edison123:
I think you have it backwards. Bigjohn is requesting that his no-load speed at 24V be cut in half. This means that he wants to cut his back-EMF constant Ke in half. The torque constant Kt of a motor must always vary with Ke, so this must be cut in half as well.
The torque generated is proportional to the armature magnetic flux, and this flux is equal to the magnetomotive force (MMF) divided by the reluctance of the magnetic circuit. The reluctance does not vary with winding (barring magnetic saturation), so flux and torque are proportional to the MMF.
The MMF generated by the coils is just n*I, the number of turns multiplied by the current. This means that Kt is proportional to the turns count n, and Bigjohn should cut his turns count in half.
If he does this with the same diameter wire, reducing the size of his winding, he cuts his resistance in half. In this case his mechanical time constant Tm [=(J*R)/(Kt*Ke)] is doubled (assuming no significant J change).
If he does this with wire of double the cross-sectional area, keeping is overall winding size the same, he reduces his resistance by a factor of 4, so his mechanical time constant stays the same.
Curt Wilson
Delta Tau Data Systems