Made a chart for newbies to understand how blades make watts

[picmacmillan]

here is a chart i made up of blade sizes in imperial and metric and also windspeed in miles per hour and what that translates into in meters per second as this is what you need to plug into the formula to understand how much power your blades can produce..Hugh states that there is another formula, but this one is more accurate and accounts for the losses incurred in a homemade blade.

          Blade Size                               Windspeed

          Feet/Meter                    Miles per hour / Meters per second

          8      2.44                        25                11.18

          9      2.74                        20                 8.9

         10      3.05                        15                 6.71

         12      3.66                        10                 4.5

         14      4.27                        9                  4.02

         15      4.6                         8                  3.58

         16      4.9                         7                  3.13

         17      5.2                         6                  2.7

                                             5                  2.24

         Formula For Estimating Blade Performance In Watts

       -Blade Power(in watts)=0.15xBlade Diameter(squared)xWindspeed(cubed)

                                                           *(cubed means to the 3rd)

  EXAMPLE:from chart above:Machine with 10' blades and 20 mph wind is as follows

              Blade Power(in watts)=0.15x3.05(squared)x8.9(cubed)

                                   =0.15x(3.05x3.05)x(8.9x8.9x8.9)

                                   =0.15x9.3x704.969

                                   =983 watts  DECENT POWER EH!

I hope this helps some newbies and maybe some others who are intimidated with the math. Just plug in your blade diameter and the wind you think you will have, and you will get how many watts your blades can produce.....pickster

[Chiron]

Is that formula for potential energy or realised?

[picmacmillan]

although all the formula's would in one way or another be potential energy because of other factors, this one has been devised to realize as quoted in hugh piggots book"The blades can only convert at best half of the wind's total power into mechanical power. In practice only about 25-35% is a more practical figure for homebuilt rotor blades.

The above formula has been devised to take in to account these percentages and as far as i can see would then be real close to realized...pickster

[johnlm]

Pic,

Since you wrote this for the newbie, You need to likely make it more clear that you are using only the metric units in your equation.  Its apparent if someone looks closely at your equation but you preface your example by stating 20 MPH and 10ft blades then jumping right into the equation with the metric equivalents.  The approximate same results are had using the equation

Watts = 0.0012 X Diameter in feet squared X mph cubed

Which is mentioned all the time.

Johnlm

[picmacmillan]

good point john...hugh suggested that we should convert it to metric as it would be more efficient...sometimes i get lost im my own madness!..thanks again johnlm..pickster

[Chiron]

Using the above formula for a z750 with a 150' blade diameter, 22MPH wind I get

0.0012 X 22500 X 10648 = 287496 or about 288kW.

The z750A with a blade radius just under 75' hits peak production at 22 MPH and I have seen it with my own eyes so it's not just a marketing claim.

That's about 38% of the actual output power. which would make the constant factor for large turbines 0.0031 instead of 0.0012.

Has anyone tried high TSR blades with variable pitch on a small turbine?

Just wondering

[Flux]

The cp of 0.15 is intended to be overall, including the alternator efficiency and matching as far as I know.  Blade output will be about double this for most home built blades.

Reasonably well made blades should easily reach a cp of 0.3.

Good blades and an efficient alternator can even manage 0.3 overall at low power but it is difficult to maintain this far up the curve with the normal arrangement optimised for cut in at low wind speed. High efficiency in the alternator results in it operating at near constant speed and the blades soon stall.

Flux

[Chiron]

We're discussing totaly different blade designs.

I wasn't implying poor design on the small fixed pitch blades, just wondering if anyone has tried variable pitch on a small machine. The weight, complexity and control drain is probably unacceptable for turbines under 5 or 10kW.

There's no "stalling" on a well designed varible pitch turbine and though the specs say 6MPH cutin there are a few that will fire up at 4 to 4 1/2 MPH and the figure of 0.0031 is at full rated power.

The power curve from 6 to 22MPH pretty much follows the Geometric curve of the available power from the wind so I suspect the effiency is pretty constant.

The gen operates at shaft speeds between 800 and 1320 RPM (20 to 33 RPM at the hub) not constant speed. No modern (1996 or later) turbine over 100 kW uses a fixed speed generator.

I'll try to get some cross section pix on the blades and you'll see what I'm talking about. The blades have no twist in the airfoil but do vary in geometry down the length.

[Flux]

Sorry if I have caused confusion, I was pointing out that the figures in Hugh's formula refer to overall power not to blade output.

I doubt if there is much data on pitch control of small machines over the range up to about 30 mph. Most operate in constant pitch up to this speed and use the pitch control to hold power down beyond this.

I also would be interested on such data if anyone has any.

Flux

[aogden]

What would be really nice is an Excel template to display a theoretical power (Watts) curve. Using the fore-mentioned theoreticl formula: Watts=Diameter squared * MPH cubed * Efficiency (where Efficiency is .0012 for nonmetric and diameter is in feet).  The MPH range could be limited on the X axis from 0-? MPH to make the curve more readable. The Y axis (dependant variable) would be power in Watts.  Please help me format this in Excel to share.  The efficiency could even be a variable and if desired one could cheeso metric or US units.  This would be really usefull in evaluating the efficiency of ones turbine system. Also see my seperate post on this subject. BTW not just usefull for newby's!