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A great-circle track is drawn on a Lambert chart between positions A and B in the Northern Hemisphere. The great-circle true track at position A is measured as 070°, while at position B, it is measured as 076°.

If the parallel of origin of the Lambert chart is 37°, what is the longitude difference between positions A and B?
  • A
    007°30’
  • B
    004°59’
  • C
    003°45’
  • D
    009°58’

Great Circle tracks are very closely approximated by straight lines on a Lambert chart, especially when near the parallel of origin, where chart convergency equals the earth convergency at that latitude.

We are given the value of convergency to be 6⁰, which is the change of direction of the great-circle track.

We can also calculate the constant of the cone of the chart, by finding the sin (parallel of origin). Constant of the cone = sin(37) = 0.602.

Convergency = Change in Longitude x Constant of the Cone

Therefore, with rearrangement,

Ch. Longitude = Convergency / Constant of the Cone
Ch. Longitude = 6 / 0.602
Change in Longitude = 9.97 degrees (press DMS button on calculator for 9⁰58’)

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