Descender Overheating?

[dougr]

Radiation would dominate in a vacuum, but in our atmosphere conduction both direct and convective exceed the radiative transfer by a good ratio unless temps are very high. The radiative constant of 10^-8 means a delta T on the order of 650 is needed for radiation to dominate.

Quick calcs:

Convective transfer: q = k A (delta T)

k for free air is about 15. A is the same for both equations. Let's assume a delta T of 200.

So q = 3000 A


Radiative transfer: q = sigma A (delta T)^4

sigma is about 5.7 * 10^-8, A is fixed, delta T is 200.

So q = 91 A

Therefore, convection alone is transferring 30 times the heat of radiation. Direct conduction is highly dependent on contact area of course, so no telling what that may be in this scenario. The A in its equation is different. Very interesting stuff and a great Q.

[ratagonia]

Radiation would dominate in a vacuum, but in our atmosphere conduction both direct and convective exceed the radiative transfer by a good ratio unless temps are very high. The radiative constant of 10^-8 means a delta T on the order of 650 is needed for radiation to dominate.

Quick calcs:

Convective transfer: q = k A (delta T)

k for free air is about 15. A is the same for both equations. Let's assume a delta T of 200.

So q = 3000 A


Radiative transfer: q = sigma A (delta T)^4

sigma is about 5.7 * 10^-8, A is fixed, delta T is 200.

So q = 91 A

Therefore, convection alone is transferring 30 times the heat of radiation. Direct conduction is highly dependent on contact area of course, so no telling what that may be in this scenario. The A in its equation is different. Very interesting stuff and a great Q.

I see your point, but...

As our colleague Professor Agostinone pointed out, it is not the 4th power of the temp diff, it is the diff of the 4th powers of the temperature - quite a different animal. Perhaps you would re-run your claim with this distinction.

Tom

[xxnitsuaxx]

I appreciate all the responses. As a liberal arts guy\law school grad I had to resort to Googling several of your responses. The takeaway message that I'm getting is that the rope's not going to melt through but I still don't want to come to a complete stop? And that no matter how hardcore engineers might pretend to be, deep down they really just want to pick out pocket protectors and work out equations on their slide rules?

[dougr]

Holy cow! Yes! Not (delta T)^4 but the difference of the temps to the fourth. Mind is failing. Sad. I was a math teacher at one time, up to Calc BC, and completely misread the equation at quick glance the other day.

The factor is 1 rather than 30 in favor of convection. Throw in direct conduction and the sum total radiation contributes is probably 20% in my guess.

I'm intrigued by this all and am going to set up a spreadsheet and take some measurements of the rap device/rope interface and see what I can come up with.

[trackrunner]

The takeaway message that I'm getting is that the rope's not going to melt through but I still don't want to come to a complete stop?

perhaps a smooth, continuous, slow speed also keeps the heat down

http://www.youtube.com/ATSadventures#p/u/3/APreETBFDHw

It wasn't much of a test. And it wasn't really very real-world.

T

you weren't using a plumbers torch in Imlay?

[ratagonia]

Holy cow! Yes! Not (delta T)^4 but the difference of the temps to the fourth. Mind is failing. Sad. I was a math teacher at one time, up to Calc BC, and completely misread the equation at quick glance the other day.

The factor is 1 rather than 30 in favor of convection. Throw in direct conduction and the sum total radiation contributes is probably 20% in my guess.

I'm intrigued by this all and am going to set up a spreadsheet and take some measurements of the rap device/rope interface and see what I can come up with.

My thesis is that the rapid increase of radiation with temperature difference makes it very difficult to get up to a temp that will soften the polyester.

I am surprised you can go to a rate for convection without using some kind of length - as convection goes up a lot with the height available, as the chimney driving effect increases...

T

[agostinone]

I appreciate all the responses. As a liberal arts guy\law school grad I had to resort to Googling several of your responses. The takeaway message that I'm getting is that the rope's not going to melt through but I still don't want to come to a complete stop? And that no matter how hardcore engineers might pretend to be, deep down they really just want to pick out pocket protectors and work out equations on their slide rules?

xxnitsuaxx--I must say you have this nerd (disguised as a canyoneer) pegged. I found myself getting all twitterpated when heat transfer entered into the discussion.

Back to your original inquiry about scorching the rope, you'll should be fine. When you are at the top of the rap you poses a certain amount of potential energy (more of it the higher the rap and the bigger the beer belly). That energy gets converted to heat on your way down. How hot it gets depends on how fast you go. Here is a helpful analogy: if you have a battery and you hook up a 10W light bulb the bulb gets hot and the battery drains. Same battery hooked up to a 100W light bulb will drain the battery faster and the bulb will get a heck of a lot hotter.

Seems to me worts case would be a long free hanging rappel that is rapped really fast and then stopped just before you touch the ground. That way the rap device is as hot as it's going to get and all your weight is mashing it into the rope.

[Bo_Beck]

I reccommend putting your prusik/autobloc on the uphill side of the descender (use a wrap3 to the fourth power) so that when you stop to let the thingy cool down and it melts through the softened polyester at least you'll still be attached to the rope......lemme think? how many rescues or fun rides have been done with a 2.....or maybe a 3 person load on a single rope with a single descender? Maybe statistics would answer some questions as well as the pure physics? Last year a rappel from the now infamous "BIRD PERCH" with two people and all gear (on the same device simultaneously) didn't end up with a melted in the middle and oh shit and we're gonna die now situation! Things get hot....so does the desert! I worry more about the 50% reduction in the strength of a rope when it is wet and the possibility of a rock clipping it when I'm on it bouncing my merry way down! (oh yeah...and folks that don't look up while on descent and realize all the maneuvering that they do cuts the shit out of ropes rubbing on edges).

[ratagonia]

I worry more about the 50% reduction in the strength of a rope when it is wet ...

I'm curious where this figure comes from?

10% to 15% seems the more reasonable figure.

Tom

[Bo_Beck]

I'm curious where this figure comes from?

10% to 15% seems the more reasonable figure.

Tom

Sterling Rope Co. suggests up to 30% loss of strength, but I saw a study at ITRS 2002 in Golden Co. that showed up to 50% loss of strength. I just do know that a wet rope is definately weaker than a dry rope and since I use 8mm single strands, my concern on occasion would be a falling rock clipping my rope. Had a 10.5mm on the 2nd to last pitch of Moonlight Buttress cut more than halfway through.

[Bo_Beck]

I'm curious where this figure comes from?

10% to 15% seems the more reasonable figure.

Tom

Not exactly 50%, and not exactly an answer to low stretch or static lines, but interesting nonetheless! Check it out.

http://www.singingrock.com/article.a...&nLanguageID=2

Will have to get my notebook from the ITRS 2002 I attended and see if I can find the study that showed up to 50%.

[ratagonia]

Not exactly 50%, and not exactly an answer to low stretch or static lines, but interesting nonetheless! Check it out.

http://www.singingrock.com/article.a...&nLanguageID=2

Will have to get my notebook from the ITRS 2002 I attended and see if I can find the study that showed up to 50%.

I am trying to track down sources for various numbers. Sterling has access to information from tests conducted by boating people, and it is not clear that these numbers translate over into canyoneering applications.

Please note the Singing Rock article is about nylon dynamic ropes. The analysis talks about the peculiar chemical properties of nylon with water.

Tom