# How to calculcute variation and compass deviation in this CDMVT problem?

Usually I can solve CDMVT problems, but sometimes I feel I'm missing something important. For example:

• I'm able to solve:
Given WCA -012, TH 125, MC 139, DEV 002E. What are TC, MH and CH?

T     V    M    D      C
125 + 2 = 127 - 002E = 125
————————W(+)——E(-)———————————->


TH=TC+/-WCA
MH=TH+/-VAR
MH=MC+/-WCA
CH=MH+/-DEV

125=TC-012 => TC = 137
MH=139-102 => MH = 127
CH =125

• Using the same method, I cannot solve:
Given: TC 183, WCA +011, MH 198, CH 200

T     V      M     D     C
194 + 4  =  198 + 002  = 200
————-W(+) —-E(-)——————->

• TH is easy 183+011=194
• Variation looks like +4 so 4W, and deviation looks like +002.
But the correct results are variation is 004E (so minus 4) and DEV is -002 not plus.

Please someone clear me up what I am missing I feel like is important and I miss something critical.

Abbreviations used:

• TN/MN: True/Magnetic North

• VAR: Magnetic variation, positive when MN comes after TN, clockwise, said otherwise when VAR is east.

• TC/MC: True/Magnetic Course. The track actually flown

• WCA: Wind correction angle, angle added to desired course to get the heading to be flown.

Thus we get:

• MH/MC = TH/TC + VAR
• MH = CH + DEV
• TH/MH = TC/MC + WCA

What are TC, MH and CH
given: MC = 139, TH = 125, DEV = 2, WCA = -12 (given are between brackets)

          C  +  D --> M  -  V --> T
Course              [139]   2    137
WCA                             [-12]
Heading  125   [2]   127    2   [125]


Answer: TC = 137, MH = 127, CH = 125
Because:

• TC = TH - WCA = 125 - (-12) = 137
• VAR = MC - TC = 139 - 137 = 2 (meaning MN is east of TN)
• MH = TH + VAR = 125 + 2 = 127
• CH = MH - DEV = 127 - 2 = 125

What are TH, VAR and DEV
given: TC = 183, WCA = 11, MH = 198, CH = 200

          T  +  V --> M  -  D --> C
Course               187    4   [183]
+ WCA                            [11]
Heading [200]  -2   [198]   4    194


Answer: TH = 194, VAR = 4 (east), DEV = -2
Because:

• MC = MH - WCA = 198 - 11 = 187
• VAR = MC - TC = 187 - 183 = 4 (so MN is east of TN)
• TH = MH - VAR = 198 - 4 = 194
• DEV = MH - CH = 198 - 200 = -2

I used the standard definition of the magnetic variation, positive when MN is eastward. You seem to prefer positive when MN is westward, just invert MH/MC = TH/TC + VAR, that is use: TH/TC = MH/MC + VAR and you'll get the same result.