Around The World in ??? Days

For today's lab,  there are two main goals: Derive the formulas for
the distance between two cities, given their latitudes and longitudes.
These formulas are to be turned in by the end of the lab period.  Make
as much progress as possible on your functions for reading the input
data and printing the list of cities (see part (a) on page 3).
Ideally you should be able to write and test them today. Distance
between citiesA  point on the surface of a sphere can be uniquely
characterized by two angles, the polar angle  and the azimuthal angle
b, as shown in the  diagram below.  We can use these angles to
estimate the "surface distance"  between two cities on Earth, given
their latitudes and longitudes.  We take the "prime meridian" through
Greenwich, England to be b=0.  Cities with E (east) longitudes will
have positive b values; cities with W (west) longitudes will have
negative b values.  Cities in the northern hemisphere will have 0 <= a
< p/2, while cities in the southern hemisphere will have p/2 < a <= p.
A city on the equator (latitude 0) has  a = p/2).
WNGraphic.838900.eps
Work out the formulas for converting a latitude (given in degrees and
minutes N or S) into an a -value (in radians).  Do the same for
converting longitudes to b-values.  I suggest implementing these
formulas either in Mathematica or in C so you can test them for
several latitudes and longitudes to see if they produce reasonable
values of a and b.  Recall that a minute is 1/60th of a degree.
Now figure out the formulas (in terms of R, a , and b) for the x, y,
and z coordinates of a point on the surface of a sphere of radius R
whose defining angles are (a, b).  Assume that the origin is at the
center of the sphere.  The z coordinate is the easiest one to figure
out.  To get the x and y coordinates, first project the (bold in the
diagram) line segment (from the origin to the point) onto the xy-plane
(that projection is also shown in the diagram).
What is the length of this projected line segment?  How can you use
the projection and the angle b to find the values of x and y?  Next,
suppose that two points P1 and P2 have (a, b) and (a, b) as their
defining angles.  Consider vectors V and V from the origin to points P
and P respectively.  Let q be the angle between these vectors.
Use your above calculation of the rectangular coordinates (x, y, z)
along with the dot product formula to derive a formula for

cos
 q
 Mathemetica can be a great help in the simplification process;  You may have to apply Simplify[] to part of the answer in order to get satisfactory results.  The final formula should not be very long.
Y<?, You should turn in a (computer or hand) written copy of all of
your formula derivations by the end of lab today.   Once we know the
radius R and the formula for q, it is easy to calculate the surface
distance between two points on the surface.  The average of the polar
and equatorial radii of the Earth is 3957 miles; the planes fly
approximately 6 miles above the surface, so we will use R=3963.

Input description  Each line of the input file (design your program to
expect at most 100 lines) will contain a city name	columns
1-18the latitudeT 	degrees	columns 20-21 	minutes	columns 23-24
direction	column  26  the longitude T 	degrees	columns 30-32
minutes	columns 34-35	direction	column  37 population      	columns 41-45  (in thousands)rate of pop. increase	columns 48-52  (it's a percent, in some cases negative)per-capita income	columns 55-58  (in thousands of dollars per year)<All of the numbers except the population growth rate and the per-capita income are integers.  The directions are single characters: N, S, E, or W.Here is a typical input line:  Essen              51 27 N     7 01 E    7452  -0.33  19.81The data file is 
cities.dat, found in the         
Winter_1994-95/CourseDocuments/c-programming/exercises/ex9.1-aroundTheWorld
directory.  If there are any clarifications or updates to this
assignment as a result of student questions, I will place them in the
same directory (and alert you via e-mail).

Strategy: You are to turn in one program that does all of the following things.   But I have broken it up into parts as a suggestion as to how you can do it in manageable pieces.    This program is not as hard as it may seem at first, provided that you start early and take it one step at a time.  Your program does not have to label the parts (a, b ,c, etc.) as such, but it should do all of the parts if you want to get full credit."You should work with the 
9-1-test-scores.c file  in the c-examples9 directory before you
begin the  C-programming portion of this assignment.  It will give you
many clues as to how to do various things in your program.

Part
(a) Design a "city" structure to hold the needed information about a
city (city name, latitude, longitude, alpha, and beta). (Perhaps you
will also want  latitude to be a structure). Then declare an array of
these city structures to hold the information about all of the cities.
We will discuss one possible approach in lab today.Write a function
to read all of the data and place it into the array, returning the
number of cities read, similar to readStudentInfo in the
9-1-test-scores.c program.  You must also write an output
function that prints some of a structure's contents.  In particular
you might want this output function's list of arguments to include one
or more argument(s) that control which members of each city structure
get printed.  This is so that the different lists that you print can
contain different information, without having to write a separate
output function for each kind of output list.

A 1990 Rose-Hulman graduate named Deming Speed has already made his millions, and after retiring to his lifelong-dream-community of Terre Haute, he plans to take a special trip.  He wants to visit the  largest cities of the world (largest populations, according to the 1993 World Almanac).  The question he thinks about in his life of leisure is, "What order should I visit them in?"  He has come up with four possible schemes:@?01)	In decreasing order of population.2)

In increasing order of wealth.  The wealth of a city is to be measured as the product of the population and the per-capita income.)	In order from northernmost to southernmost.4)	In decreasing order of predicted population in the year 2035, if we assume that the growth rates will be the same each year as listed in the data file. (He wonders if it might be a while before he really gets around to taking this trip).For each case, Deming wants to know the total miles that he will fly if he leaves Indianapolis, travels to each of the largest cities, and then returns to Indianapolis.  You have been hired to find out this information forhim.  Because Mr. Speed owns his own fleet of planes, you may assume that there is always a direct flight from city to city wherever needed.dYou have been provided with a list of the cities, their latitudes and longitudes (in degrees, minutes, and direction), populations (of their metropolitan areas, in thousands), rates of population growth (in annual percentage), and per-capita incomes (for the countries in which the cities are located, in thousands of dollars per year).  Thanks to Bryan Whitsell for collecting the statistics from the World Almanac and an atlas.For each of the four possible routes, you should print a table with one line per destination city (in the order in which the cities are visited).  That line should list (at least)the name of the city,	the value of the quantity that you are using to determine the city order (population, latitude, or wealth)	the number of miles flown to reach this city from the previous city.  	A running total of the number of miles flown so far on the entire trip.Your program should be written in such a way that it can handle any number of cities up to 100.  It should determine how many cities to use from what it reads in the data file.>?4	Write a small main() function to test your input and output functions.  I recommend that you attempt to finish Part (a) in lab today.Part (b) Write in C the function(s) to convert the latitude and longitude values to a and b values.  In order to test this feature, modify your output function from part (a) so that it can print the values of a and b.Part (c) Write a function that takes two cities as arguments and calculates the surface distance between them.  Test your function by computing and printing the distance of each city in the list from Indianapolis.  The latitude of Indianapolis is 39Ê 46' N, and the longitude is 86 9' W.

Do the distances printed by your program  seem reasonable?  Assuming that your program is correct, what could be some sources of discrepancies between the distances printed by your program and the numbers you might find in a world atlas?    You do not need to include this output in what you turn in;  it is only to give you confidence that your distance function is working.

Part (d) Print out the first table showing mileages, etc.

Part (e) Sort the cities into wealth order, and test to be sure that it works.   Print out the second listing including mileages.  Then do the same thing for latitude order.

Part (f)  Use the population rate  figures to update the population for each city to its expected value in 25 years (don't forget to compound).  Then redo part (d) based on these figures.  You should reuse as much of the code from part (e) as possible instead of having to write entirely new functions to do it all.  In fact, reusing code should be a major theme as you write this entire program.³What to turn in: Q?A1.

Your formula derivations (due today)  2.	A listing of your well-commented program that reads the input file and prints the four lists3.	The output from your program.  4.	Also email your C source program to anderson with a Subject:  line "IFYCSEM exercise 9.1 turnin".  The program, its output, and your conclusions paper should be stapled together and signed by all partners.  By signing, you attest that you participated significantly in the creation of this program, that you understand what was done, and that you could explain it to other people.ÚUnlike programs due earlier in the term, this program will not be accepted late.  You must turn in whatever you have done by the due time (Thursday at 1:30 PM).    Do not think that you can get additional credit by continuing to work into the Block 9 period on Thursday.    Suggestion:  Set up a timetable that includes plans to finish this assignment by Monday night;  then you will have plenty of time to cope with unanticipated problems.

What to turn in: Q?A1.	Your formula derivations (due today)  2.	A listing of your well-commented program that reads the input file and prints the four lists3.	The output from your program.  4.	Also email your C source program to anderson with a Subject:  line "IFYCSEM exercise 9.1 turnin".  The program, and its outpu should be stapled together and signed by both partners.  By signing, you attest that you participated significantly in the creation of this program, that you understand what was done, and that you could explain it to other people.

What to turn in:
1.	Your formula derivations (due today)
2.	A listing of your well-commented program that reads the input file and prints the four lists
3.	The output from your program.
4.	Also email your C source program to anderson with a Subject:  line "IFYCSEM exercise 9.1 turnin".  The program, and its output should be stapled together and signed by both partners.  By signing, you attest that you participated significantly in the creation of this program, that you understand what was done, and that you could explain it to other people.

Next, suppose that two points P1 and P2 have (a, b) and (a, b) as their defining angles.  Consider vectors V1 and V2 from the origin to points P1 and P2 respectively.  Let q be the angle between these vectors.  Use your above calculation of the rectangular coordinates (x, y, z) along with the dot product formula to derive a formula for 
cos
 q
Mathemetica can be a great help
in the simplification process;  You may have to apply
Simplify[] to
part of the answer in order to get
satisfactory results.  The final formula should not be very long.  THe
formula for distance in terms of
(a,
b) and
(a,b)  is what you should use in oyur C program. 
What to turn in:
Q?A1.	Your formula derivations (due today)
.	A listing of your well-commented program that reads
the input file and prints the four lists3.	The
output from your program.  4.	Also email your C
source program to anderson with a Subject:  line "IFYCSEM exercise 9.1
turnin".  The
program and its output should be stapled together and signed by both
partners.  By signing, you attest that you participated significantly
in the creation of this program, that you understand what was done,
and that you could explain it to other
people.