Accurate models of the recording properties of heads and media are essential for design and optimization.. Some of the most useful analytic models are available here in C source code.
Jones' Head Model. This is a transmission line model which gives reasonable values for the efficiency and inductance of a multiturn, thin film head. Some adjustments of the width are needed to approximate a real head. (Header file.)
Karlqvist Model. The granddaddy of all head models.
Ciureanu's Head Model. This is an extension of the Jones model which accounts for the presence of a backgap.
Szczech Head Field Model. This has been one of the most useful models for approximating the field of heads with finite pole lengths. Developed by curve fitting to a measured, and later conformally mapped, head field plot. (This implementation adds the capability of adjusting the amplitude of the undershoots associated with poles 'p' and 'q' from 0 to 100 percent. Header file.)
Potter's Head (Fringe) Field Model. An early head model by Potter. This was used for comparison by Szczech.
Bertero's Head Field Model. This is a fully analytic model of the head field for finite pole lengths. (Header file.)
Curland and Judy's Head Field Model. Iterative solution of head field using complex conformal mapping. Does not account for finite poles.
Yang and Huang's Head Field Model. Derived from a conformal mapping solution, this iterative field model is somewhat more advanced than the Curland and Judy model. The implementation here provides for equal pole lengths.
Lindholm's Equations. An amazing 3D model which closely approximates the field of semi-infinite pole heads -- but models the gap region of finite pole head well. It is especially useful when applied to pole trimmed heads. In my experience, this model gives results equal in quality to those of finite element programs -- and a lot faster. (Header file.)
Williams/Comstock Transition Model. This is one of the most used 'slope' models dealing with media transitions. It produces an estimate of the 'a' parameter for use in head/media modeling. (Header file.)
NMMM Transition Model. Noyau, Middleton, Miles and Mackintosh devised this slope model incorporating an approximation to the B-H loop of the media. More elaborate than the Williams/Comstock model, it blends the media limited and head limited regions into a single curve. (Header file.)