How to calculate height of camera and ground coverage via geometry?

Question

I have a GoPro7 that I will mount on a pickup vehicle to capture ground images with video capture.
The camera isn't top down but has about 20 (or 30) degrees inclination from the vertical axis.
I want to capture the road that is 4m in width.
Other givens would be:

Vertical Field of View: 71.0deg
Horizontal FoV: 86.7deg
Diagonal FoV: 100deg
Sensor size: 1/2.3” (6.17×4.55mm)
Aperture: f/2.8
Zoom: 0%
Frame width: 4:3

I would like to know if it is possible (and how) to calculate the needed height of the GoPro for this.

Ross Millikan · Answer

I will make a bunch of assumptions along the way along the lines of my comment. If I guess wrong, I hope you can adapt the calculation. Let us assume the camera is pivoted to the left so the 4m you want to see is equally split across the centerline of the frame. I will also assume the 4m is across the middle of the frame vertically. If the height of the camera is H the point on the ground will be H/tan(20) ahead of you. The half width of the frame is 2m, so you want 2=(H/tan(20))*tan(86.7/2), which gives H=0.77 meters or about 30 inches.

Answered by Ross Millikan on March 19, 2021

How to calculate height of camera and ground coverage via geometry?

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