Longitude Latitude Question

Excelmancan

New Member
Joined
Jun 27, 2010
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25
Hi,

I am trying to find a formula that would determine the distance (in feet) that these two coordinates varied from. In this case, to be expressed as "X" (amount of feet south) and "X" (amount of feet west) or original point. Then total distance as the crow flies.

45.5099086,-73.5638463

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45.4893274,-73.5844949

Thanks.

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DRSteele

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Excelmancan

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Jun 27, 2010
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Thanks for the reply DRSteele. No, actually I am just trying to figure out how many feet South and West these two coordinates end up at. I want to end an argument that has been going on for years with regards to St.Catherine street in Montreal. The street goes Northeast to Southwest with a dividing line at St.Laurent. All addresses "West" of St.Laurent (going towards Atwater), are called St.Catherine West. The argument goes that St.Catherine is actually more in line with North / South. This would finally end the argument. You might be familiar with this - being from Calgary.

https://www.reddit.com/r/montreal/comments/1hkmpo/why_does_north_west/
 

offthelip

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Dec 23, 2017
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If you want a reasonable flat earth type of calculation you can do this easily by using the equivalence between one minute of arc and 1 nautical mile which is about 6076 feet
To find the difference in Northing subtract one latitude from the other :
0.0205812
The multiply by 60 to get minutes and then by 6076 to get feet:
=7503.082272 feet
To find the Easting you need to take account of the fact the lines of longitude get closer together as you go North. We can do the approximately by multiplying by the cosine of the Average latitude
The average latitude is:
45.499618
To find the cosine in EXCEL we need to convert this to radians by multiplying by PI/180
The equation for this assuming the average is in cell D7is :
=Cos(PI()*D7/180)
This is: 0.700914
WE now find the difference between the two longitudes=
0.020649

We now multiply this by 60 * 6076 and the cosine of the average latitudes to give:
5276.238 feet

This is only approximate because the earth isn’t really flat. However for distance such as these the error is not large ( I haven’t Calculated what it is)
To get a more accurate answer you can use a Spherical earth model which is much more complex and even then is not absolutely accurate. A more accurate model of the earth is the elliptical model which is really hard work calculating, then you get a choice of which elliptical model you want to use.
Note I have used 6076 feet to the Nautical mile , this is an approximation too
 

Excelmancan

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Jun 27, 2010
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25
For all intents and purposes - this is a "flat" earth case, as we are talking about 25-30 city blocks.
 

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