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→Roll Period
The formula for roll period is not too difficult but is too lengthy to describe here. Generally, boats with periods less than 4 s are stiff and periods greater than 8 s are tender. Stiff boats resist rolling and capsizing, and recover quickly. Tender boats roll more, recover slowly and are less resistant to capsizing. As a rule of thumb, for comfort the minimum natural roll period should be equal to a vessels maximum waterline beam in yards. For example, a boat with a beam of 17 ft 9 in should have a minimum roll period of 5.9 s. For safety the roll period should be less.
Waves also have periods. A wave period is the time between two crests or troughs passing the same point. Typical ocean wave periods are 5 to 20 s.<ref>On Second-Order Roll Motions of Ships, Yonghui Liu, FMC SOFEC Floating System, Inc, Houston, Tx., Proceedings of OMAE03, 22nd International Conference on Offshore Mechanics and Arctic Engineering, June 2003, Cacun Mexico </ref> <ref>31. Rousmaniere, J, The Annapolis Book of Seamanship Simon & Schuster, New York, New York, Chapter 1: The boat p26-35, 1999</ref> If the natural roll period of a boat is equal to or an even interval of the wave period, then the wave periods will synchronise and harmonically amplify the roll in what is called a [https://en.wikipedia.org/wiki/Standing_wave standing wave]. At the least this will make the motion uncomfortable; at worst it will capsize the boat very suddenly. Many deep-water service boats are being designed with roll periods greater than 20 s, but generally this is not advisable.
Waves are made by wind from weather action. Long slow periods indicate the waves have travelled a long distance, so the disturbance is far away. Short periods mean it is close by.
=== Roll Acceleration ===
Roll acceleration is the force of gravity (G force) you experience during a roll. High rates of acceleration are very uncomfortable, stress the body, and make it impossible to sleep. Marchaj <ref> Marchaj, Seaworthiness, The Forgotten Factor, chapter 4, "Boat Motions in a Seaway"</ref> has proposed four physiological states: Imperceptible, Tolerable, Threshold of Malaise, and Intolerable. Malaise starts at 0.1 G, Intolerable starts at 0.18 G.