Trying (probably fruitlessly) to quantify channelling strength.
Ok, kids. I've decided to be REALLY stupid and try to do this shit again. Let's get into this.
There are very few things that are quantified in the WOT universe, especially with channelling, but I think I've come across something that may be at least some kind of visual indicator showing how channellers grow in strength and output as they climb the rankings.
We know one of the more difficult feats of the power is lifting objects with flows of air; it's considered very simple, but very difficult. We have a few examples of channellers lifting things: Moiraine lifting the gilded chair, Elayne lifting the copper kettle, Rand lifting the tent components, etc. I began wondering if the ability to lift was a possible avenue to determine strength, so I focused on two feats (or, in the case of the latter, the telling of a feat): Morgase fluttering the scarf in Malden, and Suian claiming she could lift three times her body weight at her original strength.
The reason these two are comparable is that they both represent an absolute upper limit for the lifting capacity of two channellers of the same sex, with one being the absolute lower limit of channelling. Of course, in doing this, I made several assumptions and am blatantly ignoring some issues of affinity and stressful vs. casual limits, but I got too carried away and had to just share it with someone.
The biggest issue here is figuring out the force used on the scarf; this is where assumptions need to be made the most. We know Galina was using a red scarf as a signal and that it was tied up—we're not sure against what—and that Morgase used it to draw someone in to rescue the girls. In the books, it's said the scard when rigid sideways before swinging like a pendulum and releasing to go limp. This manoeuvre took Morgase a very long time to produce and can be assumed to be her absolute limit.
The first assumption is the weight of the scarf. We don't know its material, but I'm making the assumption it's ~20-30g. I'll use 20g in my calculations and then give a full range at the end. For going taught and swinging like a pendulum, I'll figure out the force required to lift a scarf to 30 degrees to swing back and forth from a vertical resting position.
To calculate the force required in N, you'll need the following:
mass (m) x gravity (g) = weight (N)
m = 20
g = 9.81
0.020 x 9.81 = 0.1962N (Scarf's weight)
Weight (N) x Angle from vertical (Tan(90)) = Force to move the Scarf
0.1962 x Tan(30) = 0.113N (Force applied to the scarf to make it taut and swing gently)
Next, we need to figure out Suian's lifting capacity. We know she can 'lift 3x her body weight', so let's assume her body weight. She's described as 5ft5in and sturdy of build. This would put her somewhere between 140lbs and 160lbs. I'll start with 140, or 63.5kg, and go from there.
63.5 x 3 = 190.5Kg
190.5 x 9.81 = 1868.8N (Force to lift 3x Suian's body weight)
Now, we need to figure out how to go from Mogase's strength to Suian's, and how to find the non-linear increase between the two. I'll break the ranking system into 78 levels from 72(60) to ++6. Suian is 13(1), equal to 19. Morgese is 72(60), equal to 78.
78 - 19 = 59.
Now, we need to figure out how to get from Morgase's 0.113N to Suian's 1868.8N, an increase of 16512.4x. We know that increase is non-linear, so we'll use exponential multiplication:
0.113 x X****^(59) = 1868.8N
Rearrange.
X****^(59) = 1868.8 / 0.113
X****^(59) = 16512.4
X = 16512.4^(1/59)
X = 1.179 = 17.9% increase for each step.
If the scarf was 30g and Suian weighed 160lbs, the increase would be 17.35%.
Due to the way the increase is proportional to the pair, the lowest range would be if the scarf was heavier and Suian was lighter at 30g and 140lbs. This comes to 17.08%. While the greatest range of a 20g scarf and a 160lbs Suian comes to 18.18%.
The higher Morgase's scarf weight and the lower Suian's body weight, the smaller the jump proportions. I've shoved all four different models into a log graph for you to see clearly.
And if you're wondering why I'm using a log graph, it's because using a standard graph gets you this:
Not helpful...
Anyways, this is kinda stupid since channelling it is pretty abstract, but I wanted to play with it a little and see what I could make. Also, here's a list of the full scale range and a few corresponding channellers:
Any thoughts?
