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The Blade Design Equation | Wind Force and Torque Formula | Design Calculation

#science, #howto, #green, #formula, #teacher, #school, #kid, #design, #challenge, #change How to derive the design equation for the blade of a wind turbine? How to design the blade of a wind turbine? #scientistkids, #windturbine, #greenenergy, #basic, #scientist, #smartkids, #school, #teaching, #teach, #electrical, #electricity, #aerodynamic, #pressure, #force, #windforce, #3D, #3Dprinter, #3Dprinting, #genius, #geniuskids, #designer, #designinspiration, #development, #generator, #wing, #rotation, #selfsufficient, #renewable, #renewableenergy, A moving object of mass (m) and velocity (v) has a momentum of m.v. A change in momentum of an object is equal to the impulse response applied to it. A bullet fired from a gun has momentum equal to m.v given by the mass of the bullet (m) and its velocity (v). If the bullet strikes a box, there will be a change in its momentum, which is equal to m.Δv. This change in momentum results in an impulse response being applied to the box, which is equal to F.Δt. So, we have: F. Δt = m.Δv. This is Newton's Second Law of Force. Similarly, the wind has momentum that is given by the mass of the air and wind speed. The momentum of incoming wind causes the blades to rotate. Now, how to calculate how much force is applied to the blade due to a change in wind momentum? As we know, the blade will split the incoming wind into two parts, one that flows through the front part of the blade (vf) and one the flows through the backside of the blade (vb). So, the change in wind momentum is given as the mass of the air (m) times (vb-vf). As the wind passes through the blade, the wind will interact with the blade for a certain period of time (Δt), which is defined by the profile of the blade. A wider blade will result in a longer interaction period. In this case, the interaction period Δt is equal to the width of the blade (W) divided by the speed of front-wind (vf). As we derive earlier, change in wind momentum result in an impulse response being applied to the blade or F.Δt = m (vb-vf). So, after summarizing all these equations, we have obtained the equation of force that is due to wind momentum as F = [m (vb-vf)vf]/W [The force (F) is equal to the mass of the air (m) TIMES the difference between back-wind and front wind velocity (vb-vf) TIMES vf divided by the width of the blade W. Now, how much torque (T) can be produced by this wind-generated force to the blade? The wind force to a blade of length (L) will produce torque (T), which is equal to the wind force times the length of the blade (L). By substituting the wind- force formula, we can express the torque equation as seen here: T=[m]× [(vb-vf)vf]× [L/W] So, we finally derived the detail of the torque equation, which is the [a]-[b]-[c] expression of torque. [a] is the mass of the air, [b] is the air-in-motion, which is the wind velocity, and [c] is the blade itself, which is the aspect ratio of the blade. Basically, this torque equation concludes that we need air, and air in motion through the blades to generate torque to produce electricity. For demonstration, I will share the design calculation of this mini wind turbine. Before starting the design, we need to know the available wind resource by measuring the wind speed at a specific height by an anemometer. In this case, the available wind speed is 3 to 10 m/s. The minimum required torque to turn the generator is equal to 0.015 N/m. For a wind turbine to generate useful energy, the generated torque by the blade has to be higher than the minimum torque specified by the generator. So, how much torque can the blade generate? To answer this, first, we need to calculate the mass of air that passes through the blade. Mass of the air can be calculated from air mass density rho-air (ρ-air) times the volume of the air. In this case, air mass density is approximately equal to 1.225 kg/m3. On another hand, the Volume of the air is equal to the area of blade rotation times the width of the blade W. Initial blade aspect ratio [L:W] is set to 15cm:2cm. We can obtain the mass of the air is equal to 1.7gr as seen from the calculation here. Next, we calculate the air motion or the aerodynamic components of the torque. The back-wind velocity (vb) is assumed equal to the available wind speed as 3 to 10m/s. As we mentioned earlier, the blade will split the wind into back-wind and front-wind. The ratio between them is defined by the angle of attack (θ). In this case, the front-wind velocity (vf) is approximately equal to cosθ x back-wind velocity (vb). If the angle of attack θ=60o, cosθ is equal to 0.5 and we have the front wind speed to be 1.5 to 5m/s. Hence at a wind speed of 3m/s, the torque T is equal to 0.0287 N.m. As seen in the detailed calculation, the calculated range of torque is equal to 0.0287 – 0.64 N.m. This amount of torque will be sufficient to turn the generator to generate electricity.