Thursday, July 09, 2020

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One may easily estimate the weight of Noah’s Ark fully loaded by using Archimedes’ Principle and some information in Rashi to B’reishit 8:4. Rashi declared that the Ark floated with 11 amot of its hull submerged under water. He gets this from the text. The waters reached a peak above land of 15 amot (7:20) on the first of Sivan, when they began to recede (7:24). The recession continued for two months, since land was uncovered on the first of Av, 60 days later (8:5). The Ark rested on Mt. Ararat on the 17th of Sivan (8:4), after 16 days of the water level falling. Assuming a linear drop in height of the water, the rate is 15 amot in 60 days, or one amah every four days. Thus by the time the Ark rested, the water had been receding for 16 days, meaning the water level dropped four amot from its peak. Since the water level began at 15 amot above the mountain, the Ark must have had 11 amot of its hull under water.

According to Archimedes’ Principle, the weight of an object floating in water is equal to the weight of the water displaced by the object. The object is buoyed by a force equal to the weight of the displaced fluid. In the figure, the cube of water in the stationary container shown is in equilibrium because all forces on it are balanced. If the cube is replaced with a material that is denser than water, it will sink; if less dense than water, it will float. Weight of an object is equal to its mass times the acceleration due to gravity (W=mg). The latter (g) is the same for the Ark and the water, and so it cancels out of the equation. Thus the mass of the Ark equals the density of the water (ρ=1000 kg/m3 for rainwater) times the volume of the water displaced (m= ρ V). The volume of the water displaced equals the volume of the submerged portion of the Ark, which is (assuming rectangular cross-section geometry) the length of the Ark (300 amot, or ca. 150 meters) times its width (50 amot, or ca. 25 meters) times the depth (11 amot, or ca. 5.5 meters). The mass of the Ark is then 1000 x 150 x 25 x 5.5, or 20,625,000 kg., which weighs 45,375,000 lbs. or 22,687.5 tons.

By way of comparison, the largest ships on the seas today are ultra-large crude-oil tankers, which can carry up to 320,000 tons of cargo and weigh as much. The luxury liner Oasis of the Seas (Royal Caribbean) weighs 220,000 tons. Aircraft carriers such as the Nimitz or the new George H. W. Bush weigh around 100,000 tons. Of course, these are all made of steel and not wood, as the Ark was. I guess the conclusion is that the Ark was, by the standards of the ancient world, a huge ship.

Richard Schiffmiller is a musmach of YU and has a Ph.D. in physics. He has worked as a systems engineer in the electronic warfare industry for almost 40 years. He holds seven patents and numerous technical achievement awards. He has been giving a shiur in Congregation Beth Aaron for the past 30 years.