Falling down
the thought of someone riding a circus elephant in a spandex suit brings a grin to my face for some reason.
i'm not sure about all this math stuff. sure, i play a little minesweeper and count (very little) money but that's about the extent of my math skills. so if someone could be so kind as to give me a hand with these equations.
a climber, let's say his name is dude, leaves a belay on el cap leading the crux pitch of... 'imminent death', VI 5.8+ A5d. on this pitch our climber leads exclusively on hooks for exactly 60m. while standing on the last hook of the pitch, dude camly reaches a locking biner toward the fat 3/8" belay bolt when... ping... dude becomes airborne. the unfortunate dude issues forth a tremendous blood curtling scream as his body cartwheels backwards, gaining momentum. here are my questions,
1- how fast is dude going when he passes the belay?
2- what is dude's maximum speed at the end of his fall, immediately prior to deccelleration?
i'm not sure about all this math stuff. sure, i play a little minesweeper and count (very little) money but that's about the extent of my math skills. so if someone could be so kind as to give me a hand with these equations.
a climber, let's say his name is dude, leaves a belay on el cap leading the crux pitch of... 'imminent death', VI 5.8+ A5d. on this pitch our climber leads exclusively on hooks for exactly 60m. while standing on the last hook of the pitch, dude camly reaches a locking biner toward the fat 3/8" belay bolt when... ping... dude becomes airborne. the unfortunate dude issues forth a tremendous blood curtling scream as his body cartwheels backwards, gaining momentum. here are my questions,
1- how fast is dude going when he passes the belay?
2- what is dude's maximum speed at the end of his fall, immediately prior to deccelleration?
weather is occurring.
alright, i've been working on this long enough to make batguano's head hurt (read-not long). i'm trying to rounding up to 10m/s2 to make this easier.
dude falls at a rate of 10m/s in the first second, Delta d, (the change in distance, Dd) is 10m at the end of the 1st second. 20m/s in the 2nd second, Dd is now 30m. 30m/s in the 3rd second, Dd is now 60m. so 3 seconds to pass the belay.
v=squ.rt of 2(10m/s)(60m) anybody got a scientific calculator? (please excuse my dear aunt sally...)
the speed at the end of the 4th second will be 40m/s, making Dd 100m. and at the end of the 5th second, the speed will be 50m/s, making Dd 150m, which is 30m too far, so lets say around 4.5 seconds to reach the end of the rope, completing the 120m fall.
v=squ.rt of 2(10m/s)(120m)
lets see, parenthases first, yes, yes, then the exponents, uh huh, carry the one, now multiply, uh huh, yes yes, carry the one again... divide by two, uh huh, yes, yes, now add in dude's soiled underwear, making sure to drop the remainder.. uh huh, i think i've got it!
so uh...
"damn, that's a whipper", is my final answer. anybody else get that?
dude falls at a rate of 10m/s in the first second, Delta d, (the change in distance, Dd) is 10m at the end of the 1st second. 20m/s in the 2nd second, Dd is now 30m. 30m/s in the 3rd second, Dd is now 60m. so 3 seconds to pass the belay.
v=squ.rt of 2(10m/s)(60m) anybody got a scientific calculator? (please excuse my dear aunt sally...)
the speed at the end of the 4th second will be 40m/s, making Dd 100m. and at the end of the 5th second, the speed will be 50m/s, making Dd 150m, which is 30m too far, so lets say around 4.5 seconds to reach the end of the rope, completing the 120m fall.
v=squ.rt of 2(10m/s)(120m)
lets see, parenthases first, yes, yes, then the exponents, uh huh, carry the one, now multiply, uh huh, yes yes, carry the one again... divide by two, uh huh, yes, yes, now add in dude's soiled underwear, making sure to drop the remainder.. uh huh, i think i've got it!
so uh...
"damn, that's a whipper", is my final answer. anybody else get that?
weather is occurring.
In a vacume, the impact speed would be 109 Mph, though, I think one could rightfully assume Dude would be flailing wildly while falling, thus increasing his surface area, reducing his "streamline", and increasing his drag coefficient, so his actual speed would be slower, maybe 80-90 Mph. The slower speeds would also give Dude time to "evaluate" his life slightly longer and enjoy the slide-show. I'm guessing either the rope won't be able to handle that load, or the bolt will tear out of the wall. Now, I'm not privy to my physics book right now, so I can't give better values, or my Fluids book to get a closer handle on the wind resistance. But, unless Dude is very small, thereby reducing the momentum at "ropes end", there won't be much "whipping" involved. 
Oh, and Legion, that depends, is your elephant the pot-bellied elephant from the South Park episode with the 5-assed monkey?
Oh, and Legion, that depends, is your elephant the pot-bellied elephant from the South Park episode with the 5-assed monkey?
"I never saw a wild thing sorry for itself. A small bird will drop frozen dead from a bough without ever having felt sorry for itself."
D. H. Lawrence
D. H. Lawrence
thanks corey. that's 109 m/h at the moment the rope begins to absorb force.
so dude would pass the belay at 77 m/h (34.3 m/s or 123.5 km/h) did you get that too?
i'm gettin all worked up here thinking about ripping bolts out of the wall. surely the hardware would remain intact? the rope and the belay should really be able to support this. assuming it's a clean fall and there are no edges to cut the rope and dude gets caught by the belay, i would like to think nothing would fail. there are reports of people taking 300+' falls and surviving.
how could we estimate the force?
F=m a, where do we go from here?
so dude would pass the belay at 77 m/h (34.3 m/s or 123.5 km/h) did you get that too?
i'm gettin all worked up here thinking about ripping bolts out of the wall. surely the hardware would remain intact? the rope and the belay should really be able to support this. assuming it's a clean fall and there are no edges to cut the rope and dude gets caught by the belay, i would like to think nothing would fail. there are reports of people taking 300+' falls and surviving.
how could we estimate the force?
F=m a, where do we go from here?
weather is occurring.
Well, seeing as the fall factor of a 120 M fall on 60 M of rope is the same as a 20 meter fall on 10 M of rope (2), and many people have taken those, I would say you would be ok, as long as you had a couple of fatty bolts or cams for the belay. Of course, if it was A6, then both people better have base jumping gear ready to go....
Wes
Wes
"There is no secret ingredient"
Po, the kung fu panda
Po, the kung fu panda
wait a minute...
that still can't be enough information. we now know dude's velocity, but his impact force would be strictly dependant on how long it took the rope to stretch. distance over time and all that jazz.
therefore the impact force would vary depending in the specific type of rope used for the belay right? so would the force of this massive whipper be the same as a new rope's impact force as stated by the manufacturer?
that still can't be enough information. we now know dude's velocity, but his impact force would be strictly dependant on how long it took the rope to stretch. distance over time and all that jazz.
therefore the impact force would vary depending in the specific type of rope used for the belay right? so would the force of this massive whipper be the same as a new rope's impact force as stated by the manufacturer?
weather is occurring.