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Spheric ========= A Spherical Geometry Calculator and Navigation Aid Version 1.26 by J. Andrzej Wrotniak December 16, 1994 Table of Contents 1. Introduction 1.1. What does Spheric do? 1.2. PC-DOS and HP Palmtop mutations 1.3. Extended (registered) version 1.4. Disclaimer 2. The Main Screen 2.1. The History Log 2.2. The Status Line 2.3. The Fix Database Display 2.4. The F-Key Menu 2.4.1. Nested menus 2.4.2. Nested F-key notation 2.4.3. Help and Exit keys 2.4.4. The Top Menu 2.5. The Prompt Line 3. The Fix Database 3.1. Fix display format 3.2. Moving around 3.3. Finding a fix 3.4. Inserting a fix 3.5. Appending a fix 3.6. Modifying a fix record 3.7. High accuracy fix display 3.8. Deleting a fix 3.9. Saving a fix file 3.10. Loading a fix file 3.11. Sorting fixes by name or category 3.12. Sorting fixes by proximity 3.13. Clearing the database 4. Computational operations 4.1. Distance between fixes 4.2. Azimuth from a fix to another 4.3. Midpoint between two fixes 4.4. Fix at a given azimuth and distance 4.5. Intersection of two great circles 4.6. Projection of a fix on a great circle 4.7. Distance from a fix to a great arc and its circle 4.8. Distance between two great arcs 5. Data entry 5.1. Editing the input 5.2. Special characters 5.3. Entering a single fix name 5.3.1. Name completion 5.3.2. Recalling previous inputs 5.3.3. New and old fix names 5.4. Entering two fix names 5.5. Entering fix coordinates 5.6. Entering an azimuth 5.7. Entering a distance 6. The History Log 6.1. Display format 6.2. Scrolling through the log 6.3. Deleting a log entry 6.4. Clearing the log 7. Program settings 7.1. Distance units 7.2. Distance display precision 7.3. Angular modes 7.4. Sign convention 7.5. Azimuth display modes 7.6. Earth model 7.6.1. Spherical Earth 7.6.2. Elliptical Earth 7.6.3. Accounting for the ellipticity 7.7. Sound alerts 7.8. Fix category display 8. Miscellaneous operations 8.1. On-line help 8.2. Clearing history and data 8.3. Exiting the program 9. Program installation and use 9.1. The packing list 9.2. Installing Spheric on your computer 9.3. Character set compatibility 9.3.1. Screen 9.3.2. Printer 9.4. Running Spheric from DOS 10. Registration and distribution 10.1. How to register 10.2. The extra goodies 10.3. Registration fees 10.4. Distribution 10.5. Support 10.6. Improvements and new features 10.7. Credits 1. Introduction 1.1. What does Spheric do? Spheric allows you to define a number of points (fixes) on the Earth sphere and then to perform various calculations involving these fixes: distance, azimuth, arc intersections etc. 1.2. PC-DOS and HP Palmtop mutations Spheric has been originally written for the Hewlett-Packard 95LX palmtop computer. The HP95 version will also run on the HP100LX or HP200LX. It is denoted with the letters "HP" in the version number, e.g., "1.20/HP". Although the HP palmtop version will also function on "regular" DOS machines, there is a version of the program compiled specifically for them. It centers the Spheric display in the screen, uses color (if applicable) and provides function key labels. This version is designated as "PC", as in "1.20/PC". Otherwise both mutations are identical, and the HP version will run on a full screen - but without color and F-key labels. The PC version of Spheric will run on virtually all PC-DOS clones with any display. A math coprocessor, if present, will be detected and used. Most of this manual is machine-independent, i.e. relates to both the PC and HP mutations; the information specific to the HP Palmtops can be found in the supplied file SPH_HP.DOC. 1.3. Extended (registered) version Spheric is shareware; the details on its distribution and registration are given in Chapter 10. *** Some program features may be available only in registered copies of Spheric, distributed exclusively to those who paid the registration fee. These are designated with letter "R" in the version number (e.g., 1.20R/HP). *** Parts of this document referring specifically to the registered version are marked with a "***" string. *** In the current version, there is only one difference between registered and non-registered copies of the program: the size of the fix database and of the history log. As a calculator, both versions are equally capable. The registered version, however, comes with two fix data files included (see Section 10.2). 1.4. Disclaimer Although the author has extensively tested the software and reviewed the documentation, he makes no warrant or representation, explicit or implied, with respect to this package, its quality, performance, merchantability or fitness for a particular purpose, in any hardware or software environment. In no event shall the author be liable for direct, indirect, special, incidental or consequential damages arising out of the use, misuse or inability to use the software or documentation. 2. The Main Screen When you run Spheric, you will first find yourself in the Main Screen, which consists of four parts: ┌──────────────────────────────────────┐ │Fix at distance 1200mi and │ │azimuth -75°19' from HONOLULU,HI │ │ 24°42'N 176°23'W│ ├──┬────┬────┬─────┬─────┬─────────┬───┤ │ 4│ NE │ mi │ DMS │Ellip│ N = 32 │","│ ├──┴─┬──┴────┴─────┴─────┴─────────┴───┤ │ 12│ HONOLULU HI 21°19'N 157°52'W │ │ 13│ HOUSTON TX 29°46'N 95°22'W │ │ 14│ INDIANAPO IN 39°46'N 86°09'W │ │ 15│ LASVEGAS NV 36°10'N 115°09'W │ │ 16│ LOSANGELE CA 34°04'N 118°15'W │ │ 17│ MEMPHIS TN 35°08'N 90°03'W │ │ 18│ MIAMI FL 25°47'N 80°11'W │ └────┴─────────────────────────────────┘ CAL FFd Azi Mid Aim FAd Prj AAd Int TOP These are, from top to bottom, the History Log, the Status Line, the Fix Database and the F-Key Menu. The last one is sometimes taken over by prompts asking for some input. 2.1. The History Log This is the long, three-line area near the top. Every calculation performed by Spheric is displayed here. The first two lines show the input data, the third one - the result. For more details - see Chapter 6. 2.2. The Status Line This line is located below the Expression Line and contains the following information (left to right). - The number of the History Log entry currently displayed (see Chapter 6). - The default direction indicator, showing whether North or South (East or West) will be assumed when latitude (longitude) is entered without the direction letter N or S (E or W). See also Section 7.4. - Unit indicator, showing the units in which distance is displayed or expected on input (see Section 7.1). - Angular mode: DMS (degrees and minutes), Dcm (decimal degrees) or Inf (infix notation, as in 56N09). This is the mode used for display of latitude and longitude. See Section 7.3 for more. - Earth model used in calculations: elliptical or spherical. - Number of fixes currently in the database. - The comma mode indicator, ",", or an empty space (see Sections 6.1 and 7.4). 2.3. The Fix Database Display Most of the Main Screen is taken by the Fix Database Display. The fix number is shown at the left, followed by the fix name and category, latitude and longitude. The display shows up to seven fixes at the time. The Fix Database is described in detail in Chapter 3. 2.4. The F-Key Menu The bottom line is taken by the Function Key Menu with mnemonics for the function keys F1..F10. We will be referring to function keys with these abbreviations in square brackets, e.g., [Set] instead of F2. 2.4.1. Nested menus Some of the function keys do not cause any immediate action. Pressing such a key will, instead, bring up a new menu with different operations assigned to the F-keys. For example, F3, marked as [Cal], will bring up the Calculation (CAL) Menu; while that one is active, F2, denoted as [Azi], performs the azimuth calculation. The name of the currently active menu is always displayed in uppercase letters above the F1 key. 2.4.2. Nested F-Key notation Nested function key sequences are denoted in this manual with key mnemonics separated by a vertical bar; thus the operation described above would be referred to as [Cal|Azi]. As the current menu is indicated with the key mnemonic in the Status Line, [Cal|Azi] may be also interpreted as "Press the [Azi] key while the Calculation (CAL) Menu is active, i.e. 'CAL' is being displayed at the bottom left of the screen". 2.4.3. Help and Exit keys In all function key menus, F1 activates the on-line help. Because this is true for every menu, the space above the F1 key is not used for the [Hlp] mnemonic (like in previous versions of the program), but for the menu name, displayed in capital letters, e.g. "SET". In all menus F10 is used to return to the next higher menu level (the name of that menu will be shown here in caps) or, in case of the top menu, to leave the program (in this case it shows as [Exit]). 2.4.4. The Top Menu This is the F-key menu visible first when the program is executed. In addition to [Hlp] and [Exit] functions, it allows for switching to other, more specialized menus, containing groups of related operations: [Set] brings up the Settings Menu, from where different program settings can be adjusted, as described in Chapter 7 [Cal] switches to the Calculations Menu, with all the numeric operations described in Chapter 4 [Dat] calls the Database Menu, with the database operations (mostly those from Chapter 3) 2.5. The Prompt Line Some times Spheric will ask you for a numeric or textual input by displaying a prompt at the bottom of the screen, temporarily replacing the F-key menu. Data input at prompts is discussed in detail in Chapter 5. 3. The Fix Database Spheric is capable of storing up to 32 geographic locations (for short: fixes). *** The registered version can store up to 9999 fixes (if there is enough memory in the system). One of the fixes (or, sometimes, an empty record) will always be selected, i.e. highlighted. This will be always a fix within the currently displayed range. Up to seven fixes will be shown in the Fix Database Display at one time. 3.1. Fix display format Each fix is shown as one line of text. It consists of the following: * Fix name (up to eleven characters starting from a letter; all letters will be in uppercase) * Fix category, if present; up to ten characters (denoting state, country or any other information you wish) * The latitude in degrees and minutes or in decimal degrees, depending on the current angular mode * The longitude, as above Some examples of this format could be seen in the illustration in Chapter 2. Individual fixes can be displayed with higher accuracy as described in Section 3.7. 3.2. Moving around At most seven fixes are visible at a time in the Fix Database Display. Others may be viewed by scrolling the display up or down. The up- and down-arrow keys select the previous (next) fix with respect to the currently selected one. If the latter is already at the top (bottom) of the display, the displayed range will be scrolled by one record. Obviously, it is impossible to scroll above the first record in the database or more than one record beyond the last one. The Page Up and Page Down keys will take you to the top or to the bottom of the current page or, if you are already there, will scroll one page up or down, respectively. The Home and End keys will cause a jump to the top or to the bottom of the whole database. 3.3. Finding a fix In order to find a fix by its name, just start typing this name. A one-second pause (or pressing the Return key) marks the end of the input. Spheric will then jump to the first record matching what you have typed in. After that, pressing Tab will take you to the next such record (if it exists). The display will be scrolled so that the newly selected fix will be in the displayed range. You can also search for fixes with specified category abbreviation (for example, to find fixes in California, denoted with "CA" in the small database US.FIX, enclosed with the program). To do this, type a comma and then the category, e.g. ",CA". 3.4. Inserting a fix To insert a new fix into the database, press the Insert key. You will be prompted first for the new fix name, and then for its latitude and longitude. (See Chapter 5 for the details on data entry). If your answers do not contain errors, the new fix will be inserted into the database before the currently selected one. If the name you have entered already exists, Spheric will warn you about it. You will be then able to cancel the operation or to overwrite the old fix of that name. 3.5. Appending a fix Another way to add a fix to the database, instead of pressing the Insert key, is by going to the bottom of the database (the empty record following the last one) and pressing Enter. The remaining part of the procedure is as described in the previous section, except that the new fix will then be appended at the end of the database. 3.6. Modifying a fix record To change the name and/or the coordinates of a fix, select it as described in Section 3.2, and then press the Enter key. You will be prompted for the new name, and then for the new latitude and longitude. If you are renaming a fix, the new name has to be different than that of any other fix already in the database. (Entering a fix name is described in Section 5.3.) 3.7. High accuracy fix display Although fix coordinates are displayed, depending on the [Set|Ang] setting, with an accuracy of 1' or 0.01°, which is high enough for all practical purposes, sometimes you may need to view a fix in higher precision. Pressing the "." key will show the currently selected fix at the bottom of the screen, with an accuracy of 1'' or 0.0001° (depending on the [Set|Ang] setting). Any key will then bring the menu display (and functionality) back. 3.8. Deleting a fix Pressing the Delete key will remove the currently selected fix, after asking for a confirmation. 3.9. Saving a fix file Spheric will save the fix database as an ASCII (plain text) file with fix names and coordinates. This file can be then used by another program or by Spheric itself. To save a fix file, press [Dat|Sav]. You will be prompted for the file name which may contain up to eight characters. Do NOT enter the path (which will default to the current Spheric path); the program will; the program will also append the extension ".FIX" to the name you enter. If the name thus created is not a legal DOS file name, an error message will be displayed. Pressing the Tab key will recall the last file name used; the down-arrow will scroll through all .FIX file names in the Spheric directory, and the up-arrow will jump back to the first name in the list. If a .FIX file with the selected name already exists, it will be overwritten without a warning. The output file format is simple: each fix takes one line, consisting of the fix name and category (separated with a comma), a space, latitude, a space again, and then longitude. The angle notation will depend on the current angular mode (DMS, Infix or Decimal, see Section 7.3). For example, the last of the fixes from the screen shot in Chapter 2 will be written in one of the following formats: NEWARK,NJ 40°44'N 74°10'W NEWARK,NJ 40N44 74W10 NEWARK,NJ 40.7333N 74.16677W (When writing to a file, the degree symbol in the Decimal format is dropped, as in the third line.) 3.10. Loading a fix file A fix file can be loaded into the program with [Dat|Loa]. Again, you will be prompted for the .FIX file name without path as described above (including the use of Tab and arrow keys). The program will also ask, whether you want to clear the fix database first; if not, the new fixes will be appended to the database. The input file standard is the same as the output one described in Section 3.8, except that the coordinate values can be preceded by a sign instead of being followed by a letter, as in NEWARK,NJ 40°44' -74°10' NEWARK,NJ 40.73 -74.17 The sign convention (what directions correspond to "+" or "-") can be changed by [Set|+/-] (see Section 7.3), so it is also possible to have the last record interpreted as, e.g., (40.73S, 74.17E). To avoid confusion, do not switch between various sign conventions unless you really have to. 3.11. Sorting fixes by name or category Pressing [Dat|Nam] will sort the fixes in ascending alphabetical order (as per the ASCII codes of the characters). This is quite useful, especially if you intend to search for fixes by name, as described in Section 3.2. [Dat|Cat] will sort the database alphabetically by category abbreviations; within the same category fixes will be arranged by names. 3.12. Sorting fixes by proximity Fixes can be also be sorted in the increasing order of their distances from a given fix. To do this, select a fix by highlighting it in the database window and press [Dat|Prx]. The fix, distances from which have been used as the basis for the sort will be shown at the top of the database. 3.13. Clearing the database Pressing [Dat|Clr] will bring up the Clear (CLR) Menu. From here, [Fix] will clear the fix database, [His] - the history log, while [All] will clear both. 4. Computational operations Here we come to what Spheric actually does. All these operations are performed from the Calculations Menu. To get here, press [Cal] in the Top Menu. (There is also a shortcut: just press the space bar at any time, and you will jump right here.) 4.1. Distance between fixes [Cal|FFd] ("Fix-to-Fix distance") will compute the distance between two fixes. You will be prompted for both fix names. The distance is defined as the length of the great arc, connecting both fixes on the Earth sphere. Instead of the first fix name you may enter just a "+" (without quote marks). Spheric will then replace it with the name of the second fix from the previous distance calculation, compute the arc length, add it to the previous result and display the total. This way, a total length of a route defined by a series of fixes can be easily computed. 4.2. Azimuth from one fix to another Pressing [Cal|Azi] will compute the azimuth from one fix to another. You will have to identify both fixes by their names. The azimuth from fix A to fix B is defined as the angle (measured at A) between two great arcs - one running from A to the North Pole, and the other from A to B. The clockwise direction is defined as positive ("+"). The result will be between -180 and 180 degrees or between 0 and 360 degrees, depending on the [Set|360] setting. If both points have the same coordinates, or if one is exactly opposite on the sphere to the other, an error will be reported. The azimuth from the North Pole to anywhere else is 180 degrees; from the South Pole, 0 degrees. Similarly, the azimuth from anywhere to the North Pole is 0, to the South Pole, 180 degrees. 4.3. Midpoint between two fixes This point is computed with [Cal|Mid]. A midpoint between fixes A and B is defined as a fix C, located on the great arc from A to B, and such that the distances A-C and B-C are equal. You will be prompted for the names of the original two fixes (A and B), and then you will be able to assign the midpoint a name. If you do that, a new fix will be added to the database. An error will be reported if one of the points is exactly opposite on the sphere to the other. 4.4. Fix at a given azimuth and distance This operation is invoked with [Cal|Aim]. Given a fix A, azimuth angle a (any values between -360 and 360 degrees are allowed), and distance d, it will compute a new fix B, such that the azimuth from A to B will equal a, and the distance, d. 4.5. Intersection of two great circles Two great arcs may or may not intersect within their lengths, but their great circles always do (as long as they are not identical). This operation, activated by [Cal|Int], will find the intersection between the great circles to which two given great arcs belong. First you will be prompted for the names of two fixes defining the first great arc (A,B), then for those defining the other arc (C,D). You will be also given an option to assign a name to the intersection point E; in this case the fix will me added to the database. Two great circles (different from each other) intersect in two points. Out of these two possible solutions, Spheric will chose the one which is closer to the arcs involved (more accurately: to the midpoint between their respective midpoints). The result displayed in the History Log will be followed by two characters; each of them denotes the relationship of the intersection E to the first or the second arc: "*" means that the intersection belongs to (falls within the length of) the given arc "-" denotes the intersection preceding the arc's first fix "+" means that the intersection follows the arc's second fix. For example, let us consider two great arcs: the first one running from (5N,0) to (10N,0) and the second from (0,10W) to (0,5W). It is not difficult to predict, that the intersection point will be at (0,0). It will be marked with "+-", as it follows the end of the first arc, but precedes the start of the second one. On the other hand, with the first arc from (5S,0) to (5N,0) and the second from (0,5W) to (0,5E), the intersection point will be (0,0) but it will be denoted as "**", falling within the spans of both arcs. 4.6. Projection of a fix on a great circle The projection of a fix can be defined as the point on the circle at the closest distance from that fix. For example, the projection of (10N,5E) on the Equator will be (0,5E). We may be, for instance, interested in finding the point on an aircraft's route (a great arc) from Warsaw to Chicago, which is closest to London. This will be exactly the projection of London on the great arc (or its circle) Warsaw-Chicago. This computation is activated by pressing [Cal|Prj]. You will be prompted: first for the names of the fix being projected, then for the names of two fixes defining the great arc. The displayed result will be followed with a character, "*", "- " or "+" denoting whether the projection falls within the arc span, precedes its start, or follows its end, respectively. For example, if our fix is (10N,0) and the great arc runs from (0,5E) to (0,10E), then the projection will be (0,0) and it will precede the arc's start fix, so the solution will be marked with a "-". 4.7. Distance from a fix to a great arc and its circle Pressing [Cal|FAd] ("Fix-to-Arc distance") will compute and display two results: - The "passing distance": this is the distance between a fix and its projection on a great circle (see the preceding section). - The "closest distance", i.e. the distance from the fix to the closest point of the arc. The prompts and data input will be the same as in the case of [Cal|Prj], and the character flag following the result value has the same meaning as well. If that character is a "*" (i.e. the projection falls within the arc length), both results will be the same. For a "-" or a "+", the second result (greater than the first one) will be the distance between the fix and the start or the end of our arc, respectively. 4.8. Distance between two great arcs [Cal|AAd] ("Arc-to-Arc distance") will prompt you for fix names defining two arcs, and then the distance between those arcs will be computed. This is the shortest distance between any point on one arc and any point on the other. Obviously, if the arcs intersect (within their lengths) or overlap, the computed result will be zero. 5. Data entry At certain times, Spheric will prompt you for input from the keyboard. Sometimes it will be a simple Yes/No question, sometimes you will have to answer with a textual or numeric input. The prompt is always displayed in the Prompt Line, temporarily replacing the F-Key Menu at the bottom of the screen. Your answer will be also echoed here. The Yes/No questions require you to press just the Y or N key. Instead of "Y" you may press again the same key which caused the prompt to be displayed, and pressing Escape will abandon the whole operation. For example, [Dat|Clr|All] will prompt you with "Clear all?". Instead of moving your finger to the Y key, just press [All] again, and the clear-all operation will be performed. The following general rules are applicable to all other kinds of keyboard input. 5.1. Editing the input Sometimes a default (or just the previous) answer will be displayed after the prompt. The answer can be edited with use of the customary line-editing keys: left- and right-arrow, Delete, Backspace, Home and End. Pressing Escape when any input is present on the Prompt Line will clear it. The same key with no input present will exit the prompt, and the operation of which the prompted input was a part, will be abandoned. After having the appropriate input typed in, press Enter to continue. The same effect can be achieved by pressing again the same F-key in response to which the prompt has been displayed. 5.2. Special characters In all inputs involving angles, the degrees character "°" can be entered by pressing Alt+D (hit the D key, while holding Alt down). The minutes symbol can be entered as an apostrophe, but also as Alt+M, and seconds - as double quote or Alt+S. (Note that seconds are not shown in the fix database display, but the input data may use them if you wish.) Alnernatively, a "d" or "D" can be used instead of the degree symbol, as in 12d30'21". 5.3. Entering a single fix name The fix name can be typed in either upper- or lowercase; it will be converted to uppercase anyway. Leading and trailing spaces are discarded; spaces inside the name are not allowed. The maximum name length is eleven characters. The name can be immediately followed by a comma and a category abbreviation (up to ten characters), as e.g. in "PARIS,FRA". The total length of name+category is limited to 11 characters. If these limits are exceeded on input, name and/or category will be truncated appropriately and redisplayed. Pressing Enter again will accept the truncated version. For example, "STOCKHOLM,SWEDEN" will become "STOCK,SWEDEN" "NEWBIGPOINT,X" will become "NEWBIGPOIN,X". 5.3.1. Name completion Instead of entering the whole name (or name+category), you may type in just one or more of its first characters and press the Tab key. The program will then display the first matching name (as ordered in the database) on the Prompt Line, together with the category abbreviation. If more names match, subsequent uses of the Tab key will scroll through all matching names, finally returning to the first one again. If there are no matching names, the entered text will be just reformatted to uppercase. 5.3.2. Recalling previous inputs If the Tab key is pressed when the prompt line contains no input, the last used (and accepted) fix name will be displayed there. Press Enter to accept this input. Alternatively, the up- and down-arrow keys can be used to browse through the three most recent inputs. *** In the registered version, last ten inputs (not three) can be recalled. 5.3.3. New and old fix names In some situations Spheric expects you to enter the name of an existing fix (i.e. one already in the database). If this is not the case, an error message will be shown. An opposite case is also possible, when Spheric waits for a name of a new fix (different than any already in the database), but you enter an "old" one. If this happens, the program will alert you that the operation will overwrite the existing fix and you can proceed or not. 5.4. Entering two fix names This case is very similar to the one described above, except that Spheric expects two existing fix names, separated with one or more spaces. Each name can be immediately followed by a comma and category abbreviation. Pressing the Tab key will, obviously, complete just one fix name: the last one in the Prompt Line. For example, if the input is just "lo", it may be redisplayed as "LONDON,GBR ", but if it is "LO PA", then pressing Tab will bring up "LO PARIS,FRA". To get "LONDON,GBR PARIS,FRA" enter "lo", press Tab, then add "pa" and press Tab again. It can't be more simple than this. If the Tab key is pressed when the prompt line contains no input, the last used and accepted pair of fix names will be displayed there. The up- and down-arrow keys allow to scroll through three (in the registered version: ten) most recently entered fix name pairs. 5.5. Entering fix coordinates At many points Spheric will expect you to enter the coordinates of a fix. It will then display a prompt Lat, Lon: followed by the current coordinates of this fix, if the fix already exists in the database. Now the program will expect you to enter values of latitude and longitude (in this particular order), separated with one or more spaces (but no spaces within values are allowed!). The program will understand quite a variety of input formats here, and they can be mixed in almost any way you wish (the current angular mode setting does not affect this). For example, the same coordinates can be entered in any of the formats shown below: 13°30'N 5°15'W 13.5N -5°15' 13.5 -5.25 13N30 5W15 (Note that the meaning of "-" in coordinate values can be changed as described in Section 7.4.) Instead of the degree symbol, a letter "D" or "d" can be used. Any illegal input (and there are quite a many possibilities here) will cause an error sound (no message, though!) and you will be able to correct the mistake. 5.6. Entering an azimuth When Spheric prompts you for an angular value of an azimuth, it will be able to recognize input in all angular formats used by Spheric, (see Section 7.3), regardless of the current angular mode. Azimuth is always measured clockwise from North, usually from - 180 to +180 degrees, although values between -360 and +360 degrees will be interpreted properly. This does not depend on the [Set|+/-] setting (described in Section 7.4). Instead of "-" or (optional) "+", letters "W" and "E" can be used. For example, an azimuth of -90 degrees denotes the direction due West. Instead of entering "-90", you can enter "270" or "90W" here. 5.7. Entering a distance Every prompt for value of a distance explicitly states the units in which the input is expected. This depends on the current setting of distance units (see Section 7.1). The entered value may (but does not have to) contain a decimal point. 6. The History Log Every computational operation performed by Spheric is entered, if successful, into the History Log. The most recent entry is displayed in the three-line area at the top of the Main Screen. Up to 12 recent entries (in the non-registered version) are stored and can be reviewed as described in Section 6.2. *** The registered version stores up to 60 log entries. When the full capacity of the history log has been reached, each next entry will cause the oldest one to be removed from the log, and all others will be pushed up by one number. 6.1. Display format A log entry consists of three lines: the first two define the computational problem, the third shows the result. Coordinates and distances are displayed according to the current settings (see Sections 7.1-7.3). Changes to these settings will not affect the existing log entries, only those which will be added afterwards. Display of fix categories in the history log can be enabled or disabled. Switching between these two formats is done with the [Set|Com] function key sequence, and if the second mode is active, a "," symbol will be shown on the Status Line. 6.2. Scrolling through the log The left- and right-arrow keys can be used to move from one log entry to another. Pressing one of these these keys while Ctrl is held down will cause a jump to the first or to the last entry, respectively. 6.3. Deleting a log entry The currently displayed entry can be (after a confirmation query) deleted by pressing the Backspace key. 6.4. Clearing the log [Dat|Clr|His] will clear the history log, while [Dat|Clr|All] clears also the fix database. 7. Program settings To get to the Settings (SET) Menu, press [Set] while in the Top Menu. There is also a shortcut: while in the Calculations Menu, you can get directly to the Settings Menu by just pressing the Space key (press Space again to get back to the Calculations Menu). 7.1. Distance units This setting affects in what units Spheric displays distance values and in what units it expects them on input. Pressing the [Set|Uni] function key repeatedly will change distance units between kilometers (km), statute miles (mi), nautical miles (nm), minutes of arc (') and degrees of arc (°). The last two settings are useful primarily, but not only, in astronomical applications (and you thought Spheric dealt just with Earth?). One statute mile is defined as 1.609344 km, and one nautical mile - as 1.852 km. The relationship between degrees/minutes of arc and the other units depends, obviously, on the assumed Earth radius. This will be described in Section 7.6. 7.2. Distance display precision Depending on the [Set|Uni] setting, the distance results displayed in the History Log are rounded to the nearest km, mi, nm, arc' or 0.01 arc°. This accuracy is sufficient for any practical purposes but if a higher display precision is needed, [Set|Acc] can be used to switch to a mode where three more decimal digits are displayed (this is, of course, much higher a precision than that provided by the Earth model we are using). 7.3. Angular modes This setting decides how Spheric displays latitude and longitude and azimuth. It does not affect the data input (all formats will be always accepted on input). Pressing the [Set|Ang] function key toggles you between the DMS, Infix and Decimal modes. In the DMS mode angles are displayed as degrees and minutes, e.g. 23°15', in the Decimal mode - as degrees with decimal fraction, like in 23.25°. The Infix mode is similar to DMS, but the direction character follows the degree value, as in 23N15. When angular mode is changed, all entries shown in the Fix Database Display will be reformatted. The angular mode does not affect the way in which azimuth values are displayed: decimal degrees will be always used for that purpose. 7.4. Sign convention Some of us prefer to use "-" and (optionally) "+" signs instead of the N, S, W and E letters when entering latitude and longitude values. The usual convention seems to be that positive values correspond to North and East. Spheric allows this to be tailored to your personal preferences. Pressing the [Set|+/-] key repeatedly will change the sign convention from NE (where North and East are "+") to NW (North and West, often used in the United States), SE (useful for our Australian friends) and SW. One has to remember, that if a fix file using signs instead of letters is read by Spheric (see Section 3.10), it will be interpreted according to the current setting. This is important only for files generated by other programs, as Spheric always uses the letter (not sign) convention when saving fix files. 7.5. Azimuth display modes The [Set|360] function key toggles between two modes of displaying azimuth values: from -180 to 180 degrees, or from 0 to 360 degrees. This does not affect how the azimuth is defined (always clockwise from the North). 7.6. Earth model Spheric allows, in a somewhat limited way, to use either spherical or ellipsoidal model of Earth in its calculations. Pressing [Set|Ert] toggles between these two models. This may cause some delay, especially for large fix databases, as the program has to recompute the internal representation of all stored fixes. 7.6.1. Spherical Earth This model assumes that Earth is a sphere with the radius of 6367.4357 kilometers. The spherical model is useful when comparing the results of calculations by Spheric with those of other programs; it also should be used when Spheric is used for astronomical (as opposed to geographic/navigational) calculations. In the latter case the distance units should be set to degrees or minutes of arc (miles or kilometers do not make much sense on the sky!). 7.6.2. Elliptical Earth This model, often referred to as GRS 1980, assumes that Earth is an ellipsoid with the polar axis of 6356.7523 and the equatorial axis of 6378.1370 km. The geometric average of these two values is equal to the "spherical" Earth radius as shown in Section 7.6.1. 7.6.3. Accounting for the ellipticity For most purposes you may just skip this section and remember only that the elliptical model is more accurate than the spherical one. Now more explanations for those who have to know. In the first approximation Earth is a sphere. It can be, however, represented more accurately as an ellipsoid with the shorter axis about 1/300 less than the longer one. (Better approximations are also available). When dealing with the elliptical Earth, one may distinguish between two different definitions of latitude. The geocentric latitude of a fix P can be defined as the angle between the Equator plane and the line connecting P with the Earth's center. The geographic (geodetic) latitude is the angle between the Equator plane and the line perpendicular to the ellipsoid at P. It is slightly greater than the geocentric latitude (except at 0 and 90 degrees S or N, where it is the same). This is the latitude usually given for a point. Most of navigational and cartographic applications account for Earth's ellipticity just by performing their operations in three steps: (1) Translating the geographic latitude into geocentric for any points on input; (2) Doing all calculations on a sphere with some "average" radius; (3) Translating the geocentric latitude into geographic for any points on output. Spheric also follows this method, with the average radius assumed as 6367.4357 km (the same as the one for the spherical model). Such a procedure accounts for most, if not all, of the Earth's ellipticity. In principle, the shortest path length between two points can be computed on an ellipsoid with the full accuracy (a cumbersome, iterative procedure), but it would be no longer a distance along a great arc: there is no such thing like a great arc on an elliptical Earth! All other concepts used in our program are based on the concept of great arc - and this, obviously, makes sense only on a sphere. 7.7. Sound alerts Spheric uses two kinds of sound alerts: one to signal a completion of a computation and one to alert you to an error. These sounds can be disabled (or enabled again) by pressing the [Set|Snd] function key. Enabled sound is denoted with an arrow preceding the [Snd] menu entry. 7.8. Fix category display The [Set|Cat] function key toggles between the two formats of fix name/category display in the History Log, as described in Section 6.1. When the category display is enabled, a "," symbol will be shown on the Status Line, and an arrow sign will be pointing to the [Cat] menu abbreviation. 8. Miscellaneous operations Here we describe all remaining features of Spheric, which did not fit into any of the preceding chapters. 8.1. On-line help Spheric has a simple on-line help, activated by pressing the F1 key in any menu. The Help Screen contains a list of topics available. Entering the topic's first one or two letters (enough to distinguish it from others) at the prompt and pressing Return, will bring the proper help page. Some help pages will offer you a further choice of topics - the help is structured in a tree-like fashion. Pressing Return, Escape or F10 at a topic prompt (or any key in a prompt-less screen) will take you back to the next higher level or to the Main Screen. 8.2. Clearing history and data [Dat|Clr] will bring up the Clear Menu, denoted as CLR, from where three operations can be performed: [Fix] - clear the fix database [His] - clear the history log [All] - clear all (i.e. both of the above). 8.3. Exiting the program To leave the program, press [Exit] in the Top Menu. Before exiting Spheric will allow you to save its current status (including fixes, history and settings) to disk file named SPH.ENV. There will be also the final request for confirmation, with the exit prompt showing the program version and (for registered copies) the serial number. To exit quickly without saving (and with no extra queries), press Shift+F10; going to the Top Menu is not necessary to do this. The size of SPH.ENV depends on the number of fixes stored in the database and on the number of entries in the history log. SPH.ENV is automatically read in as Spheric is executed, so that you can exit the program, do something else, and reenter it without losing continuity of your work. 9. Program installation and use Installing the program requires that some or all of the distributed files are copied to your disk drive. 9.1. The packing list Whatever was the source from which you obtained Spheric, you should have the following files: SPH.EXE - the program itself SPH.HLP - the text file used by on-line help SPH.ERR - the text file with error messages SPH.DOC - the manual (you are reading it now) SPH_HP.DOC - addendum to the manual (HP Palmtops only) US.FIX - a fix file with coordinates of 30 major U.S. cities WD.FIX - a fix file with 30 major world cities WHATS.NEW - a brief list of changes since the last version READ_ME.1ST - the introductory file *** Registered copies of Spheric contain additional files: USA.FIX - a file with coordinates of 240 U.S. cities WRD.FIX - same, for 300 cities of the world 9.2. Installing Spheric on your computer This is a simple task. Just copy the files SPH.EXE, SPH.HLP and SPH.ERR to one directory, e.g., C:\SPH. If you decide to use some of the supplied data files, copy them there, too. If that directory is included in the PATH definition in your AUTOEXEC.BAT file, you will be able to run Spheric while anywhere in the system, as explained in Section 9.4. 9.3. Character set compatibility 9.3.1. Screen The only non-standard ASCII characters used by Spheric are the degree symbol (°), corresponding to the value of 248 in the ASCII table, and the graphic symbols used to draw the Main Screen. These symbols are available on the HP Palmtop as well as on desktop machines, at least these using English or International character sets (code page 437 or 850, respectively). 9.3.2. Printer Not all printers may print the above symbols correctly; this may cause minor problems in a few places of this documentation; a minor annoyance. On the HP LaserJet III (and perhaps some other models) all these problems can be avoided by setting the character set to 850 Multilingual. 9.4. Running Spheric from DOS To run Spheric we must assure that (i) DOS will find the program file, SPH.EXE, and (ii) Spheric will find its related files SPH.HLP, SPH.ERR, SPH.UNI and SPH.ENV. The first is done either by moving (with use of the CD command) to the directory where Spheric resides before running it, or, preferably, by specifying this directory in the PATH statement in your AUTOEXEC.BAT file. The second is done by keeping all files listed in (ii) above in the same directory where SPH.EXE is. 10. Registration and distribution Spheric is a copyrighted program, released as shareware. You are free to use any evaluation (non-registered) copy of it on a trial basis for a month or so. If you decide to use it afterwards, you are expected to register it (as described below); otherwise please delete it from your system. 10.1. How to register To register, send your name and address (including GEnie, CompuServe or Internet, if applicable) together with the appropriate registration fee - a check or money order (U.S. funds, drawn on a U.S. bank) to J.A.Wrotniak 2057 Happy Lane Crofton, MD 21114-1917 Please state your current version number and computer type (HP palmtop versus any other DOS machine). The basic registration fee is $30, and the complete price list can be found in Section 10.3. 10.2. The extra goodies "Yeah, yeah, I'm going to pay you some time later this year, but not now; I've spent too much for Christmas!" *** To increase chances that you keep your end of the deal, those who pay the registration fee will receive a package of extra goodies, including: *** The newest registered (enhanced) version of Spheric on a 3.5" DD or HD floppy disk *** Two additional data files, covering the USA (240 fixes) and the world (300 fixes) *** Registered copies of Spheric, denoted with an "R" in the version number (e.g., 1.20R/HP or 1.20R/PC), cannot be distributed: resold, leased, given away, placed on electronic bulletin boards etc. *** The owner may make backup copies only for his/her own use, safety and convenience. *** Every registered copy of Spheric has a unique serial number embedded inside and displayed at the program exit. Please refer to this number in all related correspondence. 10.3. Registration fees Here is the complete price list: - A single copy of Spheric (PC or HP): $30 - Both versions at the same time: $36 - The other mutation ordered later: $12 - A single update to a new version: $10 - Both updates at the same time: $12 Institutions may order multi-user site licenses at prices obtained by multiplying the above rates by square root of the number of users. For example, a site license for both versions of Spheric and for 20 users will be $40*sqrt(20) = $40*4.472 = $178.88. 10.4. Distribution You are free to distribute Spheric (only evaluation copies, without an "R" in the version number) to anyone, as long as all original files, as in the Packing List above, are enclosed. This permission extends to the electronic distribution. Please do not distribute (give away, sell, lease, post on electronic bulletin boards etc.) any registered versions of Spheric. Public Domain and shareware vendors are granted the right to include complete evaluation copies of Spheric into their libraries only if the total cost to the user stays within the limit of $6 per disk; otherwise my explicit permission is required. (I would, however, recommend contacting me ahead of time; I may already have a newer version.) 10.5. Support If you have any questions, suggestions or problem reports, I can be contacted on GEnie (J.WROTNIAK) or CompuServe (70611,2552). My email address on the Internet is "wrotniak@umdhep.umd.edu". If you do not have an access to these services, write under the address shown above. I read all letters and answer most of them. 10.2. Improvements and new features Unavoidably, the program reflects, to a large extent at least, my own needs, preferences and working habits. In your own interest, let me know what you like and dislike about Spheric, and how would you like it to evolve. 10.7. Credits Spheric has been developed in Turbo Pascal 7.0 from Borland International, and contains library code copyrighted by Borland. Some of the math algorithms used in Spheric have been borrowed from one of my other programs, Star Base, running on the Atari ST series. I have also used some algorithms I developed for various Civil Aviation applications at Aerospace Engineering and Research Associates, Inc., in Landover, MD.