The winding window is one of the hardest parameters to change in a design. Once the core geometry is set, the only freedom left is how much copper you can fit into that window. This is exactly what the fill factor measures.
What Is the Fill Factor?
The fill factor (space factor) is the share of the conductor cross-section within the total area the winding occupies. Simply put: total conductor cross-section ÷ winding area. The remaining space consists of insulation thickness, the air gap between conductors and winding irregularity.
Round conductor has a geometric upper limit: equal-diameter circles in the tightest arrangement (hexagonal packing) can fill about 90.7% of the area. When enamel thickness, inter-layer slippage and winding tolerance are added, the real value drops markedly. In flat conductor the section itself is close to rectangular; the loss comes only from corner radii and insulation thickness.
Comparison Table
| Criterion | Round conductor | Flat conductor |
|---|---|---|
| Typical fill factor | About 70 – 78% | About 85 – 92% |
| Ease of winding | High; ideal for automatic winding | Low; requires die and bending control |
| Heat conduction | Point contact, limited heat transfer | Wide surface contact, better heat transfer |
| Suitability for large section | Limited; parallel branches needed | High; large section with a single conductor |
| Skin effect | Becomes pronounced at large diameters | Controllable with thin build |
| Mechanical strength | Tendency to slip under short circuit | More stable winding as a block |
| Supply and cost | Wide stock, low unit cost | Mostly special sizes, longer lead time |
Why Does the Fill Factor Matter So Much?
An increase in the fill factor brings three results at once:
- Lower resistance: When more copper section fits into the same window, the winding resistance drops and copper loss decreases.
- Better cooling: The wide surface contact of flat conductors makes it easier to transfer heat to the core and cooling channels.
- More compact machine: The same power can be produced in a smaller volume; in e-mobility and wind applications this is a direct competitive advantage.
The Role of the Corner Radius
In flat conductor the corners can never be perfectly square; a certain radius (r) must exist. This radius is critical for two reasons. First, at a sharp corner the enamel film thins and the electric field concentrates; the breakdown risk rises. Second, as the radius grows the area lost at the section corners increases and the fill factor drops. Standards therefore define the radius within a thickness-dependent range; when giving dimensions, the radius expectation must be stated along with the width and thickness.
A Numerical Example
A simple calculation is enough to see the size of the difference. Assume the section area reserved for the winding is 2,400 mm². If 75% fill is achieved with round conductor, the total copper section in the winding is 1,800 mm². If 90% fill is reached with flat conductor in the same area, the copper section rises to 2,160 mm².
The difference is a 20% increase in cross-section. Since resistance is inversely proportional to section, the winding resistance drops about 17%; copper loss decreases by the same ratio. In a continuously running machine, this corresponds — accumulated over years — to an energy saving that can more than cover the material price difference. Moreover, lower loss means lower winding temperature and longer insulation life.
There is another side to the calculation: winding with flat conductor is slower, requires die investment and carries a high scrap risk. In high-volume production this labour difference can overshadow the energy gain. The decision is made by calculating both sides together.
Which One, When?
Round conductor is the natural choice for small and medium-section motor windings, high-volume mass production and fully automatic winding lines. Flat conductor stands out in power-transformer windings needing large sections, high-current low-voltage windings, generator coils and compact traction motors.
There is an intermediate solution too: twin/triple arrangements where several thin round or flat conductors are used in parallel. These arrangements both limit skin effect and ease winding; but transposition is needed to prevent circulating current between parallel branches.
Summary
- The fill factor is the ratio of conductor section within the winding area.
- In round conductor the geometric upper limit is about 90.7%, in practice around 70–78%.
- Flat conductor can rise to the 85–92% range; its heat conduction and mechanical stability are also good.
- The corner radius affects both breakdown strength and fill; it must be stated in the order text.
