physics problem: pendulum legnth

[layton]

What's the longest pendulum distance horizontally you could theoretically do if the follower plans on using the same rope to lower and get across. I figured 50' with a 200' rope since the follower needs 2x the amount of rope as distance to the next crack. I also assume the leader would need to belay exactly at the height of the pendulum point.

 

just curious.

[keenwesh]

you could do a penji 100 feet below your lower out point with a 200 foot rope (however far horizontally that is). The leader climbs 100 feet, lowers back to the belay, cleaning gear, and swings. once to the other spot they put the follower on belay and the second follows the penji and unties. Pull the rope through and keep sendin'.

[tvashtarkatena]

Incorrect.

 

If R is the max horizontal distance from pendi fulcrum to leader/belayer as well as the max pendulum length, assuming the leader/belayer is level with the fulcrum, then the follower when fully lowered out will be at a 45 degree angle from the leader/belayer, therefore

 

Rope Length L = 2R + R*SQRT (2) (draw it to see WTF I'm talkin bout)

 

If L = 60m, then

 

max R = L/(2+SQRT (2)) = 60/(2+1.414) =17m

 

this is the max horizontal distance from leader/belayer to fulcrum, as well as the max pendulum length for leader and follower.

 

This is best case - if the follower has to 'wind up' in the opposite direction to make the pendi happen, max R is even shorter. I've also assumed knot length is accounted for by rope stretch.

 

 

 

Edited January 24, 2014 by tvashtarkatena

[num1mc]

Depends on how steep the wall is and how big a ripper the second wants to take.

[tvashtarkatena]

I've also assumed the leader doesn't just burn a fatty and float past the pendi on his way to awesome land.

[layton]

I've also assumed the leader doesn't just burn a fatty and float past the pendi on his way to awesome land.

 

Awesome.

 

If I don't like a pitch, I lower out the length of that pitch, and pendulum so hard that I make a half circle and wind up at the next anchor.

Edited January 24, 2014 by layton

[tvashtarkatena]

I go one better - I have my buddy do that while I finish my fatty.

 

Me when you need something like this Cliff Clavenized, Keenwesh when you want to actually get up the pitch, Ivan when things suck and you need to witness something suffering more than you.

Edited January 24, 2014 by tvashtarkatena

[tvashtarkatena]

Although I gotta say I've witnessed the Big Man do some wild-assed shit that got us through.

Edited January 24, 2014 by tvashtarkatena

[ScaredSilly]

What's the longest pendulum distance horizontally you could theoretically do if the follower plans on using the same rope to lower and get across.

 

Theoretically, the length of the rope ...

 

[tvashtarkatena]

This assume you've got only one rope, per the OP.

 

Method 1

Pro: Faster, good if EZ down low, horiz reach 17m

Con: Dangler cn snag while leader penjiz, 2 fulcrums

 

Method 2

Pro: Good if EZ up high, no dangler snag, 1 fulcrum

Con: Slower, horiz reach only 15m

 

PenjiLand by PatGallagherArt, on Flickr

Edited January 24, 2014 by tvashtarkatena

[keenwesh]

the way I detailed lets both the leader and the follower actually do the pendulum, a plus for me. Penjis are super fun, running back and forth a long ways off the ground is one of the best things about climbing walls.

 

I think ya'll are really overthinking this.

[tvashtarkatena]

Both leader and follower must pendulum in the both methods I've drawn. Nobody gets out alive.

 

I didn't show anybody actually swinging and screaming is all.

Edited January 24, 2014 by tvashtarkatena

[tvashtarkatena]

Redux, with screaming pendiz. These are the only ways I could think of to do this with one rope.

 

R = max horizontal distance between the pendi fulcrum and the next anchor assuming both are at the same elevation, if only one rope is used.

 

This is a specific case where you're penjiing over to a spot directly horiz to anchor 1 at max angle of 45. Not sure how much you can push that angle practically speaking. Depends I reckon.

 

Also, if anchor 1 is higher, horiz reach is farther. If its lower, less. This is a specific case for horiz reach = vert between anchor 1 and fulcrum

 

 

 

Method 1

Pro: Faster, good if EZ down low, horiz reach 17m

Con: Dangler cn snag while leader penjiz, 2 fulcrums

 

Method 2

Pro: Good if EZ up high, no dangler snag, 1 fulcrum

Con: Slower, horiz reach only 15m

 

PenjiLand2 by PatGallagherArt, on Flickr

Edited January 24, 2014 by tvashtarkatena

[ivan]

[num1mc]

Both leader and follower must pendulum in the both methods I've drawn. Nobody gets out alive.

 

I didn't show anybody actually swinging and screaming is all.

Redux, with screaming pendiz. These are the only ways I could think of to do this with one rope.

 

R = max horizontal distance between the pendi fulcrum and the next anchor assuming both are at the same elevation, if only one rope is used.

 

This is a specific case where you're penjiing over to a spot directly horiz to anchor 1 at max angle of 45. Not sure how much you can push that angle practically speaking. Depends I reckon.

 

Also, if anchor 1 is higher, horiz reach is farther. If its lower, less. This is a specific case for horiz reach = vert between anchor 1 and fulcrum

 

 

 

Method 1

Pro: Faster, good if EZ down low, horiz reach 17m

Con: Dangler cn snag while leader penjiz, 2 fulcrums

 

Method 2

Pro: Good if EZ up high, no dangler snag, 1 fulcrum

Con: Slower, horiz reach only 15m

 

PenjiLand2 by PatGallagherArt, on Flickr

 

Where's Catbirdseat when we need him?

[bstach]

How do you get from pic 3 to 4 in method 2? It seems a few steps are missing.

[layton]

thanks for the math...

always wondered why no one ever tried to figure this out... i would think it would be well known

[tvashtarkatena]

I'm gonna try to verify with some actual route info to see what the longest horiz penjis are out there. Don't know if you can do the 45 deg. thing in practice on too many routes. Can also come up with a generalized equation for that ultra nerd. Hittin the road for a bit, back later.

 

Any steps missing in drawings should be easy to figure out. I just drew the essential states required to royally hose oneself regarding a safe retreat.

 

 

 

[layton]

you could get more than 45 degrees with a jet pack

[G-spotter]

You can get more than 45 degrees each side of vert on a playground swing, so why not on a pendulum?

 

You can't get to 180 degrees (fully horizontal on each side) unless you have solid steel bars instead of chains. Or a rope in this case.

 

Layton, you think switching out the rope for an inflexible rod would be useful for penjis?

 

http://boards.straightdope.com/sdmb/showthread.php?t=692253

Some useful links in there

 

 

[layton]

oh say, that's a good thought. lots of trees in yosemite you could haul up too

[ivan]

you could get more than 45 degrees with a jet pack

if'n you got a jet-pack, wtf you climbing for?

[tvashtarkatena]

tree+pig=trebuchet. check my math here.

[tvashtarkatena]

flat belayer reqd for max R