navigation general question 1

[gphillips134]

the chart convergency on a lambert conformal conic projection bewteen point a (3000N 01000W) and point B (4500N 03000W is 12. If the rhumb line track from A to B is 314(T), the approximate great circle track T from A to B is?

explaination please

[Jinkster]

Whats the answer and I will have a go at working it from there?

Jinkster

[OneIn60rule]

A drawing question.

In order to answer it you must draw two lines that form the LETTER "A" the third line in the letter "A" will be the great circle track.

Of course you also have to draw the RHUMB line between the two points, this will be an ARC. What you want to do is draw the ARC so that it points towards the EQUATOR.

After you've drawn it you will see that the starting RHUMB LINE track from A is LARGER than the GC track. After this all you have to do is halve the Convergence and SUBTRACT it from the rhumb line TRACK. This will give you your GREAT circle track.

Convergence formula by the way for this> SinLat (mean lat) x Change in longitude= Convergence.

I tried my best here.

[Send Clowns]

The difference between the rhumb-line track and the great circle track at either end is the conversion angle (C.A.), which is half convergence. Really you must use Earth convergence, not chart convergence, as this would concern a straight line on a chart, not a great circle. In this case they are actually the same, so C.A. is 6 degrees.

Then we need to know which end is in question - the great-circle track varies. The rhumb line will be closer to the equator than the great circle, so at A the great-circle track is greater than the rhumb-line track. This would make it 320(T). At B the track would be less, at 308 degrees.

Send Clowns
General Navigation Instructor
BCFT

[gphillips134]

answer in book is given as 264

therefore am i right in assuming 118m -12 = 106

in southern hemisphere 106-22 =84
84 + 180
= 264 bearing from NDB

[Send Clowns]

12 should not come into it - that is the convergence - the angle between meridians and therefore the change of great-circle track (or straight line on the chart, for chart convergence). You want the change from rhumb line to great circle, which must be conversion angle. Also it cannot be magnetic, as you have no variation in the question! Note I would recommend you make all calculations in True, converting to magnetic at the end if required.

Don't know where you found 118 degrees or where 264 comes from :confused: Try taking htis to your school's Gen Nav instructor, he can draw a diagram which should make it clearer.

[OneIn60rule]

I believe that either the answer given in the book is wrong or you are not posting the question properly.

Regardless, the answer is 320 degrees IF you copied the question without fault.

Yes do make sure you highlight the answer given in the book and show it to your instructor.

[ABO944]

Send Clowns

Could you check your PM please??

Thank you

[gphillips134]

disregard my last post had nothing to do with the question sorry

[Send Clowns]

Have replied now ABO. See you soon.

Happy with the answer so far, gphillips?

[paramac146]

send clowns
Would you be so kind as to explain Chart Convergency as apposed to Earth convergency. I realize that convergency=Ch Long x Sin mean Lat...I believe chart convergency is applicable to Conic projection charts given as the N factor.

[Send Clowns]

Earth and chart convergency are the same on a Lambert's chart at the parallel of origin. On the chart, though, convergence is independent of the latitude of the points chosen, as the meridians are straight. Therefore at any latitude on a Lambert's chart,

chart convergence = ch. long. x sin (latitude of parallel of origin)

This is, the angle between the two meridians as drawn on the chart. Meridians always show local true North, so this is the change in direction of True North on the chart. A straight line, crossing two meridians, will not actually change its direction. Its bearing will, however, change; the meridian from which the bearing is measured has a different direction. The difference of direction is, of course, the convergence. Therefore convergence gives change of straight-line bearing.

In a very similar way Earth convergence, the angle between two meridians on teh Earth's surface or drawn on the reduced Earth, gives change of great-circle bearing.

On a normal Mercator chart there is no convergence (the meridians are parallel) and on a Polar Stereographic chart convergence is equal to the change of longitude.

Does that summarise the situation for you?

[paramac146]

Yes perfectly...Thank you

[Send Clowns]

A pleasure :)