How to calculate chord lengths along the wind turbine blade

Updated July 20, 2017

Chord length, or the width of the wind turbine blade at a given distance along the length of the blade, is an important factor in blade design because increasing the chord will increase the amount of power generated. To calculate chord length, plug numbers into the following equation: Blade Chord (in meters) = 5.6 x R^2 / (i x Cl x r x TSR xTSR) Where: R = Radius at tip, r = radius at point of computation, i = number of blades, Cl = Lift coefficient and TSR = Tip Speed Ratio.

Plug in the number of blades your design has. Many wind turbines use two blades, which means the equation is now: Chord = 5.6 x R^2 / (2 x Cl x r x TSR xTSR).

Look at a profile curve of your wind turbine blade to determine the lift coefficient. For example, we'll use the NACA 2412 profile. This is a fairly simple, sturdy profile with a lift coefficient of 0.85. This means Cl=0.85 and our equation is now: Chord = 5.6 x R^2 / (2 x 0.85 x r x TSR xTSR).

Measure the radius at the tip of the blade in meters. With our NACA 2412 profile example, this number is 0.82 meters. Chord = 5.6 x 0.82 x 0.82 / (2 x 0.85 x r x TSR xTSR).

Determine your Tip Speed Ratio (TSR). TSR is equal to the tip speed of the blade divided by the wind speed, and it relates to the efficiency of the turbine design. If your turbine is operational, you can calculate the tip speed by measuring the rotational speed of the turbine and the wind speed. For our example, we will simply use TSR=7. For a two-blade design, a TSR of between 6 and 7 has been shown to be optimal. Now our equation is: Chord = 5.6 x 0.82 x 0.82 / (2 x 0.85 x r x 7 x 7).

Pick a length along the blade and measure the radius in meters. You will likely want to determine the chord length at a few different points along the length, and you will repeat this step for each. For a simple example, we will calculate the chord length at the tip of the blade, which we already know is 0.82 meters (the value of R). Replace r with 0.82 in the equation: Chord = 5.6 x 0.82 x 0.82 / (2 x 0.85 x 0.82 x 7 x 7). Do the math and you get 0.055 meters, or 55 millimetres. So at the tip of the blade, your chord length is 55 millimetres.

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About the Author

Erica Krimmel has been writing science-themed articles since 2006. Her work has appeared in "FishRap Live!" and online at the "Natural History of UC Santa Cruz" website. Krimmel graduated from the University of California, Santa Cruz with a Bachelor of Arts in Environmental Studies.