Calculated Elevation Angles of sites viewed from the Halona Blowhole Lookout, elevation ~400 feet.
Site lines from Halona Blowhole, Oahu.
Clear view of Haleakala prior to sunrise.
Sun rising over Haleakala, ~ 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 Haleakala's  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 Haleakala of 0.54 deg is off by from the predicted 0.657 degrees. (2) The relative heights of Haleakala peak and the peak on the island of Lanai agrees well with the predicted ratio. The Haleakala peak is observed to be ~1.5 times the Lanai peak. The predicted ratio is 0.657/0.438 ~ 1.5. Thus, observed ratio is as expected. (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 can not be 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 obscured 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 disagreement with the Haleakala peak is probably within the uncertainty 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 Haleakala 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
Haleakala
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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