5. Translating What's on Paper into Something Real

Note: For best results, read these posts in order. See menu on the right.

We're 4 posts into a wind generator project, and we still haven't mentioned something very critical... The Wind!

We know that a specific RPM produces a specific voltage and wattage. We also know Cutin is 200 RPM. Here's where theory starts to become practical: At what wind speed do we want to start charging our batteries?

Within reason, there is no right answer to that question. It depends on how much wind you expect to get at your location. I don't have a weather station at my place yet, so I rely on one from a fellow Ham Radio Operator down the street. His data is used to create the charts you see at the bottom of this blog. Looking at the last 100 days, I see that most winds typically fall between 5 and 10 MPH on average. If I want to extract anything useful from these winds, I should set my cutin to somewhere in this range.

NERD ALERT - EXPLICIT MATH REFERENCES AHEAD

For future reference, we have now set the following the following variables:

Wind speed = 5 to 10 MPH
Cutin = 200 RPM

We need more information to determine what kind of blade we need. This brings up something called TSR.

TSR, or Tip Speed Ratio is a measurement of how fast the Tip of blade is moving compared to the speed of the wind that is making it move. It is expressed as an integer based upon the following fraction:

Tip Speed / Wind Speed

Here's an easy example. If the wind is blowing 10 MPH, and the Tip of the blade is moving at 60 MPH, then you have a TSR of:

60 / 10 which equals 6/1 expressed as TSR 6

Get it? The idea of TSR isn't really any more complicated than that.

Theoretically you could design any TSR you like. But for homemade wind generators, we tend to like TSRs of 5 - 8. As TSR increases, the blades get thinner. That makes sense, since thinner blades will cut through the air faster. Because they are faster and thinner, they are also noisier. Therefore, you will find people tend to stick within the "lower" range of acceptable TSRs.

Let's take a look at TSR 5. If the wind is blowing between 5 and 10 MPH, a TSR 5 blade's tip is traveling at 25 - 50 MPH. That doesn't help us... do we have any other variables we can plug in?

That's right! Cutin! Between 5 and 10 MPH (tips spinning 25 - 50 MPH) we want 200 RPM. That is enough information to do some math with! (I warned you!)

We'll get back to TSR in just a minute. Actually, we'll work back to it. We need to determine what length of blade we're going to make. We will use that length to do the following math equations. The result will be a range of TSRs. If the TSRs are within reason, then we've found a good blade length.

Based upon a suggestion from a buddy who intrinsically knows all this stuff, I am going to guess and say I'll make 7 foot (diameter) blades. Math Time:

A wind generator tip travels in a circle, right? Our circle has a diameter of 7 feet. How far does the tip travel per revolution?

Circumference = pi(d).
7 x 3.141592 = 21.99 feet per revolution. We'll call this variable "fpr"

How fast would those tips be travelling at 200 RPM? (We add "x 60" to translate it from RPM to RPH (hours)).

(RPM x fpr x 60) / 5280 = MPH (remember, 5280 feet in a mile?)

(200 x 21.99 x 60) / 5280 = MPH

263880 / 5280 = 49.97 MPH

If we round that up to 50 MPH, we see that a 7 foot blade's tips travel 50 MPH at 200 RPM.

Remember, we said that we wanted our blades to spin at 200 RPM between 5 and 10 MPH wind? Can 7 foot blades accomplish this within a reasonable TSR? Let's find out:

5 MPH wind & 50 MPH blades = TSR10 (too high)
8 MPH wind & 50 MPH blades = TSR 6.25 (great)
10 MPH wind & 50 MPH blades = TSR5 (good)

A 7 foot, TSR 6 blade would reach cutin at 8.3 MPH
A 7 foot, TSR 5 blade would reach cutin at 10 MPH

Looks to me like the 7 foot blade is a winner!

NEXT UP: Marking and Cutting blades!