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Optimized Blade Design for Homemade Windmills
- 1 Overview
- 2 -- Engineering Calculations --
- 3 -- Regional Considerations --
- 4 -- Technical Specifications --
- 5 -- Estimated Costs --
- 6 -- Common Mistakes --
- 7 References
- The intent of this project, created in collaboration with Mech425, is to identify the best angle for flat, uniform blades that would typically be used to create homemade wind turbines
- 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.
Area of the cylinder base is calculated by:
A = 1/4 (π * D^2)
Length of the cylinder is based on the velocity of wind multiplied by time:
L = v * t
Combining these values, we are able to compute the total volume of the fluid cylinder:
V = A * L
The mass of the cylinder is based on the density of the fluid multiplied by the volume:
m = ρ * V
The Kinetic Energy can then be found by multiplying the mass of the fluid by the half the velocity squared:
KE = 1/2 (m * v^2)
This can be simplified as follows:
KE = 1/8 (ρ * π * D^2) * v^3 * t
Finally, the power in the wind is simply the energy per unit of time
P = π/8 (ρ * D^2 * v^3)
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
Length = Additional rotational force Vs. torque / momentum required to spin blade
-- 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
-- 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
- Bike chain ring
- 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)
-- 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