Hello Azalea Ellis, my main question which is definitely a single detailed question and not several questions disguised as one is:
Main question
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“Chapter 20 – Practical Will-based Casting says”
Sebastien drew a triangle, since this was transmutation—heat energy into kinetic energy.
And the maths for kinetic energy has the energy being proportional to the relative velocity squared.
Kinetic Energy = 0.5 x mass x velocity^2
From the thaum costs for lifting weight given in “Chapter 25 – Alchemy” and “Chapter 116 - Operation Defenestration”, it seems one Thaum of the Henrik-Thompson test converts to about one Joule of gravitational potential energy. And candles provide about 80 thaums per second which is like 80 Watts from a candle.
It seems possible that one Thaum would result in an acceleration that adds one Joule of kinetic energy.
Thaums = 0.5 x mass x velocity^2
velocity = sqrt( 2 * Thaums / mass )
It’s relative velocity squared. So this would mean that if you’re speeding up a projectile that weighs 1 kg (2 2/10 lb), it would be like this (ignoring energy lost in the transmutation):
50 Thaums gives 10 metres per second (22 miles per hour)
200 Thaums gives 20 metres per second (45 miles per hour)
450 Thaums gives 30 metres per second (67 miles per hour)
800 Thaums gives 40 metres per second (89 miles per hour)
5,000 Thaums gives 100 metres per second (224 miles per hour)
1,280,000 Thaums gives 1600 metres per second (3589 miles per hour) (0.9 planet Earth radius per hour)
So it looks like kinetic energy conversion would look like this if the stationary spell array was accelerating another body, where the resultant speed is proportional to the square root of the thaums. But, can a thaumaturge or artifact accelerate itself without this being a concern? Gain speed linearly proportional to the thaums? It is relative velocity in the kinetic energy equation, but if you just accelerate yourself then you’re always at rest, not moving, relative to yourself. You’re like a rocket in outer space (except rockets take matter with them that they are stationary relative to and which they push against).
Thaddeus had what looked like a floating chair, and Myriddin had a flying spell. There was also the exam question about casting a fleet-foot spell on a gryphon with an average of 3000 thaums per minute, where the thaums in effect increase kinetic energy (the wind being perhaps the relevant reference), and there are fleet-foot potions.
There was also “Chapter 30 – (A Rather Poor) Rescue” when Siobahn used the glyphs for “line,” “movement,” and “circle” to magically fix some glass missiles to a glass plane she had, and then she put her lantern away and put her conduit in her mouth and the glass missiles stayed attached when she wasn’t actively casting, like an artefact or ritual where the effect lingered.
And also the other two bits of that chapter I’m getting to are firstly when she seemed to charge up a missile before “releasing” it.
She had practiced this spell for many hours, till she could do it half asleep and at a moment’s notice. It was only slightly harder to do it now, with adrenaline rushing through her body and the wind tearing at her so hard she had to crouch slightly to avoid being knocked over. It took a handful of seconds to get the glass ball rotating so fast its jagged edges were shrieking against the pane underneath. It was easy, with such a small ball, and no sand to slow it. The hardest part was actually keeping it from shooting off under the force of its speed.
The spell array glowed slightly as she poured on more power, not totally efficient even with all her practice. The Word was too simple.
When she released the ball, it shot forward faster than she could see, exploding against the ground below, just to the side of the Morrows’ barrier.
which is another kinetic energy thing but (I’ve been re-reading PGTS (which is pretty good btw) and I’m a bit close to the beginning and) I only remember this sort of magical acceleration being in one chapter and I don’t know how it worked.
Maybe she gradually created a magical force field that would exert force. This was a few chapters after they reviewed magnetism in Natural Science.
Also, it didn’t mention there being any recoil from shooting it.
Postscript: Oh, I think I just got it. When I first read it, I imagined the missile spinning on its own axis. It may instead have been moving circularly as though swung around by a slinger, like Siobahn had recently been doing at the university. My question feels less interesting now without the mystery of the charged up kinetic energy.
And secondly there was this part which was a bit earlier
Then, she drew over a dozen more Circles on the other panes of glass in the window, with pentagons for each, along with the glyphs for “force,” “compression,” and “sphere.”[…]
[…]
[…] With the energy from the lantern, which she held up into the Circles she had drawn on the window glass, she crushed each pane into a vaguely ball-like shape of jagged, cutting edges. […] A little dribble of honey helped the balls keep their shape.
This bit also did not go into the full detail on how it worked. She drew the circle on each pane she would crush, she didn’t draw them on something else and bring the panes to it one by one. The circles would have been broken when the glass was crushed, but the spell continued. Then either the magic continued to hold shards of broken glass together, or the glass had changed shape and was solidly fused yeah maybe it’s the second one. But also honey helped somehow (transmogrification? :s ).
Postscript: Oh, maybe this is going off-topic for a kinetic energy question. I don’t want to delete all this after typing it though so I’m out-crossing it which looks okay perhaps.
Or what if someone was not creating a thaum-efficient magnet-like force to levitate a stone, but was more inefficiently channelling the thaums to create the precise upward acceleration to counteract the downward acceleration from gravity? Would that be 48 thaums per second for 1 kg? I got that number by taking the acceleration in a second and converting that to kinetic energy. In normal physics energy is conserved but what about the thaums do they go into the void or turn into heat?
I think it probably doesn’t turn into heat? If you channel thaums to accelerate something alternately left and right like a pendulum or a wagging tail then it probably just changes velocity.
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My own failing..
I couldn’t find anything referencing this in previous forum posts, but I admit that my search was very cursory. I apologize in advance if this has been covered already!
