Report No. 61308 CAPE KENNEDY PEAK WIND PROFILE ...range of from 6 to 154 kts, each block having sides of 2 kts. gration of Eqs. (12), (13) and (14) only the blocks with probability

-. ; 9%

NASA CONTRACTOR REPORT

=.

Report No. 61308

CAPE KENNEDY PEAK WIND PROFILE PROBABILITIES FOR LEVELS FROM 10 TO 150 METERS

I

Lockheed Missiles and Space Company Huntsville Research and Engineering Center 4800 Bradford Blvd. Huntsville, Alabama

September 1969

c

By J. L. WoodandW. AlanBowman

Prepared for

NASA-GEORGE C . MARSHALL SPACE FLIGHT CENTER Marshall Space Flight Center, Alabama 35812

https://ntrs.nasa.gov/search.jsp?R=19700002900 2020-06-02T01:21:36+00:00Z

I - I

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2. GOVERNMENT ACCESSION NO. 1. REPORT NO.

NASA CR-61308 4. T I T L E AND SUBTITLE

3. RECIP IENT 'S CATALOG NO.

5. REPORT DATE

CAPE KENNEDY PEAK WIND PROFILE PROBABILITIES FOR LEVELS FROM 10 TO 150 METERS

I 7. AUTHOR(S) I 8. PERFORMING ORGANIZATION REP0R.r

. September 1969 6. PERFORMTNG ORGANIZATION CODE

J. L. Wood and W. Alan Bowman I 9. PERFORMING ORGANIZATION NAME AND ADDRESS 110. WORK UNIT NO.

4800 Bradford Blvd. Huntsville, Alabama

12. SPONSORING AGENCY NAME AND ADDRESS

NASA-George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama, 35812

Lockheed Missiles and Space Company Huntsville Research & Engineering Center

, NAS8-20082 1 3 . T Y P E OF REPOR;' & PERIOD COVEREC

Contractor Report

14. SPONSORING AGENCY CODE

11. CONTRACT OR GRANT NO.

17. KEY WORDS

Peak wind prof i les Peak wind speeds Exposure periods '

j ' ' . ' ,'

18. DISTRIBUTION STATEMENT

PYLIC RELEASE - 1 I; 1 A/*& /A/ d c-

/ ' / ' , , ' E. D. GEISSLER, Director

Aero-Astrodynamics Lab, MSFC

I 15. SUPPLEMENTARYNOTES The technical coordinator for t h i s study i s M r . 0. E. Smith of the Aerospace Environment Division of the Aero-Astrodynamics Laboratory, MSFC.

19. SECURITY CLASSIF . (of this repart) l20. SECURITY CLASSIF. (of this page)

U U

Peak wind s t a t i s t i c s for levels up t o about 150 m for Cape Kennedy are presented From dis- for use i n establishing d e s i p c r i t e r i a for space vehicles and fac i l i t i es .

tr ibutions of peak winds a t 10 m and a conditional (power-law profile) equation relat ing winds a t levels between 10 and 152.4 m, a bivariate distribution function i s integrated to provide: (a) cumulative probability distributions of peak winds for seven different levels and eleven different exposure periods, and (b) cumulative joint probability distributions of peak winds a t a reference level and individual peak-wind profiles between 18.3 and 152.4 m. The cumulative distribution curves for a l l levels (10, 18.3, 20.5, 61.0, 91.4, 121.9 and 152.4 m) and a l l exposure periods (1 hour and 1, 2, 5, 10, 15, 30, 60. 90, 180 and 365 days) possess the double-exponential shape, character is t ic of Fisher-Tippett Type I (FT1) extreme-value distributions. and resu l t s are summarized i n tables of the two FT 1 dis t r ibut ion parameters, computed from each curve. exceeded decreases both with increasing height and exposure period.

This feature is i l lus t ra ted

Results indicate that the probability o f a wind value not being

2 1 . NO. OF PAGES 22. P R I C E

67

FOREWORD

This report presents the results of work performed by

Lockheed' s Huntsville Research & Engineering Center while

under subcontract to Northrop Nortronics (NSL PO 5-09287)

for Marshall Space Flight Center (MSFC), Contract NAS8- 20082.

ment of Appendix A-1, Schedule Order 28.

This task was conducted in response to the require-

The NASA technical coordinator fo r this study is Mr.

0. E. Smith of the Aerospace Environment Division of the

Ae ro- As t rodynamic s Laboratory.

ACKNOWLEDGMENTS

The authors wish to thank Mr. 0. E. Smith and Dr. G. H. Fichtl of MSFC for several helpful discussions.

We a re a lso grateful fo r the able ass is tance of Mr. J . E. Tyson of Lockheed/Huntsville who ca r r i ed out the computer

programming.

.. 11

CONTENTS

Section Page

FOREWORD

ACKNOWLEDGMENTS

INTRODUCTION

THEORETICAL DEVELOPMENT

RESULTS

USE O F THE GRAPHS

SUMMARY AND CONCLUSIONS

REFERENCES

TABLES AND FIGURES

ii

ii

1

2

7

10

1 3

15

16

iii

Section 1

INTRODUCTION

Studies of peak winds at the 10-m level observed at Cape Kennedy,

Florida, show that such extremals fit the Fisher-Tippett Type I (FT1) distribution. Because of insufficient observational data, however, s imi la r

studies have not been attempted for levels above 10 m. This report outlines

a method by which power-law profiles based on peak wind observations from

the 150-m meterological tower at Cape Kennedy, and FT1 parameters devel-

oped fo r the 10-m level and for various exposure periods can be used to find:

0 Cumulative distributions of peak winds for levels up to about

150 m- and for exposure periods ranging from one hour to one

year , and

0 Joint distributions of peak winds a t a reference level (18.3 m)

and peak wind profiles (00, lo, 20 and 3 0 profiles) extending to

about 150 m, and for exposure periods ranging from one hour

to one year.

Section 2 THEORETICAL DEVELOPMENT

* The Fisher-Tippett Type 1 (FT1) density function f o r a wind speed

and p (determined from the mean and var i - variate u, with parameters

ance of the wind sample) can be written

Figure 1, based on work by Pope (Ref. l ) , shows a distribution of 10-m ex-

t reme winds.

the curves a r e control bands (Refs. 1 and 2 ) , and the straight line is the inte-

gral of the FT1 function (Eq. 1).

that they often fit a Fisher-Tippett distribution (c.f., Ref. 3).

In the figure, the aster isks represent observed extremals ,

Experience with extreme winds indicates

Fichtl (Daniels, Ref. 4) established an empirical relationship

- 3/4 18.3 c u

Uh =‘18.3 (A) between u

peak wind speed at the reference level, 18.3 m.

variable with a mean of 0.52 and a standard deviation of 0.36.

represents a power-law profile with parameters c and 3/4 derived by s ta t is-

tical analysis of Cape Kennedy wind records f o r a specific exposure period.

the peak wind speed (m/sec) a t level h( m) and ulBe3’ the h’ The quantity c i’s a random

Equation (2)

With this much as background, cumulative distributions of peak winds

can be developed fo r various levels by combining Eq. (1) and Eq. (2) . some level h,

F o r

* In this report , probability density functions a r e represented by f(u) where u is a random variable.

2

where f(uhlc) is a probability density function with random variable u

ject to a given value of c ; i.e., a conditional probability, which may be ex-

pressed in te rms of Eq. (1) by

sub- h

f (uh C ) = a e x p -"(Uh- PI] 9 (4)

where u is a function ( h E c. For some other level h: the corresponding

probability f(u , is related to f(uh c) by the transformation al c, 1

Then, from Eq. (5) and Eq. (3) ,

It is convenient to choose h = 10m, since the 10-m FT1 parameters a and p required to determine f(u

Section 3) , and to choose h'Z18.3,since 18.3 appears explicitly in Eq. (2).

Subject to these choices, and the fact that c is normally distributed*, i.e.,

c ) b y Eq. (4) have been tabulated (Ref. 4, also see hl

- 2 2 f(c) = - 1 e-(c-c) / 2 * *

4 Fichtl , private communication.

3

then Eq. (6) can be integrated to give the probability density function

To summarize, f rom the distribution f (u

specified in Table 1, and a relationship between u

) can be determined.

) given by Eq. (1) with a and p

18.3 10

10 and u given by

Eq. (Z ) , the function f (u Next the distribution f (u,) 1 18.3

fo r any level, h, is found.

A bivariate distribution can be formed relating the wind speed a t l e v e l

h to that at 18.3 m by writing an expression s imilar to Eq. (3)

where f (u u

of the normal deviate c by the transformation

) is a conditional probability that can be expressed in t e rms h I 18.3

and where the explicit dependence among c , uh and u 18-38 viz.S

18.3 Inu -1nu

-3/4 In (h/18.3) 18.3

h c = U

follows f rom Eq. ( 2 ) . The Jacobian in Eq. (9) can be obtained by differentiating

Eq. (10)

/Uh - - - ac

In (h/18.3) - 3/4 18.3 auh u

4

c

Substituting Eqs. (3, ( 9 ) , (10) and (11) into

probability density function for any level

m

Eq. (8), and integrating gives the

u18.3) dU18.3 . (12)

The cumulative distribution, o r the probability that a peak wind speed will

not exceed some value V, is obtained by integrating Eq. (12)

V

Consider now peak wind profiles. The profile of winds from 18.3 m to

is determined by only one parameter - the 18.3 152.4 m f o r a given value of u

normal deviate c.

exceeded is equal to the probability the c will not bk exceeded.

fixed value c =C, f (u,, u18.3) in Eq. (8) is the probability that both u18.3 and

the "C" profile,'' given by Eq. (2) will occur.

is obtained by setting C = C t 30 in Eq. (2).

Furthermore, the probability that a profile will not be Then, f o r a

F o r example, the "30" profile

The cumulative distribution o r

the probability that neither u1 8.

by integrating Eq. (8)

nor the C profile will be exceeded is obtained

To evaluate Eq. (14), the a rb i t ra ry choice is made that h = 152.4 and C = E,

c t 0, F t 20, and Ct 30. -

Equations (13) and (14) were integrated numerically by Simpson's rule.

The application of Simpson's rule to Eq. (7), summing over the l imits E t 40,

5

was straightforward.

range of f rom 6 to 154 kts, each block having sides of 2 kts. gration of Eqs. (12), (13) and (14) only the blocks with probability greater

than 0.00001 were included, and the, total probability was generally about

0.9993. Figures 2 and 3 illustrate the double integration.

results of this study a r e presented in Figs. 4 through 47, and a r e discussed

in Section 3.

Equation (8) was solved in blocks over a windspeed

F o r the inte-

The general

9

Figure 2 is an example (Cape Kennedy, 30-day exposure period) of a

plot of the probability contained in the individual blocks, Rather than a density

function, the ordinate is the probability that an 18.3-m wind value l ies between

+ 2 (kts) on the horizontal axis, while a 152.4-m wind value

t 2 (kts) on the diagonal axis (unlabeled, but l ies between u

on which the lines a r e spaced at two-knot intervals, beginning at six knots).

18.3 and u18.3 U

152.4 and 152.4

Figure 3 i l lustrates the same results in two-dimensional blocks. The solid blocks represent probability greater than 0.0001, the shaded blocks

probability between 0.0001 and 0.00001, and the c lear blocks probability l e s s

than 0.00001.

6

Section 3

RESULTS

r annual

reference values "env" values

1 In < t < 24 h r s 1 d a y 5 t 5 365 days 1 In < t < 24 h r s '1 day - < t 5 3 6 5 days - - - 4

a 4.67 82 4.7668 5.3487 5.4579 b 0.0279 0.3687 0.0343 0.9170

C 9.3997 16.8799 14.9100 19.8496

d 2.3537 4.7451 1.5535 4.3462 J

..

Results of Eq. (13) are shown in Figs. 4 through 25 fo r eleven different

exposure periods. Since a straight l ine on

this graph represents an FT1 distribution, all curves are interpreted as rep-

resenting such distributions.

period figures (Figs. 4 and 15) are l inear extensions of the solid curves; this

is discussed below.

The curves are almost straight.

The dashed curves on the one-hour exposure

The 10-m a and pvalues f o r Cape Kennedy, given in Table 1, vary

with the exposure period t according to

-1 a = ( a t b In t)

p = (c t d Pn t)

The coefficients designated by "env," result f rom the interpolation of a n

envelope of maximum-monthly, bimonthly, and yearly (including hurricane

data) means and standard deviations of one- and 30-, 60-, and 365-day peak

winds, respectively. The corresponding a ' s and p 's represent conservative

7

distributions fo r design and operational purposes. They may be thought of as limit-

ing cases of peak-wind distributions that could be expected to occur (see Ref.4).

Values of a and p f o r the other levels (18.3, 30.5, 61.0, 91.4, 121.9 and

152.4 m) were determined f rom the l inear expression

by substituting values of u and y (the reduced variate) f rom two points on

each curve; they appear in Table 1 also.

Before proceeding further, several comments about exposure period

In the present context, exposure period is the interval of should be made.

time chosen f o r which the largest o r peak wind is extracted f rom a given

wind record.

in establishing Eq. (2) , o r it may be an hour, a day, a month, etc.

portance of exposure period is manifested i n the and p parameters which

vary with the logarithm of exposure period, and which determines the shape

of the FT1 distributions.

* This period may be 10 minutes (Ref.4) which was the case

The im-

Figures 26 through 47 result f rom Eq. (14). The curves represent the

(abscissa value) and the profile

These figures show clearly 18.3 joint probability (ordinate value) that u

indicated in the legend will not be exceeded.

that there is little difference between the cumulative distributions of 00 and

3 cr profiles.

Before proceeding with examples of how the results of this report can

be used (Section 4), several points should be made.

* The peak wind observed a t each level h = 18.3, 30.5, 61.0, 91.4, 121.9 and 152.4 m during an exposure period of 10 minutes was tabulated. The peak winds were assumed to have occurred simultaneously a t all levels (Fichtl, private communication).

8

I Difficulty a r i s e s f rom trying to integrate Eqs. (12) and (14) for small ~

values of uh.

period cases were affected (F igs . 4, 5, 15, 16, 26 , 27, 37 and 38).

of difficulty is the empirical expression (Eq. (2))which enters into the inte-

grated f (uh,

value of u18,3.

so the empirical relation is not meant to hold fo r u

contribution to Eqs. (12) and (14) from the range (-00, u’ ) is lost.

theoretically, the integrals must approach unity as their upper limits tend to

00, it is reasonable to assume that any computed deficit results f rom this loss.

Accordingly, the distributions were adjusted by assigning the deficit value as the cumulative distribution for uh, and by shifting the values for uh> ufi up-

ward. The curves were then completed by l inear extrapolation downward to

the 0.001 ordinate value (dashed lines in figures).

In the present study, only the one-hour and one-day exposure

The center ’

Equation (2) possesses a minimum \ for some small * Such a minimum (call i t ut ) is not ordinarily observed, h

< uh. Therefore, the

Because, h

h

Secondly, it should be mentioned that no special significance is implied

by the use of FT1 graphs for plotting Figs. 26 through 47.

used simply as a matter of convenience.

vantageous for some purposes (e.g., computer applications) to have joint

distributions in a form other than graphical.

by the l inear expression Y(c, t) = @ ( c y t ) [u18.3 - Y(c, t ) ] ; the constants

a specific 18.3-m wind and profile, may be computed f rom

The graphs were

On the other hand, it might be ad-

Therefore, each curve was f i t

p and Y appear in Table 2. Approximate joint distributions F(u 18.3, c ) Y for

* tends toward 18.3

Below this small value of u18.3,

zero.

tends toward Q) a s u

9

Section 4 USE OF THE GRAPHS

Figures 26 through 47 represent joint probability statements derived

from two conditions, viz., the 18.3-m wind is equal to a given wind A, and

the profile of the winds from 18.3 to 152.4 m is equal to a given profile B

when the 18.3-m wind is A.

the probability that both conditions exist simultaneously.

The product of these probabilities P(A nB) , is

Consider three statements of joint probability to determine how the

figures and the table can be used.

Case I

Case I1

Case I11

The probability that the 18.3-m wind A is less than a given value A', and the profile B is l e s s than a given profile B1, i n other words, neither A nor B a r e exceeded, is given symbolically by P(A - < A' n B 5 B')

The probability that at least one of the conditions in Case I is violated, i.e., ei ther the 18.3-m wind is exceeded o r the profile is exceeded o r both a r e exceeded is g i v e n b y P ( A > A ' U B > B ' ) = 1 - P ( A L A 1 n B i B 1 )

The probability that both the 18.3-m wind and the profile a r e exceeded is given by P(A >A1 n B > B') = 1 - P(A LA') - P(B AB' ) t P(A <_AI n ~ 5 ~ 1 ) .

To determine the probabilities i n Cases I and 11, choose the graph f rom Figs.

26 through 47 for the desired exposure period and the profile of interest .

Using the 18.3-m wind value on the abscissa , read the corresponding prob-

ability f r o m the ordinate o r , use Eq. (15) with p and y f rom Table 2.

Example of Case I Suppose that a vehicle must remain on the pad f o r

a period of three months and that i ts design l imits will be exceeded if the

18.3-m wind exceeds 55 kts and the profile of winds exceeds the 30peak-

wind profile. What is the probability that these conditions will not be ex-

ceeded? According to Eq.(2) with c = c' t 30 = 1.60 the profile includes

10

U < 55.0 kts 18.3 - 58.78 30.5 < U

- <, 64.32 61.0

U < 67.80 91.4 - < 70.39 u121.9 - < 72.46 . 152.4 -

U

U

Figure 34 gives joint probabilities f o r the 90-day exposure period. Fifty-

five kts on the abscissa corresponds to P = 0.92 on the ordinate for the 30

envelope or profile.

Example of Case I1 What is the probability that one o r both conditions

will be exceeded?

probability that at least one of the conditions u18,3 - < 5 5 kts and uh 5%(3O) is violated.

By subtracting 0.92 f rom 1.0, 0.08 is obtained for the

Turning now to Case 111, it is suggested that the simplest way to eval-

uate P(A > A' n B > B') is t e rm by te rm, according to the formula above.

Figure 48 is used to find the value of u152.4 that corresponds to the profile

of interest and the particular u18.3 value, o r , it may be computed directly

* a r e obtained f rom the appropriate graphs (Figs. 4-25) . is read from Figs. 26 through 47 o r computed from Eq. (15).

f r o m Eq. (2). The te rms P(A - < A') = F ( u ~ ~ . ~ ) and P ( B 5 B') = F(u152.4 1 P(A LA' fl B 5 B')

JI 7.

Alternatively, Eq. (1) could be integrated

-00

and P (A <A1) = F (ulBe3) solved, using p and a f rom Table 1.

expression f o r 152.4m would lead to P ( B 5 B') = F

A similar

11

Example of Case I11 Suppose that f o r an exposure period of 90 days,

the probability is needed that the 18.3-m peak wind is grea te r than 40 kts

and the profile is grea te r than the 00 profile. Accordingly

p ( 1 - 1 1 ~ ~ ~ 40) = F ( u ~ ~ . ~ = 40) = 0.40 (Fig. 12),

o r

a = 0.1509, p = 39.3919, F(40) = 0.40 (Table 1, Eq.(16)),

= 44.83 kts (Fig. 48 or Eq. (2)), 152.4 U

= 44.83) = 0.37 (Fig. 12), ('l 52.4 < 44.83) = p('152.4 - or

a -1 0.1463, p = 44.9120, F(44.83) = 0.37 (Table 1, Eq.(16)),

<44.83) = 0.32 (Fig.34), (u18.3 5 40nul 52.4 -

and finally

> 40nuh > Ooprofile) = 1 - 0.40 - 0.37 t 0.32 = 0.55. ('l 8.3

Section 5

SUMMARY AND C ONC LUSIONS

Integral equations were developed that describe the cumulative distri-

bution of peak winds for several levels viz.,. 10.0, 18.3, 30 .5 , 61.0, 91.4, 121.9

and 152.4 m, and keveral exposure periods viz., 1 hr, 1, 2 , 5, 1 0 , 15, 30, 60, 90, 180 and 365 days.

and time periods.

posure period.

whose coefficients a r e tabulated.

The equations a re applicable to intermediate levels

The results a r e presented in graphical form for each ex-

The curves in each figure were fitted by a l inear expression

Equations describing the joint probability that a wind value a t the ref-

erence level 18.3 m, and a given profile (OD, 10, 20, 3 0 ) will not be exceeded

a r e also derived. Results a r e presented in both graphical and tabular form.

The cumulative distributioqpresented in this rCport, of peak winds fo r

levels between 10 and 150 m and for exposure periods between one hour and

one year, possess the double exponential shape characterist ic of FT1 dis t r i -

butions.

a given value, decreases with increasing height above ground (for all exposure

periods), and decreases with increasing exposure period (at all levels).

As one might expect, the probability that the wind will not exceed

F r o m a physical viewpoint, to the extent that wind gusts associated with

individual small scale eddies can be envisioned a s simultaneously influencing

the entire planetary boundary layer a t a given station and within a given ex-

posure period, peak winds at levels above 10 m could be expected to be dis-

tributed according to a FT1 distribution with parameters given by Table 1.

However, to interpret the results obtained a s proof that peak winds above

10-m f i t such a distribution would be speculative.

13

With the reference wind u18.3 and the exposure period t fixed, joint

The distributions fo r 00, 10, 20 and 30 profiles a r e practically the same.

probability that ulae3 will not exceed a given value and none of the four

profiles will be exceeded decreases with exposure period.

14

Section 6

REFERENCES

1. Pope, J. E., "A Computer Program f o r Evaluating Extremes Distributed as Fisher-Tippett Type I,I1 LMSC/HREC A791263, Lockheed Missiles & Space Company, Huntsville, Ala., March 1968.

2. Gumbel, E. J., Statistics of Extremes, Columbia University Press, New York, 1958.

3. Thom, H. C. S., "New Distributions of Extreme Winds in the United States," J. Struc. Div., ASCE, July 1968, pp. 1787-1801.

4. Daniels, G. E., ed., "Ter res t r ia l Environment (Climatic) Cr i te r ia Guide- lines for U s e in Space Vehicle Development, 1969 Revision,11 NASA TM X-53872, George C. Marshall Space Flight Center, Ala. , 8 September 1969.

15

4

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P P * N. - m

m 0. m

x

m N Ln

t

3 8

P

d

P r-

P * Y

0. 0 0 - d

9 9 9

:

ii

*

d

d

r- N

m

2 m

Ln N - d

4 - 0.

0 N P

f m

o W m

x

m

d i P

0 o D.

:

t- 0

01

P

m

u;

m 0. 0.

x

9 m r- e

d *

r- m 0 - d

N m

9 - P

- - d

4 N m -

17

N

0

6

d n c

X

3

9 N N

Q. 0

‘“.

01 m m

d

9 9

In

m

m

<

m r- Ln

d

9

9

P m

m

N.

N d 9 d

0 *.I

I R

In In u. d:

m r- N m

Ln r- N 0

N i

x 0: m

0 N h N -i N

N

In N 9

x , u. 9 In

01 CI N.

N Q 0

d

N I- O - d

In r- 0 - d

In

I- 0 - d

W Q

0 01 4

d: c "

r-

N

Q O

e

N.

N 0 N

5 m

m 0

m m i m

x d - I x

d

< e W m

01 m - d

d

d

W w

R

E D

U

C

E D

V

A

(i

I A

1

E

.**S

.*BO

.*a?

.e99

. a90

.so9

.so0

,910

. H O

.SSO

.930

. so0

.as0

.a00

.TOO

. eo0

. 900

.400

. SO0

.ZOO

. l oo

.os0

.010

.oos

.001 0

-1

1 00

I

+

I ? ? I

*

1 !

Fig . 1 - F T l F i t of 30-Day P e a k Wind Da ta f o r Cape Kennedy

20

.o

1 .D

0

Fig. 2 - Joint Probability Curve fo r Cape Kennedy (30-Day, Annual Reference Period)

21

l e s s than 0.00001

bxv 0.0001 to 0.00001

100

90

80

70

60

50

40

30

20

10

= greater than 0.0001

10 20 30 40 50 60 70 80 90 100

18.3 (kt U

Fig. 3 - Joint Probability Plot fo r Cape Kennedy (30-Day, Annual R ef e r ence Period )

22

CACC I t m t O T C T ! M R

1. W > l S

Fig. 4 - Surface Wind Cumulative Distributions

2 3

CACC ICNNCOV C T 1 OAV

n C 0

U C

r 0

V

4

n I 4

T C

. e d 0 1n.q

0 1 8 . 3

I 3 0 . 5

e1.q

.-r.

8 9 1 . 4

0 10. ro. SO. ¶O . 00. ?O . 00

I WCltS

Fig. 5 - .Surface W i n d Cumulative Distributions

24


2 5

C A W I C W C D Y C I I DAYS

n C 0

U c f D

V

A ~ n

1

4

T C

I mtS

F'ig. 7 - Surface Wind Cumulative Distributions

26

- l.&

- 1 4 1

I- - r.0-

0 Y0.0

@ I * . ) .m

I M@tS


27

n r 0

U C

r 0

V

A

I)

I A

1 C

a 9q.n

0 ta.3 .m

a n t a

Fig. 9 - Surface W i n d Cumulative Distributions

2 8

- I )

e l D

c U

C

D Y . O b

t . 0 .c 1 . Y L

* . O L

0 . Y k

- 0 . Y O - 1

- l . Y t

t

.- I

c - t . 3 -


2 9

n

n C

U c r 0

V

4

a I

A

I C

K m T a

Fig. 1 1 - Surface Wind Cumulative Distributions

30


31

a I

n

U

c

I

n

V

4

9

I

I

1

r


32

,

# K I T

Fig. 14. - Surface Wind Cumulative Distributions

33

I.


34

'n. en. T 0- $0. i m. 0 f n- 2r)- I n '

M N T q


* * P

U

‘ r r c,

V

4

a I

4

r c

N W 1 9


1

36

I

__

.. .

. -, . .: 1.-y

=A_. 9

r r

L l

r

I

P

V

* 9

1

a

r c

-. ..

- - ------I--- .~

..

- . .

. .

- .

.

1


37

R

C

I r I,

c

r r

V

3

P

I

fi

T

, i

c

t

- -+

. .~ .... . .-

c--t----

I

en.

... .


38

a

.F r

U

r

F

P

V

4

0

I

a

1

c

.. .

I

.

. . .. ..

, -. :

1 e . 3

u-

. .- I

I--- __


39

e c P

U

c

r P

V

4

e

1

4

1

r

S

.nn

.*a¶ -%

-

.wq - --

.+n

-%In

.*yn

.3n-

.9r)n

----

-- --

--

--

.ayn

.enn ----

-700

.eon

.y""

. 4 m

-3nn

*tnn

.Inn

.n¶n

- - --

--

- -

- - n 1 n . M Y

*oar

_ - _ .

.... . . .

en-

..... .. .-__

- -I-- - , _-

- ____- - .~ _--

- ._ ...... ...

. . . . . . . . . . . . . . . . . . . . .

- .................. .......

. . .

. .- .

i ?OS en.


40

1. 1 nn.

a

c

P

U

c

c P

V

e

9

I

a

I r

c i lV'


41

.99*

0

c .nr --

I

.-?

. 9 9 y

S

-9911 -

. ) ( I 5

. qn,,

t I Y . Y b

___._

~ ... . ..

..

. .

. ~. .

I. ! I. rn. %l . 9 nn.


42

* P

I,

r P

V . a I

4

1 r

Fig.24 - Surface

4n.

uw l*

Wind Cumulative Distributions

43

*Lc I *


44

. .. . .- . ..

.. . . .-

. .

.

J

1 00'

? R 0 0 A

B 1 L

K 1 I

Fig. 26 - Surface Wind Profile Cumulative Distributions

45

P R 0 B A

B I L

I 1 Y

.**e

.**a

. **?

.**¶

.*ea

.HI

.em

.*TO

.sea

.*sa

. m a

.ma

. m a

.ma

.tea

.aoa

.5W

.400

.3w

.eo0

. a 0 0

.050

.OlO

.001

,001

.....

.............

.. -. .......

....... - .

......

.....

.....

. .

.....

.......

. . ; I

CAPE KENNLDY E 1 1 D A Y

80. ao. 40. BO.

K N O T S

...

-- . .

.__

___ . . . .

... .- . . . . -

........

. . . .-

...

......

-.

... ..

........

____.

___.

~.


.?

R 0

e A e I L

1

1 I

.m

.m

.SSl

.m

.m

.n!

.su

. S7I

.-I

.SI1

.eu

.w(

..SI

.#I

.7u

.0u

.5u

.4u

.sol

.tu

.lo(

.OS1

.oat

.Do4

.Do!

0

X

*

. ..

. .. -

-

. -.

.

.. __-

. . -

t 1 2 D A Y S

---I ---i I -+

-i

0 10. 80. SO. 40. SO. 00. eo. mo. lo..

KNOTS


47

CAPE KE NNfO Y E 1 5 D A Y S

P R 0 B A

0 I L I 1 1

.a99

.**a

,997

.**I

.w

. n s

.w

.#TO

.WO

.SI0

.uo

.ma

..IO

.ma

.7w

.000

. I W

AM

.1w

.tw

.loo ,010

,010 . 001

-001

0

0

X

*

. . . . . . - . . .

. . . .

- .

-----

___

___ __. .. -_

-- __

__ - - ._ __ .

-

-I-

- ....

- ...... .

- -. ....... ___

- . __ ........ __ . - . -. . . . .

.- ~ ................

....

.....

. . . . . .- .

__I

....... 1

-1

-4 0 10. 80 80. 40. 10. 00. TO. 00. *a. 80 . .

K N O T S

F i g . 29 - Surface Wind Profile Cumulative Distributions

4.8

CAPE K L W D Y E T 10 D A Y S

P R 0 I)

A

I)

1 L

1

1 Y

.m

...(

.ni

.m

.m

- 0 . 3

.o.I

..TI

.#I

.SI(

.91(

.m

. O N

.rat

.To(

.ow

.so(

.4o(

.SO(

.SO(

.lot

.OSM

.01a

.001

.oQl 0

- --i 10. SO. 10. 00. TO 00. ao. 8 0 8 .

KNOTS


49

i

C A N KENNEOr

. @@@

.*@8

. @@7

.*@S

*@@o

.@8S

.@80

.070

.@80

.@SO

.@SO

.eo0

.850

.eo0

,700

.eo0

.SO0

A00

.SO0

.roo,

.loo

.OS0

.o:o

.DO9

.DO1

E T IS D A Y S

0

0

X

-

* - - _

--

- --- - ---

--__

- -

- -

- ---

-

-

0

? R 0 B A

B I L

I T Y

......

80. SO. , 40.

KNOTS

B. 80 e TO. 80. M. 100.

Fig . 3 1 - Surface Wind Profile Cumulative Distributions

50

CA?E KE-DY

? R 0 9 1,

B 1

L

1 I Y

L 1 SO DAYS

eo. TO. a0 . #. 101.

KNOTS


5 1

P R 0 B A

B I L

I 1 V

. SSS

. SSI

. ssr

.*SY

. SW

.SI¶

. S I 0

.or0

.#P

.*YO

. SSO

.eo0

..YO

.ow

.rw

. O W

.YO0

A00

.SO0

.200

.IO0

.os0

.010

.OOY

.OOl

.. -

. .

0

CAPE KENNEDY E 1 60 D A Y S

I. 00. M.

F i g . 3 3 - Surface Wind Profile Cumulative Distributions

52

? R 0 B A 0 1 L 1

1 1

.m

..u

.m

.@a!

.m

.@el

.sac

. e70

.wo .*

.w

.am

.Ma

.om

.rw

.om

.5m

.4m

.so0

.tw

.loo

.os0

.a10

.W1

.Wl,

40. BO. eo. 70 eo. m. I... 10. Bo.

KNOT8


53

P R 0 D A

D I L

I I V

.em

.m

.H1

. *M

.m

. n a

.wo

.*TO

. n o

.@SO

. 8 0

.a00

.8SO

.mo

.TOO

A00

A00

.400

.so0

.a00

.loo

.os0

CAPE KENNEDY E 1 1 0 0 D A Y S

54

KNOTS


55

? I 0

h 8 I L 1 T Y

0 IO. m. 40. M. 00. m. 80. w. rwl8

1

tm.

Fig. 37 - Surface Wind Profi le Cumulative Distributions

56

? R 0 I)

A

0 I L I 1 Y


57

P R 0 B A B I L I 1 Y

CAPE KENNEDY E 1 2 DAYS (CNW


5.8

? R 0 B A m I L

I I V

.uK,

.too

.lo0

.os0

.a10

.801

mmts


5.9

c R 0 e A

e 1 L 1 I Y

.m.

. n o

.nr.

.m

. n o

.em

. n o

.*TO

. n o .

. H O

.em.

.#Q

-8SO

.em

.rm.

.em

.Baa

A00

.mo

.mo

,100

.OB0

.OlO

.oo)

0

0

X

*

I

’

.

-

-

-

-

-

-

.001---

CAPE K f r m L O Y E 1 10 D A Y S (CNV)

0 10. 80 JO 40. BO. eo. eo. 18@.

K W T B

F i g . 4 1 - Surface Wind Profi le Cumulative Distributions

60

C R 0 B I 9 I L I 1 v

.m

.m

.m

.m

.em

.a9

.aw

. mm

.wa

.No

..30

.(Do

.*so

.Do0

.mo

.a00

. $00

A00

.so0

.aw

.loo

40.- so. 00. m. a. I-. 10. 10. io .

K n o t 8


61

P R 0 B A

B 1 L I 1 Y

. B n

.sea

.ni

.nr

. n o

.ws

.e80

. B70

.WO

. H O

.w

.900

..so

.mo

.7w

CAPE KEMMEOY E I SO D A Y S (EMV)

.loo

.os0

~

-

.@IO ,001 '--- zT:+-+yf: ,001 --_ - _

ao. TO. e0 . 00. io.. 0 IO . 80. SO. 40 10.

K N O T S

Fig, 4 3 - Surface Wind Profile Cumulative Distributions

6 2

c

.m

.an

.m

.mea

. n o

.WI

.am

. n o

.w

. n o

.sso

.#o

.uo

.a0

.roo

.ow

.500

..w

.sm

.too

.loo

.OS0

.OlO ,001

,001

. ? R 0 8 A

8 1 i I 1 Y

0

0

X

'

~

'

-

__-.

'- - -- a 80. io . 40. io . 00. 10. m. n, 1m.

UmtS


6 3

P I 0 b A

b I L I 1 Y

Fig. 45 - Surface W i n d Prof i le Cumulative Distributions

CAPE KENNEDY E 1 90 DAYS (ENV)

I. r n .

64

c ? R 0 0 &

I 1 L

1 'I Y


65

CAPE K E N N E D Y E T 365 D A Y S ( E N V )

? R 0 B A

B I L 1 1 Y

0

0

X .**e

I

0 S I G M A

1 S I G M A

2 S I G N A

3 S I G M A

0 1 0 0

c

m . 8 0 . 4 0 BO. 00. ,o . eo. #. K N O T S

F i g . 4 7 - Surface Wind Profile Cumulative Distributions

66

c

Y b. I w

D s ? L L D

U w 0 1 S

1 9 2

4

w

L L V E L

it..

so-lIk 0 0 10. 1

MSFC-RSA, Ala

Fig.48 - Wind Profile Plots

67

Documents

Report No. 61308 CAPE KENNEDY PEAK WIND PROFILE ...range of from 6 to 154 kts, each block having sides of 2 kts. gration of Eqs. (12), (13) and (14) only the blocks with probability