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 it’s not a square. So my question again: How do I have to calculate with the coordinates to get a perfect square?

Thanks for your help!!
Marc

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

Look at the following map:
image

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

The same applies in IF; to get a perfect square you’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 blown… 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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😂 seriously boss? The aircraft can’t turn on a dime it will always have rounded corners. That’s as square as you’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 won’t get perfect corners. That’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 😋

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

Same… I got it in my Science Test few months back…

Could he try using projected coordinates rather than geographic coordinates to get a better local approximation? Like using UTM rather than Lat/Long… 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 “Great Circle Route”, “Napiers Wheel”, “Rhumb line Sailing” , “Plane Sailing” 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 ‘draw’ 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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It’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 it’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. It’s real easy to see from this pic of the earth in IF.

image

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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 that’s a function of the latitude. I haven’t tried this, but give it a shot…

Let’s use a simple example, Say you’re using 1deg latitude for your north south legs. If you’re at 45deg latitude you’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 you’re say at 20deg latitude, you’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 you’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 is…,
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. I’m going to create a python script to do it for me.

image

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My initial shot in the dark for the longitude scaling factor wasn’t as accurate as I thought. I was getting squashed patterns when I increased the leg count.

This formula is much more accurate…

ScaleFactor = 1/sin(90-latitude)

And yields results like this…

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 I’m only the world’s second biggest nerd.

[And, yeah, you children in the lounge are free to put that first sentence in your thread. I’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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I made the below routes on Infinite Flight using only Google Earth and Google Drive SpreadSheet apps.

They might look rough but I didn’t spend any time trimming so they should be way improved if one wishes.

Here are the coordinates to check for yourself:

2800N/13349W 2825N/13347W 2826N/13361W 2827N/13399W 2836N/13450W 2849N/13500W 2870N/13552W 2898N/13599W 2932N/13647W 2962N/13672W 3000N/13696W 3035N/13707W 3072N/13713W 3106N/13713W 3144N/13705W 3171N/13696W 3198N/13682W 3225N/13662W 3245N/13639W 3249N/13633W 3250N/13624W 3242N/13617W 3224N/13614W 3198N/13606W 3174N/13600W 3146N/13588W 3116N/13569W 3086N/13545W 3065N/13517W 3044N/13481W 3027N/13432W 3018N/13377W 3014N/13306W 3028N/13223W 3058N/13163W 3095N/13131W 3137N/13129W 3176N/13144W 3191N/13156W 3205N/13173W 3217N/13193W 3231N/13218W 3247N/13257W 3259N/13299W 3270N/13344W 3283N/13386W 3299N/13436W 3319N/13488W 3321N/13505W 3366N/13583W 3408N/13625W 3458N/13659W 3520N/13676W 3589N/13674W 3659N/13647W 3728N/13596W 3780N/13515W 3807N/13435W 3820N/13343W 3815N/13210W 3789N/13112W 3766N/13051W 3739N/13004W 3721N/12983W 3701N/12970W 3686N/12969W 3667N/12976W 3643N/12988W 3583N/13033W 3563N/13058W 3556N/13072W 3558N/13087W 3562N/13100W 3580N/13123W 3603N/13151W 3629N/13192W 3650N/13237W 3660N/13293W 3657N/13353W 3652N/13387W 3639N/13419W 3620N/13447W 3596N/13464W 3574N/13470W 3551N/13470W 3528N/13460W 3504N/13441W 3487N/13413W 3461N/13362W 3441N/13301W 3421N/13232W 3383N/13121W 3356N/13068W 3331N/13026W 3289N/12977W 3244N/12941W 3200N/12920W 3140N/12911W 3078N/12912W 3045N/12920W 3007N/12935W 2970N/12957W 2935N/12987W 2894N/13041W 2864N/13092W 2846N/13153W 2836N/13191W 2829N/13233W 2825N/13284W 2824N/13325W 2825N/13344W 2800N/13347W 2801N/13252W 2800N/13142W 2800N/13032W 2800N/12702W 2841N/12700W 2841N/12730W 2848N/12754W 2865N/12766W 2896N/12777W 2926N/12782W 2971N/12789W 3038N/12794W 3205N/12798W 3387N/12798W 3554N/12791W 3706N/12770W 3768N/12749W 3790N/12734W 3797N/12725W 3799N/12715W 3799N/12693W 3800N/12637W 3800N/12529W 3794N/12512W 3785N/12507W 3775N/12509W 3679N/12542W 3642N/12554W 3597N/12564W 3556N/12573W 3515N/12578W 3470N/12582W 3433N/12583W 3403N/12581W 3389N/12577W 3381N/12570W 3378N/12563W 3378N/12556W 3382N/12545W 3401N/12520W 3453N/12466W 3532N/12395W 3578N/12359W 3658N/12308W 3727N/12271W 3772N/12254W 3788N/12248W 3797N/12240W 3799N/12222W 3800N/12189W 3800N/12081W 3799N/12052W 3793N/12045W 3782N/12040W 3768N/12042W 3707N/12053W 3686N/12066W 3643N/12086W 3591N/12122W 3530N/12172W 3477N/12220W 3435N/12263W 3424N/12272W 3417N/12275W 3408N/12274W 3398N/12267W 3336N/12211W 3278N/12159W 3220N/12120W 3143N/12076W 3045N/12037W 2973N/12022W 2891N/12012W 2867N/12013W 2853N/12013W 2847N/12020W 2841N/12031W 2840N/12105W 2842N/12245W 2850N/12264W 2868N/12271W 2928N/12272W 2987N/12281W 3051N/12292W 3122N/12315W 3155N/12330W 3216N/12362W 3257N/12395W 3271N/12414W 3275N/12428W 3268N/12447W 3233N/12500W 3191N/12543W 3158N/12565W 3132N/12575W 3095N/12574W 3027N/12561W 2890N/12532W 2861N/12529W 2848N/12533W 2841N/12545W 2840N/12572W 2842N/12654W 2841N/12697W 2801N/12698W 2801N/12478W 2800N/12125W 2800N/11575W 2843N/11575W 2843N/11670W 2841N/11691W 2861N/11718W 2899N/11727W 2946N/11725W 3009N/11711W 3061N/11692W 3101N/11671W 3141N/11652W 3171N/11637W 3188N/11635W 3203N/11641W 3229N/11669W 3295N/11739W 3349N/11791W 3404N/11836W 3460N/11874W 3514N/11902W 3583N/11929W 3648N/11943W 3723N/11949W 3773N/11941W 3795N/11927W 3803N/11911W 3806N/11900W 3804N/11878W 3804N/11843W 3803N/11777W 3802N/11729W 3802N/11700W 3797N/11684W 3786N/11672W 3772N/11668W 3757N/11671W 3705N/11678W 3681N/11682W 3644N/11678W 3591N/11668W 3538N/11651W 3484N/11625W 3436N/11592W 3379N/11537W 3371N/11524W 3367N/11507W 3375N/11489W 3399N/11460W 3459N/11410W 3527N/11365W 3603N/11329W 3661N/11313W 3727N/11316W 3772N/11324W 3785N/11325W 3795N/11318W 3800N/11296W 3800N/11258W 3801N/11153W 3798N/11131W 3788N/11111W 3775N/11104W 3756N/11101W 3699N/11103W 3645N/11109W 3563N/11135W 3491N/11171W 3409N/11227W 3313N/11306W 3260N/11346W 3200N/11388W 3171N/11406W 3092N/11440W 3004N/11463W 2946N/11468W 2918N/11464W 2875N/11458W 2859N/11458W 2854N/11463W 2849N/11471W 2844N/11481W 2843N/11502W 2842N/11573W 2800N/11574W 2800N/11525W

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By the way, as i made it in Google Earth it looked perfect, so I guess InfiniteFlight app is also messing up with it a lot. I even modified the google earth MLK file to 2 decimal point accuracy and rounded them up, yet it still looks in perfect shape.
45 PM

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