**Tom Chavez**

Intersection of 27th Avenue and Van Buren
Elevation:

1070 ft.

Latitude:

33°27'3.91"N

Longitude:

112° 7'3.08"W

Distance to left light 60.04 Miles (317011.2'), at 204.59 degree heading

Distance to right light 64.38 Miles (339926.4') , at 210.26 degree heading

Distance to middle light 66.24 Miles (349747.2'), at 207.85 degree heading

Distance to Mountains at 3860ft elevation, 16.53 miles (87278.4') (track to left light) 24.49 degrees from mountain to Tom

Distance to Mountains at 3640ft elevation, 15.6 miles (82368') (track to right light) 30.18 degrees from mountain to Tom

Distance to Mountains at 3698ft elevation, 15.78 miles (83318.4') (track to middle light) 207.85 degrees from Tom to mountain

With this data I tried two different methods to calculate the minimum visible altitude from Tom's position to each of the three confirmed lights. First I calculated the angles by creating a right triangle from Tom to the mountains and then extended at the same angle to the full distance to each light which gave me an estimated altitude not including earth curvature (

final values in red). To add the earth curvature I used estimates provided on this web page:

http://www.davidsene...e_of_sight.html which lists height adjustment of 2380' for 60 miles and 3240' for 70 miles. This seems close enough of an approximation and I believe that it accounts not only for the curvature of the earth, but also the anticipated effect of ray diffraction.

Then I used a bastardized estimate from lost_shaman's previous calculations for each of these three lights (

final values in green). The numbers came out somewhat higher using LS's calcs versus the approximations from the above web site, but regardless of that we can see that some of the lights in the array would indeed have been visible from Tom's position for a short period of time, but probably not all and probably not for very long.

My calcs are below, hopefully you can make sense of them.

**Triangle from Tom to Mountains track to Left Light**
side a = 3860 - 1070 = 2790

side b = 87278.4

side c = *87322.98

Angle A = 1.83093 degrees

Extend side b 60.04 Miles (317011.2') to Left Light at 1.83093 degrees = 10133.78251 feet, add 2380ft from estimate = ~

12513.8' minimum visible altitude
or, using an estimation from LS's calcs:

Difference in elevation 2790 ft @ 87278.4 feet, then 2790/87278.4 = .031966672166309 arctan = 1.8309319 degrees add .6 degrees for ~curvature = 2.4tan x 317011.2 =

13286.7' minimum visible altitude
**Triangle from Tom to Mountains track to Right Light**
side a = 3640 - 1070 = 2570

side b = 82368

side c = *82408.084

Angle A = 1.78713 degrees

Extend side b 64.38 Miles (339926.4') to Right Light at 1.78713 degrees = 10606.18703 feet, add 2600ft from estimate = ~

13206.2' minimum visible altitude
or, using an estimation from LS's calcs:

Difference in elevation 2570 ft @ 82368 feet, then 2570/82368 = .03120143745143745 arctan = 1.7871308 degrees add .6 degrees for ~curvature = 2.4tan x 339926.4 =

14247.1' minimum visible altitude
**Triangle from Tom to Mountains track to Middle Light**
side a = 3698 - 1070 = 2628

side b = 83318.4

side c = *83359.835

Angle A = 1.8066 degrees

Extend side b 66.24 Miles (349747.2') to Middle Light at 1.78713 degrees = 10912.60995 feet, add 2800ft from estimate =

13712.6' minimum visible altitude
or, using an estimation from LS's calcs:

Difference in elevation 2628 ft @ 83318.4 feet, then 2628/83318.4 = .031541652264 arctan = 1.8066046 degrees add .6 degrees for ~curvature = 2.4tan x 349747.2 =

14658.7' minimum visible altitude