{ "id": 6044, "title": "Spherical or flat?", "url": "/competitions/flight2-milestone/discussion/6044", "author_name": "", "post_date": "2013-10-17T14:59:25.827Z", "votes": null, "comment_count": 4, "views": 3108, "content": "

Hi,

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I was reading through the code and it seems to me that you get a penalty for computing proper spherical distances and path on great circles (unless you give a lot of waypoints).

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I say penalty because distance on the sphere is always > distance on a flat patch. So if I would send my planes on a straight euclidean line instead of a GC and all distances are euclidean flat-grid then my fuel consumption would be lower (simply because the travelled distance is shorter, although this does not correspond to real life).

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Eg.: in flight.fs: stepToWaypoint (L76):

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 let distanceRemaining = calculateDistance (currentX, currentY) (destinationX, destinationY)

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Then if you look at spatial.fs, let calculateDistance:

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all it does is flat grid distance (adding proper units), i.e.

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sqrt((destX-CurrX)^2+(destY-CurrY)^2)

\n

 

\n

Is this right? Or is there something about easting Northing I did not understand (my code uses only latitude and longitude, so there was never a real need to get into details of easting and northing coordinate system).

", "messages": [ { "id": "32388", "postDate": "10/17/2013 14:59:25", "content": "

Hi,

\n

I was reading through the code and it seems to me that you get a penalty for computing proper spherical distances and path on great circles (unless you give a lot of waypoints).

\n

I say penalty because distance on the sphere is always > distance on a flat patch. So if I would send my planes on a straight euclidean line instead of a GC and all distances are euclidean flat-grid then my fuel consumption would be lower (simply because the travelled distance is shorter, although this does not correspond to real life).

\n

Eg.: in flight.fs: stepToWaypoint (L76):

\n

 let distanceRemaining = calculateDistance (currentX, currentY) (destinationX, destinationY)

\n

Then if you look at spatial.fs, let calculateDistance:

\n

all it does is flat grid distance (adding proper units), i.e.

\n

sqrt((destX-CurrX)^2+(destY-CurrY)^2)

\n

 

\n

Is this right? Or is there something about easting Northing I did not understand (my code uses only latitude and longitude, so there was never a real need to get into details of easting and northing coordinate system).

", "rawMarkdown": "", "votes": null }, { "id": "32391", "postDate": "10/17/2013 16:54:25", "content": "

See the bottom of this post which explains that:

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[quote]...any lats/longs inputted into the simulator immediately get converted onto a Lambert conformal conic projection [/quote]

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The wikipedia article on Lambert conformal conic projection says that:

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[quote]Pilots favor these charts because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints [/quote]

", "rawMarkdown": "", "votes": null }, { "id": "32392", "postDate": "10/17/2013 18:14:36", "content": "

Thanks Christopher! But the questions remains how long the approximation remains true? I played a bit in the old leaderboard and if I remove some random points of the 2 flights I have which crash (due to exhausted fuel), the one which crashed at the second last wp lands decreasing my $perPlane-score by 30...

\n

And generally if I remove some random points from a random flight (paths are mainly but not always on the same GC) I actually also decrease my score (by some Cents only)-->so it is only an approximation and it has an influence (although maybe only little).

\n

My grid points are separated 22km (spherical distance)...

", "rawMarkdown": "", "votes": null }, { "id": "32395", "postDate": "10/17/2013 20:42:47", "content": "

Yes, some of the differences you're seeing could be caused by the Lambert approximation.  However, another confounding factor might be how you've set the waypoint altitudes.  The simulator doesn't do a linear interpolation between waypoint altitudes...so deleting waypoints would change how long a plane cruises at  higher, more fuel-efficient altitudes.  That would change fuel consumption & cost, too.  .

\n

 

", "rawMarkdown": "", "votes": null }, { "id": "32412", "postDate": "10/18/2013 15:07:53", "content": "

Yes it does indeed, I wrote an optimization code which removes some of the 'less important' waypoints, getting my score down by 60$ (or from position 39 to 36, if I were to have submitted these routes during the competion) :-).

", "rawMarkdown": "", "votes": null } ], "comments": [ { "id": 32391, "author_name": "chefele", "author_url": "", "post_date": "10/17/2013 16:54:25", "content": "

See the bottom of this post which explains that:

\n

[quote]...any lats/longs inputted into the simulator immediately get converted onto a Lambert conformal conic projection [/quote]

\n

The wikipedia article on Lambert conformal conic projection says that:

\n

[quote]Pilots favor these charts because a straight line drawn on a Lambert conformal conic projection approximates a great-circle route between endpoints [/quote]

", "votes": null, "replies": [] }, { "id": 32392, "author_name": "sandros", "author_url": "", "post_date": "10/17/2013 18:14:36", "content": "

Thanks Christopher! But the questions remains how long the approximation remains true? I played a bit in the old leaderboard and if I remove some random points of the 2 flights I have which crash (due to exhausted fuel), the one which crashed at the second last wp lands decreasing my $perPlane-score by 30...

\n

And generally if I remove some random points from a random flight (paths are mainly but not always on the same GC) I actually also decrease my score (by some Cents only)-->so it is only an approximation and it has an influence (although maybe only little).

\n

My grid points are separated 22km (spherical distance)...

", "votes": null, "replies": [] }, { "id": 32395, "author_name": "chefele", "author_url": "", "post_date": "10/17/2013 20:42:47", "content": "

Yes, some of the differences you're seeing could be caused by the Lambert approximation.  However, another confounding factor might be how you've set the waypoint altitudes.  The simulator doesn't do a linear interpolation between waypoint altitudes...so deleting waypoints would change how long a plane cruises at  higher, more fuel-efficient altitudes.  That would change fuel consumption & cost, too.  .

\n

 

", "votes": null, "replies": [] }, { "id": 32412, "author_name": "sandros", "author_url": "", "post_date": "10/18/2013 15:07:53", "content": "

Yes it does indeed, I wrote an optimization code which removes some of the 'less important' waypoints, getting my score down by 60$ (or from position 39 to 36, if I were to have submitted these routes during the competion) :-).

", "votes": null, "replies": [] } ], "raw_markdown_by_id": { "32388": "", "32391": "", "32392": "", "32395": "", "32412": "" }, "source": "meta" }