Appendix

Wind Diverting Integrated Generator Turbine CAD Drawings

Previous Turbine Design

Wind Diverting Integrated Generator Turbine Electrical Design

Theoretical Force Calculations

The wind diverting integrated generator turbine has an inlet, denoted by index 1, and two outlets, denoted by indices 2 and 3. The velocity of wind entering the turbine is known to be 60 mph. This is a typical highway speed for a vehicle. To determine the outlet wind velocity, conservation of energy is used in the following equation:

where this describes the energy going into the turbine is equal to the energy coming out and the work done by the turbine. The power produced by the turbine is calculated through the following equation:

Combining this with the energy conservation equation and noting that the velocities at the outlets are equal, an expression for the outlet velocity is found to be:

The outlet wind velocity is found to be 12.144 m/s. To find the forces acting on the turbine itself, we use a control volume enclosing the turbine casing. Momentum equations are then used to calculate the force acting on the turbine. This calculation is based upon an ideal situation where the turbine would be able to reach the Betz limit of turbine power production. Under these assumptions, the force can be calculated to be approximately 10N using the following equation:

Here, the angle theta is the angle used at the outlet to divert the air. This can be seen in the turbine casing drawing above.

Electrical Power Theory

The electronics of this project are based on Faraday's Law of Electromagnetic Induction. The law states simply that a changing magnetic field will induce a current in a conductor. Mathematically, this is described by the equation:

Emf refers to the electromotive force, or voltage, induced in the conductor, N is the number of turns of coil the magnetic field changes over, phi is the magnetic flux, and t is time. To harness the energy present in the wind, a traditional wind turbine relies upon large airfoils to produce rotary motion with respect to a central axis. The power present in the wind is a cubic relationship with regards to the winds speed, and square relationship regarding blade length. Mathematically, it is described as:

In the equation, P represents the power available in the wind, A represents the sweep area of the blades, delta represents the density of the air, and omega represents wind velocity. Accordingly, high wind speeds equate to exponentially higher power outputs. However, the amount of power that can be successfully transformed from mechanical energy to electrical energy is limited by the Betz Limit. The Betz Limit states that a turbine's blades cannot capture greater than 59.3 percent of the kinetic energy present in the wind. Accordingly, while great amounts of power may be present in the wind, just over half of that power can actually be captured for use by electronic devices. While frictional losses in the bearing exist, they are generally fairly small. The other major source of power loss in the turbine is within the generator itself. This is due to the inclusion of iron within the generator. As the blades turn magnets around their central axis to create current, these magnets also produce negative effects in the iron supporting the copper coils and magnets themselves. These losses are known as eddy current and hysteresis losses. To reduce these losses, generators use a laminated structure. This increases the overall resistance of the iron housing without hindering magnetic field amplification, producing fewer harmful losses. Our project uses a similar structure. However, our integrated generator turbine does not produce current by applying torque to the central axis. Instead, the magnets are attached to the outer edge of the rotor. This allows for a more efficient system to be realized that otherwise could not exist in a traditional wind turbine. By minimizing losses of the turbine, more mechanical energy is transformed into electrical energy by the generator. This energy may exist in a polyphase output. A polyphase output refers to a power source consisting of multiple phases produced by the change of angle between the magnets and the coils they interact with. The turbine we created produced a single phase output. However, more phases are possible. After outputting an amount of power, that power is then stepped up or down by a transformer according to the required load. For example, if the battery is being recharged or assisted, a higher voltage is necessary and hence a step up transformer is used. On the contrary, if small electronic devices are being used, a step down transformer is used to reduce the voltage. After adjusting the power to the appropriate level for the electronics using it, the power is then rectified by a full bridge rectifier. This changes the original AC signal into a direct current signal suitable for powering traditional electronic devices.