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Running from her people. It was never unexpected, but Alynn always hurt about it.

She ran from the jeers, the shouts, the calls of "freak" and "witch". She ran away from yet another life she almost had.

More importantly, she ran from the rocks and bullets aimed at her. Stopping them dead in their tracks was all very well, but it drained. Not energy, she had plenty of that, but it tired her out - and then she wouldn't be able to run any more.

Alynn ran, considering where she'd set up her next life.

Meet Alynn. She's an almost-scientific mage: that is, her magic is partially constrained by science. You'll be seeing her frequently: this is the first of a series of weekly questions about her magical exploits.

In this question, I'm asking about some constraints I have put in place on her magic.

The system works on the basic principle of an inefficient calorie-duplicator. For every Calorie she eats, she gets another half-Calorie (2000 joules) of magical energy to use or store. Yes, she violates conservation of energy which is not very scientific, but bear with me.

For a young woman of her 17 years, that means she would normally end up with about 4 MJ of energy over the day (from a 2000 Calorie consumption).

That, to me, sounds like too much. She can store the energy, so in theory if she does no magic at all for a while she could store up massive amounts of energy.

So: how much energy might some mundane magical tasks take? Take, for example:

  • Creating a fireball
  • Stopping a bullet in its tracks
  • Lifting a 1-tonne mass 1 metre off the ground

With the data from those calculations, is 4 MJ/day too much? Will she ever use that much?

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  • $\begingroup$ It probably depends on the principal of how the energy is used to make the magic. For instance, if I try to lift a 1 ton weight, it'll take more energy than I have, but if I get a long lever it'll take hardly any energy at all. $\endgroup$ – AndyD273 Apr 23 '15 at 11:46
  • $\begingroup$ @AndyD273 100% efficient conversion - the energy the effect uses is the amount of magical energy it takes. $\endgroup$ – ArtOfCode Apr 23 '15 at 11:47
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    $\begingroup$ @AndyD273 Lifting a 1 ton weight takes the same amount of energy no matter how long a lever you have. The force required changes, but the amount of force required will be inversly proportional with the distance that the force is applied over. $\endgroup$ – Taemyr Apr 23 '15 at 12:08
  • $\begingroup$ @Taemyr Right, I understand that. But the amount of energy it takes from me is lessened. If all he wants is someone to look up force requirements or do the math for him, that's fine, but I figured it would be useful to know if there are any magical levers available. Can you magically lift with your legs? How is the force applied? If you magically lift 1 ton 1 meter, what do you do about Newton's 3rd law? Similar question: scifi.stackexchange.com/questions/83142 $\endgroup$ – AndyD273 Apr 23 '15 at 13:10
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    $\begingroup$ How does she support objects she's holding in the air? Is it like a jetpack where she has to expend energy to hold something still in the air or can she create insubstantial magical/non magical structures? if so what are their rules? can she make a magical support structure can can support iron but won't support water? If she can lift things can she compress/expand things? can she create a bubble of vacuum or a pressurized bubble of air? $\endgroup$ – Murphy Apr 24 '15 at 11:42
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I'll take this in parts.

Casting a fireball

Fireballs are a common piece of magic for any spellcaster, it seems. Since you want something based in science, you might take a look at quark-gluon plasma, which is a fifth state of matter with high temperature and/or density. Particles in QGP exist have a temperature of $2*10^{12} K$, which is $175\ \mathrm{MeV}$, or $2.804*10^{-17}\ \mathrm{MJ}$ of energy. This means Alynn can produce 280,400,000,000,000,000 such particles before she even begins to notice a drain on her reserves, at 1 MJ.

Stopping a bullet

Not surprisingly, and thankfully, someone has already done the calculation on stopping a bullet and come up with a nice number of 600 Tesla for a magnetic field to stop a copper bullet. From the equation

$\mathrm{Magnetic\ Field\ Strength} = \frac{\mathrm{Energy}}{\mathrm{Current} \times \mathrm{Distance}^2}$

We can see that if we assume a current of 1 Amp and a distance of 1 meter, you would need 600 Joules to stop the bullet. Sounds reasonable, and hardly impacts her reserves.

Lifting masses

Finally, lifting a 1-tonne mass. Since we only want to lift the weight, we can simplify the work equation to just $\mathrm{Work}\ =\ \mathrm{Force} \times \mathrm{Distance}$. We can figure out the force needed to lift the weight from $\mathrm{Force}=\mathrm{Mass} \times \mathrm{Acceleration}$. Acceleration due to gravity is $9.8\ m/s^{2}$ and the mass is 1 metric tonne (1,000 kg). Plugging back in, we get: $\mathrm{Force}=1,000 \times 9.8=9,800\ \mathrm{N}$. From this, we can calculate the amount of energy required to lift the weight as $\mathrm{Work}=9,800 \times \mathrm{(the\ distance\ lifted)}$. Of course, you could lift the weight faster by applying a greater force, but that's the minimum needed to overcome gravity.

Conclusion

Finally, you wanted to know if $4\ \mathrm{MJ}/\mathrm{day}$ was too much. Each day, Alynn could create four fireballs (or one big one), stop 6,666 copper bullets, or lift a 1-tonne mass 1 meter high several hundred times.

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  • $\begingroup$ Sorry - I meant a metric tonne. Simple calculation change though, which i'm sure I can substitute if you don't fancy editing. $\endgroup$ – ArtOfCode Apr 23 '15 at 14:02
  • $\begingroup$ @ArtOfCode I've updated my answer. $\endgroup$ – Frostfyre Apr 23 '15 at 14:10
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    $\begingroup$ Do note that 280,400,000,000,000,000 particles really isn't very many. There are on the order of 10,000,000,000,000,000,000,000,000 particles in any given square meter of air. The fireball is not going to be one of her more impressive tricks. $\endgroup$ – Saidoro Apr 23 '15 at 17:16
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    $\begingroup$ Er, cubic meter. not sure why I wrote square. $\endgroup$ – Saidoro Apr 23 '15 at 17:23
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    $\begingroup$ @Saidoro Hollywood explosions are actually gasoline-based... The pellet would probably superheat the air as it traveled, which will have other ramifications. $\endgroup$ – Frostfyre Apr 23 '15 at 17:45
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You're right - that's an enormous amount of energy. What you need to do is place (and justify) a limit on power. But let's say there is no such limit.

Your calculations are correct - ~ 4 MJ per day. If she exercises hard, she can easily up that by 50% and not gain weight.

Alynn is a 17-year-old girl. Presumably she was gently raised, and socialized to passivity and avoidance of direct confrontation. Good thing. It is only her mental reservations which keep her from being a frickin' killing machine.

Let's say she carries around a few pieces of scrap iron, or largish pebbles. If she throws one at an attacker, then boosts its velocity, how much energy does it take to do real damage? Well, a 1-oz 12-gauge shotgun slug has a kinetic energy of about 2400 joules. And if she wants to impress, you should be aware that it takes no work at all to keep an object suspended at a constant height. Force, yes - work, no. Work is force times distance; no change in gravitational potential energy means no work done, and at walking speeds kinetic energy is not an issue, any more than it would be if she simply carries the stuff. So she can walk around with a half a dozen rocks suspended over her head, ready to use. And she can use them about 800 times a day (1600 if she doesn't try to reuse them). How big is her village?

The same principle applies to artillery support. If there are any mountains close by, she can move a few boulders from the upper slopes and position them over the village she's living in. This will take awhile, since she can't move them fast, but once they're in place it takes no energy to keep them there, waiting for the command to fall.

Stopping a bullet is harder, but not for reasons of energy. A .45 slug only has 500 joules of kinetic energy, so that's all it takes to stop one, and it takes much less than that to simply divert its path. No, the problem is reacting fast enough to perform her magic on something that's moving too fast to see. Or a bullet that has been fired at her from behind.

In a pinch, of course, she can always do really scary stuff. The human brain weighs about 3 pounds. If she's willing to expend 1/10 of her daily magic ration, she can instantly raise the temperature of a person's brain by about 100 degrees Celsius (just below boiling), cooking it like a hard-boiled egg and killing him instantly. 3 lb of water raised 100 degrees F takes 300 BTUs, or just over 300 kJ. It will, of course take considerably more of her energy to raise the temperature to more than boiling, but the results would be pretty impressive, as the skull would explode. Not pretty, but an effective way to establish "Don't mess with me".

An even more energy-efficient technique would be to drain heat from an attacker. Dropping brain temperature by 20 degrees would cause instant hypothermic coma, and take only 20% the energy that heating would. As a plus (from a certain perspective), the affected individual might well recover, as flow of warm blood from the rest of the body would gradually warm the brain back up.

And if her control is really good, and she's feeling really nasty, the human eye weighs about 7.5 grams, or 15 grams total. Cooking those parts would be no trouble at all (energetically speaking). Total energy to raise one liter of water to boiling is ~ 2600 kJ. For a 15 g pair of eyes, call it 40 kJ to make them explode.

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  • $\begingroup$ Well then. I was not expecting those comparisons, but they're very useful. $\endgroup$ – ArtOfCode Apr 23 '15 at 16:18
  • $\begingroup$ @ArtOfCode - Yeah. Well, the physics of weapons effects is not something that comes normally to most girls. As I stated, you need a way to place limits on power (and force, too). I'd suggest, as a starting point, that she can apply force only a certain amount higher than her muscles can provide, and she can cause effects only on a scale that her perceptions can follow. So she can't boost an object to bullet velocities simply because she can't follow the resulting motion. Just as she can't block a bullet if she can't see it coming. $\endgroup$ – WhatRoughBeast Apr 23 '15 at 16:29
  • $\begingroup$ @ArtOfCode - And my answer might serve as the basis of the solution to her problems. She would be an ideal protector of a village from external threats, from bandit gangs up to small armies. No mercenaries who might abuse their powers, no gang of fighters who eat up the village's food - just a single teenage girl who wants to be accepted. PMS issues might be a problem, though. $\endgroup$ – WhatRoughBeast Apr 23 '15 at 16:34
  • $\begingroup$ PMS issues? I'm missing something... $\endgroup$ – ArtOfCode Apr 23 '15 at 20:57
  • $\begingroup$ You don't want to be around someone who can explode your eyeballs and who is in a really bad mood. $\endgroup$ – WhatRoughBeast Apr 23 '15 at 21:43
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Rule of thumb:

One KCal = 4 KJoules = 1 gram of TNT

So right now, she is accumulating the magical equivalent of 1kg of high explosives per day.

Whether that is a lot or not depends on what she does with it. I think that should be about 10 grenade sized fireballs per day. You can get at that by looking at the filling charge of grenades, which varies between 60 and 200g.

For stopping a bullet, compare to the propellant charge, using relative effectiveness factor.

A musket, for example, is about 12 grams of black powder in a typical charge, so about 6 grams of TNT-spellpower to stop. Modern guns are actually less powerful per shot (a rifle bullet is only 4kJ...), but obviously fire more quickly.

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  • $\begingroup$ I'm looking for something more scientific than "I think that should be about..." - why? More importantly, 1 cal = 4184J $\endgroup$ – ArtOfCode Apr 23 '15 at 14:03
  • $\begingroup$ Calories and cals and kCals are amazingly confusingly named. Apologies for the error. But anyway a grenade's filling charge ranges from anything between 60g for a Soviet F1 and 180g for an American M67. You can look on YouTube for what 100g of TNT looks like. $\endgroup$ – Fhnuzoag Apr 23 '15 at 14:11
  • $\begingroup$ As far as I know, 1 kcal = 1 cal, though it does seem otherwise... $\endgroup$ – ArtOfCode Apr 23 '15 at 14:12
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    $\begingroup$ @ArtOfCode Not quite. 1kcal=1Cal=1000 cal. In words; One kilo calorie equals 1 food calorie equal one thousands calories. The reason for the naming scheme is that calorie(cal) is defined as the energy needed to raise the temperature of one gram of water one degree. This however is such a tiny amount that it's almost never useful to talk about, one usually measures in kilo calories instead, but this gets shortened to just calories in ordinary speech. $\endgroup$ – Taemyr Apr 23 '15 at 19:34
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Lets take another tack, Lets not violate conservation of energy and add practical limitations. First it is quite easy to simply switch from a 2000 cal diet to a 3000 cal diet and convert one third of that food energy to magic. (she is a skinny gal) Next I am aware of no process of converting energy that is 100% efficient. So a reasonable way to keep her from being over powered is to assign a couple energy conversion loss factors. Firstly there is the conversion of food into magic. Thinking outloud I would use 60% for her at the moment and 30% when she hit puberty and her magic kicked in and a maximum of 80% with lots of practice. Next is the casting efficiency. Moving energy uses energy so you want the casting efficiency to be inversely proportional to the distance. you also want it to be proportional to the skill that she has with a particular task. you would also need a correction factor if she is acting on something she can't see or if she is being careless or rushed. I would also have storage loss of 5% minimum. This brings her from overpowered to just plain scary but beatable.

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For the bullet question, it would depend on what the mass of the bullet is and the distance it was fired from.

For a bullet, one estimate that I have read for terminal velocity is around 300 ft/sec (about 200 mph). Since that's a lot slower than a bullet leaves a gun nozzle, it seems that the air resistance really will have a big effect on the speed of the falling bullet.

For the lifting question, the amount of energy required depends on how quickly the 1 ton is lifted.

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  • $\begingroup$ @ArtOfCode To lift the force required would be F=mg. Energy is force times distance E=mgh. This is minimum, in real life time is relevant because the faster you lift the more kinetic energy the lifted object will need. $\endgroup$ – Taemyr Apr 23 '15 at 12:03
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Humans store normal energy all the time. Our cells store small amounts of glucose, the liver stores moderate amounts of glucose, and our bodies store large amounts of fat -- which can get converted to glucose, but that takes time. And of course, energy stored as fat weighs you down, and it can be quite bad (for a variety of reasons) if you store too much. OTOH, not having any fat reserves is also very bad. So, I'd suggest that storing magical energy should be limited, that it should take time to convert stored magical energy into useful magical energy, and that over-storage of magical energy should have consequences. That makes your system more balanced, and also adds three more nuances of magic use that you can work into your story.

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