that is totally wrong. doesn’t fit the math.
and even if the points are close to directly opposite, the two routes on the map, route A and route B
are from the same departing airports while the two routes are far apart. Mathematically the distance between them is more than 2000 miles… They can’t have the same distance. and not the same time if you look at the time of each route.
But you need to prove it mathematically as I did previously.
I’m not in a position to doubt your maths, but there appears to be something wrong in the application of it.
Keep in mind that this depends entirely on the map projection that you’re using. The picture you’re showing appears to most likely be a Mercator projection, which is notorious for that type of distortion, especially near the poles.
Basically all aviation charts use a Lambert conformal conic projection. While not a definitive source, Wikipedia gives the short version of this (Lambert conformal conic projection - Wikipedia):
Pilots use aeronautical charts based on LCC because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints for typical flight distances.
All ways of attempting to “flatten” a spherical (or ellipsoid) surface onto a flat map are not perfect and have various failings like distortions of some form or fashion. For example, the sample picture on Wikipedia for the LCC looks like this (where you can see that the distortion gets fairly extreme towards the southerly parts of it):
In your New York to Moscow example, as the route of flight has a significant amount of it north of the 50N standard parallel, using this particular map would deviate quite a bit from the great circle route, and one that was made using standard parallels farther north for the projection would be noticeably more accurate. However, both would be a lot closer than if you used the Mercator projection. (Note that most of your normal aviation charts are essentially small bits of the sample picture with the standard parallels chosen to minimize distortion for that particular region, so the distortion isn’t as severe as if you were trying to go from one end of the sample picture to the other.)
My Dear Friend,
Thank you for your attempt of understanding the math.
The idea behind your attempt to disprove the math of great circles, will not resolve the problem with the simulator, or the challenges you have in understanding the proof.
Even if the numbers are incorrect, which anyone can make a mistake… will not change the fact that you need to put an effort into disproving my point.
Otherwise enjoy putting your time into more productive challenges, that way your brain will get smarter.
Changing numbers will not change the fact that I am right.
And sorry for my productive thinking, I seem to enjoy smart arguments… rather then shallow ideas.
Thank you for your answer, and explanation.
Very true. And yes, the projection of mapping has an impact on the intentions of pilots and their efficiency in navigations, but it doesn’t change the fuel calculations in real-world physics, whereas for our simulator, the lack of accuracy in real-world physics as for the calculations of distances does impact some of us.
But there is a bug in the simulator, and the distances are incorrect.
Regarding the example you’ve posted showing distances between New York and Moscow, what about this is incorrect? 4056nm is 7511km.
I’m still really struggling to understand exactly what you think this bug is. Maybe you’d like to patronise me some more in the hope of making it clearer?
Forgive your misunderstanding…
I am not trying to patronize anyone.
Have you studied math? Do you know how to prove a mathematical statement or an idea?
I am asking because you seem to think the examples you are giving will prove that the calculations
within the map system of MSFS are correct.
Trying to show me, the distance of other routes doesn’t regard the problem I was referring to.
If other routes are showing accurate distances, it is because of the proportion within great distances that the great circle has an effect upon. 4056NM, relative to 10800 NM is a very big difference in calculations, and if you understand how great circles are calculated you will realize why the error within Numerical Calculations of great circles increases if the accuracy of the algorithm is not taken into account. By the way, that is the reason the map system in flight is having an error in the north pole and the south.
And I gave you an example of two points with three different routes between them so that it would indicate the error, not one route as you are displaying.
For two points very close to being opposite each other on a sphere (the oblateness of which is so small as to be irrelevant) claiming there should be up to 12% difference between routes relatively close together is genuinely absurd.
The shortest (great circle) distance between the two locations in your example is ~19700km (evidence below). The other part of the same great circle is the longest distance. If we take the Earth’s circumference to be a nominal 40,000km, that would be 20,300km.
The difference between the genuine shortest and longest distances between these two points is therefore about 3%. How can you expect to see a difference of “7-12%” on routes so close together? It makes no sense.
You can’t just put people (everyone, apparently) down because of your claimed superior knowledge of maths. There seems to be something fundamentally wrong with your thinking on this subject.
Also, here’s a composite of your example from google maps. The relatively small differences are consistent with MSFS…
Google maps also lets you put the midpoint on the opposide side, creating the longest route. Absolute maximum distance possible appears to be ~20,300km which corroborates the numbers above…
If anyone wants to know which website I’m using for the examples in my posts:
First, look at your first map, and look at the difference between to upper route, can you see how close it is to Alaska? and how far is your upper route from Alaska?
Your routes are not the same as the routes in the Map I displayed within MSFS.
One needs to be very accurate in thinking and estimating, in addiction to taking mistakes into consideration, And Thank you for investing your precious time to find your truth.
You’re now just splitting hairs and ignoring the points which are actually relevant to this whole question.
It’s impossible for those routes to differ in length by the amounts you’re suggesting. If you think your maths somehow proves you right, it’s simply wrong.
You need to prove it otherwise, not just presume that you are correct.
If you don’t want to prove it, I guess you already know that you are wrong.
That wasn’t a “straight line” and a great circle, it was two great circles, one east-west at the equator and one north south. The point being that the difference is insignificant.
You seem to have a fundamental misunderstanding of what a “straight line” on a sphere is. A great circle route IS a straight line on a sphere, or as close as you can get.
Yes, You are all correct, and I am wrong.
Thank you for your time and patience.
Think we need the thunderbirds ‘mole’ in the sim for this one
I am reliably informed by a diehard group of people that the world is actually flat. I must admit that on my 2D monitor it certainly appears so 
Following the interesting discussion… while still assuming (totally non-scientific)… instinctively… that routes (hiking, driving, flying…) which are not 100% identical are unlikely to have the exact (!) same length…
Now my two cents: as we are discussing flight routes we need to take into account that the earth is spinning while we fly. This means that even for the same (physical) distance say from Frankfurt to Miami it makes a big difference in flight time if we fly Frankfurt to Miami vs Miami to Frankfurt. The flight time from Frankfurt to Miami is usually much shorter as the earth rotates (west to east mainly) and thus while flying Miami gets closer and closer.
This difference in flight time also depends on which route we are taking (flying EDDF to KMIA usually over Greenland, then New Foundland and then coming down the US east coast… which by any means is not the direct route/line ) and how far north the route goes.
So as it all comes down to how much fuel we need this is yet another aspect of planning a route.
I think you can’t pretend to apply mathematics to a flightplan based on airways, because they are not always meant to follow the shorter distance between two points but to follow a standard procedure instead. As seen in the picture on first post the airways are not parallel.
Cheers
You might be a bit confused here. The Earth’s spin has an effect on wind direction and strength and therefore flight time but it doesn’t affect flight time directly.
