John, I don't think you have the right approach. I just went through this for making globes and this is what I came up with:
The radius of the lattitude circle in question is a function of the radius earth. That is, radius of x degree lattitude = cos(lattitude) *radius at equator. If the earth had a radius of 4000 miles, then the 45 degree circle radius would be 2828.427 miles. And a degree at that lattitude would be 2828.427 * 2pi/360 or 49.365366 miles. (Of course, I mean along the lattitude circle) ++ron -----Original Message----- From: John Carmichael <[EMAIL PROTECTED]> To: [email protected] <[email protected]> Date: Friday, August 20, 1999 12:17 PM Subject: length of degs./mins./secs. >Hello dialists: > >I've had another basic question that has bothered me for a while. In fact, >it is such an elementary question that I'm almost embarassed to ask it, but >as they say, no question is a dumb, just the person who asks it! And I know >none of you are judgemental. > >I am trying to come up with a simple formula for determining the length of a >degree of longitude at a specific latitude. I wish someone of you would >check my reasoning and my math to see if my conclusions are correct. > >I am basing my calculations on the premise (true or false?) that the length >of a degree of longitude is directly proportional to the latitude because >the length of a degree of longitude is maximum at the equator (90* or 111.32 >km.) and zero at the poles. (to obtain 111.32 km. as the length of one >degree longitude at the equator, I divided the circumference of the earth by >360 degrees: 111.32 km./degree=40,074.16 km./360*) > >For example, if 45* latitude (north or south) is one half the distance from >the pole to the equator, then the length of one degree of longitude at 45* >latitude would be equal to one half the length of a degree of longitude at >the equator. This is 111.32 km./ 2 = 55.66 km. Is this correct? > >Using similar logic, if I wanted to know the length of one degree of >longitude at latitude 32* 13' 18", first I need to convert this latitude to >decimals. This would be: 32.2216*. >Then I determine the percentage of the distance this latitude is from the >pole to the equator. This is: (90*-32.2216*)/90*=.64198 or 64.2%. 64.2% of >111.32 km. = 71.46 km. >Is this correct? > >32* 13' 18" is the latitude for Tucson Arizona as given by Fer in his >sundial program in his list of world cities and their coordinates. I >wondered to which part of the city these coordinates refered. Was it City >Hall, The main plaza, the geographical center or what? (Fer, if you are >reading this would you let us know?) > >If one degree of longitude at this latitude is 71.46 km. then one minute of >longitude is 71.46*/60'/deg.=1.19 km, and one second of longitude is >1.198km./60"/min.=.01985km.=19.85 meters. Correct? > >The length of a degree of latitude is the same everywhere on earth. It would >equal the circumference of the earth divided by 360. This is 111.32 km., the >same length as a degree of longitude at the equator. This makes the length >of a minute of latitude=111.32 km./60'/deg.=1.855 km., and one second of >latitude is 1.855 km./60"/min.= .03092 km.=30.92 meters. > >If this is so, then Fer's coordinates are accurate to 30 meters of latitude >and 20 meters of longitude at Tucson's latitude. Am I correct? > >This leads me to ask if this degree of precision and accuracy even >necessary. I doubt that it would even be possible to build a sundial to >these exacting requirements. When dialists label their sundials with >latitude and longitudes accurate to the second, is this not presumtious, or >are they just giving the precise coordinates of the place in which the >sundial is located? > >I think this is an important concept for all dialists to understand, >especially the beginners. You might have delt with this before I joined the >list, but I'm sure most of us who are newcomers would appreciate a replay of >the thread. > >Thanks so much, >John Carmichael >http://www.azstarnet.com./~pappas > >
