Like let’s say that we start on the cape of goodwill for example and follow the coast.
Represent each 1km with 1mm for example on our map (map size isn’t a problem just for the sake of the argument). Getting the directions of drawing off a compass exactly. And just walk around all the coasts of the world.
What type of map do we end up with in this hypothetical?
In: 5
Are maps inaccurate? Or are people using the wrong maps?
Mercator projection is the classic case. It is designed for navigation. If you use a protractor to measure an angle on the map, then followed that compass course, you would end up where you want to go (allowing for weather, terrain etc.)
It does distort the land shapes, but it is designed for accurate angles, not accurate representation of size.
Just as a screwdriver isn’t used for nails, or a hammer for screws (except in my city) it’s about picking the right tool for the job
For these small scale (very zoomed out charts) we use the Mercator projection in the maritime (actually for all paper charts, also larger scales)
The Mercator projections is basically the globe projected from the center onto a cylinder. The cylinder can then be rolled out to a flat sheet. This is stretching the drawing the more we are getting away from the equator, the classic “Greenland is as big as Africa”. But very interesting, the angles are true and makes it easy to put out courses.
We usually measure the length scale on the N/S edge of the charts, as the one end might have a significant different scale than the other when coming to precision plotting.
If you decided to make a chart with the same scale all the way, you end up making a very cubby looking chart where you can’t measure true angles or plot courses and positions easy.
When charts was hand drawn there was for a long time significant errors as it was a lot of triangulation calculation, but as the instruments and calculations got better, the maps also got better
Let’s ignore coasts and think about some extreme examples:
* You start at the North Pole, move south 1km, move east 1km, and move north 1km. On paper, you’ve made a U shape, but under ideal conditions, you’ve put yourself back at the North Pole after moving in a sort-of-triangle.
* Using this same south-east-north plan, you start near the South Pole. There is one particular area where your eastward movement completes a full circle, and you are again back at your starting point, having retraced the same path north that you took going south. [This video](https://www.youtube.com/watch?v=OOzzncDp2oE) goes into cases where your eastward movement is closer to the SP and results in multiple circles.
* There is another area about half a kilometer north where your eastward movement only completes a semicircle, and you end up over 2km away, technically on the other half of the world.
* There is yet another area further south where you also return to your starting point, but your eastward movement also crosses over your south/north path. However, this might not count since you are crossing the SP—any movement away from the SP is technically north, and any movement towards is technically south.
* Even at the equator, your south-east-north path doesn’t quite result in you being 1km away from your starting point, but you are much closer to your planned U-shape than at any other latitude.
Part of the problem is that you can never actually walk in a straight line on the surface of a globe. Your path curves into the globe by some amount. With Earth as large as it is, this curvature is almost impossible to feel.
Another part of the problem is that every east/west path that isn’t along the equator curves to the left or right. You’d probably notice this in the polar examples given above.
If you wanted to make it join up properly you’d end up having to twist around the piece of paper you were drawing it on, making it into a sphere. You’ve basically invented the globe.
To take an obvious example of what would happen if you tried to do this on a flat surface, let’s say you started at the South Pole, walked North in a random direction 5km, then walked East 5km (so a 90 degree turn), then walked South 5km (another 90 degree turn).
If you draw that on paper you would have three sides of a square. But where you end up should be the same place you started. So your 2d projection is wrong – it doesn’t join up.
I think you would just end up with a scribble.
For the sake of visualization, let’s start walking from the north pole.
– Walk all 10,000km down to the equator, then turn 90-degrees to the right.
– Now walk 10,000km along the equator, then turn 90-degree right again
– walk another 10,000km and you will arrive at the north pole, having drawn a “triangle”
On paper:
– you would draw a 1000cm line down
– then a 1000cm line to the right, forming an L shape
– then a 1000cm line up, drawing a U shape or a square with no top
– the square would also be reversed
Now imagine all the twists and turns of a coastline, left/right reversed at time, with 90-degree angles actually being 60 degree angles.
A scribble!
Simply put, your method can’t work. In general, the line generated by traversing the coast of any continent wouldn’t form a closed loop on the paper when you returned to your starting point. As a simple example, imagine a three-sided continent that reaches a point at the north pole and two other points on the equator. Two of its coast lines run due-north/south and the third runs due east/west. Drawing those three lines on a flat piece of paper doesn’t make a triangle. Using the north pole is an extreme example but the same issue will occur for all the continents. And think about what would happen if you tried to do Antarctica!
Start at north pole. Walk 100km due south. Draw a 100mm line on your map. Turn 90 degrees left. Walk due east 100km. Draw a 100mm perpendicular to the first.
Turn 90 degrees left and walk due north again. You are now at north pole again, but the map says you are 100km from north pole.
How do you intend to transcribe your motion onto paper?
By simple angle change?
The allow me to give you a simple path that should demonstrate the problem. You start at the north pole, and follow the prime meridian south. You turn 90 degrees left at the equator, and travel a quarter of the way around the Earth. You then turn left 90 degrees again, and walk another quarter.
You’re back at the north pole, having followed a ‘triangular’ path. Each corner is 90 degrees. If you were to draw this path on flat paper, your map would have two north poles on it. Your path would look like 3 sides of a square, since each corner is 90 degrees, and each side would be 10 meters long. Your start point and end point were both the north pole, but on paper they’re a quarter world (10 meters) apart.
If you were to try and trace a country using this system, walking its border, you would walk the full length and your drawing on paper would not be a full loop; your start and end points would be in different spots on your paper despite them being in the same place on Earth.
You’d end up with a discontinuous map.
The starts and ends of continents and other large land masses wouldn’t join up, by noticeable amounts. Technically even the outlines of small islands wouldn’t join up either, just the scale would mostly hide it.
You can do this at home with an orange. Draw a simple map on half of it, peel that half off and then flatten it. It’ll split in one or more places and your map lines will be discontinuous where they cross splits.
How would your map deal with hills or mountains?
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