Calculate The Tip Speed Of A Fan Blade

To determine the amount of work a fan can perform on the surrounding air, engineers must first know the number, dimensions and tangential velocity (aka directional speed) of the blades. Luckily, calculating this speed only requires two pieces of data: 1) the distance from the center of the rotor to the tip of the blade, and 2) the fan's average rate of rotation (expressed in "revolutions per minute").

"Circumference" Equals "Diameter Times Pi"

Because the fan blade's length is constant, the distance from the tip of the blade to the center of the rotor is constant. Since the definition of a circle is the collection of points that are a specific distance (i.e., the radius) from a single point, we can say the tip of the blade traces a perfect circle as it revolves around the rotor. Furthermore, the circumference of this imaginary circle traced by the tip is equal to the total distance the tip travels in one revolution.

So, to determine the distance the tip travels, multiply the distance from tip to rotor by 2. The result is the "diameter" of the traced circle. Finally, multiply the diameter by 3.141 (an approximation of the number "pi") to get the length of the circumference.

Note: At this point, make sure you convert the units of measurement into "meters." If you measured the radius in centimeters, divide the circumference by 100. If you measured the radius in inches, divide the circumference by 39.37.

Distance Traveled In One Second

Search the fan's instruction manual for the average number of revolutions per minute (rpm). If you can't find it, try visiting the manufacturer's website or calling its help desk phone center.

Once you have that figure, divide it by 60 to determine the fan's revolutions per second (rps). Multiply the rps by the circumference; the result is the meters traveled in one second by the tip of the blade--i.e., the speed of the tip (expressed in "meters per second").

To convert to "miles per hour," multiply the meters-per-second speed by 2.24.

Tags: distance from, center rotor, distance travels, divide circumference, measured radius