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[sneoh]

How large a load multiplier on the anchor(s) depends on a number of factors.  After DMan's response last night, I spent some time Googling and dabbling in Statics Mechanics for the first time in 20 years or so.  The multiplier can be greater than 1x the second's weight depending on setup, whether you belay directly off the anchor of redirected through one piece of the anchor.  The whole picture is more complicated than I am able to explain here.
When I was climbing a lot at The Gunks and swinging leads with Ajax (who outweigh me enough for consideration), I used to clip into the anchor, climb slightly higher to get a piece of pro in, clip the rope thru this piece, downclimb back to the anchor, and tie in with the rope (because I am old fashion).  I would then belay Ajax up with the rope redirected thru the higher piece.  Only I would be weighing the anchor directly.  If Ajax were to weigh the rope, his weight would be on the high pro.   When he got up to the anchor, I would hang him the remnants of my rack and he would take off, with the first piece of pro already set.  No factor of 2 fall here.  Of course we were just doing G and PG climbs where one can almost always find pro placements whenever one wants.

If you and your second habitually tie in using the rope, you might want to pay attention to pitches which are "rope stretchers".  Eric and I witnessed this when we were on L29 and the other party was on Eagle Dance.  It  appears that ED has a pitch which is pretty darn close to full 60m.  The second had tied into the anchor with the rope.  The leader was literally two feet from the next anchor when he ran out of rope. Much cussing ensued.  The second had to untie from the anchor then both simul climbed 4 or 5 feet till the leader was able to tie into his anchor (presumably with slings).  We shouted "good job" over but they were not terribly amused since we had just beaten them to L29 which was their true objective that day.  ED was the "consolation climb" for them.

[DLottmann]

People are mentioning redirecting the belay through the anchor doubles the load, but doesn't the lifting of the belayer (assuming they are hanging below the anchor) make it more dynamic, likely sprading out the impact over time. I have always been a believer in bomber belays, which makes the whole question somewhat mute, though I understand you may not have that with ice.

Also, belaying the second up, if they fall, it is not likely going to generate a lot of force. If you are worried about the belay holding then, I sure wouldn't want to be relying on it when they climb through. Once they are leading and have clipped a piece, how would belaying through the anchor increase the force? If they fell before the first piece, I would think you would particularly want the catch to be dynamic. If my leader took a fall factor 2, I would feather the belay.

Let’s focus on just one situation here, belaying a 2nd.

If you re-direct the load strand through the anchor (or a high piece set above the anchor), and the 2nd falls generating a force of “x” on the load strand, an equal force of “x” must be applied on the other side of the carabiner to prevent rope from moving.

This, equals 2x. Yes, the belayer moving may soften the catch a little, but “x” still needs to be applied on that side of the carabiner to stop “x” on the other side. That means that carabiner/pro sees 2x. It’s pretty simple physics really...

If you are directly belaying off the anchor, with Munter or “plate” style device, that carabiner/pro only sees 1x.

I hate to mention this book but FOTH diagrams this well...

Bottom line, as long as the “high-point” is absolutely bomber it shouldn’t matter, EXCEPT if you end up needing to create a haul system or escape the belay... as Strand will attest this is a rare event... however I choose to direct belay because it is more comfortable, easier to take in slack quickly (depending on the device) and with many devices I can be hands free in-between yarding slack, allowing me to eat, drink, take pictures, scratch my ass, or whatever else needs attending...

Talking about Factor 2’s if the 2nd climbs through is a separate topic IMO...

[strandman]

I believe it would generate close to 1/2 X since the load would fall somewhat on both belayer and second ?

[DLottmann]

I believe it would generate close to 1/2 X since the load would fall somewhat on both belayer and second ?

No. I can’t explain this any simpler.

If you pull 50lbs on one side, you MUST hold 50lbs on the other side. This puts 100lbs on the carabiner/pro...

[DLottmann]

Picture the type of hanging scale, like the one at Pinkham Notch people weight their packs on...

If you take a 50 lb pack and attach a sling to it, and double the sling through the hook, you need to attach a 50lb pack on the other side for the two to balance... this would make the hanging scale read 100lbs.

[strandman]

I believe the load would be somewhat shared throughout the system .. belayer... belay point and second

if the belay pulls from a seconds fall, then you are screwed

there is no such thing as a pure load in climbing and a real factor 2 fall cannot be acheived

"hands free "?  never

[OldEric]

Classic case of physics 101 vs.  the real world.  No one I know has more practical real world experience that John.  So sorry all you Newton - Einstein wanna-bees - all that classroom jazz doesn't necessarily apply here.

[sneoh]

Picture the type of hanging scale, like the one at Pinkham Notch people weight their packs on...

If you take a 50 lb pack and attach a sling to it, and double the sling through the hook, you need to attach a 50lb pack on the other side for the two to balance... this would make the hanging scale read 100lbs.

This explains the difference in forces on the master point between rappel versus being lowered.

Apologies to Eric -
as for the force on each of the two anchor pieces for a given load on the master point, it actually depends on the included ("V") angle between the two legs of the equalized anchor system.  Ideally, you want to keep this angle to 60 deg or less.  Increase the "V" angle to 120 deg and EACH anchor will be subjected to 1x the force of the load, not 1/2 as you might expect.  As for the force multiplier whether you belay directly off the anchor or redirected through the anchor, it is yet another level of analysis, too complicated for me to even try to get into here.

I agree with John that a 100% factor 2 fall would be hard to achieve in real life even belaying with a Gri Gri.

Edit/PS: Shouldn't we be talking about the impending "record-breaking, crippling" snow storm instead.  A little hysteria, perhaps?

[wivanoff]

I believe it would generate close to 1/2 X since the load would fall somewhat on both belayer and second ?

No, it's called "pulley effect" http://www.southeastclimbing.com/faq/faq_pulley.htm The load on the masterpoint would be closer to 1.66 x weight of the climber because a carabiner is a very inefficient pulley.

[frik]

This is awesome, two effing pages on how to tie off to a tree.

[pappy]

This is awesome, two effing pages on how to tie off to a tree.

The curse of the internet and sites like this is that everything gets waaaaay over thought.