A Complicated Geometry Question (No, This Is Not Homework)

Factual Questions
21

Yup. My Flerfer-Radar went straight into alert-mode.

22

By coincidence . i just watched a new report on the U2, and the pilot said the max range he can see above 60,000 ft is 260 nautical miles. And I was just reading this thread this morning. :slight_smile:

23

That is one case where it is easier to remember with imperial units.


       _____________     
1.17⋅╲╱ height(feet)  = distance to horizon in NM

So at 1 Meter, 2.12 Nautical Miles or 2.12 minutes, which is probably just as easy to remember as:


       ______________ 
2.12⋅╲╱ height(meters) = minutes.

At least this is what I used when sailing in the pre-GPS days.

24

To clarify the above that had the multiplier to change units.find the distance to the horizon with the secant-tangent theorem.

Where:

D = diameter
R = radius
h = height
d = distance


      ___________
d = ╲╱ h⋅(D + h) 

or:
      _____________
d = ╲╱ h⋅(2⋅R + h)

These assume the same units so if the Diameter is 12742 KM or 12742000 Meters

d = 3569.594 Meters

But that finds the height at the intersection point, you would have to adjust for the right angle intersection in the OP, but I wanted to clarify the distance formula I was using above.

But it is not much more work to get the rest once you have this formula.