Inrunner motor with tangential magnets polarization vs Outrunner with radial magnets polarization

The torque equation in a synchronous motor or generator is directly proportional to the stator field strength, rotor field strength and the sine of angle between them and from the area of the gap between the stator and the rotor. This is true for all rotating electrical machines. If Fs, Fr and λ be the stator field strength, rotor field strength and angle between Fs & Fr, S is a gap area, R is gap radius,  then the torque is given as

Te ~ R*S*Fs*Fr*Sinλ

Let's now evaluate these values for this we will assume that the sine is close to 1.

S = 2*PI*R*L where R gap radius, L length of motor

Fs ~ Sc*I  where Sc coil cross section,  I current density

Fr ~ B  where B is magnetic field in the gap

From which we have

Te ~ R*R*L*Sc*B*I

If we will compare motors with the same diameter, length, mass  and current density we can remove I and L form equation, then we have

Te ~ R*R*Sc*B

Let’s try to calculate this value for two different types of motors - in and out runners with the same diameter and mass.