# Optimized Blade Design for Homemade Windmills

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## Contents

# Overview

- The intent of this project, created in collaboration with Mech425, is to identify the best angle for flat, uniform blades where the primary use is for homemade windmills where there is little access to tools or when simplicity is preferred
- The project has been selected to provide support to individuals looking to generate electricity by harvesting the wind

- The target audience are people who can not afford commercially available models and have chosen to build their own

Windmills have many functions and can be operated wherever there is access to wind. Windmills use their blades, or sails, to convert the energy in wind into rotational motion. This rotational motion can either be used for direct work or converted again into electricity. Originally, windmills were used to perform the grinding at mills. Today, they are still used for this purpose but have extended their range of uses to pumping water and primarily for electricity generation, In lesser economically developed countries, the electricity generated by homemade windmills are often used to charge batteries and cell phones or operate lighting, radios and irrigation pumps.

Modern, commercially available wind turbines are tailored to address specific wind speeds and are capable of generating megawatts of electricity from each turbine. However, homemade solutions are often low-tech and have undergone little scrutiny in terms of optimization. This report intends to identify to best angle to tilt the blades in relation to the oncoming wind and what length of blade is best suited for electricity generation.

William Kamkwamba is a fantastic example of who could benefit from the analysis presented in this report. His ambition for a better life and access to scrap materials was transformed into a working device that provides both light and irrigation to his community and inspiration to the rest of the world. As more people begin to develop solutions for their own energy needs, there is great value in optimizing these devices to maximize their social benefit.

### -- Benefits of Flat Blades --

Flat blades are less common than other designs but offer significant benefits, especially in low income or remote areas. The following is a list of benefits offered by using flat blades:

- Easy to build
- Less design and local knowledge required
- Less machinery is required during construction compared to a curved design
- Less time is required for construction purposes
- Easier to ensure conformity among the blades

**-- Engineering Calculations --**

**Power Available to the Turbine**

The amount of power passing through the turbine blade area is primary dependent on the velocity of the wind and to a lesser extent, the area of the blades. To quantify the energy in the wind, we must first consider the wind to be a fluid flowing through the blades in a cylindrical shape.

The kinetic energy stored in the wind can be found according to Bournoulli's equation:

[math] KE = 1/2 (m * v^2) [/math]

In order to find the energy in the wind, we must find the mass of the cylinder. This is based on the volume of the cylinder multiplied by the density of the fluid:

[math] m = \pi * V [/math]

The total volume of the fluid that is represented by cylindrical column is:

[math] V = A * L [/math]

We can calculate the area of the cylinder's base by:

[math]A = 1/4 (\pi * D^2) [/math]

The length of the cylinder represents the amount of fluid that has passed through the windmill's swept area. This is calculated by multiplying the velocity of wind by time:

[math] L = v * t [/math]

This can be simplified as follows:

[math] KE = 1/8 (\rho * \pi * D^2) * v^3 * t [/math]

Finally, the power in the wind is simply the energy per unit of time

[math] P = \pi /8 (\rho * D^2 * v^3) [/math]

As demonstrated, the power in the wind highly related to the velocity of the wind and to a lesser extent, the diameter of the turbine blades

**Maximum Possible Efficiency**

The Betz limit was developed by Albert Betz and seeks to determine the maximum possible energy that can be derived by a device from a stream of fluid, flowing at a given speed. In the case of windmill, the maximum theoretical efficiency of a thin rotor can be found based on the following assumptions:

- The rotor is considered ideal, having an infinite number of blades and no drag.

- The flow into and out of the rotor is axial and in accordance conservation equations.

- The fluid is modeled based on incompressible flow.

The Betz limit has been able to predicted the maximum value for the power coefficient to be 0.593. This means that the theoretical limit of power removed from from the fluid is 59.3%, although current commercial wind turbines are able to achieve 40 - 50% conversion efficiency.

**Angle of blade and the resulting forces to spin the blades versus surface area exposed**

The angle that the windmill blades are tilted compared to the stream of fluid will determine how much energy can be converted into rotational motion and then be captured by the system for meaningful work. The amount of force is calculated by finding the wind pressure.

The wind pressure exerted by the wind is given by: *P* = 1 / 2(1 + *c*) * ρ * *v*^{2}

- where c is a constant and equals 1.0 for long flat plates.

The force of the wind against the windmill blade is based on the wind pressure multiplied by the area of the blade facing the oncoming flow. In the event that the blade is tilted at an angle to the oncoming airstream, then the area of the blade exposed to the fluid is reduce by a factor of *sin*θ. As such, the wind pressure calculation is multiplied by *A* * *sin*θ to obtain the force of the wind on the blades

In addition, the force of the wind converted into rotational motion is related to the angle of the blade in relationship to the oncoming fluid flow. This relationship is given by a factor of *cos*θ.

Furthermore, the blades will encounter a drag coefficient related to the angle of the blades as they rotate in their own axis perpendicular to the oncoming flow of fluid. This drag coefficient will be represented by *D* * *cos*θ.

Therefore, the combined calculation to determine the force balance on the blades is:

*F* = ρ * *v*^{2} * *A* * *sin*θ * *cos*θ * *D* * *cos*θ

An important relationship to note is that between force and θ. The combined force balance indicates a relationship between force and *sin*θ * *cos*θ * *cos*θ.

As a result, the optimal tilt of the blades would provide an angle to the airflow such that *sin*θ * *cos*θ * *cos*θ is a maximum. This value has been presented in the graph below to show how the value changes as θ is adjusted.

The angle is adjusted in radians and seems to indicate a maximum value at approximately 0.62 radians, or roughly 35.5 degrees. This translates in a maximum conversion of 38.5% of the wind force into rotational motion. Therefore, the blades should be tilted at an angle of roughly 35.5 degrees from the oncoming air stream to obtain the optimal amount of energy using flat blade windmills.

**-- Regional Considerations --**

The target regions for this technology are those of Sub Sahara Africa or alternatively for people with limited access to tools or supplies or climate in the targeted regions

such as climate, locating raw materials, etc, as well as cultural, social and political context.

Using William as an inspiration to improve his design and what was accessible to him at the local scrap yard

as cultural, social and political context – william’s story

http://changeobserver.designobserver.com/entryprint.html?entry=10707

### -- Materials --

William Kamkwamba was able to build his windmill using:

- Tractor fan

- Shock absorber

- Bicycle frame

- PVC pipe

- Bicycle generator

- Bamboo poles

- Bicycle dynamo

- Rubber belt

- Pulleys

- Bike chain ring

- Piston

- Copper wire

If the intent is to store electricity, then these additional materials are required:

- Deep cycle batteries 12V (If the user intends to store electrical energy)

- Charge controller to regulate how much the battery charges

- DC/AC Converter

- Bridge rectifier (to ensure electricity flows into batteries)

www.makeawindturbine.com/

### -- Tools --

### -- Skills and Knowledge --

-- Technical Specifications --

# -- Estimated Costs --

# -- Common Mistakes --

Wood blades - if avoidable

uneven blade shapes

placing blades too low, must be twice as high as the tops of nearby houses or placed far enough away to not be affected by the boundary layer