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# How do I compensate for planetary curvature during long distance flight?

## Question

My highschool geography teacher once told me that if you take a flight from Amsterdam to New York, you sort of fly over Iceland due to the curvature of the earth. Looking at my textbook map, this idea seemed kind of ridiculous because a straight line doesn't bring you anywhere near Iceland. You'd need curved maps or 3D maps. I don't think I outright believed him, but I have been on enough flights since to know that this effect does affect a plane's trajectory. I just still don't have an exact idea how much.

Now it seems I have a problem along a similar vein. I did a long distance data collection contract and noticed I was constantly adjusting my course because I kept tracking the indicator on the navball for the first objective. I started out at 207° and near my destination it had shifted to something like 250°. I had been flying in a giant curve because I had assumed the indicator would adjust for the curvature of Kerbin.

Ideally I only would have had to point my plane into a direction once to reach my final destination. It seems I have to guestimate instead. How do I aim for the actual shortest route to a location that's nearly on the other side of Kerbin? I assume someone made a mod for this already, but I'd like to know if there are any tricks to get pretty close to it.

Edited by Tricky14

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Just now, Plusck said:

...The NavBall doesn't have a flat map to look at and get confused. Taking your geography example, if you're standing in New York and have a NavBall on you pointing at Amsterdam, it should not be pointing due east but quite a bit north, when you fly over Iceland it will point due east, and when you arrive near Amsterdam it will be pointing quite a bit south: in other words it would be accurately taking you on the shortest route.

A navball pointing directly at any significantly distant target will be pointing at the ground - you probably don't want to go that way!
Even at ship, or walking, speed - let alone flying - navigation is all about little orbits.  Just like orbits it doesn't make intuitive sense most of the time.  The two main concepts are Great Circle Routes, which are the shortest path but with changing compass heading (eg; North-East to Iceland, then South-East to the Netherlands) and Rhumb lines, which use a constant heading but are longer.

Seems to work, I made it across the Atlantic three times.

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33 minutes ago, Tricky14 said:

Now it seems I have a problem along a similar vein. I did a long distance data collection contract and noticed I was constantly adjusting my course because I kept tracking the indicator on the navball for the first objective. I started out at 207° and near my destination it had shifted to something like 250°. I had been flying in a giant curve because I had assumed the indicator would adjust for the curvature of Kerbin.

Ideally I only would have had to point my plane into a direction once to reach my final destination. It seems I have to guestimate instead. How do I aim for the actual shortest route to a location that's nearly on the other side of Kerbin? I assume someone made a mod for this already, but I'd like to know if there are any tricks to get pretty close to it.

Actually, I would say that the NavBall indicator should be absolutely correct.

The navigation icon is - AFAIK - pointing exactly at the object you're aiming for. Therefore if you go in that direction, it will take you the shortest route.

The NavBall doesn't have a flat map to look at and get confused. Taking your geography example, if you're standing in New York and have a NavBall on you pointing at Amsterdam, it should not be pointing due east but quite a bit north, when you fly over Iceland it will point due east, and when you arrive near Amsterdam it will be pointing quite a bit south: in other words it would be accurately taking you on the shortest route.

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Just now, Plusck said:

Actually, I would say that the NavBall indicator should be absolutely correct.

The navigation icon is - AFAIK - pointing exactly at the object you're aiming for. Therefore if you go in that direction, it will take you the shortest route.

I have observed on three different contracts now that this is not the case.

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16 minutes ago, Tricky14 said:

I have observed on three different contracts now that this is not the case.

Are you really sure about that?

If you are in orbit, and the navigational point is exactly on a line between prograde and retrograde, then you will fly over the indicated point no matter what the magnetic bearing as long as the planet doesn't move underneath you. And by the time you get there your magnetic bearing will have changed.

I don't see how this can be any different in flight - apart from the fact that the atmosphere is moving both you and the target at the same time, so you don't even have to worry about the target moving out of your orbital path.

So I'd say that the only reason you had to adjust your course was because SAS was trying to keep you on a constant magnetic bearing. If you had been in perfectly level flight without SAS, your aircraft would have ended up following the navigation sign all on its own.

The only way to really check this is to move the camera on the map so that you and the target are both as central as possible on the view of the planet. Halfway there, you should be right in the middle of that view.

And also - that screenshot picture you put up is wrong. You most definitely do NOT want to follow the yellow or green lines, because they are not the shortest route.

Going back to your example, starting at 207° and ending up at 250° sounds perfectly reasonable and accurate. The red lines on your screenshot show a final bearing which is over 270°, which would be a bit much. So again, I suspect you are mistaken and that the NavBall was taking you the shortest way all the time.

Edited by Plusck

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So I tried just hyperediting an orbit using "207° from KSC" as presumed starting point:

Spoiler

Keeping SAS on prograde, this ended up with a 250° heading here:

Spoiler

So if your destination was actually between the south pole and that longish island, then the NavBall was, without a shadow of a doubt, pointing you in the right direction.

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Ah, I see. I was actually using Mouse Aim Flight, not SAS. But I suppose it has the same result.

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These guys are right. A jet has to fly along the horizon line for obvious reasons. A target indicator will appear above or below the horizon line (usually below unless you are getting close). If you fly along the horizon with exactly the same heading as the target marker at any moment, you are flying a Great Circle route "straight" toward the target. (At least as straight as you can, since you can't tunnel through the ground.) The target marker compass heading will change in flight, but that does not mean that you are turning.

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22 minutes ago, bewing said:

(At least as straight as you can, since you can't tunnel through the ground.)

With enough boosters, you can

Spoiler

Warning:  Doing so may void your warranty though.

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I've definitely followed the navball for long flights and done great circle routes. The chief nuisance was that SAS doesn't maintain a constant pitch with respect to the surface.

One confusing point is that the blue curve in the map view is based on orbital velocity, so when you're flying north, it shows you going northeast.

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9 hours ago, Hodari said:

With enough boosters, you can

Reveal hidden contents

Warning:  Doing so may void your warranty though.

I like the way you think, totally Kerbal... Forget Kerbal Space Program, we need Kerbal Tunneling Program...

Would Jeb really care about a warranty you speak of? I'm sure Jeb showing up at the KSC is enough for all warranties to be null and void.

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On earth, you don't exactly fly a great circle directly either. You break it up into a series of shorter segments you can hold a heading for. Unless you have more advanced navigation instruments than your compass. Which you need to know how to use anyway if things go wrong.

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I'm struggling in my head to decide if the rotation of Kerbin needs to be taken into account with regard to what the navball is 'pointing at'. You'd see different results if it's orbit vs. surface mode, no?

Wemb

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1 hour ago, Wemb said:

I'm struggling in my head to decide if the rotation of Kerbin needs to be taken into account with regard to what the navball is 'pointing at'. You'd see different results if it's orbit vs. surface mode, no?

Wemb

I'd say no. With one slight exception...

In orbit, obviously, then yes you need to take any target's movement into account.

However when the ground and/or atmosphere is moving both you and the target equally, then at any given time you will get closest to it by moving directly towards it, and at the end of that time interval, both you and the target will have been displaced by the same angle of rotation.

So take an example, of going from the equator to just the other side of the north pole, leaving at midday.

If it takes one second to get there, obviously you want to aim "straight" at it.

However, if it takes half a day, meaning you get there when it is midday at the target, you might think that the shortest route would not be straight, since the target will be on "your" side of the pole half a day later. That would be true if you left the atmosphere first, but not otherwise since you'd have to travel through more atmosphere to stay at "midday" and meet your target half a day later. That means going faster, and if you're going to go faster, you'd be better off going faster straight to the target and meeting it before it gets to midday.

So if you are driving on the surface, there is no doubt that aiming straight is the only way to go. If you are really high in the atmosphere, however, it might pay off to consider yourself to be suborbital and compromise, especially since the atmosphere will have a lower rotational velocity as you approach the poles. But you'll still be pushing through more atmosphere to follow what, from orbit, looks like a shorter path

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