Longitude conversion according to your latitude

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Discussion Overview

The discussion revolves around calculating the distance between two longitude points at specific latitudes, particularly in the context of sonar work and programming in MATLAB. Participants explore the necessary conversions for longitude based on latitude and seek clarification on the formulas involved.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a formula to calculate the distance in yards between two longitudes at given latitudes, noting that the distance per degree of longitude varies with latitude.
  • Another participant suggests using the formula for the radius of a circle of latitude, which involves the mean radius of the Earth and the cosine of the latitude angle.
  • A participant confirms their application is for sonar work and questions whether the same conversion factor for latitude can be applied to longitude.
  • There is a suggestion to clarify which latitude should be used for calculations, proposing the average of the two latitudes as a potential solution.
  • One participant explains how to calculate the distance along a parallel of latitude using the circumference of that parallel and the difference in longitude.
  • A later reply confirms understanding of the explanation provided.

Areas of Agreement / Disagreement

Participants express varying degrees of understanding and agreement on the methods to calculate distances, but there is no consensus on a single approach or formula. The discussion remains open with multiple viewpoints on how to proceed with the calculations.

Contextual Notes

Participants mention the need for clarity on which latitude to use in calculations, indicating potential limitations in the assumptions made about the relationship between latitude and longitude distances.

michael atlas
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I have two latitude/longitude points. They are really close together. What I want to do is find the difference between the two longitides and calculate how many yards that would be. If I did the calculation with with the two latitudes, it would be just 2025yds per minute of latitude. However, for the longitude; being that the closer you get to the poles, the closer the lines of longitude move together, you have to apply a conversion to it.

If my lat/longs were 34.34°W, 79.1°N and 34.23°W, 80.3°N Respectively, I want to find the exact amount of yards between my two lines of longitude.

If anyone had the formula to find out how many yds per minute of longitude according to what latitude I am at, I would greatly appreciate it.

Thanks,
Mike
 
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Can you not use the second formula I gave you in the other thread?

The radius of any circle of latitude (rθ) is given by the mean radius (r) of the Earth times the cosine of the angle of latitude (θ)

rθ = rcosθ

And by the way what is your application here and there ?
 
Last edited:
My application is for sonar work, programming in matlab.

When I get the answer from the other thread... I just multiply that latitude by 2025yds per degree of latitude AND longitide?

Is that true, because of the fact that I have to convert longitude given the latitude for Theta E
 
michael atlas said:
If my lat/longs were 34.34°W, 79.1°N and 34.23°W, 80.3°N Respectively, I want to find the exact amount of yards between my two lines of longitude.


At what latitude? 79.1°N or 80.3°N or somewhere in the middle?

This can all be solved quite easily if you have a good grasp of spherical co-ordinates.
 
The difference in longitude is the distance along a parallel of latitude.

Each parallel of latitude is a circle of radius rθ = r cos(θ)

So the circumference of that parallel is 2∏rθ in yards or metres or whatever and 360 degrees in angle.

So for instance the difference between 10° west and and 20° west is 10°

So this in yards is

10/360 times circumference = (10/360) * 2∏rθ where r is the mean radius in yards.

Now the latiture you use for θ is different for each point so you should take the average latitude by adding up the two latitudes and dividing by 2.

Does this make sense?
 
Yes it does.

Appreciate it.
 

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