Your drawing is completely biased. In order for that top picture to be true, you made that top side bar out of elastic..

 

The arrows in the drawings only illustrate load direction. Not suggesting anything as elastic.

The bars location above or below the axle isn't what makes the difference, its how its attached at the axle end.

The bar in the first drawing utilizes a pivot point at both ends, second image uses a solid connection, no provision to allow for pivot at the rear most end. That is what completely eliminates axles ability to rotate "ladder bar".

If it used that same pivoting connection as the top link at its axle end? it would do no more to prevent wrap then the top link.

 

I have to disagree with that the under mounted snubber style bars are not any more effective...seen lots of old cars with them producing all kinds of wheel hop at the drag strip. If the springs are soft enough to bend into an S shape they're gonna do it regardless what type bolt-on trac-bar is used so like you and I both said the full solution would be beefier springs and traction bars or something that involves welding like ladder bars or a complete linked rear axle setup.

 

Incorrect, they both are allowed to pivot on both ends. It's where the rod is located on the axle that makes the difference.

Rod on top: Pinion begins to climb the ring gear and twist the axle back, the traction bar gets put under tension, which causes the front of the spring to be put under compression. This compression causes the spring to bend up into an S shape.

Rod on bottom: Pinion begins to climb ring gear and twist the axle back, the traction bar gets put under compression, which causes the spring to be put under tension (the exact opposite of the bar on top). This "tightens" the spring -making it seem stronger then it really is. It forms a kind of triangulation which prevents the axle from turning.

The single rod on bottom can still wrap under the right conditions. You need a dual bar (ladder bar), or a full linked suspension to eliminate axle wrap completely.

Go read the article I linked, or even search around some off-road and truck pulling forums. Single bars on top do not work.
Axle-wrap almost always causes wheel-hop, wheel hop is not always caused by axle-wrap. Improper springs, poor shocks, tires, bad shackle/spring geometry can all cause wheel hop.

At worst a bar on bottom won't prevent axle wrap all that much, at best they'll eliminate most of your wrap.. At worst a bar on top will blow your u-joints right out of the vehicle, at best they'll hardly do anything.

 

Ian--- BTW I agree with your point on the under mounted bar working better if it's the type that is attached at both ends, I was only considering the snubber style bars that are just bolted to the axle and not the frame when I made the above comments.

As for the springs bending into an S shape and allowing the driveshaft to be dislodged that really shouldn't be a problem on a truck with what should be a fairly hefty leaf pack, if they're fatigued, broken, or the straps are missing then all bets are off of course.

 

Yea I understand that, top or bottom location with pivot allowed at both ends can not completely eliminate the ability of the spring to turn into an S.
A ladder bar will because it does not allow the axle to wrap because of the difference in the way its connected at the axle.

Would it help being under rather then on top? yea little bit however it can not remove it completely. Still hugely reliant on spring stiffness, if single spring or soft weak spring pack it'd be all but useless. The axle travel up while allowing spring to "S" in reaction of pinion attempt to climb ring gear.

Same effect different location, tad better yes but only because leverage is greater, has axle by top and bottom however still a weak "four link" arrangement and reliant on the spring as an integral component, one highly subject to deflection.

 

It has nothing to do with leverage. A leaf spring is much stronger under tension, then compression.

A single bar on top will make axle wrap worse in most cases. It puts even more compressive force on the spring then without.

A single bar on the bottom can only reduce axle wrap, how it reduces depends on the geometry of the lower bar and the spring setup.

 

My best experience has been with torque arm type traction bars, like the old Rancho and now LFP long bars. They bolt to the frame and then to the axle and leaf spring with their supplied hardware and brackets. These traction bars don't affect the ride quality and I don't experience any wheel hop. These are expensive, but with what I've experienced and seen with traction bars, you get what you pay for.