How efficient would it be for a magic system to be based on absorption of nearby kinetic energy?

Question

The System in General

So, the magic system involves mages being able to create semi-tangible, rope-like energy structures. I'm not gonna go into too much detail on it since this isn't the point of this question, but basically imagine it as a mix of Just Cause's tether mechanics, the Pull/Push powers from Mistborn (Minus the push), and Spiderman's webs, but made out of energy.

So, the system has an overall theme of kinetic/mechanical energy. For the sake of thematic cohesion— and in order to have a magical source that sooort of follows the first law of thermodynamics without resorting to to "they eat magically charged salt"— I came up with this idea: What if base energy for this magic system is gathered through the users absorbing nearby kinetic energy?

Now, this could work a variety of ways and have interesting effects in the environment around them. BUT, in order for them to not instantly have a secondary power that allows them to essentially freeze time (or at least motion) in a small area around them, I've decided to set a few limitations.

Levels of Kinetic Absorption

A "Weaver" (aka a magic user of this system) can absorb instances of kinetic power from around them in power proportional to their skill. So for example:

• a Weaver that is just starting would be able to absorb sound vibrations from the air around them, creating a sphere of absolute silence.
• A more advanced user could, in addition to sound, absorb more subtle movements, making swaying grass freeze around them, or falling raindrops to stop mid air or slow down in a sphere around them.
• Really advanced users could create a "Dampening field" around them that would make others feel as if they were moving through honey instead of air. In order for that to not be so overpowered, like for example making people's hearts or blood slow down and depriving them of oxygen, I'm gonna say this "absorption field" works in a projection-like way and can't pass through solid surfaces.

Extreme uses of this could allow users to walk on water, or even near-fully dampening kinetic power from around them, freezing things mid-air.

Now, I know this is basically a whole other magic system, but the more extreme examples will be kept for characters that have a legend-like status. The sound and slight dampening of small motions would be much more common.

How Effective would it be?

Now, my main question here is how long would it take to stockpile a significant amount of energy through those methods? For example, how long would it take for someone sitting down a cliff near the ocean, absorbing sound from the environment, to collect enough energy to fling themselves up it?

Would this provide too much, or too little relative power overall? And what other sources of kinetic energy would there be in an outdoors setting?

Important note: This story would take place in an Age of Sail sort of setting, on a world that's for the most part a massive archipelago.

Answer 1

One example:

Say we count ambient temperature as kinetic energy. And say someone wants to lift 100 kg by 100 m. Acceleration due to gravity is about 10m/s^2. Multiplying to get the desired gravitational potential energy, they need to absorb 100 kJ.

The specific heat capacity of air is about 1 kJ / kg K (https://www.ohio.edu/mechanical/thermo/property_tables/air/air_Cp_Cv.html).

So if they can lift the weight if they lower the temperature of 10kg of air by 10 degrees. The density of air is around 1kg / m^3 (https://www.macinstruments.com/blog/what-is-the-density-of-air-at-stp/), so this is about 10 m^3, or a sphere of 1.3m.

But maybe that's too overpowered, so let's consider sound. Sound travels, so a sphere of silence will be absorbing all of the energy entering the surface of the sphere. I found this article: https://engineering.mit.edu/engage/ask-an-engineer/can-sound-be-converted-to-useful-energy/

It says very loud sounds might be 0.01 w/m^s. Say they have a sphere of radius 10. The surface area is 4 pi r^2, so about 1000 m^2. If loud sound is hitting the sphere from all sides, that's about 10 watts. 1 watt is 1 joule / second, so it will take about 10,000 seconds to absorb 100 kJ (almost 3 hours) if they're surrounded by jackhammers. But ambient sounds are probably much quieter. Decibels are a log scale: every 10-decibel decrease in volume is a 10-times decrease in power. So realistically it will take many orders of magnitude more time to absorb the energy. Go down from 120 decibels to 70 decibels, and it will take 10000 times longer to absorb the energy - going from hours to decades.

What about absorbing the kinetic energy of moving objects? Kinetic energy is 1/2 * mass * velocity^2. I'd guess grass might wave around 0.01 - 0.1 m/s (a very rough guess), so in one instant that might be 0.00005 - 0.005 J/kg of grass. The question is how often this is refreshed - does the grass constantly absorb all of the energy from the wind pushing against it, or does the person have to wait for it to sway to absorb the energy? If they're absorbing the energy from 100kg of grass twice per second, that's maybe 1 watt, and they need 100,000 seconds (about a day) to absorb the energy. If the grass is acting like windmills, they can probably absorb more energy.

If they can directly take energy from ocean waves or large volumes of wind or large trees blowing in the wind or seismic waves reaching the surface, they could potentially absorb huge amounts of energy very easily.