well and would like to find a way to convert or rearrange a established physics equation or set of equations to represent all of the difficulty factors with the result being in, for instance, newton or watts or some other established measurement. Is there anyone who can help me to do this or should I just be satisfied with the equation that I worked out?

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Elect....Seems like one additional variable you likely need is torque....Ever hang vertically on a pair of still rings in gymnastics? Then try the "extension with arms out horizontally?? Notice a BIG difference, right??

Same idea for your fingers...a right angle at any of your knucles will be a lot harder hang than if they are bent further and so the knuckle is curled up and the angle greater than ninety degrees....and the "extension" reduced...

How about friction at the grip point...type surface, sweaty hands, shape and angle of the grip surface....

good luck, not an easy modeling project...but interesting application of physics...

You are right about the friction part...

We use powdered chalk to improve the 'grip' that we get when climbing or in this instance dead hanging but temperature does still play a role but it is a factor that is too complex for me to calculate accurately but I’d be more than welcome to hear ideas of how it could work...

Any advice on how to work the other factors (area and time) into the torque equation?

Any advice on how to work the other factors (area and time) into the torque equation?

Torque is force times distance. so a horizontally extended finger of 1" takes twice the force of one extended only 1/2"....but I have not the slightest idea how a living body reacts to the expenditure of "work"....is the first minute of exercise burning calories at the same rate as the last minute a few hours later?? Once muscles become "tired" it subjectively seems to take more effort but whether that's psychological or physiological or both....I don't know...

Yes, I understand that torque is force x distance and that the answer comes in the form of Nm and if I were going to use the torque equation in my situation then I also must be able to take the answer from the equation (X Nm) and put it into another equation that considers the area and time factors because 5 fingers under a certain amount of torque is not the same as 2 fingers under the same amount of torque. Furthermore, holding that position for 5sec or 2min is not the same either...

Yes, the more tired you get the harder it is for you to hold on but the required force to hold on is the same or...? If instead of it being a person holding on it was a machine with a mechanical finger and a certain weight it would take a certain amount of energy or force for that machine to hold on to a certain grip area, for a certain amount of time with it’s set weight and that should (some way) be able to be measured. This is what I am interested in, a equation taking these three factors (weight, area, time) into account....