Convergence
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Convergence
I am looking for a formula for calculating a correction for convergence ( particularly for northern nav).
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North Shore
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Smartass answer: G+P+S= position 
Edited to add that I (obviously) know SFA about Arctic ops..
Edited to add that I (obviously) know SFA about Arctic ops..
Last edited by North Shore on Thu Sep 20, 2007 3:54 pm, edited 1 time in total.
Say, what's that mountain goat doing up here in the mist?
Happiness is V1 at Thompson!
Ass, Licence, Job. In that order.
Happiness is V1 at Thompson!
Ass, Licence, Job. In that order.
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just curious
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Upon reception of inbound navaid or approximate midpoint of route, convergencyshall be applied to track equal to the amount of longitude crossed from departure to destination. If track is in an easterly direction, (0-179) then convergence shall be added to true heading. Conversely, if track is in a westerly direction, convergence shall be subtracted from true heading.
Note when in in the Southern Hemisphere and navigated bu reference to true south, the reverse of the above applies.
Note convergence must not be applied to departure runway heading because in the event of an emergency return to the point of departure the heading indicator will be mis-aligned with navaids and runway heading
Example flight from Resolute Bay to Mould Bay:
YRB N74 43.0 W 94.58.2
YMD N 76.14.3 W119.18.5
Amount of Longitude change equals:
119 18.5
-94 58.2
_______
24 20.3 of convergence
Track is in a westerly direction, therefore upon reception of Mould Bay Beacon indicator will be turned to the south to subtract 24. 20.3 assuming there has been no precession in the gyro, and it is indicating the correct true heading.
Note when in in the Southern Hemisphere and navigated bu reference to true south, the reverse of the above applies.
Note convergence must not be applied to departure runway heading because in the event of an emergency return to the point of departure the heading indicator will be mis-aligned with navaids and runway heading
Example flight from Resolute Bay to Mould Bay:
YRB N74 43.0 W 94.58.2
YMD N 76.14.3 W119.18.5
Amount of Longitude change equals:
119 18.5
-94 58.2
_______
24 20.3 of convergence
Track is in a westerly direction, therefore upon reception of Mould Bay Beacon indicator will be turned to the south to subtract 24. 20.3 assuming there has been no precession in the gyro, and it is indicating the correct true heading.
Hmm
I'm a little confused here.
JC your answer starts off with 'applying convergence to TRACK' but then you switch and say to apply it to HEADING. Last I checked these were two different things.
I'm gonna assume that you prob fly with the astro compass welded to the dash so your HEADING will always be bang on as you correct for that precession every 10 min. So that's covered, it's always aligned to true north.
Now the TRACK is what's always changing as you fly east or west, yes? Not on the equator but anywhere else, especially way up where you are with all those lines of longitude coming together, or converging. I think everyone sees their TRACK changing, that's why one is constantly adjusting the CDI on their GPS slaved HSI as the autopilot and GPS take us on the Great Circle route to wherever we're going.
So of course we wouldn't apply it to our HDG, especially not on the rwy since that is such a good spot to properly align our heading indicators. Instead, as you started to say, one would apply it to the TRACK if flying on airways, routes, or wherever you're going. Perhaps all of it at the half way point or maybe half at the 1/3 point and the other half at the 2/3. Sort of an ugly great circle when compared to the GPS's constant changes.
Maybe I'm out to lunch like usual, but I think the SOP's you cut and pasted that from might be little incorrect.
Hope things are going ok in your neck of the woods.
RB
I'm a little confused here.
JC your answer starts off with 'applying convergence to TRACK' but then you switch and say to apply it to HEADING. Last I checked these were two different things.
I'm gonna assume that you prob fly with the astro compass welded to the dash so your HEADING will always be bang on as you correct for that precession every 10 min. So that's covered, it's always aligned to true north.
Now the TRACK is what's always changing as you fly east or west, yes? Not on the equator but anywhere else, especially way up where you are with all those lines of longitude coming together, or converging. I think everyone sees their TRACK changing, that's why one is constantly adjusting the CDI on their GPS slaved HSI as the autopilot and GPS take us on the Great Circle route to wherever we're going.
So of course we wouldn't apply it to our HDG, especially not on the rwy since that is such a good spot to properly align our heading indicators. Instead, as you started to say, one would apply it to the TRACK if flying on airways, routes, or wherever you're going. Perhaps all of it at the half way point or maybe half at the 1/3 point and the other half at the 2/3. Sort of an ugly great circle when compared to the GPS's constant changes.
Maybe I'm out to lunch like usual, but I think the SOP's you cut and pasted that from might be little incorrect.
Hope things are going ok in your neck of the woods.
RB
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Ref Plus 10
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Correct me if I'm wrong, but I believe JC was mentioning you use TRACK (east or west) to determine whether to add or subtract convergence to your HEADING. Then again, assuming there is no change in atmospheric conditions, your track would change just as much as your heading, so convergence applied to the track or the heading would result in the same number, would it not?
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just curious
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Redbreast-
Operating in true, the track stays the same. The heading will change. This heading change is due to convergence. Track stays the same cause it's great circle.
It's not merely SOP, it is a way of life.
Way down south we run in Grid, so convergence isn't a factor.
Yes.I'm a little confused here.
Operating in true, the track stays the same. The heading will change. This heading change is due to convergence. Track stays the same cause it's great circle.
It's not merely SOP, it is a way of life.
Way down south we run in Grid, so convergence isn't a factor.
Confused? Yes, I usually am.
I will concede that heading indicators need correction in True airspace for a number of things, convergence being one of them, precession being another and probably some other reasons I ought to know of. If one was keeping a precession log, then convergence could be accurately applied to heading. I haven't come across one of those in my travels except in museums. So most people I know set their heading indicators (while in True Nav) by GPS bearing to NDB, or if they are feeling energetic - by Sun's True Bearing/Astrocompass etc, while enroute and before an approach.
Now I believe the important consideration here is the TRACK. If you fly a constant TRACK in Magnetic or True when travelling either East or West (other than on the equator) I think you are on a Rhumb line and you will end up spiralling into a pole eventually. Since we tend to fly shorter distances and don't carry enough fuel for that, great circles are the shortest way to go. These do require constant TRACK alterations both in Mag or True. The easiest way to confirm this is to look at an LE chart between two points on an air route or airway. In true airspace, they are not reciprocals - due to convergence altering the TRACKs. In magnetic airspace, there is both convergence and variation at play making the numbers different. Of course it is more pronounced over long distances at high latitudes. If you are on autopilot slaved to the GPS you can just go to sleep and it'll get you there. If you are hand-bombing it on NDB's, then at some point you need to say "We're half way along now, let's apply convergence to our track and start tracking ___ towards the NDB. It's a pretty ugly Great Circle but most people don't want to apply it at each line of longitude they cross to make it smooth. That's why GPS are slick.
JC question those SOP's - they are only written by people
and Ref+10, I think you are correct that in zero wind they would be the same. I've yet to see a day with no wind at altitude tho.
I will concede that heading indicators need correction in True airspace for a number of things, convergence being one of them, precession being another and probably some other reasons I ought to know of. If one was keeping a precession log, then convergence could be accurately applied to heading. I haven't come across one of those in my travels except in museums. So most people I know set their heading indicators (while in True Nav) by GPS bearing to NDB, or if they are feeling energetic - by Sun's True Bearing/Astrocompass etc, while enroute and before an approach.
Now I believe the important consideration here is the TRACK. If you fly a constant TRACK in Magnetic or True when travelling either East or West (other than on the equator) I think you are on a Rhumb line and you will end up spiralling into a pole eventually. Since we tend to fly shorter distances and don't carry enough fuel for that, great circles are the shortest way to go. These do require constant TRACK alterations both in Mag or True. The easiest way to confirm this is to look at an LE chart between two points on an air route or airway. In true airspace, they are not reciprocals - due to convergence altering the TRACKs. In magnetic airspace, there is both convergence and variation at play making the numbers different. Of course it is more pronounced over long distances at high latitudes. If you are on autopilot slaved to the GPS you can just go to sleep and it'll get you there. If you are hand-bombing it on NDB's, then at some point you need to say "We're half way along now, let's apply convergence to our track and start tracking ___ towards the NDB. It's a pretty ugly Great Circle but most people don't want to apply it at each line of longitude they cross to make it smooth. That's why GPS are slick.
JC question those SOP's - they are only written by people
and Ref+10, I think you are correct that in zero wind they would be the same. I've yet to see a day with no wind at altitude tho.
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Speedbird Junior
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From JAA ATPL notes:
Convergence, i.e. constant change of track is zero at the Equator (where all meridians are parallel) and maximum at the poles.
Mathematically:
convergence = change of longitude x sine mean latitude
E.g. Find convergence in track between 40N 25W and 60N 060E
a) change longitude is 60E + 25W = 85 degrees,
b) Mean lat = 60N + 40N / 2 = 50
So,
85 x Sine 50 = 65 degrees change in track.
In order to figure out whether you ADD or SUBTRACT, for northern hemisphere, draw on a piece of paper your two meridians in parallel, but sloping out from the top of the page. Say your initial track is 090T, you are eastbound, so draw the track cutting the two meridans in that direction (North top of page remember) Your start point is from 25W (left hand meridian) so draw in the angle on your 25W meridian to the 090 line..now compare that angle with the same angle on the 60E meridian..if the 60E meridian angle is SMALLER, you subtract, LARGER, you add to your original heading.
Convergence, i.e. constant change of track is zero at the Equator (where all meridians are parallel) and maximum at the poles.
Mathematically:
convergence = change of longitude x sine mean latitude
E.g. Find convergence in track between 40N 25W and 60N 060E
a) change longitude is 60E + 25W = 85 degrees,
b) Mean lat = 60N + 40N / 2 = 50
So,
85 x Sine 50 = 65 degrees change in track.
In order to figure out whether you ADD or SUBTRACT, for northern hemisphere, draw on a piece of paper your two meridians in parallel, but sloping out from the top of the page. Say your initial track is 090T, you are eastbound, so draw the track cutting the two meridans in that direction (North top of page remember) Your start point is from 25W (left hand meridian) so draw in the angle on your 25W meridian to the 090 line..now compare that angle with the same angle on the 60E meridian..if the 60E meridian angle is SMALLER, you subtract, LARGER, you add to your original heading.
Four in trail of my big brother....
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just curious
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I was looking for the mathematical formula, and it has been posted. Lot's of other good banter on the topic too. I like the idea of ,in the northern hemishpere always correct to the south. I guess the opposite holds true in the southern hemisphere. Thanks for the answers guys:)
