- Basic .
- ..........................by .Claus Nybroe
VELOCITIES IN THE ROTOR PLANE
TIP SPEED RATIO
SELECTING BLADE CHORD AND PROFILE
this rather simple method we over the years have made very efficient
blades (Cp-max measured = 0.46). Do not be afraid of the mathematics.
There are only 6 formulas and a couple of curves. All Calculations
can be performed by hand or by the means of a pocket calculator,
a spreadsheet or another small computer programme.
paper is made as an example based on known generator data from
Ian Cummings, Putnam CT.
Ian's case we start with known generator data. Alternatively
you can also start with known wind, rotor or profile data. The
formulas are all there.
- 1. INPUT DATA
- The metric (m) system
- 1000 meter = 0.625
- Power is measured
in Watts (W)
- 1 HP = 736 W
- Ian Cummings has provided us with these approximate data:
W at 700 rpm (revolutions per minute)
- 2. VELOCITIES IN THE ROTOR PLANE
- To get a first grip
of things please have a look at
- the velocities in the rotor plane
- 3. TIP SPEED RATIO
- We start by selecting
a value for the Tip Speed Ratio (TSR) which is defined as
- (Formula 1) :
- TIP SPEED RATIO
- (tip speed of blade)/(wind
- The tip speed ratio
is a very important factor in the different formulas of blade
- Generally can be said,
that slow running multi bladed wind turbine rotors operate with
tip speed ratios like 1-4, while fast runners use 5-7 as tip
Cummings wants to cut a two bladed rotor. This rotor type usually
runs very fast, so let's choose a tip speed ratio of 7.
- 4. MATCHING FORMULAS
- The task is now to
fit the known generator capacity and revolutions to the wind
speed and to the swept rotor area. Two formulas are needed:
- (Formula 2) :
- Power (W) = 0.6
x Cp x N x A x V3
- (Formula 3):
- Revolutions (rpm) = V x TSR
x 60 / (6.28 x R)
- Cp = Rotor efficiency
- N = Efficiency of
- A = Swept rotor area
- V = Wind speed (m/s)
- TSR = Tip Speed Ratio
- R = Radius of rotor
- Rotor efficiency can
go as high as Cp = 0.48, but Cp = 0.4 is often used in this type
- This concept works
without transmission. If a transmission with an efficiency of
0.95 was to be included this means that
- N = 0.95 x 0.7
Ian Cummings case the following values fit into formula (2) and
speed ratio "TSR" = 7"
speed "V" = 8.6 m/s
efficiency "Cp" = 0.4
efficiency "N" = 0.7
rotor area "A" = 2.11 M2
of rotor = 0.82 m
= 701 rpm
output = 226 W
- It took about 20 minutes
to perform these calculations and make them match on the pocket
calculator. A simple spreadsheet can also be useful.
- 5. SELECTING BLADE CHORD AND PROFILE
- The width of the blade
is also called the blade chord. A good formula for computing
- (Formula 4):
- Blade Chord (m)
= 5.6 x R2 / (i x Cl x r x TSR xTSR)
- R = Radius at tip
- r = radius at point
- i = number of blades
- Cl = Lift coefficient
- TSR = Tip Speed Ratio
- As can be seen from
formula (4) we need to know the lift coefficient "Cl "
in order to compute the blade cord. This means that we have to
select a profile. A lot of good profile data can be found in
model airplane (gliders) literature.
have chosen the NACA 2412 profile
side facing the wind is flat, which makes the profile easy to
construct. It is an effective profile with a good thickness,
which makes the blade strong.
- In order to determine
the lift coefficient we must have a look at the profile curves.
checking the NACA 2412 profile curves Cl is determined to be
0,85. Ian Cummings formula now looks like this:
= 5.6 x 0.82 x 0.82/(2 x 0.85 x 0.82 x 7 x 7))...(m)
" = 55 mm
- Now, calculate blade
chord at 2/3 x R. On a paper choose a center line at at distance
1/3 from the leading edge. Connect the the two blade chords,
and you can measure all the cords of the blade. (Illustration)
- The closer you come
to the hub you might choose thicker profile to increase strength.
Close to the hub you should also consider an extra increase in
chord in order to make the blade start easier.
- 6. ANGLES
- Have a look at the angles of the blade
where the angles for Ian
Cummings are calculated.
- Close to the hub you
should consider an extra increase in the angle of attack, in
order to make the blade start easier.