Size matters, I guess? The measuring of distance on a map.

[Reeses]

Here is the issue, in one country, I have my character moving from one side (east) to a city in the southwest. I needed to figure out the distance for so that I know how long it would take them to travel. (Horses part of the way, carriage part of the way to the halfway point) However, when I added a guide for measuring, using an idea that I thought made sense with the earth as a reference, I don't think it went the way I anticipated. So, I did the math; compared to earth my planet seems rather weirdly sized. Obviously, changing a flat plane to a sphere is kinda weird, and I don't know the math for such things.

When it comes to earth size, Google says: equatorial circumference of Earth is about 24,901 miles (40,075 km). However, from pole-to-pole — the meridional circumference — Earth is only 24,860 miles (40,008 km) around.

So, I have 1 inch = 2800 miles. My map is 18x9 Which means its 50,400 miles across, and 25,200 top to bottom.

I haven't a clue how big this would make the planet, and if anyone can help with that I'd be grateful. (yes, I am aware if I take these exact measurements I'd get an oblong planet. Which is why I need the help...)

I have a feeling, that my guide is like WAY off, and I need to find a better number of miles per inch. Though, If that is the case, my continents are going to need resizing.....

I don't know. Maybe there is an easier way to go about things? If there is, please let me know because I've been circling this drain awhile.

[waldronate]

Assuming that your map is in something like the Equirectangular projection (the special case of Plate Caree where it's twice as wide as it is high), then the N/S distance on your map is the true circumference of the sphere. Your map is just about Earth sized, as you mentioned when you said that it was 25200 miles from pole to pole.

The difference in size on Earth between the equatorial and polar measurement is due to the rotation of the planet and the mantle being a semi-plastic, deformable material (the equator is going about 1000 mi/hr). The difference between a perfect sphere and the oblate spheroid that is the Earth's true shape is about one part in 300, or not enough to be noticed for most whole-world maps.

The biggest problem with a flat map is that you can't use a flat ruler to measure distances. The horizontal scale on your map varies by 1/cos(latitude): the scale is 1 at the equator and infinite at the poles (spreading a single point out across a whole line segment). For measuring distances with a ruler on a flat map, you need a relatively local area and a projection centered on the middle of your area of interest. https://en.wikipedia.org/wiki/Map_projection is a good starting point to learn more about map projections.

There are many pieces of software that will convert your map into another projection, including G.Projector ( https://www.giss.nasa.gov/tools/gprojector/ ).

[Reeses]

Okay, I hadn't thought about the ruler thing. I should have. I knew there was distorion. Also, I had some fun playing with different projections, so thanks for that. Its actually very helpful.

But I am a little confused. I still need to measure between two points. How do I go about doing that with the scale that I have? Like, instead of the world map, if I am working with just that country, do I need a new guide?

[waldronate]

If you're reprojecting your map and using a more local area (say, just one continent or country), then you will definitely need a different guide. The notion of a "scale bar" isn't generally meaningful for most projections that are showing large amounts of your world because the scale varies from place to place, depending on the projection ( see https://en.wikipedia.org/wiki/Tissot%27s_indicatrix for a common tool used to show variance in distance and direction in different places on a projection).

Another common decoration on maps is a wind rose (that thing that points at north). Just as "scale bar" doesn't mean much for many kinds of map projections, a wind rose isn't particularly meaningful for most projections as well. A wind rose can indicate the direction of North from the point where it's sitting, but moving it around will likely require that it twist to find the proper direction (quite difficult on the printed page).