# Lat Long Coordinates System (revised)

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First, please ignore the other post with this title - i used the wrong kind of parenthesis and my numbers disappeared.I have a question about working with the coordinates system (and I hope I'm explaining this coherently). Basically, I need to make sure that I am properly calculating the exact distance between two Lat/Long points so that I can figure out the point that is exactly half way between the two points. First, I am converting to the decimal system to make the calculations easier. Therefore, the point (Lat N*41 52.0399 Long W87*16.4099) would be (Lat 41.8973 Long -87.2735) in decimal format. Given the two points of (Lat 41.8673 Long -87.2735) and (Lat 41.8673 Long -87.2599) I believe that the exact midway point would be (Lat 41.8673 Long 87.2667). Since the Lat values are the same, the midway point between the two Long values would represent the midway point between the two coordinates. How would I figure out the midway point between (Lat 41.9665 Long -87.2664) and (Lat 41.9650 Long -87.2508). In this case, neither the Lat nor Long tracks match up.The longitude values are negative numbers since this is the western hemisphere, but is it OK to disregard the sign?Thank you very much;Christine

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Yes, disregarding the sign is fine assuming both signs are the same and you replace it afterwards!The midpoint between two Lat/Lon points is merely the mean of the Lats and the mean of the Lons.** EDIT: This is, of course, unless you want to plot "Great Circle" routes between two points. If you want Great Circle, then you need to go read Ed William's Aviation Formulary at http://williams.best.vwh.net/avform.htm and be prepared for some trigonometry! **So, for the midpoint (latM, lonM) between (latA, lonA) and (latB, lonB), you get:latM = (latA + latB) / 2lonM = (lonA + lonB) / 2e.g. midpoint between (41.9665, -87.2664) and (41.9650, -87.2508):Lat = (41.9665 + 41.9650) / 2 = 41.96575Lon = (-87.2664 + -87.2508) / 2 = -87.2586== (41.96575, -87.2586).Hope this helps,--M

Expertly done Matt. Concise and to the point. (or coord if you prefer)Glenn

Matt;Thanks for the advice. Taking the means will be just fine for what I am doing because the distances are not very big. I've seen Ed Williams' formulary and when he started talking about sines and cosines my eyes glazed over. I'm glad for a simple solution. Christine

Christine:>>I've seen Ed Williams' formulary and when he started talking about sines and cosines my eyes glazed over.Just to stir a bit more..... I was a professional navigator for several years, and to do Great Circles right you also need to be introduced to Versines and Haversines...... :-)Richard

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