Navigation: How to calculate with coordinates?

Hi everyone

I have a question, which is maybe a bit stupid.

How do I have to calculate with coordinates?

Here is my example: I want to fly route which will look like a perfect square on a 2D map. Now: I tried to calculate my coordinates linear. So I started with 4700N/00800E and added 50 to East: 4700N/00850E. Then, I added 50 to North to fly upwards: 4750N/00850E.

That was my final routing:
4700N/00800E 4700N/00850E 4750N/00850E 4750N/00800E 4700N/00800E

It looked like this:

This has 4 corners, but itâs not a square. So my question again: How do I have to calculate with the coordinates to get a perfect square?

Marc

This is a question relating to the geography and maths structure of the world.

Look at the following map:

You will notice that not every square is the same size. Because the earth isnât flat, the squares of longitude and latitude get stretched and shrunk as they are applied to the earthâs almost spherical shape.

The same applies in IF; to get a perfect square youâre gonna need to calculate the distance at a specific point in the world. in the meantime, you may get better results doing this near the equator.

Good luck.

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Thank you very much, that helps a lot!

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Mind blownâŚ but you are correct in the fact that the curvature of the earth causes what would be a square to come out in a rather different shape.

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đ seriously boss? The aircraft canât turn on a dime it will always have rounded corners. Thatâs as square as youâre going to get. It takes 30 seconds to complete each of those turns.

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Yeah, I know that. I know that I wonât get perfect corners. Thatâs not even possible. My question just was whether there is an easy way to calculate the coordinates to get a shape where every side has the same length. And I got my answer đ

I got that map in my geo class and we had to label position of each letter lolol

SameâŚ I got it in my Science Test few months backâŚ

Could he try using projected coordinates rather than geographic coordinates to get a better local approximation? Like using UTM rather than Lat/LongâŚ if that makes any sense.

As pointed out the issue you have a rectangle rather than a square is because the earth is Egg Shaped (well ish , certainly not round and definatly not flat!).

Without going into too much detail here, I would recommend a lot of research on âGreat Circle Routeâ, âNapiers Wheelâ, âRhumb line Sailingâ , âPlane Sailingâ etc, there is a correlation between your latitude and the distance to travel furhter north or south in a direct line (also not allowing for the curvature of the longitude lines as the further north/south of the equator you go the closer the lines of longitude become.

There is also a corealtion between your Current Latitdue and the Cosine of the Latitude that you are aiming for in order to clauluate the exact Lat/long of a posiiton in order to make a perfect square.

In short if you want to have a perfect square on the Equator of 1nm x 1nm this is easier to âdrawâ then if you where trying to plot one 100nm x 100nm and if you starting co-ordinates 47 00 N 008 00E and you are doing a 50nm x 50nm box then it gets more complicated!

This is without getting into the subject of Mercator projection vs Gnomonic projuection.

it is a huge and very intresting subject but you will need to spend time doing your own research in order to understand why it is.

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Itâs simply a matter of how latitude and longitude are drawn on the earths surface. Latitude is the angular displacement along the earths surface referenced to the center of the earth. Since itâs referenced to the Center, the distance of 10deg at the equator is very close to 10deg at the poles. Longitude on the other hand is the angular displacement on the earths surface referenced to a line drawn between the north and south poles (roughly). As such, the distance measured at the equator for a 10deg displacement will be larger than 10deg measured closer to the poles. Itâs real easy to see from this pic of the earth in IF.

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So, if you create your FP at the equator, it will be very close to a square. As soon as you move north or south, it will become more rectangular. But you can probably get very close to a square by multiplying the longitude displacement by a factor thatâs a function of the latitude. I havenât tried this, but give it a shotâŚ

Letâs use a simple example, Say youâre using 1deg latitude for your north south legs. If youâre at 45deg latitude youâre approximately half way to the pole, so your longitude distance will be half your latitude, so use 2deg for your longitude legs. Should get you very close.

If youâre say at 20deg latitude, youâre 20/90 of the distance to the pole, so your longitude will be approximately 7/9 the size of the latitude (1 - 20/90). To equalize them, scale your longitude by the reciprocal (9/7) or approximately 1.29.

Applying that to the 45 deg latitude, where youâre 45/90 of the distance to the pole, the scaling is 1/(1-45/90) which is 2.

The formula for the longitude scaling factor isâŚ,
1/(1-latitude/90)

Give that a shot.

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I just created a flightplan using that methodology and came up this. I did the calculations and rounding in my head which probably explains the slight errors. Iâm going to create a python script to do it for me.

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My initial shot in the dark for the longitude scaling factor wasnât as accurate as I thought. I was getting squashed patterns when I increased the leg count.

This formula is much more accurateâŚ

ScaleFactor = 1/sin(90-latitude)

And yields results like thisâŚ

BTW, This was generated with JavaScript

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@GHamsz have I ever told you I platonically love you? You make me feel like Iâm only the worldâs second biggest nerd.

[And, yeah, you children in the lounge are free to put that first sentence in your thread. Iâm a big boy.]

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Hahahaha!

I love programming! Once I started, I knew there was no stopping until it was perfect!

Plus it gave me some insight and a lot of respect for what the developers of IF have done!

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Its great that you enjoy working ouot the maths behind the principle. Maths is the only pure language!

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I think I figured it out. Just spent an hour creating an Excel Sheet and calculating with your formula.

This is my first test result:

Thank you!

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