Did some searching, and answered my own question.
Rescue 101 -
If I read your post correct your school of thought is an incomplete depiction of what a MA is doing throughout the system. N2DFIRE explained the accurately, but here is another view.
1. A pulley is a simple machine that produces a 2:1 advantage (this is in a vacuum and under the correct conditions.)
2. The pulley provides this advantage whether attached to the load or when used as a COD. That is ALL pulleys is a system are multiplying forces. Your input to MA theory is correct, but your only considering the total output of the MA and not its impact on the anchor. Use the T method to trace forces to see what the anchor is actually seeing.
With that said, I'll use an example you have used. A 4:1 is commonly used attached to the end of a high-point. When used vertically it would be a 4:1. While the load is seeing a 4:1 MA, the anchor is seeing a 5:1. (Remember the pulley has no idea what end is moving the load). Therefore your anchor end is seeing on additional unit of tension (whatever that is).
This additional load is minimal, but many times it is not accounted for when teams rig an MA to an anchor to haul a load. Obviously the higher the load weight the more impact this additional unit can make.
The ideal way to use an aerial as a high-point is to run the rope up the bed of the ladder and over a pulley. This is why many manufacturers are making pulley plates that mount to the ladder. By doing this it eliminates additional multiplication of forces, eliminates the potential of torquing the ladder, and allows the ladder itself to absorb forces inline (the resultant force will point more toward the ladder vs perpendicular to the ladder). Maybe Eric Ulner will chime in on the effects of resultant forces on the ladder. I know works with Reed and would imagine they use these calculations frequently with the AV
Of course there are other methods....
Mike - If I had to go through all of that to stabilize the aerial I would devise another plan. Part of TRT is efficiency and good use of resources. Tying back a ladder, in my opinion, is neither of those. After 21 years I have learned to never say never, but let's say it would be a last resort and I would have to be lifting more than a rescuer and victim. :)
OK - correct me if I'm wrong. (I never was good at physics.)
A single pulley, hung from your platform. a 300lb load on the end. To lift the load, there will be roughly 300lbs on each side of the rope, and 600lbs on the anchor, right? The pulley used in this fashon acts as a force multiplier, and no MA is achieved, correct?
Based on this I think we all talking Apples n Apples we're just looking at them from different view points.
Let's stick with your example(s) of the 3000# car.
You are correct that if you have the car directly behind your wrecker and you run your cable down to the car, thru a snatch block, and back to your wrecker that each section of line is only carrying 1500#'s thus the 2:1 advantage. But the MA didn't make the car lighter, it just divided the work from one run of cable to two. The hook on the snatch block is still carrying the whole 3000# "load" of the car.
Now let's say the car is sitting beside your wrecker and you run your line out to a (really big) tree and thru a snatch block on the tree and then back to the 3000# car beside you. As you pointed out above; there is no MA to this system and as you begin to pull you now have 3000#'s of force throughout the cable from the car all the way to the winch. The physics in this example work the same as above - it's just the loads that have changed. Instead of having 1500#'s per line off the pulley, you now have 3000#'s on each line. So now the hook on the snatch block (and thus the tree / anchor) is seeing 6000#'s of force.
Translate that from the horizontal plane to vertical:
You are standing on the ground beside a 250# load with a pulley as a high COD on an aerial tip. One end of the rope is on the load, the other in your hands. As you begin to apply 250#'s of force into one side of the system, the load then resists with an equal 250#'s on the other side - thus the aerial tip is now supporting 500#'s of total downward pulling force (load).
This is where the concern of overloading aerials from use as a high directional comes in. The closer the angle of your pulling forces comes to 180 - the greater the doubling force on the anchor for the pulley.
These same basic principles would still apply if you were using a "complex" MA system to raise the load. The total net force on the ladder would be the weight of the load plus the input force required to lift it.
250# load with a 4:1 MA = 250# load + 63.5# input force = 313.5# tip load.
The solution to this is (as others have stated) to pull along the direction of the ladder down toward the turn table. This in turn decreases the angle between the ropes from the 180 degree position to something closer to 90 degrees and in turn reduces the overall loading force on the aerial tip.
Without having to learn complex trigonometry, vector analysis, etc. - for the "average" line firefighter a good set of general rules for aerials as High Directionals are:
1) The force on the ladder tip will ALWAYS be more than just the load
2) If you're pulling from ground to tip and back to ground (close to a 180 degree bend around the pulley) then 1/2 tip load capacity should be your MAX load weight.
3) If you're pulling from ground to tip and back down along the ladder bed (closer to a 90 degree bend) then 2/3 tip load capacity should be your MAX load weight.
Caveat to rules 2 & 3 - the angle and extension of your aerial device may affect it's tip load limits - also it WILL affect the angle of the rope around the pulley so you should take this into consideration when making your estimates on lifting capacity at every incident.
Bear in mind that these are just generalized rules and that you should have someone "do the math" for your device(s) and have them verified by the Mfg prior to making any lifts.
Hope this clears the confusion and gets us all back on the same page. As I said before I think we're all understanding how the system(s) perform - I think we're just looking at them from different points of view or looking at the force(s) on different components of the system.
The factor of "Force Multiplication" is related to the angle of wrap around the pulley. The closer to 180 degrees -the closer to double the force.
Also - all of this is theoretical load since there are various losses in a real world system that would in turn further increase the anchor (aerial device) load.
Edit - sorry so slow to reply to this one - I was writing the "book" of a post above *LOL*
About 95% of the time I have to sketch the system out on paper so I can "see" what the forces are doing before I really understand it myself.
In reading some of the various threads on here regarding Heavy Rescue / Recovery - I have learned a lot from your post - so let's just say I'm finally getting to pay a little back for a change. ;)
Am I safe in saying....If the load indicator on the platform is still in the green for load limit and there is no side loading we should be good? So we don't have to rack our brains on the MA and F, etc, etc. I'll agree though I totally draw things out many times.
Attached is the Newton's 2nd Law analysis of three MA systems for the idealized case of
* no acceleration of the load (load is already moving at constant speed)
* direct downward pull
* pulley's with 100% efficiency
Note that the force on the tip of the ladder is a maximum of twice the weight of the load for a COD, and asymptotically approaches a minimum of the weight of the load as the MA is gradually increased.
If the pull is directed along the length of the ladder instead of directly downwards, the force on the tip of the ladder will have a component along the length of the ladder. This will decrease the moment exerted about the base of the ladder (a good thing).
Also note that the forces can momentarily exceed many times the weight of the load during while it is accelerating, e.g. being moved up to a constant speed from rest. This is one of the reasons we require a minimum 10:1 SSSF in rope rescue.
Sorry to drag up an old thread but there is some great info in here. Pat Rhodes did a great video on this very subject you can find it here http://www.rescueresponse.com/store/...e-rigging.html