Lab #1 – Chapter 3, Intersection of two planes.
In this problem, the attitudes of two planes are given:
Plane A is oriented: 066, 50SE, and Plane B is oriented: N22W, 40SW.
We want to find the line of intersection of these two planes.
Approach:
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Draw the strike (i.e., structure contour) of Plane A at point A with a ruler along N66E.
Let’s draw other structural contours at 10 m vertical intervals (i.e., v = 10 m).
We need to find the horizontal spacing (distance) on the map (x) for this 10 m vertical interval.
Since Plane A dips () 50 SE, draw a right angle triangle, with the hypotenuse dipping 50 degrees,
and vertical side of 10 m. Find the horizontal distance with trigonometry using the scale of the
map (Scale: 27 mm = 100 m).
tan = tan 50 = 10m/x which gives x = 8.4 m for the horizontal spacing for contours for plane A.
Convert this 8.4m scale into mm scale on the map (2.2 mm) using the scale of the map.
Now, draw many structural contours with this spacing south of the strike line for point A.
Repeat this for Plane B, by drawing the strike of Plane B at point B with a ruler along N22W.
Repeat all above steps, and you get:
tan = tan 40 = 10m/x which gives x = 11.91 or 12 m for the horizontal spacing for plane B.
The 12 m spacing is 3.2 mm on the map, using the scale of the map.
Now, draw many structural contours with this spacing west of the strike line for point B.
Mark their elevation (e.g., 770m, 710m).
Find the points of intersection of the same elevation structural contours for plane A and B.
Connect all such points to get the line of intersection of Plane A and B.
Draw the line, and read its trend from the N side of the map.
Note: Read it from high to low (S32W).
Now determine the plunge of the line of intersection by locating a high and a low elevation along
the line (e.g., 60 m), and finding the horizontal spacing between them (25mm=93m). Draw a right
angle triangle with vertical side of 60m and horizontal side of 93m. Find the plunge with
trigonometry:
tan  = 60m/93m,which yields tan  = 0.6452, thus = 33o
So, the intersection line is oriented: S32W, 33
Find where the two planes intersect right under the Boulder Creek. Read the structural contours
at this depth, and subtract it from the surface elevation to find how far we have to drill.