Calculated Elevation Angles of sites viewed from the Halona Blowhole Lookout, elevation ~400 feet.
Site lines from Halona Blowhole, Oahu.
Clear view of West Maui Mts. prior to sunrise.
Sun rising over West Maui Mountains, ~ 7:11 am.
The rising sun can be used as a measure of angle. On the right, the Sun is seen rising above the peak of W. Maui. peak We know that the angular diameter of the Sun is 0.54 deg (~0.5 deg). Measuring the angular displacement from the observed horizon we see that the peak is about 0.54 degrees above the horizon as viewed from the Blowhole.

These preliminary observations show that the elevation angle formula yields approximately what is observed, although there are a few things to point out: (1) The observed elevation angle of W. Mauiof 0.54 deg is off by about 6% from the predicted 0.574 deg. (2) The relative heights of W. Maui peak and the peak on the island of Lanai agrees well with the predicted ratio. W. Maui peak is observed to be ~1.5 times the Lanai peak. The predicted ratio is 0.574/0.438 ~ 1.3. Thus, observed ratio is within about 13% of the expected ratio. (3) Note that the calculated elevations angles for both Mauna Kea and Mauna Loa (Big Island) are negative indicating that these peaks are not viewable from this viewing location. As expected, neither Mauna Kea or Mauna Loa has been seen at any time from this location even under the best seeing conditions. (4) During these observations both the Molokai cliffs and the Molokai mountain peaks were obsured by clouds and therefore not visible. Because of this, comparisons of these objects with the elevation angle formula could not be made.

In conclusion, the 6% disagreement with W. Maui peakis is probably within the uncertainy of the observations. Overexposure of the Sun’s image may also have been a contributing factor. The fairly good agreement with the relative sizes of the W. Maui peak and Lanai are also a good indication of the validity of the elevation angle formula. I have gone back and checked all small angle approximations made in order to derive the elevation angle formula and have verified that these approximations are valid for typical distances and heights discussed. Further observations will certainly be necessary to verify the elevation angle formula.

Elevation angles of Mountain Peaks as Observed From Halona Blowhole, East Honolulu, Oahu
West Maui
Lanai
View from Blowhole Lookout just before Sunrise, 11 Jan. 2014.

 

 

Observer Mountain/ Distance Height Lambda
Height(ft) Island (miles) (feet) (deg)
400 Haleakala 100.0 10023 0.675
400 Lanai Peak 61.2 3366 0.438
400 Mauna Kea 174.7 13796 -0.077
400 Moana Loa 183.0 13679 -0.182
400 Molakai Cliffs 27.0 1350 0.541
400 Molakai Peak 53.5 4970 0.894
400 West Maui Peak 76.0 5788 0.574

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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