The vast majority of people who go on cruises spent their time on large, stable ships in relatively calm waters, such as the Caribbean or the Mediterranean. An expedition cruise to Antarctica is a completely different experience.

Nearly every cruise to Antarctica involves a crossing of the Drake Passage, the 500 mile wide waterway that connects the Atlantic and Pacific Oceans between the southern tip of South America and the Antarctic Peninsula. The waters here can be completely calm (the Drake Lake) or savagely violent (the Drake Shake), and often times more than half of the passengers on a ship spend a day or two sick in their cabins during this crossing. Even at night, the crossing can be unbearable, as the pitching and rolling of the ship can toss passengers around in their beds.

When a ship tilts vertically along the axis running between its front and its back, this is called pitching. The amount of pitch is measured as the angle (in degrees) that the ship is tilting from horizontal.

When a ship tilts to its left or right side, this is called rolling. The amount of roll is measured as the angle (in degrees) that the ship is tilting sideways from horizontal.

My cabin was in the front of the ship, so whenever the ship was pitching, my bed would rise and fall. This sometimes happened for hours overnight, and so it almost felt as though my bed was a trampoline. But rolling was also difficult to sleep through, as it caused my bed to tilt from head to toe. Sometimes the bed would tilt in one direction, and I would slide down about eight inches so my feet were against the footboard, and then it would tile in the other direction, and I would slide up about eight inches so my arm was against the headboard.

I took all of these photographs from the ship's bridge as we crossed the Drake Passage on our way back from Antarctica to South America. The bridge is one of the best places to be on a moving ship, as the panoramic views help the body process the motion without getting seasick. I actually stood on the bridge for four and a half hours that day as the ship pitched and rolled. And of course while I was up there, I wondered how much the ship was actually rolling. I happened to take several photos, and I realized that these should be enough for us to estimate the angle that the ship was rolling.

To measure the angle of a ship's roll from a photograph, we can use the fact that the foremast (the mast in front of the bow) is built to be perfectly vertical when the ship is flat. It should, therefore, form a 90° angle with the flat horizon. When the ship rolls to the left or the right, the foremast is no longer vertical, which decreases the angle between the foremast and the horizon. The amount that this angle is decreased is equal to the ship's roll. Therefore, we can calculate the ship's roll by measuring the angle between the foremast and the horizon, and then subtracting this amount from 90°:

So in the first image above, we measure a 68° angle between the foremast and the horizon. This means that the amount of roll is 90° - 68° = 22°. So when this photo was taken, the ship was rolling 22° to the right. In the other image, we measure a 73° angle between the foremast and the horizon. This means that the amount of roll is 90° - 73° = 17°. So when this photo was taken, the ship was rolling 17° to the right.

Just a quick note: these numbers aren't perfect. The angles are going to be just a bit off because these photos weren't taken from directly behind the foremast (which is an area reserved the for the ship's crew). But they still give a decent approximation of the ship's roll.

Sample Problems

1. Use the method from above to determine the angle of roll of the ship in each of the images below. What was the greatest angle of roll observed?

2. While the ship did roll to the left, it was always less of a roll than the right-sided rolls. What factors might cause a ship roll further on one side than the other?