Wind turbine design tool

Priced as low as 9 euros per year, a tool to design the blades of a wind turbine shows the formulae for all calculations and provides the student with the ability to vary parameters, wing profiles etc. and experiment to see the effects on power, efficiency and mechanical forces. This tool might easily form part of an education in aerodynamics, energy conversion, physics, or mechanics as well as being used to design actual turbines intended to be built. It is particularly suited to amateur construction of the blades since blade sections can be printed to act as templates for cutting polystyrene foam sections which can later be glued together, painted and then coated with GRP. Don't try reusing propellors or fans; the airfoil is the wrong way round and the blade twist is also wrong.

The input design parameters that can be varied include:-

Windspeed, Turbine rotor diameter, Power coefficient, Mean windspeed, Tip speed ratio, Number of blades, Radius of station, Angle of attack, Lift coefficient, Drag coefficient, Airfoil , Practical limits on chord width, Center of mass/lift, Air temperature, Altitude, Air viscosity, Mean windspeed.

The built-in choice of airfoils include:-

Wortmann FX63-137, Selig S3021, Selig S2091, Selig-Donnovan SD7032, Selig-Donnovan SD7037, Selig-Donnovan SD8000, ARA-D 6%, ARA-D 10%, NACA 4412, NACA 4415, NACA 63-4-021, E59, NACA A=1.0 Mean line, NACA Reflex Mean line

The built-in choice of hydrofoils include:-

YS900, YS915, YS930, E817, NACA 641A412

The outputs of the program include a life-size on-screen plot of the blade section at any desired station radius showing the setting angle, chord width, and station radius. The on-screen plot can be dragged to fit parts of it within A4 page printing boundaries and then printed onto paper. Plots larger that the paper can be printed a bit at a time and later reassembled using the 20 alignment ticks printed with the chord line. The diagram is drawn with the wind going from bottom to top and airfoil moving from right to left. This then resembles the wing of a glider making forward progress in a shallow dive and maintaining altitude because of a rising air column. It is easier to understand the principles like this and also it fits better on screen!

Your design parameters and operating scenario are editable with a GUI and can be saved in XML format to a file (e.g ) for sharing with other users.

Other outputs include, not only an empirical estimation of the performance of the overall rotor, but also includes a detailed analysis of the force vectors experienced at the particular blade station radius. These detailed calculations at a point give a good insight as to the contribution of each radius and blade and permit (by integration) a more accurate calculation for the whole rotor and give clues as to how to improve it. These detailed calculations also give validation of the formula used to calculate the chord widths and setting angles in the first place.

The "Reports" menu item gives sample output showing workings of contributions for one station on one blade, with some piecewise numerical integration at the end showing the total bending force at this station and showing that the whole rotor will generate 406 Watts:-

(Source of some equations is "Windpower Workshop" ISBN 1 898049 13 0)
Variable Symbol Units Value=formula
Pi pi none 3.141592653589793
Density of fluid rho kg/m^3 1.2 (air=1.2, water=1035)
Dynamic viscosity of fluid mu kg/m/s 1.7894E-5 (air=1.8*10^-5, water=1*10^-3)
Kinematic viscosity vee m^2/s 1.4911666666666666E-5=mu/rho
Power coeff Cp none 0.2 < 0.6
free flowspeed V m/s 5.0 about 10
Diameter D metres 4.0
Yield Strength Py MPa 60.0
Beam skin thickness St metres 0.0060
Youngs modulus E GPa 12.6
Empirical Power P watts 188.49555921538757=Cp*(rho/2)*(pi/4)*(D^2)*(V^3)
Mean flowspeed Vm m/s 3.0 about 5
Empirical Mean power Pm watts 60.480000000000004=(rho/1.2)*0.14*(D^2)*(Vm^3)
Tip speed ratio tsr none 6.0 about 6
Shaft speed rpm rpm 143.2394487827058=60*V*tsr/(pi*D) (=15.0 radians/s)
Radius (station) Rs metres 0.5 <2.0
rFactor (station) rFactor none 0.25 between 0.0 hub and 1.0 tip
foil Wortmann FX 63-137
normalised hollow foil CG CG fraction of Cw ( 0.4857722337986354 , 0.043304043079590473 ) center of gravity (x,y projection)
normalised solid foil CG CG fraction of Cw ( 0.38907052676915505 , 0.04843257006300894 ) center of gravity (x,y projection)
Center C fraction of Cw ( 0.33 , 0.045 ) chosen center (x,y projection)
MidLineYAtX Cy fraction of Cw 0.05491636363636365 y coord at camber midline at chosen x
normalised foil perimeter Lp fraction of Cw 2.1124356556075714 perimeter of section (x,y projection)
normalised foil area Abn fraction of Cw^2 0.12778071034620397 area of section (x,y projection)
No. of blades B none 2.0 3 is best
AccelerationFactor Cacc none 0.3333333333333333 1/3 is normal for Betz max capture, 1.3 for props
far wake flowspeed Vfour m/s 1.6666666666666665=V*Cacc
flowspeed (at rotor) Vrot m/s 3.333333333333333=(V+Vfour)/2
Acceleration pressure needed Facc Kg/m^2 -1.3591573224600746=rho*Vrot*(Vfour-V)/9.81 (negative is normal for turbines) (=-13.333333333333332 Pascals or N/m^2)
Rotor swept area A m^2 12.566370614359172=Math.PI*diameterm*diameterm/4.0d
Rotor thrust for Facc Froter kg -17.079674637253376=Facc*A
Power one Pone Watts -558.5053606381854=Frotor*Vrot*9.81
Power two Ptwo Watts 558.5053606381854=rho*Vrot*A*(V^2-vFour^2)/2
Power three Pthree Watts 942.4777960769379=rho*A*V^3/2
Power four Pfour Watts -837.7580409572781=Frotor*V*9.81
PressureFactor Cf none 1.0 (sum of Cf for multistages should be 1.0 e.g (-1, +2) or (0.5,0.5))
INFO turbine mode (generates power)
Speed (station) Vs m/s 7.5=V*tsr*2*Rs/D
Inflow swirl angle (station) itheta degrees 0.0 positive is opposite to blade rotation
Inflow swirl tan. vel. (station) Vtan m/s 0.0=Vrot*SIN(itheta/57.3) positive is opposite to blade rotation
Induced velocity factor (station) ivf none 0.1 positive is opposite to axial flow direction
Induced angle of attack (station) ai degrees -2.161238676351317=relative windangle with induction - rel wind ang excluding induction
Equiv induced drag coeff (station) Cdie none 0.05656767942141725=Cl*SIN(-ai/57.3)
Relative flowspeed (station) Vrs m/s 8.077747210701755=SQRT(Vrot^2+(Vs+Vtan)^2)
Lift coeff Cl none 1.5 (0.5 to 1.5)
Drag coeff Cd none 0.02 (0.01 to 0.14)
Moment coeff Cm none -0.27 twisting moment coeff at 0.25 chord (-0.3 to 0.0)
Center of pressure Cf fraction of Cw 0.43000000000000005 =0.25-(Cm/Cl)
Angle of attack alpha degrees 7.0 (0 to 7)
Relative flow angle gamma degrees 21.803015408538506=ATAN(Vrot/(Vs+Vtan))*57.3
Setting angle beta degrees 14.803015408538506=gamma-alpha
Chord width Cw meters 0.38411793265705246=ABS((Cf*Vrot*(Vfour-V)*2*pi*Rs)/(COS(gamma/57.3)*Vrs^2*0.5*B*Cl))
Practical chord limit CwMax meters 0.25 limit of paper or plank size
Limited chord width Cwl meters 0.25=MIN(Cw,CwMax)
Hugh's width Hw meters 0.24170370133727231=Cwl*COS(beta/57.3)
Hugh's drop Hd meters 0.06386956051095598=Cwl*SIN(beta/57.3)
Hugh's thickness Ht meters 0.05262415677401619=Cwl*foil_thickness_fraction
Aspect ratio (station) As none 16.0=D/Cwl
Vortex induced drag (Cdi) does not exist
Profile drag (station) Cd none 0.02 for infinite aspect ratio
Total drag (station) Cdt none 0.02=Cd+Cdi
Limited reynolds number Rel none 135426.6325701647=(rho/mu)*Vrs*Cwl
Lift (station) Fs kg/m 1.4965596330275226=(Vrs^2*Cwl*rho*0.5*Cl)/9.81
Drag (station) Fd kg/m 0.019954128440366967=(Vrs^2*Cwl*rho*0.5*Cdt)/9.81
Generating force (station) Fg kg/m 0.5372813511705296=(Fs*SIN(gamma/57.3)-Fd*COS(gamma/57.3))
Change of swirl angle (station) dtheta degrees 21.141381997595577=atan(Fg*B*9.81/(2*pi*Rs))/(rho*Vrot^2))*57.3 positive is opposite to blade rotation
Outflow swirl angle (station) otheta degrees 21.141381997595577=theta+dtheta positive is opposite to blade rotation
Generating torque (station) Tg kg 0.2686406755852648=(Fg*Rs)
Flow retarding force (station) Fr kg/m 1.3969315130433766=(Fs*COS(gamma/57.3)+Fd*SIN(gamma/57.3))
Flow retarding pressure (station) Frp kg/m^2 0.4446571109233877=Fr/(2*pi*Rs) (=4.362086258158434 Pascals or N/m^2)
Net generating power (station) Pg Watts/m 39.530475412371715=Fg*9.81*Vs
Lost eddy power (station) Pe Watts/m 1.5812190164948683=Fd*9.81*Vrs
Wing loading (station) Ls kg/m^2 5.98623853211009=Fs/Cwl (=58.72499999999999 Pascals or N/m^2)
G force (station) Gs none 11.46788990825688=((Vs^2)/Rs)/9.81
Centrifugal pressure (station) Fcps Kg/m^3 13.761467889908257=Gs*rho
Static pressure (station) Fps Kg/m^2 -3.9908256880733934=-(((Vrs^2)*rho)/2.0)/9.81 (=-39.14999999999999 Pascals or N/m^2)
IntegrationLowerLimitFactor Cr0 none 0.0 (fraction of radius 0.0(hub) to 1.0(tip))
IntegrationUpperLimitFactor Cr1 none 1.0 (fraction of radius 0.0(hub) to 1.0(tip))
IntegrationLowerLimit r0 meters 0.0=Cr0*D/2
IntegrationUpperLimit r1 meters 2.0=Cr1*D/2
Tension member radius factor tmrf none 0.0 fraction of radius at which tension member attached
Tension member angle to blade tma degrees 90.0 angle of tension member to blade
Force normal (at tension member) Ftmn N 39.93591157896826=as required to give zero total moment (in thrust) at hub
Force tension (at tension member) Ftmt N 39.93591184626228=Ftmn/(sin(tma/57.3))
Force compression (at tension member)Ftmc N (6.121151060996588, 39.93591157896826, 0.0)=Ftmn/(tan(tma/57.3))
Bending moment (thrust station) Bsy Nm 70.65000787631308=Integration(Fr*(r-Rs) forall r>Rs)*9.81
Bending moment (gen station) Bsx Nm 7.77221090070569=Integration(Fg*(r-Rs) forall r>Rs)*9.81
Bending moment (weakest dir station)Bsw Nm 70.29110439055539=Bsx*sin(beta/57.3)+Bsy*cos(beta/57.3)
Bending moment (thrust no tension mem)BsyoldNm 70.65000787631308=Integration(Fr*(r-Rs) forall r>Rs)*9.81
Normalized Bending m. (thust station)Bnsy N/m 5370.15790521492=Bsy/(Cwl*Ht)
Normalized Bending m. (gen station)Bnsx N/m 590.7713397922463=Bsx/(Cwl*Ht)
Normalized Bending m. (weakest dir station)BnswN/m 5342.877393164234=Bsw/(Cwl*Ht)
Normalized Bending m. (thrust no tension mem)BnsyoldN/m 5370.15790521492=Bsy/(Cwl*Ht)
Square beam side length m. (thrust station)Sbslym 0.01400892650700429=sqrt((Bsy)/(Py*St*10^6))
Square beam side length m. (gen station)Sbslxm 0.00464644753808568=sqrt((Bsx)/(Py*St*10^6))
Square beam side length m. (weakest dir station)Sbslwm 0.013973298384831792=sqrt((Bsw)/(Py*St*10^6))
Square beam side length m. (thrust no tension mem)Sbslyoldm0.01400892650700429=sqrt((Bsy)/(Py*St*10^6))
Beam deflection m. (no tension mem)Sbdold m 0.1512185912330578= very complex
Integrated centrifugal pressure (tip)Fci Kg/m^2 55.045871559632985=Integration(Fcs forall Rs) (=539.9999999999997 Pascals or N/m^2)
Integrated friction surface area Absi m^2 1.650568394312961=total surface area all blades all sides
Integrated volume (rotor) VOLbi m^3 0.02319121701229698=total blade volume all blades
Integrated gen power (rotor) Pgrotori Watts 406.49248162246596=B*Integration(Pg forall Rs)
Integrated turbine Cp (rotor) Cpi none 0.43130191853271255=Pgrotori/powerThree
Integrated thrust (rotor) Froteri Kg 16.283755995501828=B*Integration(Fr forall Rs) (=159.74364631587295 N)
Integrated torque (rotor) Troteri Kgm 2.7624361646107083=B*Integration(Tg forall Rs) (=27.09949877483105 Nm)

You can make a polystyrene foam cutter using my instructions.
If you want to carve a blade in one piece from solid wood instead of foam sections, then you need Hugh Piggot's book "Windpower Workshop" and you can use the "Hugh's width, drop, thickness" parameters output above to apply to his cutting method.

If you fancy building a vertical axis wind turbine rather than the standard horizontal axis, then the software is still useful for calculating reynolds numbers, rpm, G-force and plotting airfoils but the theory of vertical axis wind turbines is very different.

There are detailed tutorials for using the turbine blade design module.

This wind turbine blade design tool is implemented and is available to members of Club Cycom.