[OB] Reverser Pairing Fabrials Examined

[+Hoiditthroughthegrapevine he/him]

This thread is based on a lot of analysis already done on the [OB] Flying ships thread, but since it's not a fabrial technology suitable for use to create flying ships, I think that it's best that this has it's own thread. Lots of thanks to @The One Who Connects for helping me formulate this all in a way that is clearer and that is true to the underlying physics (and man, he's a Powerpoint wizard, his PPT diagrams look amazing!)

To analyze this in depth, I have come up with a standardized set of symbols that I'll be using to create diagrams to illustrate how I think these paired reverser fabrials work:

We only have two known use cases for pairing reverser fabrials, namely the creation of an archery parapet that could be raised remotely and the use of conjoined reversers to raise archery pavilions for Roion's archers at the battle of Narak, both in WoR.

By far the best description we have for how these pairing reversers work is the scene in Chapter 35 of WoR where Navani and her ardents are conducting tests to figure out how to use this technology to raise an archery parapet. The important excerpts of this scene are spoilered below (with emphasis added) and the sketch from Navani's notebook with the inworld diagram of the archery parapet setup is included as well.)

Spoiler

She turned back to the wooden tower. Ardents at the top had activated the fabrials there, and now climbed down the ladders at the sides, unhooking latches as they went. Once they were down, workers carefully pulled the sides away on their rollers. Those were the only things that had been holding the top of the tower in place. Without them, it should fall.

The top of the platform, however, remained in place—hanging impossibly in the air. Navani's breath caught. The only thing connecting it to the ground was a set of two pulleys and ropes, but those offered no support. That square, thick section of wood now hung in the air completely unsupported.

The ardents around her murmured in excitement. Now for the real test. Navani waved, and the men below worked the cranks on the pulleys, pulling down the floating section of wood. The archer parapet nearby shook, wobbled, then began to rise into the air in a motion exactly opposite to the square's.

...

The parapet wobbled its way upward. It acted as if it were being hoisted, though it had no support at all. Finally it peaked. The square of wood that had been hanging in the air before was now down against the ground tied in place. The round parapet hung in the air instead, slightly off kilter.

It did not fall.

...

(adolin)..."How did you do it?"

"Conjoined fabrials," Navani said. "The trick was finding a way to overcome the structural weakness of the gemstones, which succumb easily to the multiplied strain of simultaneous infusion drain and physical stress. We..."

(Adolin stares blankly)...

Navani smiled, switching to layman's terms.

"If you split a fabrial gemstone in a certain way," Navani said, "you can link the two pieces together so they mimic each other's motions. Like a spanreed?"

"Ah, right," Adolin said.

"Well," Navani said, "we can also make two halves that move opposite one another. We filled the floor of that parapet with such gemstones and put their other halves in the wooden square. Once we engage them all—so they are mimicing one another in reverse—we can pull one platform down and make the other go up."

 

Also, as further clarification for this scene, here is a cropped view of Navani's notebook that deals with workings of the conjoined Archery platform fabrial:

Here is a diagram of the archery platform test where the forces at play in this paired reverser system are shown, descriptions of what is happening in each panel follows:

1. Platform A (the blue one) is 1.5 times as massive as platform B (the pink one). The Force of gravity affecting both platforms is shown as the arrow next to each platform. Platform A is experiencing a Force towards the center of Roshar that is 1.5x greater than the force affecting Platform B.
2. The pairing reverser fabrials are engaged. Platform A experiences the same Force from the acceleration due to gravity that it did in Panel 1, but in addition is now experiencing a Force directed away from the center of Roshar that is the same in magnitude as the Force that Platform B Experiences due to gravity. The result of the addition of these two diametrically opposite forces results in Platform A experiencing a Force directed towards the center of Roshar that is .5x the force of gravity affecting Platform B. Due to the fact that Platform A can't move further towards the center of the earth because's it's downward force is pushing against a much more massive object (namely Roshar), the extra force is absorbed by the platform in the form of mechanicl stress. Though Platform B is experiencing a net positive force upwards, it likewise cannot move because motion of the retardation of motion of Platform A. The net affect is no motion and mechanical stress on the reverser fabrials in both Platform A and B.
3. After the support is rolled away, platform B continues to hang suspended in the air in it's previous position, but it's really suspended in the air because of the Inverted Force of Gravity of Platform A, and though it is experiencing a net positive thrust upwards, it's motion is limited in that direction because of platform A's inability to move down due the downward force being applied to the much more massive planetary body. So workers now grab the ropes that are connected to the suspended Platform B, and begin pulling exerting an additional downward force on Platform B that is greater in magnitude than the the upwards Conjoined Force of Gravity affecting platform B. This downward force from the ropes and pulleys is inverted and experienced as upward thrust for Platform A, which is likewise greater in magnitude than the downward Conjoined Force of Gravity affecting Platform A.
4. The workers continue to pull the ropes, and the Force applied by the pulley system is still greater than the Conjoined Force of Gravity for both platforms, as Platform B is pulled down, Platform A rises.
5. After Platform B is pulled down as far as it can go, A force of tension is applied to the ropes (by securing them to the ground) such that the force of tension offsets the Conjoined Force of Gravity and equilibrium is reached (though diametrically opposed forces are still being felt by the components of the system, the magnitude of the resultant combined forces is 0, so there is no motion).

 

Just to look at another case where the same underlying principles are at play, here is another use case. This time the more massive platform, Platform A starts out on the support tower and the less massive Platform B will be the platform being raised:

1. Panel 1 shows the Force of Gravity affecting Platform A (the blue one on the support tower) and platform B (the pink one on the ground)
2. The pairing reverser fabrials are engaged and the Conjoined Force of Gravity affecting both of the platforms is shown. In this instance the Conjoined Force of Gravity for platform A is being directed down through the support tower, and through the support tower into the ground. The net effect is inability to move downwards, so the upwards motion of Platform B is likewise retarded. Also, Pulleys are attached to Platform A in preperation to wheel away the support tower.
3. Tension is applied to both of the support lines through the pulley system to exert a force that balances the net downward Force of Platform A, and the support tower is wheeled away.
4. The tension is released in the pulley lines, and platform A now only experiences the Conjoined Force of Gravity, and is pulled towards the center of Roshar. This force and motion is inverted for Platform B and it rises into the air.
5. Another view of Platform A falling due to the Conjoined Force of Gravity and Platform B experiencing the inverted force and motion of Platform A.
6. Eventually platform A reaches the ground, and it's Conjoined Force of Gravity is absorbed and turned into mechanical stress as it pushes against the surface of Roshar. Likewise Platform B comes to a stop as it's upward thrust is unable to be converted to motion because of the inability of Platform A to move.

This case is like the scene at the battle of Narak where Navani uses large rocks, dropped into the chasms to raise the archery pavillions. The rocks dropped over the edge of the cliff most likely had paired reversers that were paired with a reverser at the open front side of the pavillion. As the rock drops down the chasm (most likely attached to ropes of specific length to arrest their motion when a drop that matches the height of the pavillion was reached) the conjoiners in the archery pavillion rise. If there are any pendular effects of the rocks swinging at the end of their tether, these would probably not be too great and would eventually come to a stable equilibrium rest position.

Here's  the text of the scene from WoR chapter 82, where the archery pavillions are raised:

Quote

Behind Dalinar, soldiers gathered. Roion's archers, finest in the warcamps, had been useless in this rain. The engineers backed up at a barked order from Navani, and the workers shoved the line of some forty rocks into the chasms.

As the rocks fell, tarps jumped fifty feet into the air, pulled at the front corners and centers. In a instant, a long line of improvised pavilions flanked the chasm.

"Move!" Dalinar said, urging his horse between two of the pavilions. "Archers forward!"

Men dashed into the protected areas under the tarps, some muttering at the lack of any visible poles holding them up in the air. Navani had pulled up only the fronts, so the tarps slanted backward away from the chasm. The rain streamed down in that direction. They also had sides, like tents, so only the open faces were towards Roion's battlefront.

Just in case anyone else would like to use these diagram symbols, I've added a PPT file that has them.

Looking forward to getting into some more of the more complex systems, but I have to get some work done too. If any one has an interesting thought experiment involving paired reversal fabrials, let me know what it is (and time permitting) I'll try and figure out how it might work and quite possibly make a diagram.

Pairing fabrial Reversers Diagram Symbols.pptx

Edited February 26, 2018 by hoiditthroughthegrapevine
typos, like usual