The Mystery of Mangaia Island

Day 152/30

Noon Position: 21 52S 157 33W

Course/Speed: NNW4

Wind: NE8

Bar: 1015, falling

Sea: NE3

Sky: Typical tropical cumulus, but small

Cabin Temperature: 83

Water Temperature: 79

Sail: #1 genoa and main, close hauled on starboard

Noon-to-Noon Miles Made Good: 106

Miles this leg: 3,587

Avg. Miles this leg: 120

Miles since departure: 20,831

To my surprise, Mangaia hove into view a little before noon.

I don’t know the Cook Islands, the group we are starting to pass through today. In 2012, when I cruised French Polynesia on Murre, our 30-foot ketch of the time, I made a hard right turn at Bora Bora and sailed for home, leaving the Cooks and all the islands to the west for a later exploration.

Lacking facts, I had expected Mangaia to have all the height of a poker chip, like the Tuamotu atolls, where the palm trees on the beach are the first thing one sees when making landfall. On the chart, Mangaia and the other Cooks are round and uninteresting, and as advertised, what hove up was a bean-shaped, level-topped smudge below white cloud.

But even at twenty miles off, it stood up. So, how high is that island after all?

Of such puzzles are great pleasures made on a long passage. Ashore the answer could be found almsot while being asked. But out here our resources are limited. And time we have aplenty.

The chart was no help. It pointed out a flagpole, an airstrip, and the location of the village, but it said nothing about the land features. So, I thought to deduce height from Distance of the Horizon calculations, the formula used in pilotage to help predict when a particular lighthouse or land mass (of known height) should become visible. The square root of the height of the object times 1.17 equals the distance at which the object should pop over the horizon.

In this case, I had *that* answer; I knew how far off we were from the chart plotter. So, after some head scratching, I reversed the formula. Distance off divided by 1.17 and then squared. This gave me 292 feet. Sadly, that was just how high the island would have to be in order to be *visible* at twenty miles and did not account for how much of it was clearly sticking above the horizon now.

Next I decided to measure the height with the sextant. The reading was difficult due to the island being so indistinct, but the angle seemed to be about 9 or 10 minutes of arc. Then I spent *all afternoon* attempting to remember high school geometry and the inner workings of the Pythagorean Theorem. And failed. As it turns out, I didn’t have enough arguments for the proof.

Last resort. Bowditch. By luck I recalled a calculation for Distance by Vertical Angle (Table 15). Again, I had distance, but by putting the table in reverse, I got that for a measurement of 9 or 10 minutes of arc and a distance off of twenty miles, the height of the object should be 600 to 700 feet.

So, am I right? Is Mangaia 600 to 700 feet tall?

—

Slow going again. But winds are steady and beginning to veer east. The sooty anvil headed clouds are gone, and we are at last making way to the north. Tomorrow we should pass the northern Cooks.