BLDC Winding Calculator

This calculator determines BLDC winding parameters including turns per phase, wire gauge, fill factor, and winding factor from motor geometry and target Kv. Motor builders rewinding outrunners for drones, RC aircraft, and industrial drives use it to optimize the tradeoff between Kv (speed) and torque constant.

The winding factor $K_{w1}$ quantifies how effectively the stator winding links rotor flux. Per Hanselman's 'Brushless Permanent Magnet Motor Design' (2006), $K_{w1} = K_d \times K_p$, where the distribution factor $K_d = \sin(q\alpha/2) / (q \sin(\alpha/2))$ and the pitch factor $K_p = \cos(\beta/2)$. That form assumes an integer $q$. A concentrated winding (one coil per tooth) has a fractional $q = S/(3P) = z/n$ in lowest terms, with $S$ slots and $P$ poles, and the star-of-slots method gives $K_d = \sin(\pi/6) / (z \sin(\pi/(6z)))$ (Bianchi and Dai Pré, 2006): for 12N14P, $q = 2/7$ and $K_d = 0.966$. The 12-slot/14-pole (12N14P) configuration achieves $K_{w1} \approx 0.933$, making it the most popular drone motor topology.

The back-EMF constant relates directly to winding turns: $K_e = \sqrt{3} \cdot N_t \cdot p \cdot K_{w1} \cdot \Phi_p$ for wye connection, where $\Phi_p$ is flux per pole, $p$ is the number of pole pairs and $N_t$ is turns per phase; $K_e$ is quoted line to line, and in delta the $\sqrt{3}$ becomes 1. Kv scales inversely with turns: halving turns doubles Kv. Delta connection yields $K_v^{\Delta} = \sqrt{3} \times K_v^{Y}$ for the same coil count because line voltage is $\sqrt{3}$ times phase voltage in wye but equals phase voltage in delta.

Fill factor $K_{fill}$ measures how much of the available slot area is occupied by copper. Hand-wound motors achieve 35-45%, machine-wound reach 50-65%. Higher fill factor means lower resistance and better efficiency but requires careful wire routing. Each slot holds two coil sides, one from the coil on each tooth beside it (Pyrhönen, Jokinen and Hrabovcová, 2008, section 2.9), so slot area $A_{slot}$, wire cross-section $A_{wire}$ and $N_c$ turns per coil give $K_{fill} = 2 N_c \cdot A_{wire} / A_{slot}$. The calculator estimates the slot from the bore as for an inrunner, $0.55\pi d/S$ wide by $0.2d$ deep; an outrunner's slot is smaller, so its real fill factor is higher than the one shown.