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DME ARCs and coordinate based FMCs

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Okay, who knows their air navigation and has enough math to understand it? I'm using the Level-D 767 and I need to tweak a few SIDs and STARs for a group of islands I fly regularly. Now, being islands nav-aids are sparse so there are a lot of DME arcs to fly and since my airac is out of date I need to update these manually - or rather, I need to know how to do it manually so that I can write a SID/STAR editor for the Level-D and others. I don't mind doing this... The Level-D is worth it and it has lovely XML based navdata files which are very easy to edit, but the FMC doesn't understand DME ARCs so these appear in the SID/STAR files as multiple references to LAT:LONG coordinates... same with others like the FlightOne ATR72.It seems that in the world of Simmer FMC's the DME ARCs are usually simulated by flying point to point segments of the arc. Can you see the problem ? Help me understand this please. Assumption 1: You CANT actually specify a DME ARC in long:lat points It seems to me that when flying a DME ARC you're using a line-of-sight distance from the navaid... so, two aircraft at different altitudes would actually have a lateral seperation when flying a DME arc. for example : Aircraft 1: 8 DME at 5000 feet Aircraft 2: 8 DME at 8000 feet Surely aircraft 2 would be closer to the navaid because more of that 8DME measurement is accounted for vertically... That is, an aircraft at 8 miles altitude would measure 8DME *only* when overflying the station and an aircraft on the ground 8 miles away would also measure 8 DME. So, this being the case, the long:lat coordinates for segments of an 8DME turn are relative to altitude. Would that be a correct assumption ? If so, aircraft flying a DME ARC with a minimum of 3000 and maximum of 8000 are actually, when viewed from above, not even in the same vertical plane. Now I don't believe radio equipment on planes account for this and deliver 'ground distance' so I'm worried that my beloved Level-D 767 is flying bad arcs. Assumption 2: Many arcs in laterally confined airspaces seem to be tight on vertical restrictions so is assumption 1 accounted for. I notice many of the arcs I have to fly have a fixed altitude or a very tight range of altitudes. Is this because of the problem discussed above ? Is it recognised that DME ARCs have stacks of planes which fit on the side of a dome rather than a vertical plane and therefore the only way to use a DME ARC is to minimise vertical range in order to tighten the lateral spread ? If so, then the problems with Level-D's hack-around method of coding SIDs/STARs is probably workable. Writing my own updated SID/STAR with DME ARC: OK, so I plan to use trigonometry and great circle calculations to plot the Lat:Long of a point with a fixed distance from another point. I'm guessing that for most DME ARCs trig is fine because the great-circle discrepency is hopefully smaller than my aircrafts ability to hold a DME course. So here's the order I intend to do this : 1. Take the coordinates of the fix on the great circle (40,000km circumference) 2. Project the coordinates of the fix on a second great circle (diameter + altitude * 2) 3. Use some unknown 'donut math' to find where a line of length DME would touch the outer circle 4. Project this point back onto the first circle (no projection needed I guess) 5. Use the great circle distance algorithm to find the ground distance 6. Sweep this G.C. distance around the fix in increments that give a good segment distance for the arc 7. From iterating step 6 arrive at multiple long:lat's on the ground projection for 8 DME flown at a given altitude 5. Enter these points into the navdata in place of the arc Does that sound at all sane ? Is there a better way ? Annoyingly I just spent two whole days transcribing all of the arcs into 'long:lat' by slewing to various DME for various radials of each fix and noting the positions on paper... unfortunately, I did it all at ground level so I'm guessing that the tracks obtained are pretty much useless : / Wow, you read all the way down to here ? Cool! In your opinion : - Am I overthinking this ? - Am I on completely the wrong lines ? - For DME ARCs with a useable range of, say, 3000 -> 7000 should I prepare my arc at 3000, 7000 or in the middle at 5000... is there any standard methodology here ? - For DME arcs with entry at 5000 and descent instructions to 3600 between two points should I plot both accordingly with a skew between the two relative to the expected descent so that the measured DME remains about right on the way down instead of drifting. such that my arc would look goofy on a chart but would fly closer to the actual DME measured course ? - As regards the math, can anyone here slap me and point me to a tool, SDK, class or some published algorithm that will do this crap for me. Oh, and some other questions... Do real FMC's (or GPS AP's) perform DME arcs based on actual DME or on Long:Lat ? I mean, is this Level-D just fudging it or is there a real life application ? Oh, and before you all tell me to grow some hairy spheroids and fly the arcs myself - I do... regularly, it's great fun... but when real life intrudes it's nice to be able to switch to (L/V)NAV and let the systems take some pressure off... particularly on VATSim where pausing ain't an option. Many thanks, -Gary

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Hi Gary,Rather than over think the ARC problem have a look at this page:http://williams.best.vwh.net/avform.htmIn particular look at the formula for "Lat/lon given radial and distance". That is what I use to develop an ARC simulation.As for the altitude and line of sight affecting the lat/long position on the same radial. There is a difference in the surface distance of the ARC with a plane at 8000 feet and one at 5000 feet but I tend to think it is small, about 450 feet with that 8 mile ARC. That's what, about 3.6 wingspans of the 757? Kind of hard to see in the air from 3000 feet away. But since we are working with a sim, who cares if the difference is 450 feet or so, it's a sim and no life is threatened. The ARC will fly the same.Anyway maybe the above link will help.Good luck in your quest.Terry

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Rather than over think the ARC problem have a look at this page:http://williams.best.vwh.net/avform.htmIn particular look at the formula for "Lat/lon given radial and distance". That is what I use to develop an ARC simulation.
Wow, great link there... that pretty much nails the math down.I suppose to do great-circle at altitude all I need to do is scale up the circle appropriately.
As for the altitude and line of sight affecting the lat/long position on the same radial. There is a difference in the surface distance of the ARC with a plane at 8000 feet and one at 5000 feet but I tend to think it is small, about 450 feet with that 8 mile ARC. That's what, about 3.6 wingspans of the 757? Kind of hard to see in the air from 3000 feet away. But since we are working with a sim, who cares if the difference is 450 feet or so, it's a sim and no life is threatened. The ARC will fly the same.
So it's safe to work out 8 miles DME at ground level (or at least the routes minimum altitude) and fly that at any altitude I'm given ?Oh, well that makes things much easier. Thanks.Actually, I suppose once the data from ground-level calculations are in I can fly it and if the difference between measured DME when flying the route did happen to be too great then I could simply scale the arc points by the amount I'm off in the air and resave the procedure file... I didn't think about that *slaps forehead*
Anyway maybe the above link will help.
Greatly, thanks Terry.Okay, thanks for sharing your thoughts. I guess I'll be off now to code a tool for giving me arcs around a fix with a specified step size, min-alt, distance and fix. Then I'm gonna spend tonight attacking these new SIDs/STARs.Take care,-Gary

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Hi Gary,Rather than over think the ARC problem have a look at this page:http://williams.best.vwh.net/avform.htmIn particular look at the formula for "Lat/lon given radial and distance". That is what I use to develop an ARC simulation.As for the altitude and line of sight affecting the lat/long position on the same radial. There is a difference in the surface distance of the ARC with a plane at 8000 feet and one at 5000 feet but I tend to think it is small, about 450 feet with that 8 mile ARC. That's what, about 3.6 wingspans of the 757? Kind of hard to see in the air from 3000 feet away. But since we are working with a sim, who cares if the difference is 450 feet or so, it's a sim and no life is threatened. The ARC will fly the same.Anyway maybe the above link will help.Good luck in your quest.Terry
Nice link! I read through some of that text and now my eyes are bleeding. lol

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I might be all wet on this one but my take on DME arcs is this.DME arcs are flown at a set altitude according to the approach plate. No stacking here. Stacking was done at holding fixes. That is rare today.Before all the fancy FMCs ,etc, you flew them by hand. Enter the Arc where designated and at the proper distance.Fly the plane straight till you notice the distance change, (half a mile,mile? I don't know.) then turn in the proper direction to get the distancenailed again.Also I belive the DME arc is rarely used any more as are procedure turns. Most charts will have a notation of NOPT which means a procedure turn is not necessary. Things change over the years. The next is the current change to the ADSB system. GPS heavily involved here.P

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I realize this is old, but the way I get by it is to -IN THE FMC- Create a place/bearing/distance point for the entry into the arc or use the provided waypoint- Create a place/bearing/distance point for the exit of the arc or use the provided waypoint- Create a fix with the arc dme from the fix origin -- Fix button on FMCFLYING THE PLANE- Upon entry use hand flying or HDG SEL to follow the arc/circle on HSI - Upon exit resume LNAV or otherTakes all of 10 seconds to do,, entering into FMC that is.Roman

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I assume that you are talking about slant distance versus ground distance when referring to the DME arc distance. In all practicality it is not worth bothering worrying about.For example the difference between ground and slant distance on a 12 mile arc at an altitude of 6000ft is only 252 ft or .04 of a mile. Not worth worrying about.I use ADE http://www.airportdesigneditor.co.uk/ to plot the arc positions and obtain the lats and longs plus any tracks and distances required.It is quick and easy and the graphical representation makes it that much easier to comprehend.

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I realize this is old, but the way I get by it is to -

 

IN THE FMC

- Create a place/bearing/distance point for the entry into the arc or use the provided waypoint

- Create a place/bearing/distance point for the exit of the arc or use the provided waypoint

- Create a fix with the arc dme from the fix origin -- Fix button on FMC

FLYING THE PLANE

- Upon entry use hand flying or HDG SEL to follow the arc/circle on HSI

- Upon exit resume LNAV or other

 

Takes all of 10 seconds to do,, entering into FMC that is.

 

Roman

 

I create bearing/distance waypoints from arc entry to exit. Just increase or decrease bearing by 10 degrees until exit. Keep it in LNAV and you will fly the perfect arc everytime.

 

Jeff Smith

 

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