I am working on the problem of calculating the distance at which the vehicle's headlight beam hits the ground, if the vehicle is traveling on a Vertical curvature. However, I am bit confused if using simple trigonometric relation is a correct process here considering the surface is curved (as depicted in the two figures)
Vehicle Go up the crest:
Vehicle going down the trough:
The parameters which I already know:
- constant Slope of the curvature (both crest and trough)
- Radius of curvature
- Field of view (the angular spread of headlight)
I am actually trying to calculate "minimum visible distance" (marked in the image) wrt. to different field of view angles given a constant height of the headlight above the ground. Basically the idea is to calculate intersection of the incident headlight on the curve (minimum and maximum distance for the lower and upper ray respectively) for crest and trough scenario.
I have approached this scenario as a trigonometric problem and use the height of the headlight from the ground to calculate the minimum visible distance (Tan of the angle). However, for both the crest and trough scenario, I cannot think of the way to calculate the Maximum visible distance.
Additionally, I also have doubt, if using trigonometric relation is correct way since the vehicle is already on the curve. I have also checked civil engineer resources, however, they do not have formulation between field of view of the headlight and the minimum and maximum visible distance on the curves.
Any help is highly appreciated. Thank you.