Texas Wind Turbines

OK all of you inquiring minds and sons and daughters of physicists and engineers…. A mind wonders while driving down the road and I started to think about the wind turbines we have seen in China and across the USA.  In Palm Springs one can see an evolution in the designs as there are at least three different types of blades on the windy hillsides.

Just how fast are the outer edges of those blades turning?  If asked to do this in high school, I’m fairly certain I would not have enjoyed the task and may have turned the assignment in late, if at all….  Visiting Tucumcari, NM I was able to get the dimensions of their local wind turbine, look up the formulas on the internet and do the calculations.

So here is the data needed:
One turbine arm is 121.4 feet long
The hub to which each arm is attached is 10.5 feet wide.
The attached video is 30 seconds long and the blades make 9.66 rotations during this time.  Watch the bottom blade in the 6’oclock position.

My calculations:
The diameter is 121.4 feet + 121.4 feet + 10.5 feet or 253.3 feet.
The circumference is:  Pi or 3.14 * 253.3 feet or 795.36 feet.
9 and 2/3 rotations in 30 seconds is 19.3 rotations in 60 seconds.
19.3 rotations in a minute times the distance traveled in one rotation or 795.36 feet is 15,366.35 feet traveled in 60 seconds.
60 minutes times 15,366.35 traveled in one minute is 921,981.3 feet traveled in an hour.
921,981.3 feet traveled in one hour divided by feet per mile (5,280) gives us the miles per hour or a bit more than 174 MPH.

It turns out that the blades are hitting lots of dust particles at this high rate of speed and this wears out the tips of the blades, called leading edge erosion.  Who knew?