Magic

Magic is the phenomenon where mages use their mana to interfere with the world, a method that allows apparition of phenomena by giving appropriate stimulation to the point of application.

Modern magic is achieved through technology Operation Orb, unlike the era of legends, this allowed people to clearly understand in detail the where, the how, and to what degree of power to interfere with reality.

Some of the aspects of magic in Youjo Senki universe are noted to be a mystery such as fundamental principles related to mana and interference formula.

Mana signals can be detected by using magic, and it seems most artillery units in this world have equipment to detect mana signals and conduct magically guided bombardment. In Rhine Front, a number of Imperial recruit mages got blown away in trenches by Republican artillery because they leaked mana signal by deploying magic shield.

History
In the olden days, magic was accomplished with various magical devices where the user have to turn chemical reactions happening in nature to equations and reproduce them with their will. However, before the Industrial Revolution, the old-fashioned devices used by magicians are inefficient in comparison to their modern counterpart. They are also unlikely to be produced in large numbers.

Magic started to evolve after the Industrial Revolution when mages took the concept of a computer from the Differential Analyzer to be replicated by magic. Giving birth to operation orb that made composing formulas more convenient and efficient, it led to the standardization and uniformity of formulas used by mages.

Operation Orb
Main Article: Operation Orb

A tool used by mages to recreate miraculous phenomena through the combination of mana and analog calculation. Modernized magical devices that excelled in speed and efficiency, born from taking the design concept of the computer and compact pocket watch.

Scepter
Scepters are tools mages use when casting formulas and later evolved into formulas rifles for modern army. Formula Rifles are mainly used as a tool to cast long range formula in battle. A few highly skilled mages like Tanya von Degurechaff can fire their formulas from their fingertips. In practice, mages usually enchant bullet with the formula they wanna use so that they can cast formula at the longer distance.

Formulas
In Youjo Senki universe, formulas aren't a set of words, spoken or unspoken to invoke some magical effect. Mages have to understand how the phenomenon of formulas they intend to cast works to recreate the deeds such as miracles. It's like the way people understand how to light a fire with a lighter, thus enabling them to recreate the deed through magic.

Flight Formulas
The aeronautic magic, which allows mages to soar through the sky. This magic works by creating propulsion, forcefully raising a mage into the sky and maintaining balance while in the air. The standard altitude for flight mages is 6,000 feet and it's not recommended for them to propel themselves any higher using an ordinary orb due to thin oxygen and massive amounts of mana their orb has to bear to maintain flight. Surpassing these limitations need a multi-core orb.

Defensive Formulas

 * Passive Shell: Protects against small fragments, small caliber bullets and blast waves. Can be kept on indefinitely, also easy to cast together with other formulas. The biggest ordinary single shot it can defend against in a direct hit is 12.7 mm, but in a saturation attack, even infantry small arms can weaken and penetrate it.
 * Active Barrier: Increasing the density of the shell in one part to create a shield that can withstand machine gun fire. Whether it provides adequate protection depends on the mage's skill. Ordinary, if concentrate on defense and funnel more mana, it can withstand up to about 40 mm.

Offensive Formulas

 * Enchanted Rounds: Sealing formulas inside bullets or grenades to activate as required. Formulas can be activated with minimal mana, but the rounds need to be prepared.
 * Penetration Formula: As implied in the name, enhancing penetrating power of the rounds.
 * Homing Cluster Shot: Any bullets that imbued with this formula will split into several homing projectiles upon reaching a certain range and will seek out the target.
 * Artillery Shots: Any bullets that are imbued with this formula will have its firepower enhanced to be comparable to artillery shots. It needs several layers control equation to converge the power. With Type 95, Tanya can shoot the magic bombardment that has similar power to 28 cm gun.
 * Optical Formulas: Emits a straight heat beam. Skilled mages can refract it to change its course. Noted to be the favored formula of Republican mage for their volley of fire doctrine.
 * Explosive Formulas: Creates an explosion at any coordinate. Converted to gunpowder, the power of Heavy Explosion Formulas are 150 kilos at most.
 * Self-Destruction: Overloading one's Operation Orb with mana causing it to reach critical mass and explode, injuring the user and surrounding enemies if not outright killing them.
 * Guidance/Interference Formulas: Directing a formula's trajectory, could be used for offensive and defensive purposes. It also could be used to interfere with radio signals.
 * Magic Blade: Enchanting an item such as a bayonet with mana which makes it sharp and durable enough to cut a man or plane in two. Even a tough magic shield can't bare the attack of magic blade. It can also emerge on hands and arms.

Combustion Formulas

 * Napalm-Type: A large-scale formula that usually used in trench and unconventional war. It will cause strong mana signal, fire, huge explosion and blast. It isn't efficient in encounter battles or high-maneuver warfare.
 * Explosive Vaporization: A practical combustion formula when attacking the target in buildings.

Miscellaneous

 * Optical Decoy Formula: Creates an illusion that will interfere with the visual senses of those around the user when cast. Skilled mages can easily differentiate between what is real and the illusion, especially since this formula is inclusively targeting sight and nothing else.
 * Observation Formula: Processes data of a Mage's surroundings, uses vary from locking on target 49527.gifinates, detecting observational waves, and analyzing an enemy's mana signature. In the anime, this formula takes the form of a holographic screen while in the manga it's akin to a halo above the user.
 * Heat Detection Formula: An impractical formula that is hard to handle even for Tanya. In volume 2, she once considered shoot the enemy bombers with the attack formula paralleling this one.

Others

 * Analgesic Formula: Doping up the target with it. It can improve the target's reaction time, increase instantaneous strength, and work as analgesic.
 * Medical Formula: Easing the pain and curing light wounds. With more advanced magic treatment, it can cure the serious injury by gunshot as well.


 * Magic Interference: The spread of high-density mana that can cause the noise and jamming to the radio equipment and haze the video with static. That basically makes communication units on the battlefield where mages involve in get paralyzed or perform electronic countermeasures.
 * Magic Communication: The radio communication between mages. While using a special format with directional waves via orbs, the high density of magic remaining will create ear-piercing noise to the radio messages.


 * Dehydration Formula: In manga chapter 30, Weiss once threatened the recruits to turn them into dry fishes by this formula.
 * Voice Amplification Formula: Increasing the volume of the user.

Trivia

 * The fundamental principle of all magic formulas in Youjo Senki is noted to be not fully understood as of now.