Can I can semi accurately measure distance anywhere while using Equirectangular?

[The King of Nipples]

My map is 5500x2750px using Equirectangular and supposed to be the size of Earth but not Earth. I'm trying to make an atlas and convert it to uninterrupted Mollweide so that I can measure stuff somewhat accurately so we know how long it takes to travel. I want to know how I could size things up so I don't make something to big or small. I've come up with
4.52mi (4.52745455mi) = 1px along the equator.
9.05mi (9.0549091mi) = 1px along the I'm unsure what it is called please let me know but the polar equator if that makes any sense.
9.0549091 * 2750 = 24901
4.52745455 * 5500 = 24901
And this is kind of useless with my current understanding I've tried to use GProject and switch to uninterrupted Mollweide to measure the amount of pixels but this seems less helpful than Equirectangular because changing it from Equirectangular to Mollweide curves it up and then when I go into GIMP to measure it is harder. Am I doing it wrong? The continent I'm working on is in the position of about where Australia is in the world. Should I forget about making it Equirectangular and just make it a square I was doing that before and it seemed more useful having a linear scale for it. I've seen people make square regional maps does that have anything to do with scale being easier to find? I'm pretty new to this so any help is appreciated! If it is all over the place let me know and I'll try to clarify.

[waldronate]

For an equirectangular map, you can measure distances exactly up and down or exactly at the equator. Any angle other the up/down or left/right at the equator will cause distance distortions. Area and angle are always distorted for that projection, but the distortions gets smaller as you get closer to the equator (the horizontal scaling factor is 1/cos(latitude) for that projection).

The smaller an area that is shown on a map, the less spherical distortion will matter. A nice whole-world map will give you a good overview, while regional maps will make it easier to measure. Mollweide is a nice projection, but distortion increases as you move away from the center of projection. An interrupted map allows you to have multiple centers of projection and to place those centers of projection on places of interest to minimize distortion in those areas.

As an example, the below images show an equirectangular projection, a whole-world Mollweide, and an interrupted Mollweide (I picked interruption centers for convenience of editing rather than for any useful properties). You can see how the distortions are reduced in the interrupted version.

Untitled-1.jpg

For what you're trying to do, I recommend making a set of maps that cover your primary areas of interest. If you use a grid for each area that is consistent with a global grid, then you should be able to use your regional maps as working maps for measurements and reproject any changes to those maps back to a whole-world map that functions as a master index for your maps. It's not the most convenient system, but one of the reasons why there are so many kinds of projections and scales of maps is that they all serve different purposes.

For a lot of purposes on the scale of small continents, the Lambert Conformal Conic projection is a good enough choice.

[The King of Nipples]

So should I just use interrupted Mollweide? It seems to be more accurate and easier to measure than the uninterrupted, I picked it because I thought it looked better. I've read about people making a map and then scaling there stuff into a more accurate regional map how would one go about that? Also if you know was I correct with the scaling for the map?

[waldronate]

If the region that you're drawing isn't terribly large (you referenced an area about the size of Australia), it's reasonable to just map that region as a flat map and not worry too much about distortion. Any projection that you choose to declare it as will work because distortions are fairly small in most projections for a smallish area, especially if it's not a polar area (you need to pick certain projections for polar views). There are software tools that can take your regional flat map and reproject it onto another projection (equirectangular is a popular working format because it's very easy to apply to globes and other projections using readily-available software).

For a whole-world map, pick one that meets your intended use. If you have continental shapes and sizes that work well with interrupted Mollweide, then go with interrupted Mollweide (I think that Hammer and Hammer VII are prettier for whole-world maps, but it's a matter of opinion and the curved parallels make some folks unhappy).

[waldronate]

I just noticed that in your original post you mentioned that the scaling is half per-pixel in the vertical direction compared to the horizontal. For a whole-world map that's 5500x2750 pixels (that is, in a 2:1 width:height ratio), the scale distance vertically is exactly equal to the horizontal scale distance at the equator. The world has longitude ranging from -180 to +180 (360 degrees) across the map, but only -90 to +90 (180 degrees) of latitude going up and down on the map.

[Azélor]

It depend, what do you want to measure? Distances, area?

Mollweide if good to measure area, whether it's interrupted or plain.

[The King of Nipples]

I want to measure both.

[The King of Nipples]

Why though because 4.52745455mi * 2750 isn't 24901 what am I missing?

[Azélor]

One of the mesure is from pole to pole, it's only half a sphere in circumference (180 degrees)
The equator run along the whole planet (360 degrees) so it is twice as long.

The thing is, horizontally, you said each pixel measure 4,5 miles but 9 miles vertically. That is confusing. Why not just use 1 measure?

[Hai-Etlik]

There is no projection that will allow you to measure arbitrary distances over an entire globe. The only way to do this is to measure on a globe. You can do this physically with a tape measure on a real globe, or using software that has spherical or geodetic distance calculation like QGIS.