I'm presently in the process of developing my plans for a flintlock fantasy series. It's high magic, but one form of magic in the setting, Arcane Magic, is heavily based in science. The energy that powers it, Aethyr, can bend the laws of physics but not outright break them. (You can't turn someone into a frog with Arcane Magic, in other words.) My protagonist, Perdita, is an Arcane Engineer. She's someone who makes magical devices of an Arcane nature. Among her creations is a belt that can perform a Spell called the Sphere of Meteoric Conversion. Here's the basic idea of how it works:
When Perdita falls beyond a certain distance, the belt activates, using Aethyr to create a magical bubble around her. When she hits the ground (or any solid object larger than the average bird,) the Sphere of Meteoric Conversion converts all her kinetic energy and the kinetic energy of the surface pushing back against her (that is, the equal and opposite reaction) into another kind of energy or simply redirect the kinetic energy away from her.
By this I mean that the bubble absorbs all the energy of the impact and transfers it away from Perdita so she takes no damage, either by directing it at something other than her or by converting it into a different kind of energy which is then directed away from her.
So, the bubble may just cause all the absorbed kinetic energy to go outward from it in all directions, like a bomb going off. Or it may convert all the kinetic energy into thermal or radiant energy and release it outward in all directions. I suppose converting it into sound is also something it can do.
The Sphere of Meteoric Conversion can also direct the absorbed and converted kinetic energy in a ring or a beam. For example, when she hits, the bubble discharges a disk of light, heat, or sound along its proverbial equator. Or it may discharge a heat beam or laser beam directly up into the air. The point is that it takes the energy of the impact and turns it into something else to be used in a different way while Perdita remains safe inside the bubble.
And, before you ask, yes, the amount of Aethyr needed to create the Sphere of Meteoric Conversion is considerable, especially if she's moving at terminal velocity. The belt is going to need some time to "cool down" (not literally) before it can generate the Spell again.
Also, the Spell doesn't have to convert all the kinetic energy into just one other type of energy. It can convert some of it into radiant energy, some of it into thermal energy, some of it into sound, and just redirect any left over kinetic energy away from Perdita.
What I need help with is determining the math for the Sphere of Meteoric Conversion. I want to make sure the math holds up in the books. Also, is there anything I'm overlooking or missing with this idea? I know it's magic, but, like I said, Arcane Magic is intended to be as science based as possible.
It's going to be interesting seeing the feedback I get on this. I hope that it presents some of you with a fun puzzle, at the very least.
Edit and Update
Okay, it seems I need to clarify another point here: The purpose of the Sphere of Meteoric Conversion is to weaponize the kinetic energy of the impact in addition to preventing Perdita from taking any damage. Alternatively, it will convert the kinetic energy into something harmless so she doesn't hurt herself, her allies on the ground, or do any significant property damage. I think it will be easier to explain this with a few examples. Some things that will be applicable in all the examples are the following:
Perdita is a Half-Orc, not a Human. She's 6'7" tall and weighs about 220 lbs. The gear she usually has on her probably comes to a total of 30 lbs., minimum. (That's her leather garments, melee weapons, flintlock guns, ammunition, etc.) So, total weight is around 250 lbs.
Example 1: Perdita is up on the tower of a castle. In the courtyard below is a horde of Ghouls (basically zombies) trying to break into the front entrance of the main keep. Perdita has the Mage with her use a Spell to launch her high into the air so she then comes down in the center of the mob of Ghouls. The Sphere of Meteoric Conversion changes the kinetic energy of the impact into thermal radiation and releases it as a disk from the "equator" of the bubble. Ghouls are weak against extreme heat. Or she may have the thermal radiation released as a beam that targets one really big Ghoul that's the size of the Incredible Hulk. The point is that she uses the kinetic energy of her impact to burn some Undead.
Example 2: Perdita is on a floating island over the ocean. She gets blown off it, either by a powerful burst of wind or a Mage using a Spell. As she falls towards the water below, she see a Sea Monster rising up, its jaws open to catch her. She activates the Sphere of Meteoric Conversion and adjust it to its "Zappy" setting. When she lands in the Sea Monster's mouth, the kinetic energy is converted into a pulse of electricity.
Example 3: Perdita is on an airship and, for one reason or another, gets thrown off of it. As she falls to the ground, she sees that she is headed toward a park where an aristocratic girl is having her Quinceañera. And the birthday girl has just received a puppy as her gift from her parents. Not wanting to become a party crashing in the most literal sense of the term, Perdita activates the Sphere of Meteoric Conversion and adjusts it to its "Harmless" setting. On impact, all the kinetic energy is converted into a beam of light (perhaps visible light, perhaps radio waves or something that won't hurt anyone.) The only damage done to the festivities is in the form of extreme awkwardness.
These examples are hopefully sufficient to explain the the why of the Sphere of Meteoric Conversion. Perdita isn't just trying to protect herself from injury and death. She also wants to harness the kinetic energy of the impact in some way or just direct away so nobody is hurt and no property damage is caused. If she just wants to slow her fall so she lands safely, she'll use a different kind of Spell, but there are situations where a slow descent would be a problem, like if that would make her an easy target to shoot from the ground or if that would give someone she's chasing time to escape and hide.
Hopefully this clarifies what I'm trying to figure out with this post. Also, having some examples of how to use the equations provided would be helpful, since I'm not a physicist and don't know what all the symbols in some of the equations mean without being told first. Once I do know, then I can use the equations myself, however, so I'm not asking other people to do all the calculations for me. I hope this clears things up.