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 A UNITED STATES 
 DEPARTMENT OF 
 COMMERCE 
 PUBLICATION 
 
 *'4TH O' * 
 
 U.S. DEPARTMENT OF COMMERCE 
 Environmental Science Services Administration 
 Research Laboratories 
 
 M ESSA Technical Report ERL 140-APCL 10 
 
 Plotter Subroutine for Meteorological 
 Straight Line Flight Data (SLENDER) 
 
 HEINZ H. GROTE 
 
 BOULDER, COLORADO 
 December 1969 
 
ESSA RESEARCH LABORATORIES 
 
 The mission of the Research Laboratories is to study the oceans, inland waters, the 
 lower and upper atmosphere, the space environment, and the earth, in search of the under- 
 standing needed to provide more useful services in improving man's prospects for survival 
 as influenced by the physical environment. Laboratories contributing to these studies are: 
 
 Earth Sciences Laboratories: Geomagnetism, seismology, geodesy, and related earth 
 sciences; earthquake processes, internal structure and accurate figure of the Earth, and 
 distribution of the Earth's mass. 
 
 Atlantic Oceanographic and Meteorological Laboratories and Pacific Oceanographic 
 Laboratories: Oceanography, with emphasis on ocean basins and borders, and oceanic 
 processes; sea-air interactions: and land-sea interactions. (Miami, Florida) 
 
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 taminants; development of methods for prediction and control of atmospheric pollu- 
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rtrtENTQg. 
 
 Se 'UCl $1**^ 
 
 U. S. DEPARTMENT OF COMMERCE 
 Maurice H. Stems, Secretary 
 
 ENVIRONMENTAL SCIENCE SERVICES ADMINISTRATION 
 Robert M. White, Administrator 
 RESEARCH LABORATORIES 
 Wilmot N. Hess, Director 
 
 ESSA TECHNICAL REPORT ERL 140-APCL 10 
 
 Plotter Subroutine for Meteorological 
 Straight Line Flight Data (SLENDER) 
 
 HEINZ H. GROTE 
 
 ATOMOSPHERIC PHYSICS AND CHEMISTRY LABORATORY 
 BOULDER, COLORADO 
 December 1969 
 
 For sole by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 
 
 Price 50 cents. 
 
a. 
 
 J 
 
 i 
 
 TABLE OF CONTENTS 
 
 Page 
 
 1. INTRODUCTION 1 
 
 2. VARIABLES 10 
 
 3. GENERAL STRUCTURE 16 
 
 4. ACKNOWLEDGMENT 23 
 
 5. REFERENCES 23 
 APPENDIX A. SLENDER Lettering 24 
 APPENDIX B. SLENDER Printout 25 
 
 in 
 
PLOTTER SUBROUTINE FOR METEOROLOGICAL 
 
 STRAIGHT LINE FLIGHT DATA (SLENDER) 
 
 Heinz H. Grote 
 
 This paper describes a subroutine SLENDER that 
 works in connection with the plotting subroutine 
 CRTPLT to provide a two-dimensional plot of a 
 relatively straight flight path and four analog traces 
 of selected meteorological parameters lined up 
 with the flight path. 
 
 1. INTRODUCTION 
 
 The subroutine SLENDER works in connection with the plotting 
 subroutine CRTPLT (Tucker, 19&8) to provide a two-dimensional plot 
 of a relatively straight flight path and four analog traces of selected 
 meteorological parameters lined up with the flight path. 
 
 The flight path is approximated by a straight line that coincides 
 with the x axis. A tilted coordinate system is then plotted and marked. 
 Wind vectors and time notations are added to the flight path. The mete- 
 orological parameters are automatically scaled and marked. Figures 
 1 and 2 give examples of a plot. The legend provides the following in- 
 formation: 
 
 (1) The flight number LID is expressed as a six-digit number and 
 
 an index letter according to convention used by ESSA 1 s Re- 
 search Flight Facility. The first two digits represent the year, 
 
tmb] 
 
 PRESSURE 
 
 FLIGHT NO 80708 B LONGITUDE LOO- 258.979 DEGREES LATITUDE LA0= 40.874 DEGREES 
 
 Figure 1. Example of plot* 
 
POT TEMP 
 
 FLIGHT NO 80708 B LONGITUDE LOO- 258.979 DEGREES LATITUDE LA0= 40.87$ DEGREES 
 
 Figure 2. Example of plot . 
 
the next two the month, and the last two the day of the flight. 
 The letter stands for the particular airplane. 
 (2) The center longitude XC and latitude YC in degrees refer to 
 the small circle in the middle of the plot. These reference 
 values are brought in from the main program. Together 
 with the scale notation every point on the plot is determined 
 by this location reference under the assumption that the 
 earth's surface can be represented by a plane. 
 
 The relation between distances in geographic degrees of longi- 
 tude dX and latitude dcp to linear distance values a and b in 
 kilometers is given by the equation,, 
 
 a = C„ dX 
 
 b = C. dcp . cos cp, 
 
 where a and b are in kilometers; dX , dcp, cp are in geograph- 
 ical degrees; and C is approximately a constant with the value 
 
 C = 111.32 ( — ) . 
 
 geographical degree 
 
 (4) On the right-hand side are the notations for the physical param- 
 eter, such as PRESSURE, PR ALTIT (pressure altitude), 
 LONGITUDE, LATITUDE, TEMP (temperature), POT TEMP 
 (potential temperature). Above these notations is the unit of 
 measurement, such as mb (millibar), km (kilometers), C 
 (degrees Celsius), °K (degrees Kelvin). 
 
(5) On the left-hand side are two values , automatically genera- 
 ted, for each parameter that determine the scale. The 
 attempt was to select them so that one value is above and 
 one value below the reference (mean value) line. 
 
 (6) A scale mark for the wind unit is on the left in the center. 
 Above it is the word "WIND" and below it the value of the 
 unit length, for example, 10 M/S. 
 
 (7) The center line for longitude LO and latitude LA and 
 
 the lines next to them are marked. The notations for longitude 
 deviations from the center line LO (km) are printed at the top 
 of the flight path plot and the notations for latitude deviations 
 from the center line LA (km) are printed below the flight 
 path plot. 
 
 In some cases some notations may be omitted to avoid super- 
 position of letters and therefore difficulties in recognizing the 
 notation. 
 
 Figure 3 shows the geometry involved in tilting the coordinate 
 system. There a is the angle by which the straight line approx- 
 imation has to be tilted to coincide with the x-axis; cp is the 
 polar coordinate angle of a point on the curve, and R is its 
 distance from the zero point; X and Y are the Cartesian co- 
 ordinates of the curve point in reference to <*arth coordinates; 
 
f / 
 
 x= R cos<£ 
 
 x'=R cos(<£-a) 
 
 x' = (Rcos<£)cosa + (Rsin<£)sina 
 
 x' = xcosa 4- ysina 
 
 y = Rsin<£ 
 
 y'= Rsin [<f>-a) 
 
 y' = (Rsin<jb)cosa- (Rcos(£)sind 
 
 y' = ycos a - xsina 
 
 Figure 3. Geometry in tilting coordinate system 
 
and X 1 and Y' are the Cartesian coordinates of the curve point 
 
 in reference to the tilted coordinate system. 
 
 The resulting relations are: 
 
 X 1 = X cos a + Y sin a 
 Y 1 = Y cos a - X sin a . 
 
 The slope f (0) of the flight path with respect to earth coordinates 
 
 at the center point of the coordinate system is 
 
 ^> a a . f ( a . h) 
 
 f (0) = - k 
 
 k 
 
 2 h ^>q a 2 
 
 1 
 
 where a is the increment count, and k is the count limit. For 
 k = 2, for example, the count sequence is 
 
 a= -2, -1, 0, 1, 2 . 
 Thus the number of points is 
 
 n =2k+ 1 . 
 The lowest value that k can take is one; thus the smallest number of 
 points to determine the slope by this equation is 3. The letter h is the 
 increment in the abscissa, and f (a # h) is the ordinate for the abscissa 
 a • h . 
 
 With k 
 
 J£~a a z - 
 
 1 k (k + 1 ) (2 k + 1 ) 
 
 1-2-3 
 
one obtains 
 
 f'(0) = J> a a ' f • ( a • h) 
 3 -k 
 
 h • k (k + 1) (2k + 1) 
 
 If the average of five points is replacing the individual values, 
 
 f_2 + f-l +fi + f 2 u c 
 
 i = h = 5 • x 
 
 + k 
 
 . ( i ! i -! f „ !■ i , !- f 
 
 f(o) = 2 
 
 S^cc • ^_ 2 . ^ . . . ^ . . 2 
 
 5 h • k • (k + 1 ) . (2k + 1) 
 
 The flight path is represented by an uneven multiple of five points. 
 Table 1 shows the use of the coordinate points. 
 
 From this distribution of points the interval h is computed as 
 
 X IPQ ■ X IQ 
 
 h = ^ * 5. 
 
 IP - 1 
 
 As long as the average curve has a slope between -45° and +45° or 
 between 135° and 225 , the abscissa values are used to determine h. 
 If the slope of the average curve is between 45° and 135° or between 
 225° and 315°, the ordinate values are used to determine h. The re- 
 sult ing slope is then reversed to obtain the slope with respect to the 
 abscissa. 
 
Table 1. Use of Coordinate Points 
 
 Total Number 
 
 Number of 
 
 Number of 
 
 Number of 
 
 First 
 
 
 
 Lower 
 
 Upper 
 
 Center 
 
 Value 
 
 of Points 
 
 Intervals 
 
 Limit Point 
 
 Point 
 
 of a 
 
 
 IP - 1 
 
 IQ 
 
 IPQ 
 
 IR 
 
 -KP 
 
 n 
 
 KA + 1 
 
 15 
 
 14 
 
 1 
 
 15 
 
 8 
 
 -1 
 
 16 
 
 14 
 
 1 
 
 15 
 
 8 
 
 -1 
 
 17 
 
 14 
 
 2 
 
 16 
 
 9 
 
 -1 
 
 18 
 
 14 
 
 2 
 
 16 
 
 9 
 
 -1 
 
 19 
 
 14 
 
 3 
 
 17 
 
 10 
 
 -1 
 
 20 
 
 14 
 
 3 
 
 17 
 
 10 
 
 -1 
 
 21 
 
 14 
 
 4 
 
 18 
 
 11 
 
 -1 
 
 22 
 
 14 
 
 4 
 
 18 
 
 11 
 
 -1 
 
 23 
 
 14 
 
 5 
 
 19 
 
 12 
 
 -1 
 
 24 
 
 14 
 
 5 
 
 19 
 
 12 
 
 -1 
 
 25 
 
 24 
 
 1 
 
 25 
 
 13 
 
 -2 
 
 26 
 
 24 
 
 1 
 
 25 
 
 13 
 
 -2 
 
 27 
 
 24 
 
 2 
 
 26 
 
 14 
 
 -2 
 
 28 
 
 24 
 
 2 
 
 26 
 
 14 
 
 -2 
 
 29 
 
 24 
 
 3 
 
 27 
 
 15 
 
 -2 
 
 30 
 
 24 
 
 3 
 
 27 
 
 15 
 
 -2 
 
 31 
 
 24 
 
 4 
 
 28 
 
 16 
 
 -2 
 
 32 
 
 24 
 
 4 
 
 28 
 
 16 
 
 -2 
 
 33 
 
 24 
 
 5 
 
 29 
 
 17 
 
 -2 
 
 34 
 
 24 
 
 5 
 
 29 
 
 17 
 
 -2 
 
 35 
 
 34 
 
 1 
 
 35 
 
 18 
 
 -3 
 
 36 
 
 34 
 
 1 
 
 35 
 
 18 
 
 -3 
 
 37 
 
 35 
 
 2 
 
 36 
 
 19 
 
 -3 
 
2. VARIABLES 
 The following variables, listed alphabetically, enter the sub- 
 routine: 
 IFS A six-digit number that determines the scaling. The center 
 
 two digits are without signficance and serve only as a separa- 
 tor. The first two digits are the plotting scale values LSC. 
 SC = 50. 0/LSC is the factor with which the coordinates X and 
 Y (km) are multiplied to obtain the plotting coordinates WX and 
 WY in the 1024-point CRTPLT-system. The last two digits 
 are the wind scale values LWS. W = 50. 0/LWS is the factor 
 with which the wind components OWX and OWY are multi- 
 plied to obtain appropriate values in the 1024-point CRTPLT- 
 system. For IFS=0 automatic scaling is obtained. Then the 
 coordinate factor is SC = 1024. / SPAN, where SPAN is the 
 largest span (km) in either abscissa or ordinate direction. 
 The wind scale W is given below. 
 
 0. 5 for WMAX larger than 100 m/sec; 1. up to 100 m/sec; 
 2. up to 50 m/sec; 5. up to 20 m/sec; 10. up to 10 
 m/sec. The wind factor LWS = 50. 0/W. 
 IM number of measurement points. 
 
 IT a 500-word array for the time of the measurement. 
 
 10 
 
IT has seven digits. The first is a 1 needed for printing; the 
 next two are the hour in 24-hour notation; the following two 
 digits represent the minutes, and the last two represent the 
 seconds. 
 
 KT record spacing (sec) . 
 
 LID flight identifcation array of eight words, as follows: 
 
 LID (1) two digits representing the most significant digits 
 of the year of the flight. 
 
 LID (2) number of the month, incremented by 1000 to main- 
 tain leading zeroes in printing. 
 
 LID (3) number of the day, incremented by 1000 to main- 
 tain leading zeroes in printing. 
 
 LID (4) airplane identifier in Hollerith notation. (The air- 
 plane identifier B is thus expressed as 1 HB. ) 
 
 LID (5) day in two digit presentation. 
 
 LID (6) the first eight letters of the month in Hollerith 
 notation. (The month of September is thus ex- 
 pressed as 8HSEPTEMBE. ) 
 
 LID (7) extension of the month for the eventually missing 
 ninth letter in two-digit Hollerith notation. If the 
 month has less than nine letters LID (7) = 2H 
 (For the month of September LID (7) = 2HRa • ) 
 
 LID (8) equal to LID (1) and containing the last two digits 
 of the year. 
 
 MW determines the spacing of the wind vectors on the plot. 
 
 MW = 1 means that a wind vector is drawn for every co- 
 ordinate point. 
 
 11 
 
MW - 2 indicates that a wind vector is drawn for every second 
 coordinate point. 
 
 MT spacing of the points on the plot (sec). By means of the equa- 
 
 tions 
 
 MI = MT/KT 
 MI = MI*KT , 
 
 it is assured that the spacing of the points on the plot MT is 
 
 always an integer number of the record spacing KT. At the 
 
 same time MT determines the time increments of the time 
 
 prints. These increments are 
 
 1 min for MT £ 10 , 
 
 5 min for 10 < MT< 60, and 
 10 min for 60 £MT . 
 
 MY not used. 
 
 OWX 500-word arrays. To save memory spaces, OWX and OWY 
 
 change their meaning in the program. In the input they rep- 
 resent the wind coordinates (m/sec) with respect to the 
 earth coordinate system. In the course of the program, OWX 
 and OWY change their reference to the tilted plotting coord- 
 inate system. 
 
 WMAX largest wind speed (m/sec) to be represented. This value 
 
 is used for automatic scaling of the wind vectors as explained 
 under IFS. 
 
 WXA x- and y- components of the bias wind. 
 
 12 
 
WYA if WXA = WYA = 0. the wind vectors on the flight path rep- 
 
 resent the wind actually measured. If the bias wind vector 
 has a value, the wind vectors at the flight path are the differ- 
 ence between the measured and the bias wind. 
 
 X, Y 500-word arrays. To save memory spaces, X and Y change 
 
 their meaning in the program. In the input they represent 
 the flight path coordinates (km) from the reference point with 
 respect to a plane earth coordinate system. In the course of 
 the program, X and Y change their reference to the tilted plot- 
 ting coordinate system. 
 
 XC, YC longitude and latitude of the center point in geographical de- 
 grees. This value is printed on the legend. 
 
 YM(J) largest deviation of each of the four parameters (which are 
 plotted as traces) from the respective mean value ZA. 
 YM(5) = provides the mean value reference. 
 
 Z a matrix of 500 x 5 representing the four meteorological param- 
 
 eters to be plotted and the reference line. The sequence is 
 
 Z(l) pressure (mb). 
 
 Z(2) pressure altitude (km). 
 
 Z(3) temperature (°C). 
 
 Z(4) potential temperature (°K). 
 
 ZA(J) mean value of each of the four meteorological parameters to 
 
 be plotted. 
 
 13 
 
The variables in the main program and SLENDER are compared 
 
 in table 2. 
 
 The following variables are used for plotting: 
 
 IX, IY, XH flight path 
 
 KX, KY, XH trace of four meteorological 
 
 parameters 
 
 KX, KYL, XH zero abscissa lines for traces 
 
 WX, WY, MN wind vectors 
 
 XA, YA, KM longitude grid 
 
 XB, YB, KN latitude grid 
 
 XD, YD, (KZ) scaling letters on abscissa 
 
 3H+0( circle marks © denoting points 
 
 XE, YE, LN on the flight path 
 
 XF, YF, (LF) dimensions of parameters 
 
 XG, YG, NG, LG lettering of parameter names 
 
 XJA, YJA, JLX longitude scaling 
 
 XJB, YJB, JLY latitude scaling 
 
 XK, YK, (IZ) time numerals 
 
 XKL, YKL, NQ, legend letters 
 KL 
 
 XKQ, YKQ, (KQ) legend inserts 
 
 XLA, YLA, LA lettering of wind scaling 
 
 XNA, YNA wind scale line 
 
 14 
 
Table 2. Comparison of Variables 
 
 Main Program 
 
 SLENDER 
 
 AY 
 
 IFS 
 
 IW 
 
 JJ 
 
 KY 
 
 LID 
 
 LT 
 
 MM 
 
 MT 
 
 OLA 
 
 OLO 
 
 OX 
 
 OY 
 
 OWX 
 
 OWY 
 
 YM 
 
 WBX 
 
 WBY 
 
 WMAX 
 
 Z 
 
 ZA 
 
 IFS 
 
 MW 
 
 IT 
 
 MY 
 
 LID 
 
 MT 
 
 IM 
 
 KT 
 
 YC 
 
 XC 
 
 X 
 
 Y 
 
 OWX 
 
 OWY 
 
 YM 
 
 WXA 
 
 WYA 
 
 WMAX 
 
 Z 
 
 15 
 
3H+0I 
 
 XNA, YNA 
 
 XP, YP 
 
 3H+0( 
 
 XR, YR, LL 
 
 XZ, YZ, ID 
 
 end points of wind scale 
 
 ordinate lines 
 
 circle marks O 
 
 points on the flight path for 
 
 which the time is printed 
 
 limits of the plot and identifica- 
 tion of the user 
 
 3. GENERAL STRUCTURE 
 
 zero plus 16 
 
 105 
 
 16 
 
 1610 
 
 1622 
 
 1623 
 
 1630 
 
 1640 PLUS 2 
 
 1650 PLUS 2 
 
 1660 PLUS 3 
 
 1718 
 
 2518 
 
 2518 PLUS 4 
 
 41 
 
 Data input 
 
 Values for time print 
 
 Flight path approximation 
 
 Conversion of path coordinates 
 
 Determination of scale factors 
 
 Path scaling 
 
 Location of time letters 
 
 Plotting of flight path with circle 
 marks and time notations 
 
 Conversion of wind components 
 and plotting of wind vectors 
 
 Wind scale 
 
 Longitude grid and scaling 
 
 Latitude grid and scaling 
 
 Plotting of coordinate grid 
 
 Scaling and plotting of meteor- 
 ological parameters 
 
 16 
 
45 
 
 49 
 51 
 
 Determination and plotting of 
 scale marks for meteorological 
 parameters 
 
 Lettering of parameter plots 
 
 Lettering of legend 
 
 T iming 
 ITC 
 
 IZA 
 IZC 
 IZD 
 
 time of the first data point that enters the subroutine 
 in six letter notation. The variables represent sets 
 of two. 
 
 hours. 
 
 minutes. 
 
 seconds. 
 
 The time ITC is then converted to seconds, represented by IZE. 
 Since the plotting time sequence is MT, the time IZF for the first point 
 to be represented on the plot has to be an integer multiple of MT. The 
 largest value that IZF can take is 86400 (midnight). 
 IZG 
 
 IZH 
 IZI 
 IZM 
 JY (1) 
 
 IZN 
 
 time increment with which time numbers are printed 
 on the plot. 
 
 time of the last point on the plot. 
 
 number of points to be plotted. 
 
 first time number to be printed. 
 
 time of plot points (sec) (later converted to hour- 
 minute -second notation). 
 
 time number, composed of the four letters IZO, 
 IZP, IZS, IZT. 
 
 17 
 
LJK 
 
 = 2™. Since Hollerith quantities with three characters 
 are used in the plot routine, integer values have to be 
 shifted by five characters for conversion (Control Data 
 Corporation, 1967, 1. 1, "Wind Structure"): 
 
 6 
 
 6 
 
 6 
 
 6 
 
 6 
 
 6 
 
 6 
 
 6 
 
 Flight path approximation 
 IP 
 
 IQ 
 IPQ 
 
 IR 
 
 KP 
 
 HX 
 
 SY 
 
 COA 
 
 number of points that can be used for insertion into 
 the approximating equation for the flight path. IP 
 has to be an integer multiple of five. 
 
 number of the first point to be used. 
 
 number of the last point to be used in the flight path 
 approximation. 
 
 number of the center point between IQ and IPQ. 
 
 first value of - a in the approximating equation. 
 
 approximation intervals. The one with the largest 
 absolute value is selected for further computations. 
 
 sum of weighted function values. 
 
 slope f'(0) of the approximated flight path = tangens 
 of the slope angle. 
 
 cosine and sine of the slope angle. 
 
 Scaling 
 
 IFS scaling selector (see sec. 2) 
 
 Plotting of Flight Path 
 
 ZX 
 
 ZY 
 
 mean values of abscissa and ordinate. (Central point 
 of plot. ) 
 
 18 
 
wx 
 
 IX 
 IY 
 
 XR 
 YR 
 
 XE 
 YE 
 
 XK 
 YK 
 
 scaled plot coordinate points. Their subscript is 
 incremented by two in order to accommodate later 
 the wind vector and points. 
 
 coordinate points in the integer plotting system. 
 
 circle marks on the flight path for time points. 
 
 circle marks on the flight path to denote a time 
 printout. 
 
 time numerals. 
 
 Plotting of Wind Vectors 
 
 WX 
 WY 
 
 XLA 
 YLA 
 
 XNA 
 YNA 
 
 end points of wind vectors. A wind vector extending 
 beyond the plot dimensions is omitted. 
 
 wind scale letters. 
 
 wind scale. 
 
 Longitude Grid and Scaling 
 
 YV ordinate for end of grid. 
 
 YVA ordinate for grid lettering. 
 
 XM abscissa span of grid line. 
 
 XIMIN 
 XIMAX 
 
 extremes of longitude values (km). 
 
 JXSP longitudinal span (km). 
 
 J XE longitudinal increment. 
 
 JXD absolute value of longitudinal increment (initial). 
 
 19 
 
JXG 
 JXX 
 JXZ 
 JAX 
 JNX 
 JXM 
 XT 
 
 XA 
 
 JLX 
 
 JXN 
 
 XJA 
 YJA 
 
 YIMIN 
 YIMAX 
 
 JYSP 
 
 JYE 
 
 JYD 
 
 JYG 
 
 JYF 
 
 JYZ 
 
 flag has sign of JXE with value one. 
 
 quantized value of longitudinal increment. 
 
 final value of longitudinal increment. 
 
 scaled projection of longitudinal increment on abscissa. 
 
 one -half the number of longitudinal increments. 
 
 total number of longitudinal increments. 
 
 abscissa of center of longitudinal lines. (For marked 
 lines the grid is extended by 10%. ) 
 
 abscissa of grid of longitudinal lines. If the abscissa 
 is outside the plot, the grid is shortened to extend 
 only to the borderline of the plot. 
 
 letters denoting longitude values. 
 
 = 2JXM + 1. Example: JXM = 8 Then: 
 
 K = 1, 3, 5, 7, 9, 11, 13, 15, 17 
 
 4f 4^ 4f 
 
 JXM-1 JXM+1 JXM+3 
 
 longitude scale number coordinates. (Numbers that 
 would not fit on the plot are omitted. ) 
 
 extremes of latitude values (km). 
 
 latitudinal span (km). 
 
 latitudinal increment. 
 
 absolute value of latitudinal increment (initial). 
 
 flag with value one, denoting sign of JYE. 
 
 scale factor. 
 
 final value of latitudinal increment. 
 
 20 
 
KDX abscissa increment. 
 
 KX abscissa variable. KX (1) is chosen, so that the 
 
 curve has equal margin to left and right. 
 
 KYO bias value of ordinate to locate the curve into its 
 
 proper space. 
 
 KYL ordinate of reference abscissa. 
 
 Determination and plotting of scale marks and letters 
 
 XL abscissa values for scaling marks and letters, 
 
 XD XL as three-dimensional matrix to facilitate lettering. 
 
 EX scale values for ordinate, 
 
 EM-ME ordinate scale factor. 
 
 MB (1, J) upper 
 
 scale value » 
 MB (2, J) lower 
 
 YD ordinate of scale marks and numbers, 
 
 KZ lettering of scales. 
 
 Lettering of plots 
 
 XF coordinates of dimension letters. 
 
 YF 
 
 LF dimension letters 
 
 (some in lower, some in upper case). 
 
 XG coordinates of parameter name letters. 
 
 yg 
 
 LG parameter name letters, 
 
 XP ordinate lines. 
 
 YP 
 
 21 
 
JBX 
 
 JNY 
 
 JYM 
 
 XU 
 
 XB 
 
 JLY 
 
 XJB 
 YJB 
 
 scaled projection of latitudinal increment on 
 abscissa. 
 
 one-half the number of latitudinal increments. 
 
 total number of latitudinal increments. 
 
 abscissa of center of latitudinal lines. 
 
 abscissa of grid of latitudinal lines. (For marked 
 lines the grid is extended by 10%. ) If the abscissa 
 is outside the plot, the grid line is shortened to 
 extend only to the border line of the plot. 
 
 letter denoting latitudinal values. 
 
 latitude scale number coordinates. 
 
 Scaling and plotting of meteorological parameters 
 
 F-YM largest deviation of parameter from its mean value. 
 
 E scale factor. 
 
 F 
 
 E 
 
 <; o.oi 
 
 10, 000 
 
 £ 0.02 
 
 5, 000 
 
 < 0.04 
 
 2, 500 
 
 < 0. 1 
 
 1, 000 
 
 ^ 0. 2 
 
 500 
 
 <; 0.4 
 
 250 
 
 <; 1 
 
 100 
 
 <; 2 
 
 50 
 
 <, 4 
 
 25 
 
 < 10 
 
 10 
 
 <, 20 
 
 5 
 
 ^ 40 
 
 2. 5 
 
 > 40 
 
 1 
 
 22 
 
Lettering of legend 
 
 XKL legend coordinates 
 
 YKL 
 
 NQ legend character specification 
 
 KL legend letters 
 
 KQ legend insert letters 
 
 XKQ insert coordinates 
 
 YKQ 
 
 4. ACKNOWLEDGMENT 
 The author wishes to thank Mrs. J. M. Tucker for her assistance 
 in the debugging of the presented work. 
 
 5. REFERENCES 
 
 Tucker, J. M. (19&8), Cathode ray tube plotter subroutine, ESSA 
 Tech. Memo. RLTM-OATS 3. 
 
 Control Data Corporation (1967)^ 3800 Computer Systems Reference 
 Manual: FORTRAN. 
 
 23 
 
APPENDIX A 
 SLENDER Lettering 
 
 1 
 
 F 
 
 -492 
 
 2 
 
 L 
 
 -480 
 
 3 
 
 I 
 
 -468 
 
 4 
 
 G 
 
 -456 
 
 5 
 
 H 
 
 -444 
 
 6 
 
 T 
 
 -432 
 
 7 
 
 
 -420 
 
 8 
 
 N 
 
 -408 
 
 9 
 
 O 
 
 -396 
 
 10 
 
 
 -384 
 
 11 
 
 (8) 
 
 -372 
 
 12 
 
 (0) 
 
 -360 
 
 13 
 
 (7) 
 
 -348 
 
 14 
 
 (0) 
 
 -336 
 
 15 
 
 (3) 
 
 -324 
 
 16 
 
 
 -312 
 
 17 
 
 (B) 
 
 -300 
 
 18 
 
 
 -288 
 
 19 
 
 
 -276 
 
 20 
 
 
 -264 
 
 21 
 
 L 
 
 -252 
 
 22 
 
 O 
 
 -240 
 
 23 
 
 N 
 
 -228 
 
 24 
 
 G 
 
 -216 
 
 25 
 
 I 
 
 -204 
 
 26 
 
 T 
 
 -192 
 
 27 
 
 U 
 
 -180 
 
 28 
 
 D 
 
 -168 
 
 29 
 
 E 
 
 -156 
 
 30 
 
 
 -144 
 
 31 
 
 L 
 
 -132 
 
 32 
 
 O 
 
 -120 
 
 33 
 
 
 
 -108 
 
 34 
 
 = 
 
 - 96 
 
 35 
 
 
 - 84 
 
 36 
 
 (2) 
 
 - 72 
 
 37 
 
 (5) 
 
 - 60 
 
 38 
 
 (8) 
 
 - 48 
 
 39 
 
 . 
 
 - 36 
 
 40 
 
 (9) 
 
 - 26 
 
 41 
 
 (7) 
 
 - 12 
 
 42 
 
 (9) 
 
 
 
 43 
 
 
 12 
 
 44 
 
 D 
 
 26 
 
 45 
 
 E 
 
 36 
 
 46 
 
 G 
 
 48 
 
 47 
 
 R 
 
 60 
 
 48 
 
 E 
 
 72 
 
 49 
 
 E 
 
 84 
 
 50 
 
 S 
 
 90 
 
 51 
 
 
 108 
 
 52 
 
 
 120 
 
 53 
 
 
 132 
 
 54 
 
 
 144 
 
 55 
 
 
 156 
 
 56 
 
 L 
 
 168 
 
 57 
 
 A 
 
 180 
 
 58 
 
 T 
 
 192 
 
 59 
 
 I 
 
 204 
 
 60 
 
 T 
 
 216 
 
 61 
 
 U 
 
 228 
 
 62 
 
 D 
 
 240 
 
 63 
 
 E 
 
 252 
 
 64 
 
 
 264 
 
 65 
 
 L 
 
 276 
 
 66 
 
 A 
 
 288 
 
 67 
 
 O 
 
 300 
 
 68 
 
 = 
 
 312 
 
 69 
 
 
 324 
 
 70 
 
 (4) 
 
 336 
 
 71 
 
 (0) 
 
 348 
 
 72 
 
 
 
 360 
 
 73 
 
 (8) 
 
 372 
 
 74 
 
 (7) 
 
 384 
 
 75 
 
 (4) 
 
 396 
 
 76 
 
 
 408 
 
 77 
 
 D 
 
 420 
 
 78 
 
 E 
 
 432 
 
 79 
 
 G 
 
 444 
 
 80 
 
 R 
 
 456 
 
 81 
 
 E 
 
 468 
 
 82 
 
 E 
 
 480 
 
 83 
 
 S 
 
 492 
 
 24 
 
APPENDIX B 
 SLENDER Printout 
 
 SUo^nUTlNP" SL^N'^P ( Tt"S s|_ T^»^ T »»•".<' »MT * TT s T •%'•'•' * v , 
 i Ym, Xr > Yr »WXa » WY A » Z a • X , Y « nWX s O'a'Y » Z »mY ) 
 roMMf)w/i /TX»TY»tZ»i^X»<Y »KYL»WXtWY t Xv »Yv 
 n T mfnS'T ON p ( c ) » r K ( 4. 1 » t T ( * ) * t T "» ( * ) s T X ( i C C ) 9 T Y ( i C " ) s I Z ( 1.0 C J » 
 
 1 JI.X ( 1?1 » JLY( 1 7 1 sjY( TOO) sjZf^O) ,MV(41 ,la (o ) , 
 
 -> ^(io),vx(iO;.) tKY( 1 ?Ti sKYLf "I 00) ,krYO( A } s'^Zf isA s£l sLI'M *») s 
 
 ■* L p ( 24) »LG(7) f MA (6. ) »" D ( ?»4) >Nr:( * ) sNQ(M »OWX ( c ~^ ) »OWY( 5.00) s 
 
 4 '''X( Q00 ) sVY(900 ) sX (*0 n ) sXA(?4) »X°( ?h) »XD(?,4»6')»XF(5) ^XF( 74) » 
 
 ^ XU( sH) sX|_(*) »X|..A( Q\ »XVA( -J) sXZ (•>) »Y( kOC) ,Ya (7&) ,Y=(.?41 »Y^C»4»ft] 
 
 -7 yc-( R 1 »Ytr ( •>/, ) , Y^-( 7 i , Yja f 1 -> ) »Yjc (T5 ) , Y* ( f^n, .v^do,, 
 
 a Yla(o) iYm(r) »Y,ma( 7) *YP(Q ) »YR(iOO> sYZ(->) »Z(=0C»c) ♦Z.Mai 
 
 r> a T A ( ric - 1 . , 1 nQ # s m,% iQ/) 
 
 n A T A (T^ = ?pi_iu # r,o^T c r XT.677C DM^p-a-a^n^ipj 
 
 OAT ft (!JK' = 107' : »741P.?A) 
 
 DATA (KL=83HFLIGHT NO LONGITUDE L00= . DEGREES 
 
 i l_ATITUO p LA0= . DFGRFFS) 
 
 hat A (<Y0 = c >??s71 7 s 307,102 ) 
 
 H A T A (|_A = ^U + l«.l ,1U + '1T ^MJ-^^^U^P^,",^ ,^U-(_~M,'5LJ4.^/,,'3q-|- C} 
 
 r>ATA ( LE=6 ( ^H+0 ' ) ^M + ^^'STCJH + ^^l s ° ( 7M+ n # ) , 
 
 n.*T A ( LG=8HPRFSSURF,pHP t 5 A.LTTT»c j MLO^'"-I T U rN »"i L - lir »PHL /v TI TUDF » 
 1 4HTFVD,RHP0T -TFMP ) 
 
 Oat A (NG=1 »0,0»0»0»1 ) 
 
 OAT A (NQ=I1 »0»0»C,C, 1 )• 
 
 OAT A ( XF=6 (4 54.0 )» 6(466.0 ) »6(47p.0) 96 ( 490.0) ) » 
 i f YF=4(4' 2 0.0»??R.0» 1 i n .0»-1 1 0.0» -l QC '. n » -'900.0)1 
 
 n a t a ( xn=? ( 4O6 . ) 9 3°4 .0 »4O0 . s406 . »4^4. 9AO* . ) » 
 
 1 (Yf*-:^O^ t ^, 1 pc; .r» ?(90. 0)» - Qr . * -77*,^, -47^ # 0l 
 
 OAT A (X<L=-AQ4.^) » ( YKL = - 5 1 1 • 5 ) 
 
 r>ATA (X^0=-P74.^s -' a 6?.0» -350.0s -??P.09 -326.09 -302.0s 
 
 1 _q^.O, _7i,^, _fc?.P, -5C,% -26.0s -?4.0, -?.0, 
 
 ? ^ ? 2 . « 334.0s * 4 6 . n 9 370.0s 3 8 ? . 9 *°4.C)»(YlC0 = ! o (-511.5n 
 
 ^ aT a ( XL A =-400. 5 9-4PTfe, 5 »-47C.K s-4A Q . * s- c i i . r s 
 1 -too, c ,-471; # c; S-4A-5 # c ,_ A c i t c ) , ( Yi a=a ( _c ".^ 1 , - ( - V '\" ) ) 
 
 ^aTa (XNA=-^ii. c s-46T. Ci )9(YNA=7(LnO,0) ) 
 
 HAT A (XZ = ^n.^s- c '"'''. ,:; )9(YZ = c; n. i:; »- c '''' 1 . c ) 
 
 haTA (YP=4QO,0s ^^^.^s ?«^.0s 1^^.0s-t 75.0s-7OK,0s-330.0»-4o0.^) 
 
 XV! M=X TMJN=YM 1 M=YT^ 1^=1^306 
 
 XmaX = XtmaX=YmaX=YtmaX=-1 c "9 06 
 
 M r > = 
 
 TTr= IT ( V) -1000000 
 
 AfT=vT/vT 
 
 v t = m I ■«■ < T 
 
 T 7 a = Tjr/ i 0^0 
 
 I7»= ITC-IZA*1000C 
 
 25 
 
i i 
 
 ;L 
 
 :"IC 
 
 T 7 r = t Z n / i 00 
 
 T Z^= T Zd-t Zf* 1 00 
 
 lZ^=TZ«i*^A0O+TZr*!t04-TZn 
 
 IZF=( ( IZF-1 )/MT+l )*MT 
 
 IZG=?0 
 
 T^ (WT.LE.1C) !ZG=6 
 
 tc (MT.fie.f,^) TZr--*00 
 
 IZV=( ( IZE-1 )/IZG+l )*IZG 
 
 TZm=(iZp+(tv-t)*kT) /mT#VT 
 
 T 7 T - f T7U_r7n /MT4.1 
 
 TZ r =!Z--B£&00 
 
 T Z M = I Zm— PictOO 
 
 d^C^ ) JY( T + i i =jv( i + i i 
 101 » 104 
 17 r 
 
 \' = JZ ( < ) /?6.0C 
 
 n = T Z M / 1 
 
 ) JZ (<+3 ) =J7 ( K+i ) -<>*/,■ 
 
 IZI={ IZH-IZP) /mt+1 
 
 T F ( T Z c . r, r . p 6 4 o 1 
 IF ( IZ M .^.«^00). 
 JY( n = TZF 
 JZ(1 )=IZM 
 
 J=1 
 
 Iff = 1 
 
 no 10* I=1»IZI 
 
 JY( T+ 1 )=.JY( J )+MT 
 
 T c ( JY( T + i 1 . r - r . 
 
 IF ( JY( I ) .EQ.JZ(K) ) 
 
 jZ K + 1 )=JZ(K ) 
 
 T^ ( JZ(k: + i ) - r - 
 
 7. 
 
 1 
 
 7 
 
 ZO= JZ ( * 1 -TZN'*^A0 r 
 
 Z P = T Z O / A 
 ZS=IZR/1C 
 7T= TZP-TZS*] 
 
 71 != TZO- TZo*£0 
 ZV= IZG/AO 
 
 Z ( < ) = T Z M * 1 n ' J- T 7 D - 
 
 Z(J )=IZO*IJK 
 
 Z ( J-t-1 1 = tZp^-T Jf 
 
 Z ( J+^ ) = tZS-*t ji< 
 
 Z( J+3)=IZT*IJK 
 
 = J+^ 
 
 = K + 1 
 
 '.»A = JY( T ) /^OO 
 
 V'' D - j y ( T ) - T '-'■' a -x- -5 A 
 
 '«./("= T W c /6 ' ; 
 
 ' A T)= IWR-I WC*60 
 
 Y ( T ) = T W a #1 0+ 1 \'-!f * 1 + J ''.'^ +■ 1 .00 n ^ 
 
 ON.TINUE 
 
 P=( IM+5 )/ 10*1 0-5 
 
 Q='( JM-ID )/2 + l 
 p = ( TD-1 ) /?j_ T Q 
 
 Y=0.0 
 QM=TQ+2 
 
 - a a / 
 
 n o 
 
 . j Z U + ] ocooo 
 
 26 
 
KA=-KP-1 
 
 HX=(X(TDO)-X( TO] ) ' ( TD-1 )*s. 
 
 uv-(Y(iDn)-V(p)] /(to_i ) *R # f! 
 
 DO 109 1=1 ♦ IV 
 X c = X c + X ( I ) 
 
 1 ^o rnMT T N't J^ 
 
 X^=XS/T M 
 
 Y c = . r. 
 
 DO 11 I=1»IM 
 Y^=YS+Y( T ) 
 it r r\ K' J T N U c 
 
 YO=YS/'T^ 
 
 |C ( ad^(mY),^-T, aDC; ( l, X) ) 1?»li 
 
 12 CO 13 I=IQV»IPQ»5 
 
 KA=KA+1 
 
 <;Y-SY+>^A*"( (X( I-->)+X( I-i )+X( T }+X ( t + 1 )+X( T + -»n /c.O-XO) 
 
 to f- n m T T |vi U r 
 
 HX = HY 
 
 GOTO 1.6 
 ] a DO \ c i I = 1QY » I D 0» c 
 
 k" a = K a + 1 
 
 c V= ^y + <A*( (Y(I-?)+Y( 1-1 )+Y(I )+Y( I + l)+Y(I+?n/ c .0-YC) 
 i c roN'T T^'U C 
 -, A p=SY/HX/KP/(<P + 1 ) ' (KP+KP + 1 )*^»P 
 
 jc (VS.FO.1 ) P=I ."/ D 
 
 cq=S0PT( 1 .0+P*P ) 
 
 rnA=i .0/50 
 
 SI A=p/S0 
 
 njp TAT"' T = 1 » T M 
 
 X I = X ( I ) - X 
 Yt = Y ( t y-Yo 
 
 ir (Xt/.T,Xt"aX\ 
 t c (XT.LT.XT V TN1 
 
 J r ( YT ,r,T.YT VAX 1 
 
 T^ ( YI .LT.YTMIN ) 
 X ( I ) =x I *CO* +Y I *? ! 5 
 Y ( I ) = Y I * r ft - X T * c ' T - A 
 
 Tr (X(n/-T.X"« Y ! 
 rr (X(n,LT,XMT M ) 
 
 Tcr (Y(T)/.T,Y"AX) 
 
 IP (Y(I).LT.YMIN) 
 
 ui" r^M T T Ml jr. 
 
 ZX=( X^TM+Xv.AX ) /?.0 
 ZYs( Y^TMj-YVftX ) /' . r 
 
 I r ( i f r > . N E . n ) 1 6 2 , 1 f ? 1 
 
 [yc = IFS-L^C*U 00'". 
 
 Xt""X=Xt 
 X T " TM = X T 
 Y T * •' A X = Y t 
 Y tmtn=YT 
 
 X M a X = X ( T 1 
 y- T M_X ( T ) 
 
 Y»' *X = Y ( t i 
 YVIN=Y ( I ) 
 
 27 
 
1 A91 
 
 £>? 
 
 1 f, 01 
 
 1 6? c 
 
 1 6° 
 
 <T^ = * . 'V !_ ? r 
 
 r.nTO i if?? 
 
 XS°= adMX^AX-X^T*' 1 
 
 Y^D=4PS(V\iiX-YMTM)*=,' A 
 
 CDAN! = VAX1 (X C P »Y C -P) 
 5C= 1024,0 /SPAN 
 LSC=50.0/5C 
 
 IF (WViX.LE.lOO.C ) 
 T tr ( wmaX . L r • c 0.Cy 
 
 w=i *o 
 
 W = 7.0 
 
 20,0) 
 
 1 
 
 ) 
 
 w=.i 
 
 100,H 
 
 IOC 
 
 IF (WMAX.LF. 
 IP (W^AX.LF. 
 
 V = — "3 
 
 L = 
 L L = 1 
 
 TV=T+T-1 
 
 vy (TM)=(X(Ti-ZXi*sr 
 
 TV ( I ) ='*'X (IW)+^1?. n 
 ^vipij-iYlTi-ZViifCr 
 
 IY( I ) =WY( IN) +512.0 
 Tr ( Tj( T i ,rn,jY (| \ ) ) 
 •y co-> X^(LL) = IX(I)- r -n 
 YR(LL)=IY( I )-512 
 L L. = L L + 1. 
 T^ (TT(Tj,F^,jZf^"n) 
 
 < = i<r+4 
 
 KK=KK+1 
 
 L = L+1 
 
 XF(L )= ! '.'X( IN) 
 
 Vp (|_ )='.vY( TV ) 
 
 Xi' ( K* ) = '»/X ( T v. ) _i 7 # 
 
 x < ( k + 1 ) = w x ( i * ) 
 X<(^4.7)=vx(H!)+n,^ 
 XK(K+3 )= l "'X( IN)+?4.G 
 r p n t J M !j F 
 
 V < = x + "3 
 LN=L 
 Xu=T w 
 
 CALL r D T D L T 
 
 r * !_ L r ° T ° i... T 
 
 C&I..L P Q TDLT 
 
 r B L L C ° T ° L T 
 
 OP 16*0 K=1»MK 
 
 Yv(/) = _io t 
 
 r A |_ L r P T d L T ( , C; » I Z { < ) » i » c ) 
 
 PALL r 9 T o l T (Xv(K),Yk'( l M»"!»' , »'i) 
 
 CX 7 ,V7 , ^ . Trs, 7 j 
 
 ( X M . i . ? , t y , t y . 1 P ) 
 
 ( 
 
 ^H+'M 
 
 ) 
 
 ( X r ,Y r 
 
 28 
 

 1660 
 
 1 701 
 1702 
 
 (0,0»'3H+ n ( »4»* ) 
 (XP,YR,LL*0,1 ) 
 
 1640 CONTINUE 
 CALL f~PTDlT 
 CALL CRTPLT 
 
 M = -l 
 
 JMsl-MW-MW 
 
 no 1 A*0 1=1 »IM»MW 
 
 I M=IN+MW+MW 
 
 xw=nwx( t ) 
 
 YW=OWY( I ) 
 
 OWX ( T.) =XW*COA+YW*S I a 
 
 OWY( I )=YW*COA-XW*SI A 
 
 WX(M) =WX( IN) 
 
 WX(M+1 )=WX(M)+OWX ( I )*W 
 
 T cr ( aqS(WX(m+1 ) ) .^T.SI 1 . c ) 
 
 1641 WX(M+1 }=WX(MJ 
 W V (M) =WY( IN ) 
 WY(M+1 )=WY(M) 
 GOTO 165 
 
 164? WY(M)=WY(TM) 
 
 WY (M+1 ) =WY ( M ) +DWY ( I ) *V 
 
 IF ( ad s ( WY ( V+l ) ) . GT . m 1 . 5 ) 
 1650 CONTINUE 
 
 MN=M+1 
 
 r ALL CRTPLT (WX»V.'Y»VN»i »9) 
 
 LWA=LW5/10 
 
 LWo = LWS-LWA*l 
 
 LA (5 ) = LWA*UK 
 
 IF (LWA.FQ.O) LA(5)=?H+0 
 
 LA ( a ) =LWR*IJK 
 
 no I 660 LZ = i »Q 
 
 TALL rPTD(_T (0,0»LA(|_Z) »1»5) 
 
 1641 » ! 6 A ? 
 
 1641 »1 6 C 
 
 CALL CRTPLT 
 CONTINUE 
 CALL CRTPLT 
 rn\_\_ rPTDLT 
 CALL CRTPLT 
 YV=iOO,G 
 YVA=l.i*YV 
 XM=YV/P 
 XNsYV*P 
 
 JXSP = XTV!AX-XI MU 1 
 JXE=JXSP/11 
 jXn=TAPS( jXrj 
 
 JXr,= i 
 
 ic (jXr.LT.O) 
 
 jXr=l0 
 
 IF (jXn.f-T.^0) 
 
 JXD=JXD/1^ 
 
 JX C =JXF*1 
 
 (XLA(LZ) ,YLA(LZ) »1»1 ,1 ) 
 
 (0,O,?H+0T >1> R ) 
 (XNA»YNA»?»0»1 ) 
 (XNA»YNA,2>0»9) 
 
 jXr,=-i 
 1 7 •? 9 1 7 ? 
 
 29 
 
GOTO 1701 
 170^ IF (JXn.|_F.50) JXX=* 
 I c (JXh.lf.pO) JXX = ? 
 IF (JXD.LE.10) JXX=1 
 JXZ=JXX*JXF*JXG 
 JAX=JXZ/COA*SC 
 JNX=JXSP/JXZ/2 
 JXW=JN'X+JNX 
 XT(1 )=-JNX*JAX 
 DO 1704 1=1, JX^ 
 XT( 1+1 )=XT( T )+JAX 
 
 1704 CONTINUE 
 JXN=JX^+JXM+1 
 <r=0 
 
 DO 171 6 <=1 >JXN»? 
 
 KC=KC+1 
 
 XA(K)=X.T(KC)-XM 
 
 YA (!<)=-YV 
 
 IF (Xa(K) .LT.-51 1.5) 17041,170a? 
 
 17041 YA(K)=(-XA(K)-A5S(XM)-511.5)*P 
 XA(K)=-511.5 
 
 17042 IF (XA(K) .GT. 511.5 ) 17043,17044 
 17 04? YA(K)=(-XA(K)+ABS(XM)+511.5)*P 
 
 XA (K) =51 1.5 
 17044 I r (K.fo.JXm-1) 17C^,T"706 
 
 1705 JLX(l)=3H+0- 
 Jt_X(2)=JXX*IJK 
 JLX(3)=2H+0 
 
 IF (JXF.GF.10) 
 JLX(4)=?m+0 
 IP ( jXc,r,c #1 00) 
 Jt_X(5) = ?H+0 
 r-nTo i7i0 
 
 1706 IF (K. C 0.JXM+1) 
 
 1707 JLX( 6 ) =?H + Oi_ 
 JLX( 7)=3H+00 
 JLX( 8)=3H+00 
 GOTO 1710 
 
 ]70r ip (K.FO.JXm+3) 
 
 1709 JLX(9)=3H+0+ 
 JLX(lOi=j L X(?) 
 JLX( 11)=JLX(3) 
 JLX( 12)=JLX(4) 
 
 1710 XA(K+1)=XT(KC)+1.1*XV 
 YA(K+1)=YVA 
 GOTO 171? 
 
 171 1 XA (K + l )=XT(KC)+XVl 
 YA (kf + l )=YV 
 
 1712 IF (XA(K+1) .LT.-511.5) 
 
 1713 XA(K+1 )=-511.5 
 
 YA(K+1)=(-XT(KC)-AF5(XM) 
 
 Jl_X(*M = 3H+00 
 JLX( 4) =?M+no 
 
 1 707,1 70P 
 
 1700,1711 
 
 1713,1714 
 
 •511 . ^)*P 
 
 30 
 
171 ^. 
 
 1715 
 
 1716 
 
 17161 
 
 1716? 
 
 1 71 64 
 
 1716^ 
 
 17166 
 
 1 7 1. 7 
 
 1718 
 
 2501 
 2 502 
 
 ?50^ 
 
 XJA( 1)=XA( JXM 
 XJA( 2)=Xfl (JXM 
 XJA(3)=XA( JXM 
 XJA(4)=XA( JXM 
 
 IF (XA(K+1) .GT.511.5) 1715*1716 
 
 XA(K+1 )=511 .5 
 
 Ya (K + l ) = (-XT(<r )+APS(XN)+5!l . *)* D 
 
 CONTINUE 
 
 )-12.0 
 
 ) 
 )+12.0 
 
 )+24.0 
 IF ( (XJA(l).L T. -439,5). OR. (XJA.U).GT. 442.0) ) 
 
 XJ* ( 1 )=-51 1. .5 
 
 XjA(2)=-499.5 
 
 XJA( 3 )=-487.5 
 
 XJA(4)=-475.5 
 
 XjA(5)=-46^.5 
 
 JLX( 5 )=3H+0- 
 
 XJA(6)=XA( JXM+2 )-12.0 
 
 XJA( 7)=XA ( JXM+7) 
 
 XJA(8)=XA(JXM+2)+12.0 
 
 IF ( (XJA(6) .LT.-511.5).OR. (XJA(P).GT.&4?.0) ) 
 
 JLX(6)=JLXC7 )=JLX(8) = ?H+0 
 
 XJA(Q)=XA( jXm+4)-1 ?.0 
 
 XJA( 10)=XA( JXM+4) 
 
 XJA( 11 )=X'A( JXM+4) + 12.0 
 
 XJA( 12 )=XA( JXM + 4) +24.0 
 
 IP ( (Xja (R) .LT.-51 .1.5 ) .OR. (XJA( 1] ) .GT. 442.0) ) 
 
 JLX(Q)=JLX(1C)=JLX( 1 1 )=JLX(1? )=?m+0 
 
 no 171 7 <=i,l? 
 
 YJA( K)=YVA 
 
 CONTINUE 
 
 DO 1718 <=1>12 
 
 TALL roTD(_T (0»0» jLX(kT) »1 »5 ) 
 
 CALL CRTPLT ( X JA ( K ) , Y JA ( K ) * 1 » ♦ 1 ) 
 
 CONTINUE 
 
 jYS D =YTMAX-Y!MT!\i 
 
 JYE=JYSP/11 
 
 jYn=lAoS( jYF) 
 
 JYr-=i 
 
 IF (JYF.LT. 0) 
 
 JY C =10 
 
 IF (JYn.GT.50) 
 
 JYD=JYD/10 
 
 jYc=jYc*i 
 
 GOTO 2501 
 
 IF (JY^.l^.^0) 
 
 IF (JYO.LF.20) 
 
 IF (JYD.LE.IO) 
 
 JYZ=jXY*jYF*jYn 
 
 JBX=JYZ/SIA*SC 
 
 JNY=JYSP/JYZ/2 
 
 JYM= JNY+JNY 
 
 17161 »1716? 
 
 17163 »17164 
 
 17165»17166 
 
 JYG=-1 
 
 2502,2 503 
 
 JXY=^ 
 JXY=? 
 JXY = 1 
 
 31 
 
XU(1)=-JNY*JBX 
 nn 2^04 I=1»JYM 
 XU(I+1)=XU( I )+JRX 
 2504 CONTINUE 
 
 JYN=JYM+JYM+1 
 
 KC = 
 
 po ?5l f K=l »JYN»? 
 
 KC=KC+1 
 
 XR(<)=XU(KC)-XM 
 
 YP (<)=YV 
 
 IF (Xp<K).LT.-511.5) ?*041»?^04? 
 7 = 041 Yo (<) =(-Xr(K)-a°S ( XN)-*H # 5) /d 
 
 Xn(K)=-'M 1. .5 
 ? = 04? if (Xr(K) .GT.511 •? ) ?50^?>?=044 
 2 5 043 YB(K)=(-XB(K)+ABS(XN)+511.5)/P 
 
 XB(K)=511.5 
 25044 IF (K.EQ.JYM-1) 2505*2506 
 ?«$0«n jlY( 1 )=*h+0- 
 
 JLY( 2)=JXY*IJK 
 
 JL.Y(3 )=2H + 
 
 IF (JYF.GE.10) Jl_Y(?)=3H+00 
 
 JLY(4)=2H+0 
 
 IF (JYF.GE.100) JLY(4)=3H+00 
 
 JLY(5)=2H+0 
 
 GOTO 2 510 
 2506 IF (K.EQ.JYM+1) 2507*2508 
 ?*07 JLY(6)i=^H+0L 
 
 JLY(7)=3H+0A 
 
 JLY(8)=3H+00 
 
 GOTO 2510 
 2508 IF (K.EQ.JYM+3) 2509*2511 
 ?e,0o J|_Y( O) =^H+0 + 
 
 JLY(l0)=JLY(7) 
 
 Jl.Y( n )=JLY(3) 
 
 JLY( 12)=JLY(4) 
 ?5"|0 XR(K+I )=XU(KC)+1 . .I*XN 
 
 YB(K+1)=-YVA 
 
 GOTO ? c l? 
 
 2511 XB(K+1 )=XU(KC)+XN 
 Yd(k+1 )=-YV 
 
 2512 IF (XR(K+1) .LT.-511.5) 2513*2514 
 ?<^1^ Xo (< + i )=-*! ] .5 
 
 YB(K+1)=(-XU(KC)-ABS(XN)-511.5) /P 
 
 2514 IF (XB(K+1).GT«5-11.5) 2515*2516 
 
 2515 XB(K+1)=511.5 
 
 2516 
 
 YR(K+1 ) = (-XU(KC) + ABS(XM)+5U.5) /P 
 
 CONTINUE 
 
 XJB( 1)=XB( JYM J-12.0 
 
 Xjo( ? )=XR( JYM ) 
 
 Xjo( ^ )=XQ( JYV )+l?.n 
 
 XJR(4)sXo(JYM )+24.0 
 
 32 
 
) .OR- (XJB(4) .GT.442.CO) ?5161»25162 
 
 2 ~ 1 6 1 
 
 162 
 
 IF ( (XJ«(1 ) .LT.-45C 
 XJ C ( 1 ) =-4 5C • < 
 XJ Q { 2) =-4 33.0 
 
 X i " ( -? j = _ /. 7 c , o 
 X |n ( A } = -&"i&.C 
 Xjc ( c i--/. 0?.0 
 
 . ) I Y ( G 1 = "3 U + P - 
 
 XJ a ( 6 )=X C ( J v " + ? )-12«0 
 XJP ( 7)=X° ( JYM+2 ) 
 
 xj- ( ° ) =x^ ( JYV+? i+i ?.r 
 
 IF ( ( XJ n ( fi ) .LT.-450. ) .OR. ( XJ C ( « ) .GT.^42. 
 ? q . 1 6^ JL.Y ( 6 ) = JLY ( 7 ) =JLY ( Q . ] =?w+C 
 "? = 1 A A X J 1 ^ ( i =X^ ( JY-v+4 1-1 ?. - 
 
 XJR( ci =x n ( JYM+4) 
 
 X.jn ( 10 J =X^ ( JYV+4 ) 
 
 XJP( 11 )=X 3 ( JYM+4J+12.C 
 XJD( 1 7 ) =X n ( JYV + '-) +24. P 
 
 IP ( (XJ D (p).LT.-/- = ". r, ).^P.(XJ^(n ) .r-T.44? 
 JLY( n ) =JLY( i ) =JLY ( i i )=JLY( i ? ) =?M-i-C 
 n n 2 517 k' = ] » 1 2 
 
 Y | n ( < ) - _ Y V A 
 
 rnM| t mi ic 
 
 ^O OE1Q /si ,17 
 
 CALL CRT D LT ( C »" , JLY ( < ) , 1 ,5 ) 
 
 fALL rr? T^LT ( X jn ( ^ j , yjd ( kT ) » i , n , i) 
 
 ) ) 
 
 ?K-|f-2,?E1A& 
 
 ) ) 
 
 7 c . 1 6 : 
 
 "3 C 1 f C 
 
 ?M f a 
 
 9 r. 1 "7 
 
 KVsrJXN + 1 
 
 f M=JY W +1 
 
 r a i_ L r ° T ° L T 
 
 r M_ L r D T R L T 
 F ( c ) = n . o 
 
 ( X A , Y A , / M , 
 
 (Xo,yn ,/v, 
 
 F=YM( J ) 
 
 J= 
 
 
 
 ^ a 1 . 
 
 
 
 P(J)=1 .0 
 
 
 aC 
 
 T c ( r . I - . t . '~ ) 
 
 ■31,-3-3 
 
 1 
 
 r = r*i- # - 
 r>=n-*i r, ,P 
 r, n t ? C 
 
 
 "3 9 
 
 T r (p.LF-AO.Oj 
 
 ~( J) = ?. C 
 
 
 T r ( r . 1 r , -3 Q , j 
 
 ~ ( J 1 = r • " 
 
 
 I - ( r .L c .^.n) 
 
 nj)=iO. 
 
 
 T ^ (c.^T. A.^l 
 
 -3 "3 , "3 
 
 -3 -a 
 
 P( J)=r( jj *n 
 
 
 ■2£ 
 
 k' f> X = i ■ ' 6 / T V" 
 
 
 
 fXt 1 ) = ( 1 074-^^X 
 
 * T v ) / 7 
 
 
 no A 1 J= 1 , A 
 
 
 
 DO 40 1 = 1 , I v 
 
 
 
 KX( 1+1 )=KX( I J+K 
 
 ^Y 
 
 
 ^Y( T 1 ="Y~ ( Ji^7 ( 
 
 T »J1 * =■ ( J 1 
 
 33 
 
41 
 
 4 71 
 
 W>0 
 
 431 
 
 k'YL.t T ) ="<rYO{ J) 
 
 r^f- 1 T t Ml. JF 
 
 CALL C^TPLT ( XH , 1 . , <X , KY , 1 8 ) 
 
 <~ a L L r °TDi_T ( X u , . , v X , '< Y L > 1 « ) 
 
 fOMT T ^ ' !j ^ 
 
 XL(1 )=<X(1 )-5.12 
 
 X[ _( 7 ) =KX ( 1 )-40? 
 
 XL(3 )=<X( I )-480 
 
 XL (4) = KX( 1 ) -468 
 XL ( c ) = ''X ( i i-i^ 
 XL (6 ) = <X ( 1 . ) -444 
 r>^ L 7 Y = i , f- 
 n^ 6.7 J=l ,4 
 
 r>n 
 
 42 
 
 1 = 1 
 
 4 21,422 
 
 O.C/^Jl/A^MZ'.f.nn 
 4 7 4 , 4 7 r > 
 
 Xn( I ,J,K) =XL (< ) 
 
 47 roMjJMijir 
 
 On 4 3 J = l ,4 
 
 FV = p< ( J)* c .O.C/F( JJ 
 
 IF (ZA( J) •EQ.O.O) 
 v«{ i , J)=0 
 r -oTn 4^4 
 
 Mir-Fk' ( J) *Z A { ,M * ( 1 . 0- 
 apn, yn ( j , J ) =Mp/VF*VF 
 T rr (WR[1,J),cn t 0) 
 
 4 24 MO (2,J)=-^E 
 
 GOTO 426 
 
 i^ Yn( i , J,i ) = {yn(i , Jy -Za ( J)*="< ( J) )**( Jl /^'< ( J)4-KY0( J>-ei*5.0 
 
 Yt>( ?,j,i ) = (vc(?,j)-za ( jo*c (J) )* r ( J) /c-k 1 ( j)+<yri(-j)-^i ?.o 
 
 p r* u "* < = 7 , 6 
 no 4^ t = 1 , 7 
 Y"M I , J,K) =YH( I , J, 1 ) 
 
 /, O rOMTTMtJF 
 
 DO 431 1=1 ,2 
 
 n r> 4 Q i J = ] , 4 
 
 <Z( I ,J,1 )=3H+0- 
 
 (~ P N T T m ! J f 
 
 nn 44, 1=1,7 
 
 y A A = m n ( j , i ) / i 
 
 "Z ( T » 1 ,7 ) =KA a *t j< 
 
 K- ft c = M D ( T , 1 ) -y A A * 1 " 
 
 KAC = KA D /1 •" 
 
 ^ Z ( T , i , -a ) = k A r * T J '< 
 
 KAD=KAR-KAC*lGO 
 
 K A F = K A / 1 
 
 KZ( I » 1 ,4) =KAE*IJK 
 
 <Z{ I ,1 i«5) =KAF*IJ< 
 
 K ( < A . fl . c . ) 4 ■= 7 , 4 ' "2 
 
 34 
 
Li~> "Z ( T » "" » 7 1 =^Z ( T , i ,^> ) 
 ^Z(T»1,^)=KZ(Ij1»4) 
 \(Z ( T , i ,4 1 =" Z ( T ♦ 1 » k 1 
 "Z ( T » i , c ) =?U + 
 
 433 KZ ( I ,1 ,6 )=2H+C 
 
 KAG=MB< I 9?) /lOOr 
 KZ( I »? »?) =KT &G*T JK 
 
 '/ A U| = M D ( ]■ , 7 ) _ V \ r. # ■] 3 
 
 kMT = KAH/lQO 
 
 "7 ( T , ? ♦^ ) = < ft t *t JK 
 
 rZ ( T f ?»4) =^H+0. 
 
 KAJ=KAH-KAI*100 
 
 KAJA=KAJ/1G 
 
 <Z ( I »">,=; ) =KA JA*T JK 
 
 KAJR = t<AJ-k'AJA*lC 
 
 •<Z ( J , 7 >* ) = <A JP*t j< 
 
 IF (KAG.EQ.O) 43^,435 
 h?L k'Z{T»^j?)=i«fZ(T»'3»^) 
 
 , <'Z(T,~>,'^m='''Z(T,' 7 »4) 
 
 <Z( I »?»45 =KZ ( I »?»5 ) 
 
 " Z (I»?»«i)=<Z( I » "> » M 
 
 KZ ( I »?»6 ) = ?H+3 
 4 3^ <Z ( I »3 »2)=3H+C+ 
 
 IF ( Vq-( I >3) .LT.C) <Z(I »^»?)=?H+0- 
 
 y A, 1/ = J A d 5 ( M D ( J , <* ) ) / ] 
 
 kf A (_ = T A D S ( *' n ( T » "3 ) ) — '< A. K # 1 
 
 x A |_ a = y a L / T 
 KZ( I »3»4) =KALA*IJK. 
 KZ ( T »^ »* ) =-au+0. 
 < A j_ ° = K A L - K A L A * ]. 
 
 ^Z(T»°»^)=KAL a *Tji<' 
 IF (KAK.EQ.O) 436,4 3 7 
 4-*a <Z(T5^»' a )=!<Z(T»^,4) 
 
 kZ ( T »' a 9* ) =kZ ( I »-3 ,a ) 
 
 KZ( I 9* ,6 ) =?H+C 
 437 <Ay = MB( I ,4)/lC00 
 KZ( I ,4,2) =KAM*IJK 
 K - a N = M Q ( T » A. ) -K A m#] 00° 
 KAO=KAN/ 1 30 
 KZ ( T »4,'> ) =<a.O* T JK 
 KAP = <AN-i< A0*1 30 
 KAPA=KAP/10 
 
 V Z ( T , A. , 4 ) = K A D A * T J 1/ 
 <Zl T »A,^ ) =^M + 0. 
 
 KAPB=KAP-KAPA*10 
 kfZ( T »4»6) =Kado#tj^ 
 IF (KAM.EQ.O) 4 3 P , 4 4 
 A^n krz ( T »4,7) =<Z( T »&»•» 1 
 <Z ( T >4 ,^ ) =KZ ( T ,^,4 ) 
 
 35 
 
«7_( I ,4»4)=KZ( 1,4,5) 
 KZ (I ,4,5)=KZ( 1,4,6 ) 
 <Z( I ,6,6)=?H+0 
 
 DO 4 5 1=1,48 
 
 C&LL CRTPLT (0,0,<Z( I ) ,1 ,5 ) 
 
 r&LL ^QTD|_T (Xn( i> »Y^( T ) » 1 »1 »U 
 6* CONTTN!U r 
 
 D^ 46 1=1 ,6 
 
 CALL CRTPLT ( , , LF ( I) , 1 » 5 ) 
 
 CALL CRTPLT ( XF ( I ) , YP ( I ) , 1 , 1 » ! ) 
 h c ro^TTNU c 
 
 n n 6 "7 T = "? » t 6 
 
 rALL rRjD.LT ( n » ft »L c ni» R » R ) 
 
 r«LL ^ n Tni.T (Xc(n»Yc(I),i»l»l) 
 6 "7 CONTINUE 
 
 no 6 Q T = *> 7 , ? 6 
 
 rALl cpTdlT (OiMjinj]^) 
 
 r/\LL ^pTP!...T (X^( I 1 ,Yp( T 1 * 1 » "" » 1 ) 
 
 CONTINUE 
 
 r>n 6° 1 = 1,7 
 
 r A| L roTo L T (Xr-(J ) )YM! ) »w^»Lr-( T )»i 
 
 r PA'T T MlJF 
 
 4? 
 
 60 
 
 c U 
 
 XP( I ) =XL( 1 ) 
 
 5 CONTINUE 
 
 r ,M l rPT D LT (XP»YD»n,"» Q ) 
 KQ("l)=LlD(l)*UK 
 KQA=LID( 2)-lCG0 
 KQq = KG.A/ 1'J 
 
 K or = fcf O A — ^ O n * 1 
 KQi(3 ) =KQC*IJK 
 <OD=Lir>(3)-lC00 
 KQE=KQD/10 
 
 <Q(6 ) =<QF*IJ< 
 
 f ncr - v pr> _ v. Q r # 1 
 
 n( ^ ) =^0^^-! J" 
 KO(6)=Ll r >(4)/60o6 
 
 K0(7)=?H+ r 
 ip (Xr.LT.O.Q) 
 <OG=ARS( XC) 
 i<;Olj = <00/ 1 '"'0 
 KP ( a i =<0W#TJ< 
 
 k'0J=K0!/1 • ■ 
 
 ,/ n ( n ) - v o J * t j v 
 
 <0^ = K.QI-KQJ^10 
 
 KG( 1C")=KQ<*UK 
 
 v^l =Ar>5( xrj*i 000. C 
 
 i^n(7i=''H+0- 
 
 36 
 
KO ( i U ) =^w + 0- 
 
 KQM=KGL-KQG*1000 
 
 KCN=KQM/10C 
 KQ( 11)=KQ.N*IJK 
 
 <o ( 1 7 ) =<QP* J J< 
 
 <Q0= KQO-KQP-x-10 
 
 ("^(U) =?H+0 
 
 Tc (Yr.LT.O.O) 
 
 i/np = ap.S ( Yf 1 
 
 KOS=KQR/10 
 
 ^n( ] 5 )=KO$*lJ< 
 
 KOTsKQR-k'QS-H-lO 
 
 KO( 16 ) =KOT*IJK 
 
 k- nu= a p s ( Y C ) * 1 # 
 
 KQV=KOU-KQG#l COO 
 
 kTOW=KQV/1 CO 
 
 KQ( 17) =KQW*IJ.K 
 
 <QX=KOV-<OW*10C 
 
 <QY=<QX/1C 
 
 KQ( 18)=KQY*IJK 
 
 KQZ=KQX-<QY*10 
 <0(1 Q) =KQZ*ij}( 
 
 CALL CRTPLT ( XKL » YKL »NQ ♦ <L > 1 ) 
 
 n n ^i i = i » i q 
 
 CALL r^TDLT (0,0»KO(!)»1»=) 
 
 (XKQ( I ) ,YKQ( I ) »1 »0»1 ) 
 
 CALL CRTPLT 
 m rOMTTNUF 
 
 CALL C9TDLT 
 FND 
 
 >?0 > 
 
 37 
 
 GPO 888-780 
 
PE N N STATE UNIVERSITY LIBRARIES 
 
 AOQOOTEOiit,^