# Winding factor

*The winding factor for a specific winding expresses the ratio of flux linked by that winding compared to flux that would have been linked by a single-layer full-pitch non-skewed integer-slot winding with the same number of turns and one single slot per pole per phase. The torque of an electric motor is proportional to the fundamental winding factor.*

The winding factors are often expressed for each space harmonic. If a winding factor is referred to without reference to a harmonic number, the fundamental winding factor is addressed. In the Emetor winding calculator, both the fundamental winding factor as well as the winding factor harmonics are calculated.

The winding factor $k_w$ can generally be expressed as the product of three factors, the pitch factor $k_p$ (sometimes also called coil-span or chording factor), the breath coefficient or distribution factor $k_d$, and the skew factor $k_s$: $$k_w=k_p\cdot k_d\cdot k_s$$

The **pitch factor** $k_p$ reflects the fact that windings are often not fully pitched, i.e. the individual turns are reduced in order to decrease the length of the end-turns and do not cover a full pole-pitch (also called chorded).

**Example:**

2-pole 6-slot winding with coil span of 3 slot pitches (i.e. full pitch): $k_p=1.0$

2-pole 6-slot winding with coil span of 2 slot pitches: $k_p=0.866$

2-pole 6-slot winding with coil span of 1 slot pitch: $k_p=0.5$

The **distribution factor** $k_d$ reflects the fact that the winding coils of each phase are distributed in a number of slots. Since the emf induced in different slots are not in phase, their phasor sum is less than their numerical sum.

**Example:**

2-pole 6-slot winding with 1 slot per pole per phase: $k_d=1.0$

2-pole 12-slot winding with 2 slots per pole per phase: $k_d=0.966$

2-pole 18-slot winding with 3 slots per pole per phase: $k_d=0.96$

2-pole 24-slot winding with 4 slots per pole per phase: $k_d=0.958$

2-pole winding with an infinite number of slots per pole per phase: $k_d=0.955$

The **skew factor** $k_s$ reflects the fact that the winding is angularly twisted, which results in an angular spread and reduced emf.

Especially squirrel-cage induction motors have their rotor bars skewed by one slot-pitch in order to reduce the winding factor harmonics introduced by the slotting of the stator.

According to our definition of winding factor (*The winding factor for a specific winding expresses the ratio of flux linked by that winding compared to flux that would have been linked by a single-layer full-pitch non-skewed integer-slot winding with the same number of turns and one single slot per pole per phase.*), the winding factor of these single-layer full-pitch non-skewed integer-slot windings with one single slot per pole per phase must be 1.0!

**Examples of winding layouts that have a winding factor of 1.0:**

Single-layer 2-pole 6-slot integer-slot winding.

Single-layer 4-pole 12-slot integer-slot winding.

Single-layer 6-pole 18-slot integer-slot winding.

Single-layer 8-pole 24-slot integer-slot winding.

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