Deadhang Equation

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Joined: Sat Jan 03, 2009 3:46 pm

Deadhang Equation

Postby electerr » Sat Jan 03, 2009 3:49 pm


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... ... hang_time/

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?

Thanks in advance

Posts: 31
Joined: Sat Nov 01, 2008 4:19 am

Re: Deadhang Equation

Postby kaosgrace » Wed Jan 14, 2009 11:27 pm

You're on the right track for your formula. Actually, I think you have it exactly right.

What you're looking for if you want to incorporate time is impulse (I=F*t, measured in N*s), which is what's used to measure the propulsive ability of e.g. model rocket engines. If you want to incorporate area, you divide by the area of your fingers to get impulse per square meter, which isn't exactly a commonly-used physical quantity in and of itself but can be computed fairly easily for other things that have a force and time component like the aforementioned engines.

So in the end you get m*g*t/A, which would be in N*s/m^2 or kg/m*s or pascal second, an ugly unit to be sure but a perfectly legitimate SI quantity which happens to be the unit for dynamic viscosity (not that that has any application to your predicament). It's also been used in at least one study with the physical meaning you're looking for (impulse area density): so it's not completely outside the range of meaningful physics although it is a little odd.

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