- Email: [email protected]
Improved extreme wind prediction for the United States
Journal of Wind Engineering and Industrial Aerodynamics, 41-44 (1992) 533-541 Elsevier
533
Improved e x t r e m e wind prediction for the U n i t e d States J. A. Peterka Civil Engineering Department, Colorado State University, Fort Collins, CO 80523, USA Abstract
An investigation of sampling error due to short data records was investigated for the fastest mile of wind records used to form design wind speeds for the U.S. The data for 29 stations in the midwest were checked for statistical independence and for trend over the geographical area. A supcrstation was formed from the stations containing 924 station-years of record, and 10,000 years of record with the same Type I distribution were generated by random function generator. The simulated data was shown to have the same distribution of predicted 50-year speeds, if divided into 25-year long records, as occurred for the 29 real stations. The analysis showed that the major variation in predicted 50-year wind speed from station to station is the sampling error. It also showed a method for effectively removing most of the sampling error. 1. INTRODUCTION Most structures in the U.S. are designed using wind speeds defined in local building codes. The trend in building codes is toward adoption of provisions of the ANSI A58.1. 1982 standard [1] (now being replaced with the similar ASCE 7-88 [2]). Thus the wind map contained in the national standards is the primary source of design wind speed definition in the U.S. This wind map, shown in Figure 1, was developed for use in the ANSI A58.1-1982 wind load standard, and has not been published in the archival literature. At locations away from the hurricane coast, the map has a minimum speed of 70 mph (31.3 m/s) fastest mile of wind at 10-m (shaded area) and maximum values of 90 mph (40.2 m/s). The map in Figure 1 was generated by the ANSI wind load sub-committee using extreme wind analysis at 129 airports presented by Simiu et al. [3] and using hurricane simulation data for the gulf and Atlantic coasts. The analysis of winds away from the hurricane coast was based on Type I extreme value analysis of fastest mile of wind records obtained from the National Climatic Data Center. Only data at airports were used where exposure errors would be minimized. The data were corrected to a common elevation of 10 m, and were screened for errors. The largest speed each year, regardless of wind direction, was used in the analysis. The stations averaged 31.5 years of record with a range of 10 to 54 years. 0167-6105D2/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
534
Figure 1. Extreme wind speeds in the U.S. [1]. Discussions of the errors in prediction of extreme winds using a Type I distribution are presented in Simiu and Scanlan [4] and Cook [5]. Type I distributions converge to the true value as the sample size increase,~. More than 1000 samples is desirable. Errors caused by short data records are called sampling errors, and can be significant for typical wind data records of 20 to 40 years. The purpose of this research was to examine this issue and to find a method to reduce the sample error. 2. ANALYSIS The current analysis considered 29 stations in the midwest, Figure 2. This is a relatively dense area for station coverage in the U.S. Figure 3 shows a contour plot of 50-year fastest mile speeds taken from the analysis of Simiu et al. [3]. A small high speed area in excess of 85 mph (38.0 m/s) dominates the center of the region at Indianapolis, Indiana, due to two high wind speed events of 83 and 93 mph (37.1 and 41.6 m/sj corrected to 10 m in a 34 year record. Nearby, to the northwest, is a low contour area at Chicago, Illinois, where the highest two wind events in 35 years of record are 56 and 59 mph (25.0 and 26.4 m/s). The Chicago station, Midway Airport, is in a suburban area more shielded than Indianapolis, but that factor is not likely to account for the 37 percent difference in maximum wind speed.
535
•
~
!
ol
|l •
Figure 2. Twenty-nine stations used in the data analysis.
80
65
70
Figure 3. Fifty-year wind speed contours in mph for the 29 stations (1 mph = .447 m/s).
536 The average yearly maximum fastest mile of wind at the two stations are 55 mph (24.6 m/s) at Indianapolis and 47 mph (21.0 m/s) at Chicago. This 15 percent difference could be primarily the result of surrounding roughness differences. Corrections for upwind roughness has not been addressed in this research, and is a needed future analysis. The large variation of wind speed with small geographical distance was not believed to be valid by the committee which constructed Figure 1 as evidenced by the smoothing of contours in the design map. It was hypothesized in this research that much of the variation in predicted 50-year wind speed from station to station is due to sampling error, i.e., that most of the variation is a direct result of the short data records. In order to investigate sampling error, the data were first normalized to remove any trend. The mean yearly fastest mile at each station is shown in Figure 4 as a parabolic least squares surface fit. Variations of individual stations from the fit surface had a standard deviation of 3.28 mph (1.47 m/s) indicating that the trend is real, but that variations from it are significant. The extent to which local upwind roughness at individual stations can explain the trend was not included in this study. The lines of constant velocity are roughly perpendicular to a common path of winter storms, which may or may not provide physical insight into the process. Figure 4 was used to remove the small trend in the data, adjusting each station by the ratio of the ensemble mean to the surface fit at the station.
,,,,,¢>
55
53
52
5 w
50 Figure 4.
49
48
Surface fit to mean yearly fastest mile speed in mph (1 mph = .447 m/s).
537 The next step in the analysis was to determine the extent to which the stations are statistically independent. Each station was compared to all other stations by calculating a correlation coefficient for the years in which corresponding data was available for at least six years. The set of correlation coefficients is shown in Figure 5. Most of the correlation coefficients are close to zero. The few that are not near zero do not represent adjacent stations, and some are for stations at almost the full distance of the array; i.e. the highest correlations appear to be obtained by chance. The implication of the figure is that the 29 stations are statistically independent of one another.
CORRELATION BETWEEN STATION PAIRS Actual Station Data 8 0 ~ 0-
~. 60
"
°:t 10 . . . . . O
r
4).6 ~).4 4).$ -0.2-0.1 0.0 0.1 '0.2'0.8'0.4'0.5'0.6'0.7'0.8 CORRELATION COEFFICIENT
Figure 5.
Correlation coefficients for all combinations of the 29 stations.
While it can be concluded that the stations are statistically independent, they still sample the same kind of climate, and even the same storm systems. Synoptic scale events that affect one station often affect another. Thus, the stations represent roughly the same climatology, with the trend removed as discussed above. The stations can then be thought of as 924 samples of a single station representing the climatology of this region, rather than a series of short records which must be treated separately. Statistical support for this view has been presented by Dorman [6] who concluded that all nonhurricane U.S. stations in Simiu et al. [3] represented just five wind categories. He did not attempt to categorize the data by geographic region. In this analysis, all 29 stations with trend removed are considered to represent 924 years of data at one station. Figure 6 shows the fit of a Type I distribution to that data. The fit is quite good.
538 2 9 SIAfI()Ixl COMB NED DAIA
L(3
I OO . . . . . . . . . . . . 9()
o~
~q()
. - .....
C)
7()
j
~
'
;
° >
FC) C
n(1 qf3
.a''"
I lJi Itl __J
I/'1
I.tJ I-.
l!
4()
j
..50 2O I (.t () --4
......... t -2
........ t.............. t . . . . . . . . . I ......... 0 2 4 Y VARIAI rZ
I ............ I ........... ~
Figure 6. Type I extreme value fit of fastest mile wind data to 924 samples. In order to investigate the validity of the approach used, a large data set with the same statistical properties as those identified for the real 924 station-year set was needed. This set of data could be analyzed in the same way as for the real stations to observe the characteristics of short records in a known statistical environment. The fit to the data of Figure 6 was used to generate approximately 10,000 years of data using a random function generator to obtain samples which fit the distribution. This record was divided into 377 segments of 25 years each to simulate typical lengths of record for real stations. The first 25-year record was correlated with each of the other 376 records; the resulting correlation coefficients are presented in Figure 7 and compared to those of the real stations from Figure 5. The agreement is good, indicating that the variation in correlation coefficient observed in the real stations is likely due to chance. A Type I fit was made to each of the 377 segments to predict 50-year recurrence winds. A histogram of predicted winds from the 377 segments is shown in Figure 8. Also shown is the histogram of the 29 ac~ :~i stations. The comparison is performed in the adjusted data (trend removed) for the real stations so that the variation in Figt,re 8 is due to the sampling error associated with short records. The variation in predicted 50-year wind speeds is about the same for both sets of data. A similar result was obtained for 35-year long records and for the same analysis conducted for 100-year winds. The results of this graph indicate that the variation in 50-year wind speeds shown in Figure 3 is likely due mostly to sampling error. It also shows the validity of combining several stations with independent records of a similar climatology into a single "supe rstation."
539 CORRELATION BETWEEN STATION PAIRS Actual and Simulated Data gou) 80-
O 63"
.rill i I I I I ! 1 lib i i I II IrL
50or) u,. 40O n- 30Lu m =E 20-
z
, _
_.,iil i i i
10-
-0.5-0.4-0.3-0,2-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
CORRELATION COEFFICIENT
i F-"] ACTUAL STATIONS
SIMULATED STATIONS I
Figure 7. Comparison of correlations between sets of real and simulated stations. COMPARISON OF 50 YEAR WIND SPEEDS Actual and Simulated Winds 0,14~
o ¢~
,, 0.1
. 0.08 0.06-
~~oo,
Id _
0
.
|... I!,.
_ .
59 61 63 65 67 69 71 73 75 77 79 81 63 85 87 89 91
10 M FASTEST MILE WlNO SPEED, MPH
I
I ACTUAL STATIONS
SIMULATED STATIONS I
Figure 8. Comparison of 50-year winds from 25-year long records from 29 real and 377 synthesized stations.
540
The superstation data fit to a Type I distributior, was used to predict the 50oyear recurrence wind for the superstation. This speed was then distributed to the map area with the adjustment factors used to remove the trend discussed above. The resulting distribution of 50-year speeds is shown in Figure 9 with solid lines. The speed contours from Figure 1 are shown with dashed lines. The exact location of the solid lines may be influenced too severely by the edge conditions of the map area, and may change somewhat when a larger area can be treated. For this reason, the lines are not now recommended for design purposes, particularly near the edges of the area treated.
80
\
75
80
/: 70
Figure 9. Fifty-year fastest mile speeds at 10-m predicted by the current analysis (solid lines) and by ANSI A58.1-1982.
There are two significant limitations on the proposed analysis method. First, the data have not been corrected for site exposure; wl~ile all locations are at airports, some exposure correction may be appropriate. Site exposure corrections are planned for future work, but are not trivial. For example, some stations show a trend in time which may be due to changing upwind characteristics. It is not clear that simple roughness change models are adequate for corrections due to upwind roughness where peak winds are from nearby downbursts, and complex terrain is expected to significantly affect readings. Second, use of short records of 20 to 40 years to predict longer term return winds cannot include any long-term climatological trends if such trends do exist. However, such analysis can set a baseline for examination of possible future changes.
541 3. CONCLUSIONS Figure 8 indicates that sampling error from short records is probably the primary source of variation in predicted 50-year winds among the 29 stations, with the exception of the small trend removed for this exercise. It also shows that the variation in predicted 50-year wind speeds for 25-year long records is quite large, ranging from below 65 to above 85 mph. It appears that a re-examination of U.S. wind speeds using the approach outlined in this research has the potential to significantly reduce the uncertainty in wind speeds used for building design. Some care will have to be taken in this application, since not all areas of the country may be as climatologically uniform as the area selected for this study. 4. ACKNOWLEDGEMENTS This research was performed as part of the Colorado State University/Texas Tech University Cooperative Research Program in Wind Engineering with the support of the National Science Foundation, NSF Cooperative Agreement BCS-9045652. The resevxch was conducted with the able assistance of Brenda Sower, undergraduate research assistant, who developed much of the software and analyzed an initial set of data, and Lenore Matsumoto who extended the analysis to a larger data set. 5. REFERENCES
1 ANSI, Minimum Design Loads for Buildings and Other Structures, American National Standards Inst. Standard ANSl A58.1 1982 (1982). 2 ASCE, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers Standard ASCE 7-88, Revision of ANSl A58.1-1982 (1988). 3 E. Simiu, M. J. Changery and J. J. Filliben, Extreme Wind Speeds at 129 Stations in the Contiguous United States, NBS Building Science Series 118, NBS (1979). 4 E. Simiu and R. H. Scanlan, Wind Effects on Structures, 2nd edition, Wiley, NY, 1986. 5 N . J . Cook, Designers Guide to Wind Loading of Building Structures, Part 1, Butterworths, London, 1985. 6 C. Dorman, United States Extreme Wind Speeds - A New View, Jl. Wind Engr. and Ind. Aero., 13 (1983) 105-114.
533
Improved e x t r e m e wind prediction for the U n i t e d States J. A. Peterka Civil Engineering Department, Colorado State University, Fort Collins, CO 80523, USA Abstract
An investigation of sampling error due to short data records was investigated for the fastest mile of wind records used to form design wind speeds for the U.S. The data for 29 stations in the midwest were checked for statistical independence and for trend over the geographical area. A supcrstation was formed from the stations containing 924 station-years of record, and 10,000 years of record with the same Type I distribution were generated by random function generator. The simulated data was shown to have the same distribution of predicted 50-year speeds, if divided into 25-year long records, as occurred for the 29 real stations. The analysis showed that the major variation in predicted 50-year wind speed from station to station is the sampling error. It also showed a method for effectively removing most of the sampling error. 1. INTRODUCTION Most structures in the U.S. are designed using wind speeds defined in local building codes. The trend in building codes is toward adoption of provisions of the ANSI A58.1. 1982 standard [1] (now being replaced with the similar ASCE 7-88 [2]). Thus the wind map contained in the national standards is the primary source of design wind speed definition in the U.S. This wind map, shown in Figure 1, was developed for use in the ANSI A58.1-1982 wind load standard, and has not been published in the archival literature. At locations away from the hurricane coast, the map has a minimum speed of 70 mph (31.3 m/s) fastest mile of wind at 10-m (shaded area) and maximum values of 90 mph (40.2 m/s). The map in Figure 1 was generated by the ANSI wind load sub-committee using extreme wind analysis at 129 airports presented by Simiu et al. [3] and using hurricane simulation data for the gulf and Atlantic coasts. The analysis of winds away from the hurricane coast was based on Type I extreme value analysis of fastest mile of wind records obtained from the National Climatic Data Center. Only data at airports were used where exposure errors would be minimized. The data were corrected to a common elevation of 10 m, and were screened for errors. The largest speed each year, regardless of wind direction, was used in the analysis. The stations averaged 31.5 years of record with a range of 10 to 54 years. 0167-6105D2/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
534
Figure 1. Extreme wind speeds in the U.S. [1]. Discussions of the errors in prediction of extreme winds using a Type I distribution are presented in Simiu and Scanlan [4] and Cook [5]. Type I distributions converge to the true value as the sample size increase,~. More than 1000 samples is desirable. Errors caused by short data records are called sampling errors, and can be significant for typical wind data records of 20 to 40 years. The purpose of this research was to examine this issue and to find a method to reduce the sample error. 2. ANALYSIS The current analysis considered 29 stations in the midwest, Figure 2. This is a relatively dense area for station coverage in the U.S. Figure 3 shows a contour plot of 50-year fastest mile speeds taken from the analysis of Simiu et al. [3]. A small high speed area in excess of 85 mph (38.0 m/s) dominates the center of the region at Indianapolis, Indiana, due to two high wind speed events of 83 and 93 mph (37.1 and 41.6 m/sj corrected to 10 m in a 34 year record. Nearby, to the northwest, is a low contour area at Chicago, Illinois, where the highest two wind events in 35 years of record are 56 and 59 mph (25.0 and 26.4 m/s). The Chicago station, Midway Airport, is in a suburban area more shielded than Indianapolis, but that factor is not likely to account for the 37 percent difference in maximum wind speed.
535
•
~
!
ol
|l •
Figure 2. Twenty-nine stations used in the data analysis.
80
65
70
Figure 3. Fifty-year wind speed contours in mph for the 29 stations (1 mph = .447 m/s).
536 The average yearly maximum fastest mile of wind at the two stations are 55 mph (24.6 m/s) at Indianapolis and 47 mph (21.0 m/s) at Chicago. This 15 percent difference could be primarily the result of surrounding roughness differences. Corrections for upwind roughness has not been addressed in this research, and is a needed future analysis. The large variation of wind speed with small geographical distance was not believed to be valid by the committee which constructed Figure 1 as evidenced by the smoothing of contours in the design map. It was hypothesized in this research that much of the variation in predicted 50-year wind speed from station to station is due to sampling error, i.e., that most of the variation is a direct result of the short data records. In order to investigate sampling error, the data were first normalized to remove any trend. The mean yearly fastest mile at each station is shown in Figure 4 as a parabolic least squares surface fit. Variations of individual stations from the fit surface had a standard deviation of 3.28 mph (1.47 m/s) indicating that the trend is real, but that variations from it are significant. The extent to which local upwind roughness at individual stations can explain the trend was not included in this study. The lines of constant velocity are roughly perpendicular to a common path of winter storms, which may or may not provide physical insight into the process. Figure 4 was used to remove the small trend in the data, adjusting each station by the ratio of the ensemble mean to the surface fit at the station.
,,,,,¢>
55
53
52
5 w
50 Figure 4.
49
48
Surface fit to mean yearly fastest mile speed in mph (1 mph = .447 m/s).
537 The next step in the analysis was to determine the extent to which the stations are statistically independent. Each station was compared to all other stations by calculating a correlation coefficient for the years in which corresponding data was available for at least six years. The set of correlation coefficients is shown in Figure 5. Most of the correlation coefficients are close to zero. The few that are not near zero do not represent adjacent stations, and some are for stations at almost the full distance of the array; i.e. the highest correlations appear to be obtained by chance. The implication of the figure is that the 29 stations are statistically independent of one another.
CORRELATION BETWEEN STATION PAIRS Actual Station Data 8 0 ~ 0-
~. 60
"
°:t 10 . . . . . O
r
4).6 ~).4 4).$ -0.2-0.1 0.0 0.1 '0.2'0.8'0.4'0.5'0.6'0.7'0.8 CORRELATION COEFFICIENT
Figure 5.
Correlation coefficients for all combinations of the 29 stations.
While it can be concluded that the stations are statistically independent, they still sample the same kind of climate, and even the same storm systems. Synoptic scale events that affect one station often affect another. Thus, the stations represent roughly the same climatology, with the trend removed as discussed above. The stations can then be thought of as 924 samples of a single station representing the climatology of this region, rather than a series of short records which must be treated separately. Statistical support for this view has been presented by Dorman [6] who concluded that all nonhurricane U.S. stations in Simiu et al. [3] represented just five wind categories. He did not attempt to categorize the data by geographic region. In this analysis, all 29 stations with trend removed are considered to represent 924 years of data at one station. Figure 6 shows the fit of a Type I distribution to that data. The fit is quite good.
538 2 9 SIAfI()Ixl COMB NED DAIA
L(3
I OO . . . . . . . . . . . . 9()
o~
~q()
. - .....
C)
7()
j
~
'
;
° >
FC) C
n(1 qf3
.a''"
I lJi Itl __J
I/'1
I.tJ I-.
l!
4()
j
..50 2O I (.t () --4
......... t -2
........ t.............. t . . . . . . . . . I ......... 0 2 4 Y VARIAI rZ
I ............ I ........... ~
Figure 6. Type I extreme value fit of fastest mile wind data to 924 samples. In order to investigate the validity of the approach used, a large data set with the same statistical properties as those identified for the real 924 station-year set was needed. This set of data could be analyzed in the same way as for the real stations to observe the characteristics of short records in a known statistical environment. The fit to the data of Figure 6 was used to generate approximately 10,000 years of data using a random function generator to obtain samples which fit the distribution. This record was divided into 377 segments of 25 years each to simulate typical lengths of record for real stations. The first 25-year record was correlated with each of the other 376 records; the resulting correlation coefficients are presented in Figure 7 and compared to those of the real stations from Figure 5. The agreement is good, indicating that the variation in correlation coefficient observed in the real stations is likely due to chance. A Type I fit was made to each of the 377 segments to predict 50-year recurrence winds. A histogram of predicted winds from the 377 segments is shown in Figure 8. Also shown is the histogram of the 29 ac~ :~i stations. The comparison is performed in the adjusted data (trend removed) for the real stations so that the variation in Figt,re 8 is due to the sampling error associated with short records. The variation in predicted 50-year wind speeds is about the same for both sets of data. A similar result was obtained for 35-year long records and for the same analysis conducted for 100-year winds. The results of this graph indicate that the variation in 50-year wind speeds shown in Figure 3 is likely due mostly to sampling error. It also shows the validity of combining several stations with independent records of a similar climatology into a single "supe rstation."
539 CORRELATION BETWEEN STATION PAIRS Actual and Simulated Data gou) 80-
O 63"
.rill i I I I I ! 1 lib i i I II IrL
50or) u,. 40O n- 30Lu m =E 20-
z
, _
_.,iil i i i
10-
-0.5-0.4-0.3-0,2-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
CORRELATION COEFFICIENT
i F-"] ACTUAL STATIONS
SIMULATED STATIONS I
Figure 7. Comparison of correlations between sets of real and simulated stations. COMPARISON OF 50 YEAR WIND SPEEDS Actual and Simulated Winds 0,14~
o ¢~
,, 0.1
. 0.08 0.06-
~~oo,
Id _
0
.
|... I!,.
_ .
59 61 63 65 67 69 71 73 75 77 79 81 63 85 87 89 91
10 M FASTEST MILE WlNO SPEED, MPH
I
I ACTUAL STATIONS
SIMULATED STATIONS I
Figure 8. Comparison of 50-year winds from 25-year long records from 29 real and 377 synthesized stations.
540
The superstation data fit to a Type I distributior, was used to predict the 50oyear recurrence wind for the superstation. This speed was then distributed to the map area with the adjustment factors used to remove the trend discussed above. The resulting distribution of 50-year speeds is shown in Figure 9 with solid lines. The speed contours from Figure 1 are shown with dashed lines. The exact location of the solid lines may be influenced too severely by the edge conditions of the map area, and may change somewhat when a larger area can be treated. For this reason, the lines are not now recommended for design purposes, particularly near the edges of the area treated.
80
\
75
80
/: 70
Figure 9. Fifty-year fastest mile speeds at 10-m predicted by the current analysis (solid lines) and by ANSI A58.1-1982.
There are two significant limitations on the proposed analysis method. First, the data have not been corrected for site exposure; wl~ile all locations are at airports, some exposure correction may be appropriate. Site exposure corrections are planned for future work, but are not trivial. For example, some stations show a trend in time which may be due to changing upwind characteristics. It is not clear that simple roughness change models are adequate for corrections due to upwind roughness where peak winds are from nearby downbursts, and complex terrain is expected to significantly affect readings. Second, use of short records of 20 to 40 years to predict longer term return winds cannot include any long-term climatological trends if such trends do exist. However, such analysis can set a baseline for examination of possible future changes.
541 3. CONCLUSIONS Figure 8 indicates that sampling error from short records is probably the primary source of variation in predicted 50-year winds among the 29 stations, with the exception of the small trend removed for this exercise. It also shows that the variation in predicted 50-year wind speeds for 25-year long records is quite large, ranging from below 65 to above 85 mph. It appears that a re-examination of U.S. wind speeds using the approach outlined in this research has the potential to significantly reduce the uncertainty in wind speeds used for building design. Some care will have to be taken in this application, since not all areas of the country may be as climatologically uniform as the area selected for this study. 4. ACKNOWLEDGEMENTS This research was performed as part of the Colorado State University/Texas Tech University Cooperative Research Program in Wind Engineering with the support of the National Science Foundation, NSF Cooperative Agreement BCS-9045652. The resevxch was conducted with the able assistance of Brenda Sower, undergraduate research assistant, who developed much of the software and analyzed an initial set of data, and Lenore Matsumoto who extended the analysis to a larger data set. 5. REFERENCES
1 ANSI, Minimum Design Loads for Buildings and Other Structures, American National Standards Inst. Standard ANSl A58.1 1982 (1982). 2 ASCE, Minimum Design Loads for Buildings and Other Structures, American Society of Civil Engineers Standard ASCE 7-88, Revision of ANSl A58.1-1982 (1988). 3 E. Simiu, M. J. Changery and J. J. Filliben, Extreme Wind Speeds at 129 Stations in the Contiguous United States, NBS Building Science Series 118, NBS (1979). 4 E. Simiu and R. H. Scanlan, Wind Effects on Structures, 2nd edition, Wiley, NY, 1986. 5 N . J . Cook, Designers Guide to Wind Loading of Building Structures, Part 1, Butterworths, London, 1985. 6 C. Dorman, United States Extreme Wind Speeds - A New View, Jl. Wind Engr. and Ind. Aero., 13 (1983) 105-114.