Stewart Corman
1st March 2008, 21:48
Well folks, I have been perturbed for quite a while about the fact that the old Jacobs, the Bergey Excel and now DaveB's 18 footer "Wincharger" behave so decently in spite of the fact that they all have constant cord width. I think I just found out why!
I knew my original xls file had bogus simplistic equations to calculate lift and drag, so I bit the bullet and spent some real time playing mental masterbation.
I cannot attach my latest incarnation of the calculator with the enhancement of a double regression curve fitting to the JavaFoil polar plot data because it is too large to be uploaded here
if you want a working version,
try to download xls from here:
http://www.otherpower.com/images/scimages/7526/turbine_RE_.xls
For those not into the math:
A simplistic overview is that for a given airfoil shape, like the NACA4425 I chose, JavaFoil performs an analysis of lift (Cl) and drag (Cd) for a set of AOA at each of different Reynold's numbers ( related to speed across an airfoil width). Since my caculator lets you plug in turbine diameter, TSR and WS ..the numbers for AOA and RE# calculated are never what is exactly on the chart ..so a math function has to "guesstimate" the inbetween numbers.
there is a screen shot of what it looks like at bottom here
there is also a diagram of what real "lift" is, and it is my bone of contention that L/D ratio doesn't tell the right story ..there is an angle involved here and it is NOT the AOA, but rather the incident angle of the apparent wind.
Both the lift and drag get "projected" onto the horizontal axis which is the direction of rotation. This has been added to my spreadsheet as "net lift" where the equation is on that chart as below.
Net lift = L sin(phi) -D cos(phi) where phi = appar wind Angle
Any lift that is greater than zero, will give torque to the turbine rotor.
This is NOT true for airplane calculations to keep an airplane from falling out of the sky. Soooooo, if you look at the chart numbers, you can compare lift at five different stations along the blade for three configurations:
1) 3:1 taper non-twist 3 to 9 inches
2) constant cord 6 inches
3) 3:1 taper with 12 degrees of twist
if you look at the "net lift" numbers, you see that twist lowers drag near root, but kills lift near the tip
constant cord is actually the best here, because if lift is a force, then force x lever arm = torque and it has more lift near the tip
quick note: the twist section allows you to choose any linear twist ...make it zero and you get the same as the top section
I have NOT played around with this long enough to fully determine under what conditions each will be a better performer, but in low WS, low RE# becomes a problem as lift Cl starts falling fast ...so a tapered blade is probably the most advantageous for large mills in low WS
Caveat Emptor - There may be errors in my calcs...and with this dataset, you can't have RE# higher than 300K or so, or the approximations go haywire, so you can't throw in high WS
Stew Corman from sunny Endicott
I knew my original xls file had bogus simplistic equations to calculate lift and drag, so I bit the bullet and spent some real time playing mental masterbation.
I cannot attach my latest incarnation of the calculator with the enhancement of a double regression curve fitting to the JavaFoil polar plot data because it is too large to be uploaded here
if you want a working version,
try to download xls from here:
http://www.otherpower.com/images/scimages/7526/turbine_RE_.xls
For those not into the math:
A simplistic overview is that for a given airfoil shape, like the NACA4425 I chose, JavaFoil performs an analysis of lift (Cl) and drag (Cd) for a set of AOA at each of different Reynold's numbers ( related to speed across an airfoil width). Since my caculator lets you plug in turbine diameter, TSR and WS ..the numbers for AOA and RE# calculated are never what is exactly on the chart ..so a math function has to "guesstimate" the inbetween numbers.
there is a screen shot of what it looks like at bottom here
there is also a diagram of what real "lift" is, and it is my bone of contention that L/D ratio doesn't tell the right story ..there is an angle involved here and it is NOT the AOA, but rather the incident angle of the apparent wind.
Both the lift and drag get "projected" onto the horizontal axis which is the direction of rotation. This has been added to my spreadsheet as "net lift" where the equation is on that chart as below.
Net lift = L sin(phi) -D cos(phi) where phi = appar wind Angle
Any lift that is greater than zero, will give torque to the turbine rotor.
This is NOT true for airplane calculations to keep an airplane from falling out of the sky. Soooooo, if you look at the chart numbers, you can compare lift at five different stations along the blade for three configurations:
1) 3:1 taper non-twist 3 to 9 inches
2) constant cord 6 inches
3) 3:1 taper with 12 degrees of twist
if you look at the "net lift" numbers, you see that twist lowers drag near root, but kills lift near the tip
constant cord is actually the best here, because if lift is a force, then force x lever arm = torque and it has more lift near the tip
quick note: the twist section allows you to choose any linear twist ...make it zero and you get the same as the top section
I have NOT played around with this long enough to fully determine under what conditions each will be a better performer, but in low WS, low RE# becomes a problem as lift Cl starts falling fast ...so a tapered blade is probably the most advantageous for large mills in low WS
Caveat Emptor - There may be errors in my calcs...and with this dataset, you can't have RE# higher than 300K or so, or the approximations go haywire, so you can't throw in high WS
Stew Corman from sunny Endicott