Horizontal cam placements

From the Metolius Powercam booklet:

"When placing cams in horizontals, always place the outboard cam lobes on the bottom. This will result in a much stronger and stable placement".

Why? Wouldn't the individual placement dictate orientation? Use of free body diagrams encouraged.

i would amend their statement to say 'when possible place with outermost lobes down, however if the opposite orientation provides a significantly better placement then use that instead'

The one thing i can think of is that (in my experience) the outer lobes of a cam tend to open as a cam walks while the inner lobes tend to retract. Ever seen a fixed tcu with the head flipped? oriented the way they say, it walks to work right with the load. see the pictures

thanks larry for the solidworks drawings, i was having a bit of trouble picturing what the booklet was trying to describe =)

Thanks for the CAD. I’m still not convinced this orientation matters…I don’t see any difference in the loading 

Is it because of the walking? Or the loading if a fall happened?

Use of free body diagrams and axes would be much appreciated.

This is still up for debate per this Instagram post  

Maybe the person who wrote the Metolius booklet just has some personal opinion or half-baked logic. Seems unlikely to me that it matters.

If you imagine a shape like the truncated pyramid on the dollar bill, obviously it's going to be more stable if it's resting on the large base rather than upside down on the tip. So maybe that was just their intuition, and they convinced themself that it was right.

Let's set up a coordinate system like the one below, with x being straight out of the crack, y up, and z being to climber's left.

If the roof of the crack didn't exist, and the thing was just sitting there on a ledge, then you'd have some tiny F_y<0 from gravity acting directly on the cam's own mass. If you then applied a nonzero F_z (with either sign), the cam would tend to topple. Let's say F_z is greater than zero, so that the torque is τ_x>0 (counterclockwise, by the right-hand rule, as seen by the climber). Then the orientation with the wide part on the bottom would be more stable. It would take a bigger F_z to rock it past the point where its center of mass was beyond its base of support. For a smaller F_z, and assuming there was enough friction to keep it from sliding in the z direction, it would rock up so that its weight was resting on the bottom corner at climber's left, then fall back down rather than toppling. The better stability comes from the relatively large lever arm of the wide lobe.

But in reality, the crack does have two sides, which makes it seem pretty questionable to me that that intuition is relevant. Suppose you put the cam in the other orientation, wide side up. Then if you apply the same τ_x>0, what will happen is that one of the lobes on top (the one at climber's right) will press up against the top surface, and will have just as big a lever arm as before.

Of course it's possible that there is some kind of internal mechanical fact about the cam that makes the orientation better, like the axle is stronger against a force in a certain direction, or the outside lobes are actually physically stronger. But their word "stable" makes it sound like that's not what they're imagining.

Maybe think about the problem where the downward force isn't directly vertical but is offset by x degrees left or right...

E MuuD wrote:

Maybe think about the problem where the downward force isn't directly vertical but is offset by x degrees left or right...

That's what it means to have a z component.

Thanks for the diagram, Ben. I agree with your reasoning: the existence of the roof of this crack means that force is equally distributed along the top and bottom sides; showing that the orientation shouldn't matter.  Even if the Applied Force (Fz) wiggles along the Y axis, it's still balanced out. 

Thus we can consider this case closed :) 

http://web.mit.edu/custer/www/rocking/cams/cams.body.html

Ben Crowell wrote:

Maybe the person who wrote the Metolius booklet just has some personal opinion or half-baked logic. Seems unlikely to me that it matters.

If you imagine a shape like the truncated pyramid on the dollar bill, obviously it's going to be more stable if it's resting on the large base rather than upside down on the tip. So maybe that was just their intuition, and they convinced themself that it was right.

Let's set up a coordinate system like the one below, with x being straight out of the crack, y up, and z being to climber's left.

If the roof of the crack didn't exist, and the thing was just sitting there on a ledge, then you'd have some tiny F_y<0 from gravity acting directly on the cam's own mass. If you then applied a nonzero F_z (with either sign), the cam would tend to topple. Let's say F_z is greater than zero, so that the torque is τ_x>0 (counterclockwise, by the right-hand rule, as seen by the climber). Then the orientation with the wide part on the bottom would be more stable. It would take a bigger F_z to rock it past the point where its center of mass was beyond its base of support. For a smaller F_z, and assuming there was enough friction to keep it from sliding in the z direction, it would rock up so that its weight was resting on the bottom corner at climber's left, then fall back down rather than toppling. The better stability comes from the relatively large lever arm of the wide lobe.

But in reality, the crack does have two sides, which makes it seem pretty questionable to me that that intuition is relevant. Suppose you put the cam in the other orientation, wide side up. Then if you apply the same τ_x>0, what will happen is that one of the lobes on top (the one at climber's right) will press up against the top surface, and will have just as big a lever arm as before.

Of course it's possible that there is some kind of internal mechanical fact about the cam that makes the orientation better, like the axle is stronger against a force in a certain direction, or the outside lobes are actually physically stronger. But their word "stable" makes it sound like that's not what they're imagining.