Tim Lovett April 2004. Original Excel calculation by Jim King 2004.
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STILL WATER BENDING MOMENT
Uneven Loading
If all the cargo was stored in the middle of the ship, the hull would experience bending (sagging) even without waves (still water). For this reason, the loading and unloading of a cargo ship must be carefully monitored to ensure the loads are within safe limits. In the case of Noah's Ark, the cargo is not very dense, (e.g. iron ore), so uneven loading is not much of a problem. The water and food storage would be the heaviest loads on the ark, and it would be prudent to distribute this cargo in sealed storage areas throughout each level. This saves handling and makes it easier to control vermin, with the added benefit of a controlled static loading as food is consumed during the voyage.
Uneven Buoyancy
The ideal loading situation is when the cargo matches the buoyancy forces of the hull along its entire length. This can be difficult when the hull is a streamlined shape. Noah's Ark was probably not like this, so buoyancy is expected to be fairly constant throughout the length of the vessel.
Still Water Bending Moment Conclusions
The following calculations (Jim King) indicate static loading is negligible compared to the wave bending moment. The highest static moment (2250 tf.m) does not occur near the center where the wave bending moment is maximum, but lower values of 1800 to 1900 tf.m. These are calculated at station 9 should be added to the wave bending moment.
Static Bending Moment = 1873 / 66750 = 2.8% of wave bending moment.
Hence the static bending moment adds only 3% to the wave bending moment in the worst case. However, since sagging dominates wave bending (ABS), the hogging effect of the static loading actually reduces the total bending moment slightly. The static loading acts to equalize the ABS wave loading.
Summary
Maximum Bending Moments.
|
Type |
Hogging (tf.m) | Sagging (tf.m) |
| ABS Wave BM | 67 009 | - 65 071 |
| Static BM | 1 907 | 1 770 |
| Net BM | 66 979 | -65 238 |
So in this arrangement, static bending moment is negligible.
CALCULATIONS
Estimated Ark Loading. For more details see Cargo
| Hull | 5333 | tf |
| Water | 2000 | tf |
| Dry Food (grain) | 2400 | tf |
| Dry Food (Hay) | 600 | tf |
| Enclosures | 4000 | tf |
| Ramps | 200 | tf |
| Passages | 200 | tf |
| Animals | 400 | tf |
| Weight | 15133 | tf |
Loads were estimated for 20 stations along the length of the Ark. This approximation assumes a more open area at bow and stern, where the structure is less critical. At this early design stage, this is assumed to be the best place to put access ramps, ventilation shafts, pumps, winches etc. Another advantage is that the ride is more comfortable amidships, so this is where the animals would be best located.
| Shear and Net Bending Moments | |||||||||||||||||
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| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 6.86 | 680.985 | 266.65 | 240 | 60 | 50 | 10 | 626.65 | -54.335 | -372.738 | 8133.936 | -8376.09 | 7761.198 | -8748.83 | |||
| 2 | 13.72 | 765.0572 | 266.65 | 240 | 60 | 50 | 10 | 626.65 | -138.407 | -1322.21 | 16267.87 | -16752.2 | 14945.66 | -18074.4 | |||
| 3 | 20.58 | 755.7159 | 266.65 | 240 | 60 | 250 | 10 | 25 | 851.65 | 95.93414 | -664.103 | 24401.81 | -25128.3 | 23737.71 | -25792.4 | ||
| 4 | 27.44 | 756.7538 | 266.65 | 240 | 60 | 250 | 10 | 25 | 851.65 | 94.89621 | -13.1155 | 32535.75 | -33504.4 | 32522.63 | -33517.5 | ||
| 5 | 34.30 | 756.6385 | 266.65 | 200 | 240 | 60 | 250 | 10 | 25 | 1051.65 | 295.0115 | 2010.664 | 40669.68 | -41880.5 | 42680.35 | -39869.8 | |
| 6 | 41.16 | 756.6513 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5.00128 | 1976.355 | 48803.62 | -50256.6 | 50779.97 | -48280.2 | |||
| 7 | 48.02 | 756.6499 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -4.99986 | 1942.056 | 56937.55 | -58632.6 | 58879.61 | -56690.6 | |||
| 8 | 54.88 | 756.65 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5.00002 | 1907.756 | 65071.49 | -67008.7 | 66979.25 | -65101 | |||
| 9 | 61.74 | 756.65 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5 | 1873.456 | 65071.49 | -67008.7 | 66944.95 | -65135.3 | |||
| 10 | 68.60 | 756.65 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5 | 1839.156 | 65071.49 | -67008.7 | 66910.65 | -65169.6 | |||
| 11 | 75.46 | 756.65 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5 | 1804.856 | 65071.49 | -67008.7 | 66876.35 | -65203.9 | |||
| 12 | 82.32 | 756.65 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5 | 1770.556 | 65071.49 | -67008.7 | 66842.05 | -65238.2 | |||
| 13 | 89.18 | 756.65 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5 | 1736.256 | 56937.55 | -58632.6 | 58673.81 | -56896.4 | |||
| 14 | 96.04 | 756.65 | 266.65 | 200 | 250 | 10 | 25 | 751.65 | -5 | 1701.956 | 48803.62 | -50256.6 | 50505.57 | -48554.6 | |||
| 15 | 102.90 | 756.65 | 266.65 | 250 | 10 | 25 | 551.65 | -205 | 295.6557 | 40669.68 | -41880.5 | 40965.34 | -41584.8 | ||||
| 16 | 109.76 | 756.65 | 266.65 | 240 | 60 | 250 | 10 | 25 | 851.65 | 95 | 947.3557 | 32535.75 | -33504.4 | 33483.1 | -32557 | ||
| 17 | 116.62 | 756.65 | 266.65 | 240 | 60 | 250 | 10 | 25 | 851.65 | 95 | 1599.056 | 24401.81 | -25128.3 | 26000.86 | -23529.2 | ||
| 18 | 123.48 | 756.65 | 266.65 | 240 | 60 | 250 | 10 | 25 | 851.65 | 95 | 2250.756 | 16267.87 | -16752.2 | 18518.63 | -14501.4 | ||
| 19 | 130.34 | 756.65 | 266.65 | 240 | 60 | 50 | 10 | 626.65 | -130 | 1358.956 | 8133.936 | -8376.09 | 9492.892 | -7017.14 | |||
| 20 | 137.20 | 680.985 | 266.65 | 240 | 60 | 50 | 10 | 626.65 | -54.335 | 986.2176 | 0 | 0 | 986.2176 | 986.2176 | |||
| Tot | 14989.24 | 5333 | 2000 | 2400 | 600 | 4000 | 200 | 200 | 400 | 15133 | -143.764 | ||||||
Data: Jim King 2004
