Guidebook 2 DRL 9 has a quick and simple method of calculating directional drilling problems.
This problem asks for MD given TVD, as well as MD if the well turns vertical. The GB shows both the radius of curvature calculation (2,865 ft) as well as the max inc (17.9 degrees).
The MD calculation is as follows:
1,500 + 17.9/(2/100) + [8,200 - 1,500 -2,865sin(17.9)]/[cos(17.9)]
1,500 - 895 + 6,119 = 8,514 ft (C).
In the second part of the problem, if the well turns vertical from 8,200 ft TVD using the same DLS, the 895 ft is merely inverted. So just take the build calculation (inc/build) already done and use it on the drop section. If we start at 8,514 ft, that's 8,514 + 895 = 9,408 ft (C).
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