How much can a magician lift if constrained by her own body's energy?

Question

In Christopher Paolini's Inheritance Cycle ( the Eragon books ), magic works in a very specifically defined way. A magician can only use magic as far as his own bodily strength would be able to take him/her. (For this reason, it is impossible to raise someone from the dead because that takes more power than a single person would have.)
If a magician was in a weakened state, his/her powers would weaken accordingly; and when magic is used, the magician tires accordingly.

Assuming a world where magic works in this way, what would happen if a magician like that tried to lift a heavy weight? What constraints would there be?
I'm specifically interested in how much this magician could lift, how high, and for how long?
Assume normal human strength/endurance.

---

I've learned from the comments below that my question above (which I left untouched, for reference) is unclear, so allow me to clarify. I do not care about Eragon's capabilities. Also, an answer to this question does not require any canonical knowledge of the Inheritance Cycle.
I'm trying to build a world in which magic works as described above -- I only mentioned Eragon as an aid to explanation.

So.....let's assume that the mechanics of magic in my world are such that magical actions taken use the biological energy available to the magician, at the time that he is working his magic. I would like to know how much force that is, assuming a fit, well-rested, adult male human being. This is not the same as the amount that the average man would be able to lift, because in this case we can use muscles and energy not normally used by men to lift with -- let him throw literally all of his energy into lifting this weight. The magician's height doesn't matter.

How much can my magician lift?

Answer 1

Let's do Some Physics!

So, you want to use magic to push things around, eh? And the magic is only as "strong" as you are?

Well, let's get some things straight.

First, we're looking at the power a human can output. That's not force, not energy, but how much energy you can put out over the course of a period of time. In theory, a person can move a rock of any size, it may just take them longer than they can live. (Other forces may prevent them from making progress, but let's get back on topic).

Anyways, I'm assuming the magician in question can just transfer a particular amount of energy (as defined by the power they produce) to some other object without losses. This would mean a magician could direct their heat energy to an object kinetic or potential energy, without any losses. I'm also assuming that magicians must continue to input energy to systems they're affecting or else the magic effects immediately cease, and the objects in question behave as normal. (This prevents floating objects from floating indefinitely and requires more work from your magic users.)

Maximum Power Output of a Human

In terms of body heat, a human puts out anywhere from 75 W to 870 W from body temperature alone. (much more than a lightbulb!). That means a wizard has around 800 W to fool around with from his body heat alone! Obviously, a wizard would need to elevate their body temperature before casting spells to take full advantage of that 800 W.

Humans are more than just heat sinks. We can put out around 400 W of mechanical power (for around an hour) if we're well-trained. Less well trained individuals go for around 50-150 W during the same course, though, so the individual's condition matters.

Wait, what about burst strength? That's when you focus your efforts into one task, and you focus as much power as you can into one push or lift. That sounds like a question weightlifters can answer to me! Take a look at the wikipedia page for weightlifting records. It looks like a world-class weightlifter (of weight category ~77 kg) can do the clean & jerk event with about 200 kg! Assuming this action is done it in about 2 seconds, and you are the same height as Oleg Perepetchenov, that's (200 kg * 9.8 m/s^2 * 1.64m / 2s) a whopping 1,597.4 W!

As a favorite thought exercise has reminded me, you technically don't do any work holding a thing up. However, if the additional potential energy the object gets from being higher comes from the person, then yes, the magician will still loose energy. (The added potential energy is $mgh$, where $m$ is the mass of the thing they're holding up, $g$ is acceleration due to gravity, and $h$ is how much higher the object is. If you do that over time, then you get power, measured in watts!) So I'm running with that assumption for holding things up.

What Can I Do With How Many Watts?

For 75 W, you can:

• Lift a household cat (a little on the fat side) above your head in 1s (I'm not responsible for where the cat goes after that.)
• Throw a stool
• Toss a baseball at at 70 mph (not enough to be in the major leagues, but a respectable pitch.)
• Hold that same domestic cat you threw up to head height for 1 second. (If you're putting out 75 W constantly, then the cat will stay up!)

For 800 W, you can:

• Raise a house cat 17.5m (about 57 ft, or 19 yards) in 1s (that's pretty high!)
• keep a house cat at ~13,000 m above its normal height (until you run out of energy).
• Hold a 50 kg (110 lbs.) weight above your head (until you run out of energy).
• Throw a baseball at 105m/s or ~234 mph.

For 1,600 W, you can:

• Throw a baseball at 150 m/s, or ~335 mph (or 0.43 Mach, with 1.0 Mach being the speed of sound)
• Lift 200 kg above your head (that's enough for 2 large men!)
• Raise a house cat 50,000 m in 1 second. (the boundary for outer space technically starts around 100km, or 100,000 m)

Obviously, if you did any of these things slower, or for less time, you would use less power (less watts).

Why am I picking on house cats? I just chose something familiar. Please don't use this magic on cats!

Answer 2

So in Eragon (this is my single favorite magic system) the caster is limited by the power in his/her own body. We are not talking mana, or spells per day or anything like that. Think of it as life force, or if you want to go all chemistry think ATP.

• A caster using a spell to complete a task loses energy proportionally to what it would take to do the job manually. I want to lift a 5 lb rock 5 feet off the ground. I won't do the physics (because I can't remember the formulas) but I am sure someone here could sort out the joules.

• Using too much energy, more than the caster has, kills the caster. Casting strength is based off of physical strength/endurance and triggered by mental or verbal (or both) command. Intelligence is important though, the way you trigger it (the words you use to form the spell) can be more or less efficient, just like doing work manually.

So generally speaking it is easy to say that the answer to this question is pretty straightforward. It takes as much energy as it would have to do it manually. There are some additional considerations though. If you are using magic to say, lift a giant boulder, a magician says the word and BAM its up off the ground (given they have the power to do so). Now a non-magician has to actually do the lifting, which may be more difficult as its harder to lift awkward objects etc.

So I would say that pure physical formulas apply to casters whereas non-casters would be less efficient in their use of energy. As for your specific question:

I'm specifically interested in how much this magician could lift, how high, and for how long?

Hard to say. Those are not linear variables, height would be irrelevant for a caster (I think???) as 2 feet off the ground is no different than 50 since you're just fighting gravity. Would a caster moving it up to 50 feet while a normal person held it two feet off the ground be equivalent??? The weight of the object dictates how long and vice versa. If you have a specific scenario in mind feel free to share it.

From the web:

Any time you lift an object, you do work against gravity. We use the same formula for work that you already know (Work = force × distance), but it’s expressed in a slightly different form: Force is written in the form mg, where m is mass and g is the acceleration due to gravity, 9.8 m/sec2. We use h for height because only the vertical distance an object moves matters for calculating work against gravity. Did you know...If you have to lift a new sofa to a second-floor apartment, the work done against gravity is the same whether you haul it straight up the side of the building with ropes or take a longer path up the stairs. Only the vertical distance matters because the force of gravity is vertical. Found here

Looking at your newer question I managed to find this. Someone better at physics will have to do the math.

lets say we have an 80kg human. the maximum energy that can be released is if there was a total mass conversion.

E=mc^2 (we'll assume momentum is zero) E= 80*9*10^16 =7200000000000000000 J =7.2 EJ(exa-joules)

Answer 3

Great answers from @James & @PipperChip.

I have three pieces to add, in support of and to provide further elucidation on, the answers given (I love numbered lists btw :D).

Effectively, to develop the most clearly defined magic for your world, determining the following would be very useful:

1. Determine the amount of time energy can be collected from the body to produce the magical force. The answer varies greatly if you determine the caster can collect the energy for a nanosecond or if they can collect it for 10 seconds... these time frames are many orders of magnitude different in power levels. Energy output (how much energy is available to lift an object in our case) must be measured in a time frame to be meaningful. NOTE: you could use this to determine how powerful the user of magic is... maybe there are people who can collect the energy over a longer time period, thus making them much more powerful than someone who can collect it for only a nanosecond. Maybe this even takes practice, so the more skill you have, (vs innate ability), the more time you can collect power.
2. Determine if the energy is only kinetic, heat, electrical, etc... energy (since the body produces all of them... or even potential chemical energy...). Based on the answer provided by PipperChip combining the heat production of the body, (a by-product of the combined energy usage by all of the processes that mean someone is alive), as well as the potential for kinetic energy produced by the muscles, would produce a very different level of power than just heat energy.
3. I would suggest one more thing that I think is a very important part of developing this concept: what is the resulting effect on the caster? If I convert all of the heat energy my body produces for 3 seconds, do I then get cold? If I convert all of the heat energy built up in my body (not just that emanating from my body but also the heat in all parts of my body) do I freeze? If I convert potential chemical energy in my cells do I get sick or die on the spot?? Alternately, if I convert the potential chemical energy in my fat cells only, do I lose weight? (side note: I suspect our fat cells may contain quite a lot of chemical energy if applied all @ once... also without fat I've heard it said we would die... so using up all the energy in just our fat cells may be life threatening as well).

Hope this is helpful & I like your more specific idea even better than the one in the Eragon series.

Answer 4

I'm going to approach this from the perspective of stored energy in a human body (for anyone else who might be interested in this) since it's relatively simple to convert calories to joules.

So here's the math.

1lb of human fat = about 3500 calories
200lb person with 15% body fat = about 30lbs of fat
That's 105,000 calories.

1 calorie = 4184 joules
105,000 calories = about 440 million joules of energy

1 joule is the energy required to lift 1kg to a hight of 10cm

Therefore, with 440 million joules we can lift 220kg to a hight of 200km

So yeah, if my math is correct, your magician could probably launch three people into orbit simultaneously!

Notice, there's no mention of how long it would take to do this, because in Newtonian mechanics, work done is a component of the force applied over a distance regardless of the time it takes to move it that distance. Your magician's "power" is limited by how quickly he can access the potential energy in his body and distribute it, as well as how fast he can replenish it.

As mentioned in some comments as well, "holding" an object in place takes no energy, so once moved, if the object is not allowed to expend it's potential energy it will remain at rest.

You will probably also want to consider the effects on the magicians body. A human can move a mile on about 150 calories and that can be fairly tiring. Imagine the exhaustion if you were to quickly expend 105,000 calories. Saying that, most of the exhaustion is caused by the chemical processes required by the body to convert stored energy into kinetic energy, so if you bypass that with magic you might not feel the tiredness.

On a side note, this is why it's so hard to lose weight.

Answer 5

Humans have 81,500 kilocalories on average on their entire body and the body consumes 2000 kilocalories on average on a day.

If you were to consume 2000 kilocalories on magic, that be 8368000 jouls which translates in Watts consumed per second.

This is enough to power a freezing spell for 16 minutes to freeze a person or keep some food fresh.

All those Watts could also be used to lift cats into space as suggested by @PipperChip