Mid-Latitude Sailings
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Because the math is easier when you flatten the earth out

Alright, so Mid-Lat sailings are basically a combination of Plane Sailings and Parallel Sailings, so if you can do those, you should be able to do this.
If you're given 2 positions and asked to find Course and Distance:
Step 1: Find l (the diff. in lat, in '), DLo (the difference in long., in ') and Lm (the middle latitude between the two positions, in minutes and tenths)
Step 2: Calculate using what you know, as of right now the only equation (see right) you have all the info for solves for p (departure, ie. DLo converted to nm), so do that.
Step 3: Now that you've got p, you can solve for C (course angle) and D (distance) independently.
Step 4: C is only your course angle, not your actual course, so you need to figure out your actual course now.
-If you are headed NE, add the C to 000 (ie. North)
-If you are headed SE, subtract the C from 180
-If you are headed SW, add the C to 180
-If you are headed NW, subtract the C from 360
If you are given a starting position and a Course and Distance:
Step 1: You can solve for l and p already using the sin functions at right. Do that, you'll need them to move on.
Step 2: Now that you know l (the diff. in lat.) you can find the lat. of your end position, and you can also find your Lm. To find Lm, follow the same steps as below, but only apply l/2 (half the l).
-If in S lat and headed N, subtract l from Lat 1
-If in S lat and headed S, add l to Lat 1
-If in N lat and headed N, add l to Lat 1
-If in N lat and headed S, subtract l from Lat 1
Step 3: Now that you know Lm and p, you can solve for DLo using the bottom equation.
Step 4: Apply DLo to your Long 1 to find your final longitude.
-If in W lat and headed E, subtract DLo from Long 1
-If in W lat and headed W, add DLo to Long 1
-If in E lat and headed E, add DLo to Long 1
-If in E lat and headed W, subtract DLo from Long 1



Departure; the horizontal distance between your starting and ending longitudes in nautical miles


Course angle; the angle between your course and your meridian of longitude


Distance; the actual distance traveled along your track line, in nautical miles


"Little L"; the latitudinal distance between your starting lat and your ending lat, in minutes of latitude or nm (1 min of lat = 1nm)


the "Mid-Latitude," this guy lies vertically halfway between your starting and ending latitudes and is derived by applying half of l to either known latitude


"Difference in long."; this is the horizontal distance in minutes between your starting longitude and ending longitude

sin C = p/D
cos C = l/D
tan C = p/l
p = DLo cos Lm