Wichita State University Libraries
SOAR: Shocker Open Access Repository
Wind Energy Reports, no.4
Center for Energy Studies
Wind Characteristics of the Western Part of Kansas
Mark T. Long and Gary C. Thomann
Wichita State University
__________________________________________________________________
Recommended citation
Jong, Mark T. and Gary C. Thomann. Wind characteristics for the western part of Kansas. Wichita, Kan:
Wichita State University Wind Energy Laboratory, 1978.-- 42 p.
Digitized by University Libraries and posted in Shocker Open Access Repository
Citable Link: http://soar.wichita.edu/dspace/handle/10057/5996
Terms of use: in the Public Domain
WER-4
WlND ENERGY REPORT NO.4
HIND CHARACTERISTICS FOR THE
WESTERN PART OF KANSAS
by
MARK T. JONG
and
GARY C. THOMANN
WlND ENERGY LABORATORY
WlCHlTA STATE UNlVERSlTY
WlCHlTA, KANSAS
FEBRUARY, 1978
Wind Energy Report No . 4
WER-4
WIND CHARACTERISTICS FOR THE
WESTERN PART OF KANSAS
by
Mark T. Jong
and
Gary c. Thomann
Wind Energy Laboratory
Wichita State University
Wichita. Kansas 67208
February, 1978
Sponsored by Wichita State University and the State of Kansas
TABLE OF CONTENTS
page
INTRODUCTION . . . . . . . . . . . . . . . . . . . .
THE WINO SPEED DISTRIBUTIONS AT THE VARIOUS STATIONS
1
. ..
.. . .
THE ANNUAL AVERAGE WINO SPEED AND THE ANNUAL AVERAGE
WIND POWER OENSITY . . . . . . . . . . . . . .
MONTHLY AVERAGES OF WIND SPEED AND POWER
THE HOURLY VARIATION IN IIIND SPEED AND WIND POIIER
DENSITY. . . . . . . . . . . . . . . . . . .
4
5
. . . . • . . . 16
. . . ..
16
THE WIND DIRECTION DISTRIBUTION AND THE ENERGY AVAILABLE
AS A FUNCTION OF WIND DIRECTION . . . . . . . . . . . . . ..
21
THE AVERAGE ANNUAL ENERGY DISTRIBUTION. . . . . . . • . . . . . .
25
SUMMARY AND CONCLUSIONS
. . . . . . . . . . . • . . • . . . . . . 35
REFERENCES . . . . . . . . • . . • . . . . . . . . . . . . • . . . 36
APPENDIX A . . • . . • . . . . . . . . . . . . . . . . . . . . . . 37
WIND CHARACTERISTICS FOR THE WESTERN PART OF KANSAS
Mark T. Jong and Gary C. Thomann
Wind Energy Laboratory
Wichita State University
Wi chita, Kansas 67208
INTRODUCTION
A determination of the power which will be supplied by a wind generator
operating in a wind regime requires knowledge of the statistics of that
wind distribution. From such wind speed statistics, it ;s possible to determine the expected values of the total yearly energy the generator will produce (its plant factor), its expected output at different times of the day
and at different times of the year . and the expected intervals when it will
be producing rated power, no power. etc. The design of a wind generator
also depends on wind speed statistics. The operating point (rotor speed)
and rotor size are usually both optimized for the wind distribution the
generator ;s to operate in.
The wind direction distribution is also important, particularly for
siting wind generators. Siting locations are often selected to enhance the
effect of the wind from certain directions. The placing of a generator on
a hill or ridge is an example.
In a preceding report,l the wind distribution for Wichita, Kansas was
estimated from "ata taken by the National Weather Service (NWS) during the
years 1968 through 1973. There appeared to be considerable variation in
the energy in the wind from year to year. To illustrate this pOint, the
Wichita average wind power density for each of the years 1968 to 1973 is
shown in Table I. These calculations are from measurements taken at a height
of 25 ft. There is approximately a 30X variation from the low to high values
Table I.
The yearly average power density in the wind for
Wichita, Kansas, for the years 1968 to 1973 measured at a height of 25 ft above ground level.
Year
Power
1968
193 W/m 2
147 W/m 2
1969
182 W/m 2
188 W/m 2
1970
1971
167 W/m 2
177 W/m 2
1~2
1973
1
2
for these six years. Because of this large variation it appeared that data
taken over a longer period of time should be used to obtain a reliable estimate of the mean yearly energy in the wind and also to obtain a more complete
idea of year to year fluctuations.
It was also desired to obtain data for stations other than Wichita,
Kansas. Enough data was sought to enable an estimate to be made of the
energy in the wind over the western half of Kansas. in particular the southwestern quadrant of the state. since it appears that this is the best Kansas
area for wind generated electricity. Data was ordered from the National
Weather Service at Ashville. North Carolina. for the sites of Wichita,
Goodland, Russell, and Dodge City in Kansas; La Junta. Colorado, and Dalhart,
Texas. The location of these stations ;s shown in Fig. 1. These stations
more or less encircle the southwestern part of Kansas.
\
COLORADO
Goodland
KANSAS
0
Russell
0
0
La Junta
0
~~eCj~
0
Wichita
OKLAHOMA
0
Dalhart
TEXAS
Figure 1.
Location of the stations where wind data was obtained.
3
Data was obtained from NWS in the form of 9 track computer compatible
tapes which contained wind speed and direction along with a variety of other
meteorological data. Computer programs were written to strip off only the
wind information for processing.
Information about the stations from which data were obtained is shown
in Table II.
An attempt was made to obtain data over the period 1948 to
1975. For some stations, data over this complete range of years did not
exist. Data for years later than 1975 is not yet digitized and available
for distribution. The air density, used for energy calculations. was calculated from the average temperature and the altitude. This information
is shown in the table also. At several of the stations the height of the
wind measuring instruments was changed during the 1948 to 1975 period. The
heights of the instruments at various times are shown in Table III. Unfortunately, during the time recorded data was available for Dalhart and
La Junta, there is no record of anemometer height at these stations. This
is also true of the Russell data for a few years.
For comparison purposes, all data was scaled to a height of twenty-five
feet. The La Junta and Dalhart data was not changed; it is hoped that the
anemometer height was near 25 ft. All the Russell data was scaled as if the
anemometer height was 29 ft. For scaling it was assumed that wind speed increases with elevation as the one-seventh power of height; this dependenc p
appears to be reasona~le, although other variations of wind speed with
height are also used.
The mlS data was recorded hourly up through 1964 and at intervals of
three hours for years later than 1964. Comparative calculations were made
during these years to see if there was any difference between results obtained using hourly data and results obtained using only data every third
hour. Calculations were made of annual average speed and power, monthly
average speed and power, wind direction distribution, velocity frequency distribution, and speed direction correlation. There was no discernible difference in any of the calculations, so only three hour data was used for the
Table II.
The location of each of the stations from which wind data
is presented, its elevation, average temperature, air
density, and the years for which the data was available .
WICHITA
RUSSELL
DODGE CITY
GOODLAND
DALHART
LA JUNTA
LATITUDE
37°39'N
38°52'N
37°46'N
39°22'N
36°01'N
38°03 1 N
LONGITUDE
97°25 1 W
98°49'W
99°58'W
101°42'W
103°31 'W
103°33 1W
ELEVATION
AVERAGE
TEMPERATURE
AIR DENSITY
YEARS OF
DATA
1321 ft
1864
2582
3922
3989
4190
56.6 of
55.2
54.9
50.5
55.9
54.4
1. 18 kg/m 3
1. 16
1.13
1.10
1.09
1.08
54-75
50-75
48-75
48-64
49-54
48-64
4
Table III.
Changes in wind instrument height at
each of the stations.
Wichita
32 ft (to 7/26/67)
25 ft (7/27/67 to present)
Dodge Ci ty
58 ft (1/1/48 to 4/12/61)
20 ft (4/13/61 to present)
ft (1/1/48 to 5/11/49)
ft (5/12/49 to 6/9/60)
ft (6/10/60 to 3/23/64)
ft (3/24/64 to 5/18/65)
ft (5/19/65 to present)
Goodland
43
25
31
35
20
Russell
29 ft since 8/24/53
La Junta
20 ft since 4/1 0/64
Dalhart
23 ft since 4/11/63
calculations throughout this report. The only exception ;s that hourly data
was used to calculate the variation in the wind speed throughout the day,
since it was felt that three hour data would be too coarse for this analysis.
THE WIND SPEED DISTRIBUTIONS AT THE VARIOUS STATIONS
Wind speed distributions~ or velocity frequency curves as they are sometimes called, give either the probability or the number of hours per year
that the wind will be in a particular velocity range. For the various stations Figures 2 - 7 show the number of hours per year and the probability
that the wind speed will be in the one knot range centered around each wind
speed. A listing of the values is also given in Appendix A. Units of knots
are used because NWS records in those units. The hours shown for zero knots
would actually be the amount of time the wind was between zero and one-half
knot. The large number of hours shown for zero knots in comparison to the
hours shown for the other low wind speeds may be due partly to starting friction in the anemometer. It would seem reasonable that the points in these
figures should lie along a smooth curve. i.e., it doesn't seem that there
should be any sharp breaks in the probabil ity curve. In these figures, the
points do not lie along a smooth curve. probably due to the limited number
of samples available. There have been some attempts to fit easily described
curves to the wind distribution data. One distribution that has been used
is the Weibull distribution described by Eq. (1).3
p(V)dV
(1 )
5
In the equation, p(V) is the wind speed probability density function, V is
the wind velocity, and p(V)dV is the probability the wind speed is between
V and V+ dV.
a and 6 are scale factors that are adjusted to make the curve
fit the data. A least squares fit is used to fit this equation to the observed data. and the curves are shown in Figures 2 - 7. Zero wind velocities
are excluded for fitting the curves.
As can be seen from the curves, in some cases the fit is not good, particularly in the case of Dalhart and Russell. The best fit is to the Wichita
data. The sum of the squared errors is shown in Table IV. where the error is
expressed in probability units.
Table IV.
The sum of squared errors between the velocity frequency
data and the fitted curve.
a
a
Wichita
12.0
2.2
Russell
12.9
2.4
Dodge City
12.5
2.4
Goodland
12.0
2.3
La Junta
8.7
2.1
1.81 x 10- 3
3.76xl0- 3
Dalhart
13.8
2.2
1.17x 10- 2
Sum of Squared Errors
1.01 x 10- 3
9.71 x 10- 3
5.34xl0- 3
THE ANNUAL AVERAGE WIND SPEED AND THE ANNUAL AVERAGE WIND POWER
DEr~SlTY
The average wind speed and power density for each station calculated
from all available data ;s shown in Table V. The power density of the wind
(the power in the wind per unit area) is given by Eq. (2),
where P is the power density, V is the wind velocity and p is the density of
the air. This equation holds for any consistent set of units. The values
in Table V are determined by calculating the power density at each wind
speed, multiplying this value by the number of hours in the year the wind
was at that velocity, summing for all wind velocities, and dividing by the
total number of hours in the year to obtain the average power density. The
air density is in general a function of altitude, temperature, and humidity.
For calculations here values of p were determined from the average temperature and humidity at each station. These values are listed in Table II.
Essentially, the average power density calculation is done using Eq. (3)
where
6
...,.,
~
m
,.,'"
"-
-
~
.~
~
.0
m
"
0
Wichita
a = 12.0 knots
a = 2.2
.<=
800
.0
0
~
0.
.09
0
700
600
Figure 2.
0
0
.08
.07
Velocity frequency data for Wichita showing wind speed and
the hours or the probability the wind is in a one knot range
centered on that wind speed value. The curve is given by
Eq. (1) and adjusted for a least squares fit to the data.
7
10t1 hrs
~
m
"""
~
-
0
.~
~
.~
~
.c
m
.c
0
~
0
Russell
0=12.9 knots
6 = 2.4
~
800
0
0
~
c.
.09
70
08
600
07
0
.06
0
500
0
0
05
400
0
.04
30
0
0
0
.03
0
0
200
.02
100
01
o
o
00
o
°LL__L -__~__~__-L__-L~~~~O
o
Figure 3.
5
10
15
20
25
30
35
Velocity frequency data for Russell showing wind speed and
the hours or the probability the wind is in a one knot range
centered on that wind speed value. The curve is given by
Eq. (1) and adjus ted for a 1east squa res fit to the data.
8
.-800
.c
m
.c
o
~
Dodge City
a = 12.5 knots
.09
6 = 2.4
o
o
Q,
o
.08
.07
o
.06
.05
.04
o
.03
o
200
.02
100
.01
0
0
0
00
5
Figure 4.
0
00
0
10
15
20
25
30
0
35
0
Velocity frequency data for Dodge City showing wind speed and
the hours or the probability the wind is in a one knot range
centered on that wind speed value. The curve ;s given by
Eq. (1) and adjusted for a least squares fit to the data.
9
o
919 hours
..c
~
.c
o
Goodl and
• = 12.0 knots
6 = 2.3
800
~
Co
.09
700
.08
600
.07
500
.06
o
.05
40
0
0
300
.04
0
.03
20
.02
10
.01
00
0
0
0
0
0
Figure 5.
5
10
15
20
25
0
0
0
30
00
0
35
Velocity frequency data for Goodland showing wind speed and
the hours or the probability the wind is in a one knot range
centered on that wind speed value. The curve is given by
Eq. (1) and adjusted for a least squares fit to the data.
10
~
.-.--
>,
1230 hrs
"'">,
~
[,
~
~
.a
.a
~
'"0
~
0
~
~
Oa1hart
0= 13.8 knots
6 = 2.2
800
a.
. 09
.08
700
o
600
o
.07
o
.06
500
.05
400
.04
o
o
300
o
0
.03
o
o
200
.02
0
100
0
.01
0
0
0
0
0
0
0
0
Figure 6.
0
5
10
15
20
25
0
30
0
0
35
0
0
40
Velocity frequency data for Dalhart showing wind speed and
the hours or the probability the wind is in a one knot range
centered on that wind speed value. The curve is given by
EQ. (1) and adjusted for a least squares fit to the data.
11
.05
400
.04
300
0
.03
0
200
0
.02
0
100
0
.01
0
0
0
0
Figure 7.
0
0
5
10
15
20
0
00 0 0
25
0
0
30
35
Velocity frequency data for La Junta showing wind speec and
the hours or the probability the wind ;s in a one knot range
centered on that wind speed value. The curve ;s given by
Eq. (1) and adjusted for a least squares fit to the data .
12
Table V.
The yearly and grand average wind speed, power density,
pattern factor and standard deviation about the grand mean
for the six stations.
Year
Speed
m/ s
Power
W/m 2
Pattern
Factor
---
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
-------------
-------------
5.97
6.09
5.92
5.37
5.44
6.07
5.78
5.24
5.18
5.02
5.55
5.31
5.29
5.54
5.73
5.20
5.55
5.51
5.44
5.46
5.49
5.49
207
222
200
164
168
242
201
158
142
132
172
153
155
181
193
147
182
188
167
177
181
183
Mean
5.53
Stand.
Dev.
,tand.Oev.
IMean
Dodge City
Ru ssell
Wichita
Speed
Power
Ke
Speed
Power
Ke
---
---
-----
241
194
162
178
185
230
211
208
189
200
157
204
208
190
143
181
256
203
216
213
199
160
193
210
165
209
233
249
1.77
2.02
1. 94
1. 73
1.64
1. 56
1.53
1.63
1. 56
1.60
1. 55
1. 59
1. 52
1.87
1. 73
1. 59
1.64
1.69
1. 70
1. 71
1.62
1.67
1.71
1.77
1.64
1.66
1.69
1.63
Ke
---
---
1. 67
1.69
1. 65
1.82
1. 79
1.86
1. 79
1.87
1. 75
1.80
1. 73
1. 75
1. 79
1.82
1. 76
1. 79
1.82
1. 92
1. 78
1.87
1.87
1.88
5.79
5.24
4.89
5.36
5.15
6.00
5.97
6.22
5.44
6.02
5.48
4.95
5.68
5.18
6.55
5.93
6.16
6.17
6.11
5.45
6.39
6.13
5.40
5.84
5.96
6.05
261
178
139
162
166
207
205
222
155
205
166
139
178
209
249
184
210
212
225
152
235
222
157
191
194
204
2.34
2.16
2.06
1.83
2.12
1.66
1.68
1. 61
1.68
1.64
1. 76
1.99
2.01
2.62
1.54
1.53
1.55
1. 57
1.72
1. 64
1.57
1. 68
1.73
1.66
1.59
1. 61
6.22
5.54
5.29
5.66
5.84
6.39
6.26
6.10
5.99
6.06
5.65
6.12
6.25
5.64
5.26
5.87
6.52
5.99
6.10
6.04
6.02
5.55
5.85
5.96
5.63
6.07
6.26
6.49
178
1. 79
5.73
193
1. 78
5.95
200
1.68
0.29
22.0
0.07
.465
33.2
0.268
0.33
27.8
0.118
0.0521
.124
.039
0.081
0.172
0.150
.055
.139
0.070
-----------
13
Tabl e V.
Continued.
Dalhart
Goodl and
Year
I
Speed
m/s
Power
W/m 2
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1971
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
6. 58
6.08
5.49
5.20
5.62
6.19
5.23
5.68
5.41
4.99
5.08
5.53
5.66
5.20
5.45
5.83
6.15
310
Mean
~tand.
Dev.
Stand.Dev.
1~lean
262
176
156
175
224
144
194
160
134
139
Pattern
Factor
Power
Ke
Speed
Power
Ke
---
---
---
---------------------------------------
109
104
121
80
67
63
157
172
2.62
2.92
2.95
2.59
2.49
2.89
3.06
3.45
2.42
3.11
2.84
3.45
2.93
2.43
1. 74
2.09
2.03
-----
-------------------------------------------
4.26
4.05
4.24
3.85
3.69
3.45
4.57
4.53
4.41
3.80
3.66
3.47
3.37
3.73
4.30
4.01
4.51
Ke
2.00
2.13
1. 95
2.03
1.80
1. 73
1.84
1. 95
1.86
1. 99
1. 95
1. 92
1.83
1. 97
1. 93
1.84
1.80
5.76
6.47
6.79
6.83
7.27
6.88
218
328
354
338
431
354
---------------------
---------------------
-----------------------
5.61
187
1. 91
6.66
337
0.439
46.5
0.101
0.513
.0782
.248
.0529
.on
---
In
---
Junta
Speed
-------------------------------------------
181
151
170
198
228
La
2.11
2.24
2.09
1. 96
2.08
2.02
111
92
75
n
60
68
74
72
101
-----------------------
-----------------------
-------
2.09
4.00
94.3
2.71
68.7
0.056
0.403
32.3
0.473
.204
.0269
.101
.343
0.175
---------
-------
---
14
P = pVJ/2
where V3 is the average value of the cube of the wind.
written as it appears in Eq. (4).
P = pK e'fJ/2
(3 )
Eq. (3) could be re(4)
where V is the mean wind speed and Ke is the energy pattern factor. defined
as
(5)
If Ke ;s known, the power density can be calculated directly from the mean
wind speed; the complete wind distribution is not necessary for power calculations. Values of Ke are also shown in Table V. Also shown are standard
deviations for each parameter . The standard deviation. o . of a statistical
variable is a measure of the spread of the parameter about the mean. Eq. (6)
shows the formula for calculating the wind speed standard deviation.
N
"L (Vi -V)
_ 2
a
=
1
(6)
N- 1
Vi ;s the average wind speed in the ;th year. N is the total ~umber of samples (years) available, and V is the averaQe over all years.
Several conclusions can be inferred from Table V. As an aid in the
following discussion, the overall average speed for each station, the overall
average power density, the standard deviation about the average speed and
average power density, and the average energy pattern factor are rewritten
in Table VI. The average wind speeds for all the stations in Kansas are
comparable. The wind speed at Dalhart is considerably higher than that at
the Kansas stations. However, the measurement at Dalhart is based on only
six years data and must be treated with some skepticism. In addition, the
height of the anemometer at Dalhart during the measurement period is not
known. Wind speeds seem to be increasing toward the southwestern part of the
state. as indicated by the slightly higher wind speeds for Dodge City and the
much higher speeds for Dalhart. This agrees with the data shown in Fig. 8,
where power density is displayed for the central United States. This graph
\','ns made from sUlTlllarized NWS data. 2 The power densities for the Kansas sta ..
tions are all around 200 W/m2, and this seems to be a reasonable value to
assume for the western part of the state, with somewhat higher power densities available in the southwestern part of the state and the nearby areas in
Oklahoma and Texas. These values are for a height of 25 ft above the ground.
At higher elevations, where large turbines would operate, the power density
is greater. For example. at a height of 100 ft above the ground the power
density would increase to 360 W/m2 and to 490 W/m2 at a height of 200 ft if
it is assumed that the increase in wind speed is proportional to the oneseventh power of the height. There are indications that this relationship
15
Table VI.
The overall mean wind speed and power density and standard
deviations about these means for each station.
Wichita
Russell
5.53
a (speed). mls
Power Density, W/m 2
Dodge
City
Goodland
Dalhart
5.73
5.95
5.61
6.66
4.00
.29
.465
.33
.439
. 513
.403
178
193
200
187
337
94.3
a (power). W/m 2
22.0
33.2
27.8
46.5
68.7
32.3
Ke
1. 79
1. 78
1.68
1. 91
2.09
2.71
Average Speed. mls
La Junta
"
000
o
o
8
0
o
0>0
Figure 8.
Wind power density in Watts/m2 for the central United
States calculated from summarized NWS data.
16
holds up to at least 500 ft over flat terrain. 2 At well selected sites.
such as the crests of hills and ridges, higher densities might be available
than those determined directly by the wind speed versus height relationship.
The average wind speed and power density at La Junta ;s considerably
lower than that of the other stations and little wind power appears to be
available this far west. The decrease in power density in the westerly
direction can also be seen in Fig. 8.
The standard deviations about the power density mean in Table VI show
that considerable variations in year to year power output could be expected.
If it were assumed that the yearly average power density was normally distributed with an actual mean and standard deviation as shown in Table V, then
the yearly power density would vary from the mean by an amount larger than
the standard deviation 32% of the time. For example, with this assumption,
the yearly average power density for Dodge City would be outside the range
170 to 230 W/m during approximately 30% of the years measured. An examination of Table IV for the yearly power densities for Dodge City shows that
the power density is indeed outside this range nine of the twenty-eight years
for which data is available.
MONTHLY AVERAGES OF WIND SPEED AND POWER
The monthly average wind speed and power for each station are shown in
Table VII. Each monthly average is obtained by averaging all data in that
particular month, i.e. all Januarys are averaged together, etc. The energy
pattern factor for each month at each station is also included in the tables.
Means and standard deviations calculated over the twelve months, and the
standard deviation divided by the mean,3re also included. Typically, monthly
data shows highest wind speeds occurring in the spring of the year, either
March or April, and lowest wind speed occurring in the summer, either July
or August. The power available in the windy months is about twice that
available in the calmer summer months. Exceptions are Russell, which does
not show quite as large a month to month variation, and La Junta, which shows
a much larger change from spring to summer. It will be seen throughout this
report that the La Junta wind characteristics differ considerably from those
at the other stations. Dalhart shows a very high wind speed in June, but it
would be hard to say that this is a long term trend because of the limited
amount of data used for the calculation.
THE HOURLY VARIATION IN WINO SPEED AND !IINO POWER DENSITY
Typically, there is a considerable variation in the surface wind during
the day in the great plains area of the United States. The data which was
available at hourly intervals (before 1964) was used to determine the variation in wind speed and wind power density throughout the day at the six stations. The wind speed at each hour for the stations is shown in Table VIII.
All the hourly data available at each station was used; the total number of
years of data available is also shown in the table. This data is also plotted
in Fig. 9. Examination of the table or the figure shows a considerable hourly
variation, with a low in wind speed occurring in the early morning and a peak
in the afternoon. The ratio between the maximum and minimum power densities
for the stations is summarized in Table IX. As can be seen from this table,
17
Table VII.
The average wind speed, power density, and power factor for each
month for the six stations. Overall averages. the monthly deviation about the mean and deviation divided by the mean also included.
Month
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Mean
Stand.
Dev.
Stand.Oev.
IMean
V,m/s
Power
DensiV
P,W/m
Power
Factor
5.47
5.71
6.33
6.44
5.73
5.52
4.94
4.96
5.14
5.40
5.42
5.32
5.53
174
198
258
262
189
170
116
121
143
170
169
167
178
.470
.085
Speed
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Mean
Stand.
Dev.
:>tand.Oev.
IMean
V
P
Ke
V
P
Ke
1.83
1.83
1. 73
1.69
1. 73
1. 73
1.65
1.69
1.80
1.84
1.82
1. 90
1.77
5.48
5.73
6.43
6.35
5.90
5.92
5.69
5.57
5.76
5.90
5.57
5.39
5.77
176
197
275
254
199
194
166
159
178
191
177
162
193
1.85
1.82
1.80
1. 73
1.68
1.63
1. 56
1.60
1.62
1.85
1. 78
1.80
1.73
5.79
5.99
6.66
6.72
6.26
6.12
5.50
5.36
5.79
5.79
5.84
5.76
5.97
194
206
294
286
227
212
151
143
177
179
198
182
203
1.77
1. 70
1.77
1.68
1.64
1.64
1.61
1.55
1.62
1.63
1.77
1.69
1.67
45.4
0.07
.329
36.1
0.104
.414
48
0.071
.255
.0395
.057
. 187 0.060
.0692
.235
.0435
Ke
Goodland
Month
Dodge City
Russell
Wichita
Dalhart
La Junta
V
P
Ke
V
P
Ke
V
P
Ke
5.40
5.59
6.35
6.38
5.95
5.79
5.31
5.23
5.48
5.18
5.45
5.31
5.62
176
189
286
276
213
189
145
140
162
144
195
164
190
2.05
1. 99
2.05
1. 95
1.86
1. 79
1.77
1.80
1.81
1. 90
2.21
2.01
1. 93
6.70
6.50
7.40
7.14
7.13
7.79
6.32
6.12
6.38
6.16
5.93
6.40
6.66
366
334
494
432
416
472
248
227
249
246
237
324
337
2.26
2.25
2.26
2.20
2.12
1.85
1.82
1.84
1. 78
1. 95
2.10
2.29
2.06
3.60
3.99
4.70
4.79
4.47
4.25
3.83
3.62
3.67
3.54
3.81
3.67
4.00
74
96
167
155
114
96
69
59
62
62
94
85
94
2.93
2.82
3.00
2.62
2.39
2.32
2.27
2.31
2.32
2.61
3.17
3.21
2.66
.415
48.3
0.133
.575 97.7
.200
.446
35.4
0.352
.0738
.254
.0688
.0863
.0971
.112
.376
0.132
.290
18
the power varies by about a factor of two for the Kansas stations. The variation at La Junta ;s higher . The variation at Dalhart ;s extremely large, a
factor of over three between the maximum and minimum power densities. The
reason for the higher ratio at Dalhart than at the Kansas stations is not presently known.
Table VIII.
The average wind speed and power density at each hour for the
six stations. Every hour data available before 1964 used.
Exact years of data used shown under each station .
.
Hour
(CST)
12AM
1
2
3
4
5
6
7
8
9
10
11
12PM
1
2
3
4
5
6
7
8
9
10
11
Wichita
1954-1964
Speed Power
(m/, ) (W/m2)
5.02
4.95
4.86
4.84
4.78
4.74
4.75
5.01
5.51
6.04
6.32
6.44
6.53
6.59
6.69
6.71
6.64
6.30
5.81
5.32
5.10
5.09
5.09
5.04
135
134
129
129
126
125
124
139
170
210
236
247
258
265
275
275
261
233
190
154
141
140
141
139
,I
I
,,
iI
Russell
1950-1964
Speed Power
Dodge City
1945-1964
Speed Power
5.23
5.16
5.12
5.12
5.07
5.04
5.03
5.21
5.65
6.10
6.36
6.46
6.52
6.55
6.57
6.54
6.37
5.98
5.55
5.13
4.98
5.07
5.18
5.20
5.65
5.58
5.53
5.47
5.44
5.42
5.44
5.49
5.82
6.17
6.41
6.48
6.54
6.57
6.61
6.58
6.44
6.26
6.00
5.74
5.67
5.72
5.75
5.72
154
150
146
145
141
139
139
149
185
223
249
261
268
269
271
267
245
212
178
149
138
144
153
150
168
160
157
152
149
148
151
159
190
229
254
265
272
271
275
272
255
235
207
181
176
175
175
174
19
Tabl e VIII.
Hour
(CST)
12AM
1
2
3
4
5
6
7
8
9
10
11
12PM
1
2
3
4
5
6
7
8
9
10
11
Continued. The average wind speed and power density at
each hour for the six stati ons. Every hour data available
before 1964 used. Exact years of data used shown under
each station.
Goodland
1948-1964
Speed Pow~
Dalhart
1949-1954
Speed Power
La Junta
1948-1964
Speed Power
(m/s)
(W/m )
5.23
5. 17
5.15
5.05
4.98
4.95
5.12
5.49
5.81
6.08
6.24
6.33
6.38
6.43
6.44
6.34
6.02
5.75
5.38
5.22
5.26
5.35
5.36
5.31
148
144
146
140
137
136
146
172
203
234
251
260
266
269
267
254
224
201
170
156
158
162
159
153
6.06
5.87
5.70
5.57
5.51
5.41
5.37
5.54
6.06
6. 70
7.22
7.50
7.60
7.74
7.86
7.99
8.01
7.84
7.43
6.91
6.65
6.61
6.47
6.32
3.68
3.65
3.53
3.48
3.48
3.48
3.52
3.70
3.84
3.89
3.98
4.02
4.20
4.43
4.59
4.73
4.75
4.65
4.40
4.18
4.05
3.96
3.88
3.81
242
218
200
189
193
175
175
196
260
349
417
472
500
528
534
541
543
497
422
322
291
288
275
261
66
65
61
57
59
60
60
71
83
91
104
109
119
135
138
144
143
132
117
107
97
88
82
74
20
9
8
,,
7
'- -,
" ,,
,
6
~
e-
• 5
"'"
'"
0-
'"
"c
4
:.
Wichita----
Russell----
3
Dodge City- · - ·
12AM
4
8
12PM
Goodland- ·· - ··
Dalhart----La Junta---
4
8
Central Standard Time
Figure 9.
The hourly variation in wind speed for the six stations .
21
Table IX.
The ratio of minimum to ma ximum power density during the
day for each of the six stations. Also shown are times
when lowest and highest wind speeds occur.
Station
Ratio
Wichita
2.2
2.0
Goodland
Dodge City
Russell
Dalhart
La Junta
1.9
1.9
3. 1
2.5
Time of Low
Wind Speed
Time of High
Wi nd Speed
6AM
6AM
5AM
5AM
5AM
3AM
2PM
2PM
2PM
2PM
4PM
3PM
THE WIND DIRECTION DISTRIBUTION AND THE ENERGY AVAILABLE AS A FUNCTION OF
WIND DIRECTION
In many cases the siting of a wind generator would consider the wind
direction distribution. Optimum sites can usually increase the local wind
speed when it is blowing from certain directions and it is advantageous to
select sites to enhance the winds which occur most frequently. For example,
the data to be presented in this section will show the wind in Kansas to be
often from either the north or south, but less frequently from an east or
west direction. Threfore. a site would usually be selected with emphasis on
enhancing the north/south winds; a ridge running east to west would probably
make a good site in Kansas. Of course, if a site can be found which enhances
the wind from all directions it would be ideal; such sites are not always
available. however. considerabl~ gork has been done on site selection and
is reported in the 1i terature. 4. •
Wind direction distributions for the six stations are given in Figs.
10-12. NWS groups directional data into 22 . 5° segments. so that grouping
is used here. The wind direction distribution in each case is for winds
equal to or greater than five knots; lower velocity winds are of little importance for wind turbine operation . The wind roses show that for all stations except La Junta the wind direction is southerly the largest percentage
of the time and from a northerly direction the next largest percentage. For
example, if in Wichita the directions S, SSE, SSW. N. NNE, and NNW are all
grouped together, 66% of all the winds over five knots are accounted for.
The other Kansas stations have somewhat similar distributions. except for
Goodland, which shows somewhat more evenly distributed winds. Dalhart shows
a distribution dominated by the winds from the S and SSW directions. with
less of a north wind component . As usual. La Junta shows a completely different distribution, with winds from the east and west dominating the distribution.
22
N
WICHITA
20%
15
E
W
:<! 5 knots
S
N
RUSSELL
20%
15
10
w
E
~
5 knots
S
Figure 10,
Wind direction distribution for Wichita and Russell for
wind speeds greater than or equal to 5 knots.
23
N
DODGE CITY
O~
15
10
E
:;" 5 knots
s
N
GOOOLANO
o
w
Figure 11.
15
E
;;. 5 knots
Wind direction distribution for Dodge City and Goodland
for wind speeds greater than or equal to 5 knots.
24
N
DALHART
15
~
E
w
5
~nots
N
LA JUNTA
0%
15
5
10
E
w
~5 ~nots
s
Figure 12.
Wind direction distribution for Dalhart and La Junta for
wind speeds greater than or equal to 5 knots.
25
It ;s also possible to calculate wind energy as a function of direction.
This energy distribution is probably a better criteria for wind generator siting than is the distribution of the wind velocity. The yearly average energy
density available from each 22.5° angular segment ;s plotted in rose patterns
in Figs. 13, 14 and 15. The energy diagrams indicate essentially what the
wind direction distribution diagrams do~ only more emphatically.
THE AVERAGE ANNUAL ENERGY DISTRIBUTION
From Eq. (l), and the number of hours the wind is blowing at a particular speed it is possible to determine the average annual energy available in
each wind speed increment. The results of these calculations for the six
stations are shown in Figs. 16 - 21. Each point in one of these figures represents the average yearly energy in a one knot range. A Weibull distribution curve was fit to this data, with the two parameters selected to minimize
the sum of the squared errors. The resulting curve is plotted as a solid
line in the figure. Previously, a Weibull curve was also fitted to the wind
speed data shown in Figs. 2-7. These curves can also be used to calculate
the energy distribution. The results are also shown in Figs. 16- 21 as
broken lines. As can be seen from these figures considerable amounts of
energy are available at wind speeds well above the mean wind speed. This
effect is. of course. caused by the power being dependent on the cube of
wind velocity.
Table X lists the total average yearly energy calculated from the actual
data. from the Weibul1 distribution curves fit to the energy data. from the
~'Jeibul1 distribution curves fit to the velocity data. and the percentage
errors between the energies calculated from the actual data and the curves.
The actual energy calculations and those from the curve fit to the energy
data agree very closely. However, significant differences occur between
these calculations and the total energy which is estimated from the curves
fit to the wind speed data. Since it is usually the energy in the wind which
is of the most concern, curve estimations to the wind distribution should
probably be done on an energy basis.
Table X.
The total yearly average energy estimated from the data, from
the least squares fit of a Weibull distribution to the energy
data. from a least squares fit of a Weibull distribution to the
vel?city data, and the percentage difference between the energy
estlmated from the actual data and that estimated from the curves .
Wichita
Russell
Dodge
Citv
Goodland
Dalhart
La Junta
Total yearly average
energy from data
1560
kW-hr/m2
1610
1690
1700
2930
805
Total yearly average
energy from fi t
to energy data
1560
(0%)
1610
(0%)
1690
(0%)
1700
(0%)
2920
(-0.34%)
804
(-0.12%)
Total yearly average
energy from fi t
to velocity data
1430
(-8.3%)
1610
(-3.6%)
1480
(-12.4%)
1280
(-24.7%)
2030
(-30.7%)
488
(-39.4%)
26
N
WICHITA
400 kW-hr/m 2
00
200
W
E
S
N
RUSSELL
400 kW-hr/m 2
00
W
Figure 13.
E
Energy/direction roses for Wichita and Russell showing the
yearly energy contained in each 22.5° segment of the wind.
27
N
OOOGE CITY
400 kW-hr/m 2
300
w
E
s
N
GOODlAND
00 kW-hr/m 2
300
w
E
s
Figure 14.
Energy/direction roses for Dodge City and Goodland showing the
yearly energy contained in each 22.5 0 segment of the wind.
28
N
DALHART
400 kW-hr/m2
W
E
N
LA JUNTA
300
200
w
Figure 15.
100
E
Energy/direction roses for Dalhart and La Junta showing the
yearly energy contained in each 22.5° segment of the wind.
29
WICHITA
0
120
energy fit
0
.
....
E
~
._-- -velocity fit
\,
\,
'\
80
"",
'".
~
>-
'"
'"zw
-
\,
~,
100
N
= 18.8, e = 3.5
a
60
w
0
\,
1
40
\. 0
,
20
i
0
5
~
~
~
10
15
20
25
30
35
40
WIND SPEED, KNOTS
Figure 16.
The energy distribution as a function of wind speed for
Wichita. Each point represents the yearly average energy
in a one knot range. A least squares fit to the data is
shown by the dashed line with the solid curve showing the
energy distribution curve resulting from the curve originally fit to the velocity data.
30
Isa
6
23S .7S
6
/\
,
\
~
120
RUSSELL
.
------energy fit
a = 18.2, 6 = 4.1
-- - -- - -
o
o
0
\,
~
100
N
0
E
-~
~
velocity fit
80
•
'".
0
~
>
'"'"z
'"
'"
60
0
•
~O
40
0
0
0
10
0
•
\
•
~•
\
0
,
20
~
~
a
5
10
15
20
0
25
0
~
0
~
30
0
00
'-
35
0
0
40
WIND SPEED, KNOTS
Figure 17.
The energy distribution as a function of wind speed for Russell.
Each point represents the yearly average energy in a one knot
range. A least squares fit to the data is shown by the dashed
line with the solid curve showing the energy distribution curve
resulting from the curve originally fit to the velocity data.
31
0
DODGE CITY
12
energy fit
a = 19.3,
,
O~,
10
N
-,.
~
80
.
~
\
\
>-
'"'"z
"'
"'
3.4
- - velocity fit
- -
\,
\,
E
.c,
-
e=
60
,
0
,
\
\,
,
40
0
I
,
20
0
\,
0
\,
o
0
000
0000
/....
10
15
20
25
30
35
40
WIND SPEED, KNOTS
Figure 18.
The energy distribution as a function of wind speed for Dodge
City. Each point represents the yearly average energy in a one
knot range. A least squares fit to the data is shown by the
dashed line with the solid curve showing the energy distribution
curve resulting from the curve originally fit to the velocity
data.
32
o
GOODLAND
120
------energy fit
o
a = 20.7,8= 3.0
-- - -
o
- - velocity fit
100
,
N
E
\
~
'-
,
~
80
,
'"
~
>-
'"'"z
"'
"'
0\
60
~
,
\
\
\
.I
.I
40
,
I
,
20
,
~
5
0
10
15
20
25
0
00
\,
I
0
00
0
"30
0
0
0
00
35
0
40
WIND SPEED. KNOTS
Figure 19.
The energy distribution as a function of wind speed for Goodland.
Each point represents the yearly average energy in a one knot
range. A least squares fit to the data is shown by the dashed
line with the solid curve showing the energy distribution curve
resulting from the curve originally fit to the velocity data.
33
1
'"6 '19 rt' 'n
6
140
'\
j.
DALHART
0/, \
0 = 26.4. B = 2.7
I, 0 0\• 0 ---·-velocity fit
,
0
120
energy fit
a
100
0
N
e
~ 80
,
-"
I
I
0
,
\
\
\
'"
~
-
>-
'"
'"
\,
0 0
0
~ 60
I0
w
,
0
J,
I00
40
0
\0,
o \
0
,
\0
,
20
•
j0
,
10
0
0
\,
1
0
0
0
15
20
25
30
0
0
0
'--
35
40
45
50
WIND SPEED. KNOTS
Figure 20.
The energy distribution as a function of wind speed for Oalhart.
Each point represents the yearly average energy in a one knot
range. A least squares fit to the data is shown by the dashed
line with the solid curve showing the energy distribution curve
resulting from the curve originally fit to the velocity data.
34
LA JUNTA
120
_ _ _ _ _ energy fit
a
= 18.5, 6 = 2.4
_ _ _ _ _ velocity fit
100
Figure 21.
The energy distribution as a function of wind speed for La Junta.
Each point represents the yearly average energy in a one knot
range. A least squares fit to the data is shown by the dashed line
with the solid curve showing the energy distribution curve resulting from the curve originally fit to the velocity data.
35
SUMMARY AND CONCLUSIONS
The Kansas stations show power densities of from 175 to 200 W/m2 at a
height of 25 ft. Using the 3/7 power law, a 200 W/m 2 power density would increase to 360 W/m 2 at a height of 100 ft and to 490 W/mZ at 200 ft. There appears to be an increase in power toward the southwestern corner of the stat~:
Confirming this ;s the very high power density at Dalhart, Texas of 337 W/m
at an assumed 25 ft which scales to an extremely high 820 W/m 2 at 200 ft. However, the Dalhart data cannot be considered reliable since little is known about
the station and data is available over only a five year period. It does seem
reasonable to assume that power densities of at least 500 W/m2 at a 200 ft
height are available in the southwestern part of the state. It is possible
that areas exist with even higher power densities and it ;s almost certain that
there will be individual sites with higher energies available, since the NWS
station locations are not usually selected with high wind velocities as a consideration.
The Kansas stations and Dalhart show energy direction distributions dominated by winds from the south and north and it seems clear that siting should
consider enhanCing the winds from these two directions.
The La Junta. Colorado wind distribution differs considerably from the
other stations, presumably because it is further west. It is not known if a
sudden change in wind characteristics occurs with western movement or whether
the change is gradual, but it seems evident from this data and from other publi~hed data that the wind energy decreases in Colorado when compared with that
available in the western half of Kansas.
Further investigation will consider the study area in more detail. An effort will be made to determine if there are areas with considerably higher wind
energies than those at the stations considered here and to locate individual
sites with higher energies. A search will be made for more wind data in the
southwestern part of the state and an attempt will be made to select individual
sites from maps of the area. A measurement program may then need to be undertaken; the necessity for measurements will probably depend on the amount of
existing data which can be located.
36
REFERENCES
1.
Thomann, G.C. and M.T. Jong. "Wichita. Kansas Wind Characteristics
Estimated from 1968-1973 NWS Data; Performance of the NASA 100kW
Prototype Wind Generator in the Wichita Wind Regime." WER-l,
~Iind
Energy Laboratory, Wichita State Universtiy. Wichita. KS, January
1977 .
2.
Reed. J.W., "Wind Climatology," Proc. Second Workshop on Wind Energy
Conversion Systems, Washington, DC, 1975.
3.
Justus, e.G., IIAnnual Power Output Potential for lOO-kW and l-MW Aerogenerators," Prac. Second Workshop on Wind Energy Conversion Systems,
Washington, DC, 1975.
4.
Golding, E.W., The Generation of Electricity by Wind Power, Philosophical
Library, New York, 1955.
5.
Simmons, n.M., Wind Power, Noyes Data Corp. Park Ridge. New Jersey, 1975 .
6.
Astley, J., et.al .• "Aspects of Wind Flow in Urban and Rural Boundary
Layers," Royal Met. Soc. Canf. on Urban Meteorology. McQuarrie
University, Sichey, N.S.W., February 1977.
37
APPENOIX A
The velocity frequency distributions for the various stations showing wind
speeds and the hours/year the wind is in a one knot range around that wind
speed.
Russell
1950-1975
Wichita
1954-1975
Oodge City
1948-1975
Speed
(knots)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Hours
IB5"""
4
43
227
385
525
619
686
712
617
687
484
544
493
487
442
342
316
240
180
148
93
86
58
51
35
22
19
10
8
7
3
2
2
1
0.4
Probabi 1i ty
0.0005
0.0050
0.0265
0.0449
0.0612
0.0721
0.0800
0.0830
0.0719
0.0801
0.0564
0.0634
0.0575
0.0568
0.0515
0.0399
0.0368
0.0280
0.0210
0.0172
0.011 0
0.0100
0.0068
0.0059
0.0042
0.0024
0.0022
0.0012
0.0009
0.0008
0.0003
0.0002
0.0002
0.0001
0.0001
Hours
296
5
32
168
241
434
521
454
863
372
1061
256
766
326
483
597
437
272
513
76
280
38
88
41
31
40
17
7
21
4
13
2
3
2
1
3
Probability
Hours
Probabil ity
0.0006
0.0038
0.0198
0.0285
0.0513
0.0616
0.0536
0.1020
0.0440
0.1254
0.0302
0.0905
0.0385
0.0571
0.0705
0.0516
0.0321
0.0606
0.0090
0.0331
0.0045
0.0104
0.0048
0.0037
0.0047
0.0020
0.0008
0.0025
0.0005
0.0015
0.0002
0.0003
0.0002
0.0002
0.0004
10
53
180
250
368
484
635
718
746
703
577
591
520
559
474
388
279
284
201
174
142
78
78
55
42
34
26
0.0011
0.0061
0.0207
0.0287
0.0422
0.0555
0.0729
0.0824
0.0856
0.0807
0.0662
0.0678
0.0597
0.0641
0.0544
0.0445
0.0320
0.0326
0.0231
0.0200
0.0163
0.0090
0.0090
0.0063
0.0048
0.0039
0.0030
0.0015
0.0017
0.0007
0.0014
0.0003
0.0006
0.0003
0.0002
47
13
15
6
12
3
5
3
2
Goodland
1948-1964
Speed
(kngts)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Hours
Probabi 1itv
10
52
257
332
438
518
618
644
660
919
522
523
502
375
424
308
347
221
135
195
81
103
89
53
48
36
19
28
13
25
5
9
8
4
7
0.0011
0.0061
0.0301
0.0388
0.0512
0.0606
0.0723
0.0754
0.0773
0.1075
0.0611
0.0612
0.0587
0.0439
0.0497
0.0361
0.0406
0.0259
0.0158
0.0228
0.0094
0.0120
0.0105
0.0062
0.0055
0.0042
0.0023
0.0033
0.0015
0.0030
0.0006
0.0010
0.0009
0.0004
0.0009
~
La Junta
1948-1964
Dalhart
1949-1954
Hours
t!T
15
67
313
220
370
294
527
301
672
1230
217
568
335
593
215
427
585
147
215
102
263
130
172
163
37
84
24
98
25
62
52
10
24
7
32
18
5
10
7
6
2
8
9
2
4
1
2
3
10
0
Probabil ity
0.0017
0.0076
0.0357
0.0257
0.0422
0.0335
0.0601
0.0343
0.0767
0.1403
0.0247
0.0648
0.0382
0.0667
0.0246
0.0487
0.0668
0.0167
0.0245
0.0116
0.0300
0.0148
0.0196
0.0186
0.0042
0.0096
0.0027
0.0111
0.0029
0.0071
0.0059
0.0011
0.0027
0.0008
0.0036
010020
0.0005
0.0011
0.0008
0.0007
0.0002
0.0009
0.0010
0.0002
0.0004
0.0001
0.0002
0.0003
0.0011
0.0000
tlffiS
28
161
666
691
877
769
793
659
623
823
257
358
213
197
221
139
137
88
44
67
22
34
21
20
21
17
4
9
2
11
2
3
3
1
5
Probabil ity
0.0035
0.0201
0.0831
0.0862
0.1094
0.0959
0.0990
0.0822
0.0777
0.1026
0.0321
0.0469
0.0266
0.0246
0.0276
0.0173
0.0171
0.0109
0.0056
0.0083
0.0027
0.0043
0.0026
0.0025
0.0026
0.0022
0.0004
0.0011
0.0002
0.0013
0.0003
0.0003
0.0004
0.0001
0.0006
38