r/geography • u/Carrot____ • 15h ago

Question Any good Mercator Maps for distance?

I'm trying to find the distance between London and Sydney on the Mercator Projection, I have the great circle distance on both a sphere and a WGS 84 ellipse so those are not needed. If anyone can find a source where I could make this calculation this would be very helpful thank you :D.

P.S. I'm writing this for a research paper so that's why I'll need a source...

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u/Petrarch1603 15h ago

Your post is confusing, do you want a map or a distance? If you're writing a research paper you should first write more clearly.

If you want a map you could probably make a custom hotine oblique mercator projection. Ask claude to make you a proj4 projection with this projection. Then use those parameters in QGIS. It might look a bit weird as those two cities are near antipodes. You'll probably want to rotate the map so that the route is horizontal. Also you'll want to trim a lot as the map will become extremely distorted at the edges.

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u/Carrot____ 15h ago

Sorry for the confusion, Ideally I'd like a map so I could do the measuring myself, though if someone is able to provide a distance and a source that would be helpful too. I'll take a look into what you suggested, thank you.

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u/TheNordicMage 13h ago

I'm sorry what? Your chosen projection doesn't affect the litteral distance between two points.

If you just want a simple distance then just take the two points, latitude and longitude in wgs84 and calculate the distance between them assuming the eath to be a perfect sphere (it isn't, but that works for most people) using the Haversine (great circles) formula.

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u/Petrarch1603 13h ago

Vincent’s formula would probably be better if this is for a research paper

Edit: vincentys

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u/TheNordicMage 13h ago

True, but Vincentys formula is also tricker to understand, and we are talking about distances between entire cities here so personally I at least wouldn't see the need for the increased accuracy.

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u/Shevek99 9h ago

You can use Pythagoras theorem.

One leg is given bu the difference in longitude λ

b = Rx (λ2 - λ1)

the other by the difference in latitude ϕ, through the equation of Mercator projection

h = Ry (ln(tan(π/4+(ϕ2)/2) - ln(tan(π/4+(ϕ1)/2))

and

D = √(b² + h²)