Maximum blade speed

[windy]

 I asked this question about maximum blade speed a awhile ago and this is the response I got.

The usually accepted rule of thumb is 80 m/s tip speed before significant wind erosion occurs (even this should only be with leading edge reinforcement of some kind or another). This does not consider mechanical strength, but if you have done a good job and balanced it well, the wind erosion will probably be the limiting factor.


So, to convert from 80 m/s tip speed to RPM, realize that the tip speed is rotational speed times the radius, so the rotational speed (omega, in radians per second) will be the tip speed divided by the radius. To convert from radians/sec to RPM, you need to multiply by 60 seconds/minute * 1 revolution / 2 pi radians.


So, RPM = tip speed / radius * 60 / 2 pi, or tip speed / radius * 9.55.


For 16' (4.9m) diameter @ 80 m/s tip speed, RPM = 313 RPM

For 10' (3.0m) diameter, RPM = 501 RPM.

So, if your 10 footer is turning 700 RPM, that's a tip speed of 112 m/s or 250 mph, which is really pushing things.
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 Am I doing something wrong?  I can't get the same numbers for RPM in the given examples. 80 meters per second is equal to 179 MPH. 179 MPH( tip speed) / 8'(radius of 16')*9.55=213 RPM. The example shows 313 for the 16 foot blade.
 Could any one help me out with this?

Thanks!
windy

[RP]

Here's what I get in Excel using the following formulas:

Radius in meters = radius in ft*12*2.54/100

Ts is the Tip speed in M/s

RPM = Ts/(r*2*pi)*60

r(ft)   r(M)         Ts    RPM
8      2.4384      80    313.2971321
5      1.524        80    501.2754113

This doesn't use radians at all and I don't know where the 9.55 comes from.

After converting the radius in feet to meters, multiplying by 2 and by pi, you have the circumference of the circle the tip travels in during one revolution.  If you divide the tip speed in M/s by this distance you have the number of revolutions the tip travels in one second.  Next, multiply by 60 to get revolutions/minute.

[SparWeb]

It's a great question, and well worth checking if you want your blades to last a long time.  I witnessed a dramatic blade erosion problem after 1 year of my first turbine.  Obviously it was running too fast.

Your calculations are spot on.  Perhaps it helps to think of 80 meters per second in terms of the speed of sound.  Since the sound barrier is pretty noisy, destructive, and dangerous, it's something to stay away from.  340 m/sec at sea level.

So you can say your blades shouldn't exceed "0.25 Mach"  if it helps.  Sounds more cool that way, too.

[Flux]

The 80 m/s is a sensible figure for quiet running and low tip erosion . If you can live with more noise and are prepared to protect the tips then you can go faster without a lot of drop in performance.

This used to be an issue before neo, but with neo and normal loading the speeds cane well below this except at cut in.

If we need to go back to ferrite magnets then the issue will crop up again. For larger machines it will be a speed increasing transmission but for smaller ones then it may be cheaper to consider higher tip speeds. Not much trouble up to 100 m/s on load as far as noise goes if you shape the tips ( gets noisy running light).  Tip protection then becomes more of an issue.

Flux

[windy]

RP,

 Thanks for the reply. That formula makes more sense.

windy