Size a rotor from the power you want: 500 W at 8 m/s and 35% capture needs a radius of 1.20 m, a 2.4 m rotor turning about 381 RPM at a tip speed ratio of 6. Then twist each blade so its pitch is the flow angle arctan(1 ÷ local speed ratio) less a 7° angle of attack, which is 26.7° at a quarter of the radius and 2.5° at the tip, with the chord widest at the root, 15 to 20% of the blade length, tapering to 8 to 10% at the tip.
Part of Advanced Wind Turbine
A blade’s length sets how much wind it sweeps, its twist keeps every section at a working angle, and its chord sets how much lift each section makes.
Length Comes From The Power And The Design Wind
Power from a rotor is P = Cp × ½ × ρ × π × R² × v³, where Cp is the fraction captured (35% for the home-built rotor in Wind Power), ρ = 1.225 kg/m³, R the rotor radius and v the design wind speed. Solving for R:
R = √(P ÷ (Cp × ½ × ρ × π × v³))
For P = 500 W at v = 8 m/s: Cp × ½ × ρ × π = 0.35 × 0.6125 × 3.1416 = 0.6735; times 8³ = 512 gives 344.8; 500 ÷ 344.8 = 1.450, and √1.450 = 1.204 m, which is 1.20 m to three figures. The rotor diameter is 2.41 m. The same check run backward reproduces the Wind Power page: a 2 m rotor makes 345 W at 8 m/s.
The design wind is the speed at which the rotor reaches its target. At 5 m/s the same rotor makes 500 × (5 ÷ 8)³ = 122 W, so choose a design speed near the wind you will often have, not the storm wind (Average Wind Speed & Power Curve).
Rotor speed follows from the tip speed ratio, ω = λ × v ÷ R. At λ = 6: 6 × 8 ÷ 1.204 = 39.9 rad/s, which is 39.9 × 60 ÷ 2π = 381 RPM. Rotor speed is proportional to wind speed at a constant λ: 238 RPM at 5 m/s, and 571 RPM at 12 m/s. The blade’s strength has to cover the fastest case (Carving Wooden Blades).
If the hub radius is 0.2 m (an assumed value), the blade is 1.204 − 0.2 = 1.0 m long.
Twist Follows The Flow Angle At Each Station
Along the blade the local speed ratio is λ_r = λ × r ÷ R. The flow angle is φ = arctan(1 ÷ λ_r), and the pitch to set is β = φ − α, with α = 7° as the middle of the 5 to 10° working range from Airfoil Profile (Lift vs Drag):
| Station r ÷ R | Local ratio λ_r | Flow angle φ | Pitch β (α = 7°) |
|---|---|---|---|
| 0.25 | 1.5 | 33.7° | 26.7° |
| 0.40 | 2.4 | 22.6° | 15.6° |
| 0.60 | 3.6 | 15.5° | 8.5° |
| 0.80 | 4.8 | 11.8° | 4.8° |
| 1.00 | 6.0 | 9.5° | 2.5° |
Twist from root to tip is therefore about 24° between a quarter radius and the tip. The carrier gives 20-25° at the root and 3-5° at the tip, and the Wind Power page gives 20-35° and 0-5°. The table agrees in kind: steep at the root, nearly flat at the tip. The exact figures depend on α and on where “root” is measured; inboard of about a quarter radius the section is mostly hub and structure, and many builders stop twisting there.
Chord Is Widest At The Root
The carrier’s chord rule is 15 to 20% of the blade length at the root, tapering to 8 to 10% at the tip. For a 1.0 m blade that is a root chord of 15-20 cm and a tip chord of 8-10 cm. Taking 18 cm at the root and 9 cm at the tip with a straight taper, the chord at the middle, 0.5 m out, is (18 + 9) ÷ 2 = 13.5 cm.
Method: Lay Out The Blade
Step 1: choose P and the design wind, and compute R and RPM as above. Step 2: draw the blade plan with stations every 10 cm from the hub, and write each station’s chord from the linear taper. Step 3: compute β at each station and write it beside the chord. Step 4: make a template for each station’s cross-section and a pitch gauge set to its β. See Carving Wooden Blades or Sheet Metal Blades. Step 5: weigh every blade; they must match within 1 to 2% (Blade Balancing).
Common Mistakes
- Designing for the maximum wind — the rotor then underperforms in the winds you actually have.
- Taking the root angle from the carrier but the tip angle from a different table.
- Making the rotor bigger than the tower and the alternator can bear: doubling the diameter quadruples the swept area and the loads.
Safety
Speed doubles the load four times over
At 381 RPM the blade is already fast; if the rotor runs away to twice that speed, the centrifugal load on each root bolt is four times higher. Design the hub for the runaway speed, not the design speed (Dump Load & Overspeed Protection).
What’s Next
- Learn next: Carving Wooden Blades to turn the drawing into wood
- Combine with: Permanent Magnet Alternator, which must match the rotor’s RPM