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# Wind Turbine Calculator

What's the difference between HAWT and VAWT?How to calculate the power generated by a wind turbine?Revenue from the wind turbine powerWhat's the torque in an HAWT or a VAWT turbine?FAQs

This wind turbine calculator is a comprehensive tool for determining the power output, revenue, and torque of either a horizontal-axis (HAWT) or vertical-axis wind turbine (VAWT). You only need to input a few basic parameters to check the efficiency of your turbine and how much it can earn you.

You can use our tool as either a HAWT or a VAWT calculator — to change the turbine type, simply choose your desired turbine from the drop-down list at the top of the calculator.

If you're interested in renewable energy in general, our hydroelectric power calculator and solar panel calculator may be useful for you.

## What's the difference between HAWT and VAWT?

In horizontal-axis wind turbines, or HAWT for short, the blades rotate around a horizontal axis. These are the most common onshore wind turbines, commonly placed on hills and in other areas that receive a lot of wind, but are also widely used offshore. Vertical-axis wind turbines (VAWT), on the other hand, rotate around a vertical axis.

The efficiency of horizontal-axis turbines (ratio of wind power to output power) is typically higher, but they do have some drawbacks. Since the blades are subject to the force of inertia, which changes in direction, they receive an alternating load which is often detrimental to the blades' integrity. Additionally, the generator is placed far above the ground, which makes repairs and maintenance costly.

## How to calculate the power generated by a wind turbine?

To calculate wind turbine power, you need to estimate two values: the available wind power and the efficiency of the wind turbine. Multiplying these two values produces an estimate of the output power of the wind turbine. Below you can find the whole procedure:

1. Sweep area of the turbine.

Before finding the wind power, you need to determine the swept area of the turbine according to the following equations:

For HAWT:

$A = π \times L^2$

For VAWT:

$A = D \times H$

where:

• $L$ — Blade length — the radius of the horizontal-axis turbine;

• $D$ — Diameter; and

• $H$ — Turbine height.

2. Calculate the available wind power.

Once you know the swept area, you can find the available wind power according to this formula:

$P_\mathrm{wind} = 0.5 \times \rho \times v^3 \times A$

where:

• $A$ — Sweep area;
• $\rho$ — Air density, assumed to be 1.225 kg/m³ by default (you can change it by clicking on advanced settings);
• $v$ — Wind speed — the typical usable range is approximately 3-25 m/s; and
• $P_\mathrm{wind}$ — Available wind power.

3. Finding the efficiency of the turbine.

You can find the total efficiency of the turbine as follows:

$\footnotesize \begin{split} \mu = (1 - k_\mathrm{m}) \times (1 - k_\mathrm{e}) \times (1 - k_\mathrm{e, t})\\\times(1 - k_\mathrm{t}) × (1 - k_\mathrm{w}) × C_\mathrm{p} \end{split}$

where:

• $C_\mathrm{p}$ — Turbine efficiency (it must be lower than the Betz limit (59.3%), and is typically between 30-40%);

• $k_\mathrm{w}$ — Wake losses due to neighboring turbines and the terrain topography, typically 3-10%;

• $k_\mathrm{m}$ — Mechanical losses of the blades and gearbox, typically 0%-0.3%;

• $k_\mathrm{e}$ — Electrical losses of the turbine, typically 1%-1.5%;

• $k_\mathrm{e, t}$ — Electrical losses of transmission to the grid, typically 3%-10%;

• $k_\mathrm{t}$ — Percentage of time out of order due to failure or maintenance, typically 2%-3%; and

• $\mu$ — Real efficiency.

Efficiency is usually expressed as a percentage, but you input it into the formula as a fraction (for example, 30% = 0.3).

4. Calculating the output power.

To find the wind turbine power, simply multiply the efficiency by the wind power available:

$P_\mathrm{output} = \mu \times P_\mathrm{wind}$

## Revenue from the wind turbine power

Let's assume you also want to know the revenue you can expect from your wind turbine. It depends mostly on the electricity tariff — that is, how much you will earn per one kWh generated by the turbine. Once you know that value, the calculation is straightforward:

$\mathrm{revenue} = \mathrm{tariff} \times P_\mathrm{output}$

## What's the torque in an HAWT or a VAWT turbine?

The torque (or the force causing the rotation of the blades) is calculated from the tip speed ratio (TSR) of the turbine. You can find it using the following formula:

$\tau = \frac{P_\mathrm{output}}{\rm RPM} \times\frac{30}{\pi}$

where:

• $\rm RPM$ — Revolutions per minute; and
• $\tau$ — Torque.

To calculate the number of revolutions per minute, use these equations:

For HAWT:

${\rm RPM} = 60 \times v \times \frac{\rm TSR}{\pi \times 2 \times L}$

For VAWT:

${\rm RPM} = 60 \times v \times \frac{\rm TSR}{π \times D}$
FAQs

### How do wind turbines work?

Wind turbines convert the kinetic energy from the wind into electricity. Here is a step-by-step description of wind turbine energy generation:

1. Wind flows through turbine blades, causing a lift force which leads to the rotation of the blades.

2. The central rotor shafts, which are connected to the blades, transmit the rotational forces to the generator.

3. The generator uses electromagnetic induction to generate electricity as it receives the rotational forces.

4. The energy generated is then transmitted through a cable system running down the turbine.

5. The energy passes through the grid connection, where some voltage adjustments might be made and distributed to power homes or buildings.

### How do I calculate wind turbine power?

The equation used to calculate wind turbine power is:

Power (W) = 0.5 × ϱ × πr² × Cp × CF × v³

where ϱ is wind density in kg/m³, πr² is the swept area of the turbine, Cp is the power coefficient, CF is the capacity factor and v is the velocity of the wind in m/s.

### What size of a wind turbine is needed to power a house?

One 5-15 kilowatt wind turbine is sufficient to power a house. This will also depend on how much electricity your house consumes or which kind of electrical devices you have in your house.

### How much energy can a wind turbine produce per day?

A range of 1.8-90 kWh of energy can be produced by a wind turbine, depending on its energy capacity and size. The table below shows energy output generated by wind turbines of different power capacities:

Wind turbine capacity

Output

100 W

1.8 kWh

200 W

3.6 kWh

300 W

5.4 kWh

400 W

7.2 kWh

500 W

9 kWh

1,000 W

18 kWh

3,000 W

54 kWh

5,000 W

90 kWh

### How much energy does a 500W wind turbine produce?

9 kWh per day as the actual output. A 500 W wind turbine has 12 kWh rated output (the total energy capacity).

Since wind turbines are highly dependent on other factors such as wind strength, weather conditions, and many more, they can only produce up to 80% of their original rated output. Hence, we look at their actual output as the real energy generated.

### How much does a wind turbine cost?

Wind turbine prices range between 2 million and 4 million dollars, depending on their size and energy generation. Once purchased, wind turbines also require maintenance costs of up to 50,000 dollars.