Q: In Overlooking View, Touko mentioned "even I can't fly without a broom", please tell us about the details of the magecraft involved in flying with a broom.

A: Basically it is a transportation method involving using magical energy as fuel. Within it, there is the Jet Method, which achieves maximum air speed transiently. There is also the low-cost Ether Sail method. The current new method of transportation involves planting a magical anchor at the destination, and the magus will be pulled toward it, like being pulled by a retracting elastic band. This is the Anchor Attraction Ascension method designed by Touko Aozaki (Patented, commonly referred to as "Touko Travel").
... Although Touko was only half-serious there, broom is still a Mystery that is supported by "Magic Foundation - Black Magic" over the entire world. Female magi can easily achieve magical properties such as "foot not making contact with the ground" and "repelled by the earth" when employing a broom. Furthermore, gravity can be reduced to about 1/6 of normal by using an ointment of witchs' which enhances the effect of "repelled by the earth" mentioned previously.
In other words, a broom is an item that enables "hovering". The source of propulsion varies depending on the magi. Nowadays there is a trend among female magi to research new methods of flight. However, in recent years, there has not been any new innovation that could trump Touko's ridiculously sophisticated method of travel.

TYPE-MOON Fes. Official Pamphlet 10th Anniversary Q & A Booklet