In another thread, someone asked if tubing spars were sufficiently strong
to withstand the force of the wind on the blades and admittedly,
I hadn't done any calcs on this and just went by gut feel.
Please feel free to poke holes in any assumptions/equations/conversions I have used.
Here are some specifics and presumptions using some worst case scenarios:
turbine diameter 18 feet
three blades @ TSR=6
furl at 20mph
steel spar tubular dimensions : 1.25"OD, 0.065" wall thickness
soft steel because (hot dipped ?) galvanized
I will now work backwards to get the applied loads:
at 20mph, 100% wind energy = 10KW, so 40% eff = 4KW
for TSR = 6 , rotation @ 20mph = 315rpm
power conversion: 4KW/(746w/hp) = 5.4 hp
torque= hp x 5252 / rpm = 5.4 x 5252 / 315 = 90ft-lbs
since 3 blades, 30ft-lbs exerted by each blade
modulus of elasticity of mild steel is 29,000 Kpsi
yield strength steel = 35,000 psi
from the tubing geometry:
section modulus Z = .068 in^3
maximum stress for cantelevered beam is :
s = weight x length / Z where W x l = torque???
if so, then
s = 30ft-lbs x 12in/ft / .068 in^3 = 5,300 psi
if above are correct, then this tubing is at 15% of the 35,000 yield
How do you apply safety factors??
I have little concern for the first set of 10 foot blades
which obviously have much less power associated with them
note that real tubing is closer to 1.375 diameter (slightly better specs by 23%)
If I choose 6 blades and TSR <= 5,
lowers rotation to 220rpm max but now has more torque,
BUT the force is distributed over 2x more spars (or not exactly?)
I have not accounted for the bending back of the blades towards the tower
( or have I??)
Did I miss anything obvious??
Stew Corman from sunny Endicott