 Supercells are rotating thunderstorms that can cause tornadoes and hail. The most widely accepted theory for storm spin-up produces a pair of counter-rotating supercells. But such pairs are rarely observed in the troposphere, and a theory is needed that produces a single supercell. A new mathematical model called vertical rotating draft has been developed that includes the gross features of a supercell in highly idealized form. This new model produces a single supercell. Principal ingredients of the model include rotation about a vertical axis, horizontal convergence in the middle troposphere caused by the compression of sinking air parcels, buoyancy, and the Coriolis force. When these ingredients are used in fluid dynamic equations, the horizontal pressure gradient is found to be zero, and air parcels move along inertial circles projected on a horizontal surface. This circular motion gives the model an inertial oscillation that appears to have been overlooked in previous supercell models. The inertial oscillation consists of a long quiescent phase when the draft diameter is large and rotates anti-cyclonically, and a short intense phase when the draft diameter is small and rotates cyclonically. One cycle of mathematically driven animation represents 13 hours of quiescent phase and 5 hours of intense phase. During the intense phase of the inertial oscillation, the rotating draft resembles a supercell. Rising parcels of air expand, causing the draft to expand and rotate anti-cyclonically. The updraft changes to a downdraft, contracts, and rotation becomes cyclonic. Downdraft is driven by evaporative cooling and updraft by condensational heating. Expanding flow interacts with the Coriolis force to produce anti-cyclonic rotation during the quiescent phase. Contracting flow interacts with the Coriolis force to produce cyclonic rotation during the intense phase. Additional physical ingredients of the model include translation of the rotating draft and vertical wind shear. The rotating draft moves at a constant height above the surface of the earth. The intense phase has a small buoyant draft, cyclonic rotation, marked by a track that turns to the right. This right turn is a salient feature of actual supercells. The quiescent phase has a large negatively buoyant draft with anti-cyclonic rotation. Latent heating changes the downdraft to an updraft in the middle of the intense phase. This flow reversal interacts with the vertical wind shear to cause the right turn. The latent energy required to support this inertial oscillation is greatest during the quiescent phase when the draft diameter is large. A supercell storm that produced one and one-half centimeter hail is documented by radar echoes spaced 30 minutes apart. These echoes become increasingly stronger as the supercell builds. The track turns to the right, hail is produced, and strong echoes are recorded. The echoes then weaken as the supercell dissipates. Application of the mathematical model starts in the middle of the quiescent phase. The first weak radar echoes are in theory created by a growing updraft in a predominantly downward airflow. After the turning point, the strong echoes and hail are created in theory by a predominantly upward airflow. Data from the documented supercell storm generally support the intense phase of the model. However, the quiescent phase of the model is not supported by the storm data, possibly because the quiescent phase requires too much latent energy. The new mathematical model called vertical rotating draft has an inertial oscillation with an intense phase that resembles a single supercell. This intense phase starts with a predominantly downward flow that causes the draft to contract and spin up, partly by action of the Coriolis force. More research remains to be done. The predominantly downward flow that theoretically occurs before the turning point in a supercell track needs to be detected and measured. This down flow, if confirmed by measurements, would strongly support this new theory for the spin up of supercell storms.