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Victor Reijs' workflows

Victor Reijs' workflows by Victor Reijs is licensed under CC BY-NC-SA 4.0

Introduction

Remember this web page is indicative/provisional; the findings are still under investigations, verification and trying to finalise things. So no rigths can be gotten from it;-)

• DHM formula
  That formula is not being evaluted on this web page, as it does not provide an absolute or relative result. It gives a yes or no if a single obstacle causes a speedfactor below a certain value (95 or 90%).
  
• Inspired by Steve Temple's method
  Of the obstacles their Intercept height (IH) at the mill are determined. Using these Intercept heights in a logarithmic ABL. Two sub methods are used to determine SpeedFactor
  
• Using Evert-Jan Laméris' method
  The obstacles' height above H_DMH is determined. Adding these above H_DMH heights together gives and idea of the lossfactor. After normalising them one can derive a kind of SpeedFactor (1-lossfactor/normalisation).
• Inspired by VR's speedfactor formula
  The linear speedfactor formula is derived from Beljaars' tables.
• Using the experimental data of Nageli
  The exponential speedfactor formula based on Nägeli's result of Dichte Wand.
• Using Ezra van der Elst's method
  The exponential speedfactor formula based several theories and experiments.
  

General idea of the VR workflows

For each 1deg direction (from 0 to 360deg in steps of 1deg) the (midpoint, average, minimum or maximum [default]) height of a DSM 'segment' at a certain distance from the mill is determined (based on DSM). This provides height profiles (each of 1deg) from the mill to the border of a circle (in test environment max. 400m). One can determine the z_0m using Davenport&Wieringa [2000, TABLE 2]:

And here the text is converted to a graph for solid obstacles:


For each above mentioned methods, the following is done:

• Inspired, as a basis, by Steve Temple's method and logarithmic ABL
  
• From this height profile (heights are increased with an effective height factor: C_eh [called C_d by ST]), several individual obstacles are being recognised for which the Intercept height (IH) at the mill is determined (in the test environment a linear Wake decay rate of 50 is used and no distinction between house or tree). Two sub methods are used:
  
• aVR_abl[#obstacles,C_eh,ap,z_0m]
  Using the obstacles' Intercept Heights (excl. C_eh), the product of speedfactor is determined by an logarithmic ABL.
• aVR_st[#obstacles,C_eh,ap,z_0m]
  Using upto 11 obstacles sorted with Intercept Heights (incl. C_eh), the speedfactor is determined using the stacking ABL function coded by Steve Temple [Temple, 2025]).
• The Speedfactors of ten profiles (each of 1deg) are averaged into a (10deg) sector.
  
• Using, as a basis, by Evert-Jan Laméris' method (rVR_ejl[SF])
  From this height profile, individual obstacles are being recognised for which the above H_DMH height at the mill has been determined (in the test environment a linear Wake decay rate of 50 and c=0.15 is used). Adding in each 1deg profile these above H_DMH heights together gives an idea of the SpeedLoss.
  The lossfactor of ten profiles (each of 1deg) are averaged into a (10deg) sector. After normalising them, one can derive a kind of speedfactor (1-lossfactor/normalisation). This speedfactor is not an absolute value yet, so not 100% comparable with SpeedFactor. For comparing with other speedfactor methods, one can only look at the whole form of the curve.
  
• Inspired, as a basis, by VR's speedfactor formula (aVR_belj[SFmulti,z_0m])
  From this height profile, individual obstacles are being recognised for which the speedfactor at the mill has been determined (a variable but lineair Wake decay rate is used). The speedloss formula is derived from Beljaars tables.
  The speedfactor of ten profiles (each of 1deg) are averaged into a (10deg) sector. One can derive a kind of speedfactor by multiplying each speedfactor at all distances over the radius. This speedfactor should be close to an absolute value, but the there is a Speedmultiplier (for high speedfactors = 3) which migth need alignment. So, it might not be 100% comparable with SpeedFactor, but it should be close.
• Inspired, as a basis, by Nägeli (aVR_nag[C_l,z_0m])
  From this height profile, individual obstacles are being recognised for which the speedfactor at the mill has been determined (an exponential Wake decay rate is used). In this implementation, the SpeedFactor formula is derived from Nägeli 'Dichte Wand' (which has an optical porosity of 10-15%), by using/interpolating the below colored curves (C_l=1):
  
  The speedfactor of ten profiles (each of 1deg) are averaged into a (10deg) sector. One can derive a kind of speedfactor by multiplying each speedfactor at all distances over the radius. This speedfactor should be close to an absolute value. It migth be that C_l needs alignment.
  Nägeli is by the way independent of z_0m (it has a fixed 0.03m), a factor K_n (called by EvdE: K) has been added to include this dependability.
• Using, as a basis, Ezra van de Elst's method (rVR_evde[z_0m])
  This method is based on several theories including Jensen's theory on wind turbines [1983] and Nägeli (wake behind a fence), resulting in an exponential decay of the wake.
  From this height profile, individual obstacles are being recognised for which the above H_EVDE height at the mill has been determined using a speedfactor =1. Adding in each 1deg profile these above H_EVDE heights together gives an idea of the SpeedLoss.
  The lossfactor of ten profiles (each of 1deg) are averaged into a (10deg) sector. After normalising them, one can derive a kind of speedfactor (1-lossfactor/normalisation). This speedfactor is not an absolute value yet, so not 100% comparable with SpeedFactor. For comparing with other speedfactor methods, one can only look at the whole form of the curve.
  
• For all methods: A weighted (using normal distribution) average is then used over five 10deg sectors. These weighting maps the normal distribution of wind directions in actual wind. The weighted average gives an idea of the Speedfactors (reduction of the wind in that sector direction).
  Remark: The weighting of anemometer readings still needs some though.
  
• From this the powerfactors-radar can be determined (SpeedFactor³). Both, speed and power, are presented in graphs in Excel.
  Important to understand that the powerfactor-radar is not a good indication of the Effective Usable Energy (EUE: one needs to include the windrose).
  
• In a seperate spreadsheet an indication of the EUE (Effective Usable Energy) is given. The type of sail system determines the efficiency (C_e) of the sails.
  

Conditions

It is important to realise that methods based/related on the DHM formula or Beljaars tables have the following constrains:

• Distance X should be longer than the cavity boundary (X  > 15*H) (Beljaars, page 12); and H larger than 10*z_0m (Beljaars, page 15).
• H should not be larger than 2.5*z (for 90%) or 3.5*z (for 95%) (Beljaars, Figure 5.1).

Trees in the neighbourhood of the mill are difficult to simulate using DHM formula. Be aware of this!

Differences between methods

Methods start with r(elative) are relative to something (unknown). As it are not absolute values, one could compress or enlarge (aka normalise) these curves for comparing with a(bsolute) curves.

Method	Based on	Reference	Arithmatic	Knobs	Ceh	c	wake decay	n
aST	Stacked ABLs	Absolute	ABL(IHi)	Ceh,ap,n,z0m	1.4	NA	linear	50 (95%)
aSTanemo	wind	Absolute	U/Uref	scale,z0a	NA	NA	NA	NA
aVRst	Stacked ABLs	Absolute	ABL(IHi)	Ceh,ap,n,z0m	1.4	NA	linear	50 (95%)
aVRabl	Multiply ABLs	Absolute	ABLIHi	ap,n,z0m	1	NA	linear	50 (95%)
rEJL	DHM	Relative	HDHMi	c,n,z0m	1	0.2 (95%)	linear	50 (95%)
rVRejl	DHM	Relative	HDHMi	SF,n,z0m	1	0.2 (95%)	linear	50 (95%)
aVRbelj	Inverse DHM	Absolute	SFVRi	SFmulti,n,z0m	1	(1-SpeedFactor)*3	log function on H/z0m	depending on H/z0m (95%)
aVRevde	exp	Relative	Hbouwi	z0m	1	NA	exponential	NA
aVRsmanemo	wind	Absolute	U/Uref	scale,z0a	NA	NA	NA	NA
aVRCFD	simulation	Absolute	RANS	many	NA	NA	NA	NA
aAEGMCFD	simulation	Absolute	RANS	many	NA	NA	NA	NA
aVRnag	exp	Absolute	SFNagi	Cl,z0m	1	NA	SF(0), SFmin and SF(X)=linear and exponential	NA

VR workflow

Get a DSM of an area around the wind mill.

• Preferable 400m in radius (as that is the recommended radius for DHM-formula). A resolution of 1m in N-S and E-W direction sounds enough.
  
• Download a GeoTIFF: preferrable first echo from a DSM service:
  • The UK DSM is here (e.g. lidar_composite_first_return_dsm-2022). To get the coordinates of the mill, use Google Earth and OS Maps (UK Ordnance Survey grid).
  • The Dutch DSM is here (AHN-4). To get coordinates of the mill, use RD coördinaten
  • The German DSM is here (bDOM20). To get coordinates of the mill, use ETRS89/UTM (and correct zone, as described in the meta data of bDOM20: e.g. [EPSG:]25832 [which is ETRS89/UTM zone 32])
    
  • Get Grid North or (meridian)convergance for UK maps and Dutch maps and German maps
    
• Make a DSM csv by using an application to convert GeoTIFF [tif] into csv (a small R program [GeoTIFFtoCSV.R] has been made to do this).
  Important: Make sure that the mill is in the centre of the resulting CSV.
  The csv file has the following setup:
  
  • column 1 (A in Excel): The North-South coordinates [m]
    
  • row 1 (1 in Excel): The West-East coordinates [m]
  • content first diagonal cell (B2 in Excel): The name of the mill
  • content second diagonal cell (C3 in Excel): Meridian convergance [deg]
    
  • Size of the csv matrix at this moment: max 800 rows, 800 columns
  This can take some time; downloading the GeoTIFF and then converting: some 5hour/location of 800*800m.
  Remark: This is likely due to inefficient coding of the raster package. Might try terra (of same authors)
  
• Workflow in Excel (takes some 90sec for a circle with radius 400m for all methods, while all methods except  aVR_st take 30sec):
  
• an Excel table to determine for a direction:
  
• the height profile;
• the z_0m;
  
• the individual obstacles;
  Check the heigtht of ground level (certainly when long and wide obstacles [woods, housing blocks, etc.])
  
• Intercept height of upto 11 obstacles at the mill (aVR_st);
  
• sum of H_DHM heights (rVR_ejl);
  
• product of speedfactors (aVR_abl, aVR_belj and aVR_nag).
  
• for aVR_st: a pivot table to sort on Intercept heights
• the CTRL_SHIFT_M macro to generate the speed- and powerfactor-radar (with 1deg segments, averaged into 10deg sectors)
• present the weighted 10deg sectors for SpeedFactor and Powerfactor.
  
• Te Effective Useable Energy (depending on the actual wind rose at the mill) can be determined.

Further steps

• Include this data in the Excel spreadsheet (in the workbook DSM). The mill is in the middle of the picture.
  

  	Impington, UK	Fosters Mill, UK	Upminster, UK	De Hoop, NL	Rijn en Lek, NL	De Zwiepse Molen, NL	Makkinga’s Mölle	Labbus, DE
  DSM
  Intercept height > Mill height
  Size DSM	800*800m	500*500m aSTanemo measurements are in wintertime	800*800m	500*500m	500*500m	500*500m	800*800m	800*800m

  
  
• Default parameters used for each mill:
  
  
• Determine the height profile in the speedfactor-radar of 360deg (in steps of 1deg). Impington's and Makkinga’s Mölle's example for the close to North direction (blue line) and including the automatically detected obstacles (yellow dots: effective heights) and significant Intercept heights at mill (red crosses):
  

  Impington, UK	Makkinga’s Mölle, NL

  
  This is automated by a macro (CTRL_SHIFT_M) for the whole speedfactor-radar (directions of 0deg to 360deg in steps of 1deg) and averaging them into 10deg sectors with a weighted averaging over 5 neighboring sectors.
  
• The macro (CTRL_SHIFT_M) makes a radar of the SpeedFactor and Powerfactor for this VR_xxx methods:
• orange-dashed based on ST method: aVR_st best match with aST: ap=0.6 (aerodynamic porosity, called by ST: C_p) and C_eh=1.4 (effective height, called by ST: C_d) for upto 11 obstacles;
  
• orange-dotted based on ST method (using all obstacles): aVR_abl
• black-dashed based on rEJL method (using all obstacles): rVR_ejl
  
• red based on VR speedfactor method (using all obstacles): aVR_belj
• blue based on Nägeli's graph (using all obstacles): aVR_nag
• The aligning of results has been done as follows:
• An alignment in the major wind direction (SW) is prioritised
  
• If CFD simulations or anemometer measurements available: the other methods were aligned in such a way that all results were within a range of 20%.
  This 'forces' the standard deviation (1sigma) to around 4%.
  
• If no CFD simulations or anemometer measurements available: the method that has the least less-deterministic 'knobs' is used as reference: aVR_st.
• Method that only provide relative results (rEJL method and rVR_ejl) were normalised in such a way that the min and max matched the min and max of the other curves. Be aware of this normalisation!
  
• Comparison (if available) with: aST (orange; using 2 obstacles), aST_anemo (green dashed), rEJL (black), aAEGM_CFD (yellow), aVR_CFD  (green), aVR_smanemo (orange crosses; using smartmolen).
  <right click a picture, to see a larger version in another browser window>
  Remember the powerfactor is ONLY looking at the physical environment, it does not include the actual wind at location (windrose). When including the windrose, the picture changes considerable!
  

  Factor	Impington, UK	Fosters Mill, UK	Upminster, UK	De Hoop, NL	Rijn and Lek, NL	De Zwiepse Molen, NL	Labbus, DE
  Speed factor for 400m radius
  Power factor for 400m radius
  Remarks	mp @ anemometer height There is an optimum by shrinking aST with 10deg; 20deg shrinking was seen when evaluating CFD against aST.	mp @ anemometer height No shrinking angle for aST is relevant.	mp @ anemometer height	mp @ windshaft height rEJL data is here rEJL is based on old AHN-1	mp @ anemometer height	mp @ windshaft height rEJL data is here rEJL is based on AHN-4	mp @ anemometer height

• In the above speedfactor graphs there are still differenc eun explained (for instance aVR_na for Rijn en aVR_nag and aVR_belj  Lek and De Hoop compared to aVR_st). Reason(s) still unknown
  Remark: something to find out.
  

Some considerations/improvements

• If one uses a DTM (Digital Terrain Model) instead of a DSM (Digital Surface Model), one should see a SpeedFactor=1 (as there are no buildings/trees) using any model:
  
• aST (orange curve) used 2 obstacles in his Excel. Below one can see the difference between 2, 3 and 11 obstacles using aVR_st (orange-dashed curves):
  

  #Obstacles	Impington, UK
  11 obstacles used in aVRst
  3 obstacles used in aVRst
  2 obstacles used in aVRst

  
  
• If we change the height of the measurement point at Upminster and Impington; at height of tip top sail, around shaft height); to bottom of the down sail we seen the following differences:
  

  Height (mp) measurement point	Upminster, UK	Impington, UK	Rijn en Lek, NL
  +6.75m
  windshaft @ 15m, 15m, 22m
  -6.75m
  All heights @ direction 235deg

  For all methods the speedfactor has been lowered for a lower measurement point height (as expected). Each method and each mill though reacts slightly different (remember the bottom graphs show a direction fo 235deg only):
  
  • For Upminster: aVR_nag & aVR_st & aVR_abl look to stay close to each other.
    
  • For Impington: aVR_belj & aVR_st & aVR_abl look to stay close to each other.  And are not far from aVR_CFD.
    
  • For Rijn en Lek: aVR_nag & aVR_belj & aVR_st & aVR_abl look to stay close to each other. 
  The range is mostly with 20%.
  
• A test with z_0m fixed or variable per segment:
  

  Impington, fixed z0m	Impington, variable z0m

  A difference for some sectors of around 10%.
  
• A test is being conducted by removing and adding obstacles (so future and past areas can be simulated). Some results are here around Makkinga’s Mölle and De Hoop:
  

  Trees	Makkinga’s Mölle, NL	De Hoop, NL
  With currrent tree(s)
  Without tree(s)
  Remarks	There is only a small difference due to the 19m tree around 23m in 200deg.	There is only a small difference due to the some 12m high trees around 50m in SW

  
  
  

Conclusions

• Underlaying DSM data:
  
• The AHN-4 data for rEJL curves map better other methods than the AHN-1 data.
• One can add or remove obstacles (by simple editing the CSV file in Excel).
• As a DSM is based on grid coordinates (northing and easting), one needs to include compensation of Grid North.
  
• Power or Speed
  
• When looking at the powerfactor, the differences between the methods becomes larger/clearer (this because power is speed³)
• See how low the PowerFactors are for all mills in the WS direction (the most general wind direction). This shows how deteriorated the mill's possible production has gotten.
• One can see that the EUE (so including the actual windrose) is totally different then the powerfactor-radar.
  
• A function to determine the EUE: Effective Useable Energy on the wind shaft ([un]leafed, possibility of turning [losses&safety; depending on windspeed reported by METeo or by mill's anemometer], working hours, function [without toll, grinding, sawing]) is implemented, based on above (leafed or unleafed) speedfactors; and the speed and angle distribution ((over a period of 25 years, using Open-Meteo at a 9km grid).
  Remark: No Weibull distribution is needed as the distribution is derived from Open-Meteo.
  
• An example of a graph displaying the speedfactored speed [m/sec] and angle [deg] distribution at Impington:
  

  Number of hour blocks per sector with a certain speed	EUE per sector

  
  With: EUE [W] = 0.5 C_e ρ π R² V³, where C_e is the efficiency factor (for traditonal wind mill sails around 0.1 [Prinsenmolen-Committee, 1958, Fig. 32], and for Russian sails [somewhat closer to Billau] it is around 0.3 [Prinsenmolen-Committee, 1958, Fig. 36]), ρ is air density [1.225 kg/m³], R is the sail stock length [m] and V is the wind speed [m/sec].
  Calculatiing the EUE using the speedfactored wind speed for each sector and the useable hour blocks in a year; one gets the EUE in kWh per year.
  The power loss (P_situation1/P_situation2) is independent of C_e or R; only of the different V for each situation.
  Also an evaluation at De Hoop has been done (with and without trees).
• One can see that the EUE (so including the actual windrose) is totally different then taking the powerfactor-radar.
• Impington and Foster as in-situ reference:
• It has the most data (calculated or measured); aST, aVR_CFD, aVR_smanemo, rVR_ejl, aVR_belj, aVR_nag, aVR_abl and aVR_st. So this mill's data will for now be used as a kind of benchmark.
  
• Using 3 obstacles instead of 2 can decrease the SpeedFactor by some 10%. Increasing the number of obstacles (max.11) this gives an additional 5% increase at some directions.
• aVR_st and aST are similar for Impington but not for Fosters Mill.
  aST does not have trees in the North-East and South-East corners for Fosters Mill. This might be a/the/one??? reason.
• Absolute and relative SpeedFactors:
  
• The speedfactors rVR_ejl, aVR_belj, aVR_nag, aVR_abl and aVR_st have the same shape of curve.
• For absolute Speedfactors, for a radius of 400m the SpeedFactor can be some 5% lower than for 250m around the mill.
• R(elative) Speedfactor methods (such as rVR_ejl) are more difficult to compare. The shape of the curves though looks ok, except for De Hoop (but that one is using the old AHN-1).
• Aligning knobs:
• The following method priority has been given to get a benchmark alignment based on Impington enviroment:
1. Anemometer measurements (aST_anemo and aVR_smanemo) with meteorological wind data (Open Meteo)
2. aVR_CFD simulation
   
3. aST formula (as it has it been matched in anemometer measurements).
• The methods were aligned based on minimising the average difference with aVR_st. This gives the standard deviation (1sigma) is 1 to 14% (average 5%).
• z_0m is depending on the wind direction (aka windward built-up area).
  The maximum difference between a well chosen average z_0m and an z_0m depending on the segments is around 10%.
  
• EvdE talks about a K_n somewhere between 5 (within built-up area) and 9 (outside built-up area). If mapping aVR_nag on aVR_st this needs in my function a K_n between 3.5 and 9. A relation with z_0m can be established: K_n = -10.465 * z_0m + 10.18 (looking at 8 mills).
  So is K_n really an orthogonal knob? On this web page it is decided that it only depends on z_0m.
• Comparing to aVR_st:

• aVRst	aVRbelj	aVRabl	aVRnag
  ap=0.6	SFmultiplier=2 - 4	ap=0.6	Cl=1.7 - 3.8
  Ceh=1.4	Ceh=1	Ceh=1.4	Ceh=1

  
  
• The standard deviation is between 1% and 14% (average 5%) after optimising the knobs (SFmultiplier, C_eh, C_l, ap).
• The aVR_st needs a Aerodynamic Porosity (ap) of 0.6 (for all obstacles, can't distinguish yet) to map more or less aST. The ap should be around 0 (houses) and 0.6 (trees) according to Temple [2025, chapter 3].
• The aVR_st at Impington needs an Effective Height coefficient (C_eh, due to the displacement zone) of 1.4 (for all obstacles, can't distinguish yet) to map more or less aST. The C_eh should be around 1.5 (houses) and 1.3 (trees) according to Temple [2025, chapter 3]. Some poeple talk about Effective height coefficient between 1.5 and 3; is this the vertical momentum exchange values between 1.5 and 3 [Hertwig, 2019, page 263]?
  Remark: Is Effective Height coefficient same as Vertical momentum exchange (−u'w') value? I don't think so.
  
• If using DHM formula, simulation or in-vivo speedfactor-radars (like aVR_CFD, aVR_belj, rVR_ejl and aVR_nag) the C_eh = 1; as the DHM formula, simulation and experiment include the effect of the displacement zone.
  
• The aVR_abl is close to aVR_st. Also both speedfactors are similarly depending on the number of obstacles.
  Remark: aVR_abl needs to be verified theoretically.
• The variability of the knobs can be explained by:
  
• ap and C_eh: referencing to CFD and actual anemometer measurements
• SFmultiplier (on average 2.8): is it close to the graphical value of 3 derived from Beljaars
  
• C_l (on average 2.8): this makes the speedfactor curves closer to Nägeli's Lockere Wand (with z_0m=0.03m and op=0.5 -> ap~0.62). The aerodynamic porosity seen in aST_vr (ap=0.6) is thus close to Nägeli's.
  
  The difference could be explained, because a) Nägeli used a 25m long fence, while most houses/trees will be closer to 5 to 10m wide; and b) the parametrisation of the Nägeli curves could have been beter included in the Excel function.
  
• The height dependency of the methods is not that far of from simulted with aVR_CFD, the difference fits also within the standard deviation of the methods.
  Investigate the height dependency and see what method is closest to CFD.
• Influence height and distance
• It is important to realise that obstacles near the mill and around the same height of the mill, will introduce turbulance. Turbulence is not include in any of the formula related to above methods. For that, one would need CFD or a specific formula that will look at turbulence (not [yet] available at this moment).
• Obstacles just outside the circle (in above calculations 400m) are of course not included, but one really would need to check if no high obstacles are present (e.g. looking if those nigh obstacles have an intercept heitth higher than the mill height).
  
• Proper benchmark data/method:
  
• It will be needed to understand the fine tuning of the knobs used for each method, this will allow a proper benchmarking.
  
• The main problem is that there is still a lack of good reference/comparison/verification values, such as perhaps CFD of actual measurements (and even these two have their issues).
  Which method is the best reference: CFD or local anemometer or ???
• General finding
• Would be good to have automatic house/tree determination from the DSM.
  Some ideas are floating around how to do this;-)
• Relative methods (such as rVR_ejl) are difficult to evaluate at a quantative level. The form of their speedfacctor radars though match more or less the absolute methods'.
  
• Important to keep evaluating/validating methods for more mill biotopes with CFD and/or anemometer measurements. Smartmolen has four (soon five) mills with anemometers.
  Impington, Rijn en Lek, Labbus and Upminster have been evaluated.
• Increasing the number of obstacles in the aVR_st evaluation does not have that much influence. So methods that use only the 2 or 3 highest obstacles still have reasonable results.
  
• Remember the curves look to be close,  because they were adjusted in such a way that they were close! The variability of the knobs allows this, as long as they can be more or less  explained!
• Many variables/knobs have been tried and tested both CFD and above methods; they all align in some way.
  
• An indication of the Effective Useable Energy is given.
• If one starts with published values of knobs; all methods can be close enough to each (ranging from simple formula to complex simulations and anemometer measurements). The standard deviation seen in that way is as expected (say 1sigma around 5%) for a real-live process. Some mills (Rijn en Lek, De Hoop) have a larger error, reason not yet investigated.
• If one compares two or more environments, the relative value become important. If the aerodynamic system is relatively linear between these environments; all unknown method parameters will be divided out, and thus the values of these parameters become a little less important (again: as long as we are in a linear environment)!
  
• Like with a lot of real-live processes, one is not really able to catch reality into simple knob (see above knob evaluation). Monte Carlo method (using proper distribution for each knob) is essential in such cases.
• So the variation seen by the many methods (different calculations methods, CFDs by different people and in-vivo measurements) is relatively small (say 1sigma around 5%). This also maps with the experience that CFD parameters can vary quite a lot without changing the outcome a lot. So it is nice to be in a relatively 'insensitive' environment.
  

References

Davenport, Alan G. et al.: Estimating the roughness of cities and sheltered country. In: 12th applied climatology. 2000.
Hertwig, Denise et al.: Wake characteristics of tall buildings in a realistic urban canopy. In: Boundary-Layer Meteorology 172  (2019), pp. 239-270.
Jensen, N.O.: A note on wind generator interaction. In: (1983), issue RISO-M-2411.
Prinsenmolen-Committee: Research inspired by the Dutch windmills. H. Veenman 1958.
Temple, Stephen: Mill Biotope mathematics. In:  Version 5 (2025).

Acknowledgements

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