Rolling Period of Ark?

Baraminological Note · For Sea-Farers .... · Rolling Period of Ark? · Ark : empty weight and freighted weight, number of couples on the Ark. · Small Tidbits on Ark, Especially Mathematical

A passenger ship will typically have a long rolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a rolling period of 6 to 8 seconds.

From My Sea Time: Q.What is roll period of a ship and on what factors does it depends ?

Roll Period Time (T) = (K * Beam^2) / sqrt (GM)

Or, from wiki:

T = 2pik / sqrt(gGM)
g = gravitational acceleration
k = radius of gyration about longitudinal axis
GM = stability index

Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a given axis, depending on the relevant application. It is actually the perpendicular distance from point mass to the axis of rotation.

Now, I had written in the previous stability related article that ...

"I was out, I calculated that total weight of Ark with load when waterline was 15 cubits up was 50,970 metric tons. I took into account that there were three storeys on Ark, and considering foot tons and calculating for even distribution of weight over three storeys, I got it to a centre of gravitation of either 21.37 feet above keel/bottom, if lowest storey count as ten feet up, or if the foot tons are zero because the height is zero, 18 feet above bottom."

18 - 21 feet up = centre of gravitation.



Problem is, what distance values do I take into account for root mean square distance to the point marked 18/21?

I'll go with three points on the height times three points on the sides. Nine points overall in their distance to the centre of gravitation.

In the middle, where diagonality is not an issue, the three points are high, middle and low. Not marked.

60 - 21 = 39	60 - 18 = 42
30 - 21 = 9	30 - 18 = 12
21	18

Each side has same values, so each following value is counted twice in the mean. High, middle, low on each side is abbreviated as h, m, l.

392 + 502 = h2	422 + 502 = h2
92 + 502 = m2	122 + 502 = m2
212 + 502 = l2	182 + 502 = l2
1521 + 2500 = 4021 = h2	1764 + 2500 = 4264 = h2
81 + 2500 = 2581 = m2	144 + 2500 = 2644 = m2
441 + 2500 = 2941 = l2	324 + 2500 = 2824 = l2
1521 + 81 + 441 + 2(4021 + 2581 + 2941) = 21129	1764 + 144 + 324 + 2(4264 + 2644 + 2824) = 21696
21129 / 9 = 2347.67	21696 / 9 = 2410.67
sqrt(2347.67)= 48.45	sqrt(2410.67) = 49.10
2 * 48.45 * pi = 304.42	2 * 49.10 * pi = 308.50
32.174 ft/s2 * 21 = 675.654	32.174 ft/s2 * 18 = 579.132
sqrt(675.654) = 26	sqrt(579.132) = 24.07
304.42 / 26 = 11.71	308.50 / 24.07 = 12.82

So, unless I totally got the way of calculating radius of gyration wrong, the rolling period of the Ark, according to the formula given in wiki, would have been between 11.71 and 12.82 seconds. Recall that first sentence?

A passenger ship will typically have a long rolling period for comfort, perhaps 12 seconds while a tanker or freighter might have a rolling period of 6 to 8 seconds.

In other words, God saw to it, they were fairly comfy on the Ark, whenever the natural rolling period prevailed!

On the road to St James, on a day when I was crying, a man trying to comfort me told me "God gives his what they need, but not too soon / just a little less, so they don't feel spoiled". God measly? Er, no.

If I got the calculation right, the rolling period of the Ark was that of a passenger ship, or even somewhat slower.

Of course, I am not a ship captain and can have got it wrong, but if you are into ships, see for yourself!

Hans Georg Lundahl
Nanterre UL
St. Narnus of Bergamo
27.VIII.2018

Bergomi sancti Narni, qui, a beato Barnaba baptizatus, primus ab ipso ejusdem civitatis Episcopus ordinatus est.