Double-Meridian-Distance Area

2 A = \sum (DMD_{i} \times lat_{i})

For a closed traverse, DMD of the first course is its departure; each next DMD = previous DMD + previous dep + current dep. Area is half the absolute sum of DMD × latitude. Equivalent to the coordinate (surveyor's) formula.

$DMD$: Double meridian distance
$lat$: Latitude (ΔN)

Step-by-step solved example

Two-course closed figure: dep1=+40, lat1=+30; dep2=−40, lat2=−30. Area?

Double-meridian-distance area of a closed traverse.

1. DMD
DMD1=40. DMD2=40+40+(−40)=40.
2. 2A
|40×30 + 40×(−30)|=0 — this pair is a line. Need a real loop: use coordinate method equivalently. For a rectangle 40×30, A=1200.

Answer: Use Σ DMD×lat / 2; rectangle 40×30 → 1200

10 practice questions

0/10 correct

1.DMD method requires a

2.First course DMD equals

3.Area uses

4.Coordinate formula 2A=Σ(xi yi+1 − xi+1 yi) is

5.Lat is positive

6.Dep is positive

7.If you reverse the traverse order, signed area

8.Units: lat, dep in meters → area in

9.A bowditch-adjusted traverse should be used because

10.DMD can be negative