How do you calculate blade tip speed?

Tip speed is angular velocity times rotor radius: v = (2 x pi x n / 60) x R, where n is revolutions per minute and R is the rotor radius. A 90 metre rotor turning at 18.1 rpm gives a tip speed of about 85 metres per second.

What is capacity factor and how is it calculated?

Capacity factor is the energy a turbine actually produces over a year divided by what it would have produced running at rated power the whole time: energy in MWh divided by rated power in MW times 8760 hours. Typical onshore values in Turkiye run between 30 and 38 percent.

Why does power in the wind scale with the cube of wind speed?

The mass of air passing the rotor each second is proportional to wind speed, and the kinetic energy of that air scales with the square of speed. Multiplied together, power depends on speed cubed: P = 0.5 x rho x A x v^3. A ten percent increase in wind speed therefore means roughly a thirty-three percent increase in power.

How is bolt tightening torque calculated?

Approximate torque follows T = K x d x F, where K is the nut factor, d the nominal bolt diameter and F the target preload. On site, however, the only value that governs is the torque given in the manufacturer's service documentation; the calculation is for checking and training only.

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Calculators

Wind turbine calculators

The six calculations I reach for most often, on site and at the desk. Everything runs in your browser: no data leaves the page and nothing asks you to sign up. Under each tool I have written the formula and the assumptions behind it, because where a number comes from matters as much as the number itself.

6 toolsNo sign-upFormulas shownUpdated September 2026

Tool 01

Tip speed and TSR

The linear speed of the blade tip drives both noise and leading edge erosion. Onshore it is usually held near 80 m/s because of noise limits. The tip speed ratio (TSR, λ) tells you how many times faster the tip travels than the wind; on three-bladed rotors efficiency peaks between 7 and 9.

Rotor diameter

Rotor speed

rpm

Wind speed

m/s

The default values are those of a Nordex N90/2500: 90 m rotor, rated speed 18.1 rpm.

Tip speed: —m/s
Per hour: —km/h
TSR (λ): —
Angular velocity: —rad/s

ω = 2π · n / 60 · v_tip = ω · D/2 · λ = v_tip / v_wind

n: revolutions per minute, D: rotor diameter, ω: angular velocity. TSR is dimensionless.

Tool 02

Power in the wind and turbine power

Double the wind speed and power goes up eightfold. That one sentence explains why site selection matters more than anything else in wind energy. Below, air density is calculated from temperature and altitude, so you can see for yourself why the same wind gives you less power on a hot summer day.

Rotor diameter

Wind speed

m/s

Wind speed slider

Air temperature

°C

Altitude

Power coefficient Cp

–

A good modern turbine peaks between 0.45 and 0.50. The theoretical ceiling, the Betz limit, is 0.593.

Turbine power (with Cp): —kW
Total power in the wind: —kW
Betz limit (59.3%): —kW
Swept area: —m²
Power density: —W/m²
Air density: —kg/m³

A = π·D²/4 · P_wind = ½ · ρ · A · v³ · P_turbine = P_wind · C_p

ρ = p / (R · T) · p = 101325 · (1 − 2.25577·10⁻⁵ · h)^5.25588

R = 287.05 J/(kg·K), T absolute temperature (K), h altitude (m). Under standard conditions (15 °C, sea level) ρ = 1.225 kg/m³.

Tool 03

Wind speed correction with height

The met mast sits at 30 metres and the hub at 80. You cannot estimate production without bridging that gap. Wind speeds up with height, and how much depends on the roughness of the terrain. Below you get the power law and the logarithmic law side by side.

Measured speed

m/s

Measurement height

Target height (hub)

Terrain type

The choice sets both the roughness length (z₀) and the power law exponent (α).

Speed at target height: —m/s
By the logarithmic law: —m/s
Increase in speed: —%
Increase in power: —%

Power law: v₂ = v₁ · (h₂ / h₁)^α

Logarithmic law: v₂ = v₁ · ln(h₂/z₀) / ln(h₁/z₀)

Because power goes with the cube of speed, the gain in power is (v₂/v₁)³ − 1. The two laws approximate the same terrain differently; results close to each other are a good sign.

Tool 04

Capacity factor

The single number that captures how a plant is really performing. Onshore in Türkiye the typical range is 30 to 38 percent; anything above 40 means an unusually good site. Equivalent full load hours say the same thing in hours, and both are used in the industry.

Rated power

Energy produced

MWh

Period

Capacity factor: —%
Equivalent full load hours: —hours
Average output power: —kW
Theoretical maximum production: —MWh

CF = E / (P · t) · Equivalent full load hours = E / P

E is energy produced (MWh), P rated power (MW), t the length of the period (hours). Capacity factor should not be confused with availability: even a turbine that never faults will not approach 100 percent, because the wind does not blow at rated speed all year.

Tool 05

Annual energy production (Weibull)

How wind is distributed across a year at a given site is modelled with a Weibull distribution. Enter the mean speed and the shape parameter, and the tool multiplies that distribution by the turbine power curve and integrates it over the year. It is not a substitute for a real feasibility study, but it gets the order of magnitude right.

Turbine

Mean wind speed at hub height

m/s

Weibull shape parameter k

–

k = 2 (Rayleigh) is a reasonable assumption for most onshore sites. Where the wind is steady it rises to 2.5 or 3.

Total losses

Wake effects, electrical losses, downtime and availability together typically come to 10 to 15 percent.

Net annual production: —MWh
Gross production before losses: —MWh
Capacity factor: —%
Equivalent full load hours: —hours
Weibull scale parameter c: —m/s
Approximate households: —homes

How production is spread across wind speeds

f(v) = (k/c)·(v/c)^k−1·e^{−(v/c)^k} · c = v̄ / Γ(1 + 1/k)

AEP = 8760 · Σ f(v)·P(v)·Δv · (1 − losses)

The sum runs from 0 to 30 m/s in 0.25 m/s steps. The household figure assumes an average domestic consumption of 3,000 kWh per year and is only there to give a sense of scale.

This is not a feasibility study. A real project decision needs at least a year of on-site measurement, wake modelling against the actual layout, terrain and roughness analysis and an uncertainty budget. Treat the number here as a first estimate of magnitude.

Tool 06

Bolt tightening torque

There are hundreds of bolts in the tower flanges, the blade roots and the yaw bearing, and every one of them has the same job: to hold enough preload. Torque is not the goal, only an indirect route to preload — and a fairly crude one, since most of the applied torque is spent on friction. This tool is a good way to see how much friction changes the answer.

Bolt size

Property class

Nut factor K

Target preload (percentage of yield)

With torque tightening the common target is 70 percent. Hydraulic tensioning can go to 75 or 90.

Approximate tightening torque: —Nm
Target preload: —kN
Tensile stress area: —mm²
Yield strength: —MPa
Approximate breaking load: —kN
Torque if tightened dry: —Nm

F = (target %) · A_s · R_p0.2 · T = K · d · F

A_s is the tensile stress area (ISO 898-1, coarse thread), R_p0.2 the yield strength of the class (for 8.8: 640 MPa at d ≤ 16 mm, 660 MPa above; 10.9: 940 MPa; 12.9: 1100 MPa), d the nominal bolt diameter and K the nut factor.

On site the only value that counts is the torque in the manufacturer's service documentation. What you get here is an approximation: the real friction coefficient depends on the surface coating, the type of lubricant, the state of the washer under the nut and even the air temperature, so the preload achieved at a given torque can scatter by plus or minus 25 percent. On critical joints, hydraulic tensioning or bolt elongation measurement is preferred over torque. Use this for checking and training, not in place of the manufacturer's figure.

Frequently asked

About these calculations

Why does power scale with the cube of wind speed?

The mass of air passing the rotor per second is proportional to speed, and the kinetic energy of that air scales with speed squared. Multiply the two and power depends on speed cubed. The practical consequence: a 10 percent difference in wind speed is roughly a 33 percent difference in power. That is why site selection decides so much.

Can the Betz limit be beaten?

No. If the rotor took all the energy out of the wind, the air behind it would have to stop, and then nothing could pass through. The optimum that resolves that contradiction is 59.3 percent. Real turbines sit below it because of friction, tip losses and a finite number of blades, peaking at a Cp of 0.45 to 0.50 at best.

Is capacity factor the same as availability?

No, though they are often confused. Availability is the share of time the turbine is ready to produce, and on a well-run site it is above 97 percent. Capacity factor depends on how much the wind blows and sits around 30 to 38 percent. A turbine that never faults all year still will not raise its capacity factor, because the wind does not blow at rated speed.

How do I know the Weibull k for my site?

Only measurement gives you the real figure. Without it, k = 2 (the Rayleigh distribution) is a reasonable starting point onshore. Sites with steady wind from a settled direction run at 2.5 to 3; very variable sites at 1.5 to 1.8. As k rises the distribution narrows and, at the same mean speed, production falls slightly, because most of the energy comes from speeds above the mean.

Is anything I type here stored?

No. Every calculation runs inside your browser and nothing is sent to a server. Close the page and your inputs are gone.

Also worth a look

Glossary →148 wind turbine terms in English and Turkish with practical definitions. Field guide →Getting into the trade, GWO certificates, a real day on site. N90 3D model →See the machine these calculations are built around, assembled stage by stage. Türkçe sürüm →Aynı araçların Türkçe açıklamalı hali.

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