Egyptian crescent-shaped sailing boats
                                               A  typical problem of short-plank boats

Given two rectangular ´ships´. One a straight ´longship´, the other a typically crescent-
shaped egyptian river boat. Both loaded with a granite block of 12000 kg in the midst.
Both boats lay over a length of 10 meters in water. The longship immerse 0.6 m and
the crescent-shaped one 1 m into the water.

It is shown that the typically in a crescent-shaped manner bent river boat is less
endangered by tensions along the hull than a straight-lined boat.
(An ingenious idea to construct * optimal* riverboats if only short planks are available)
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A short calculation

            

Supposed a swimming rectangular * bark* (10 x 2m) loaded midship with 12000 kg.
Thereby 12 cbm water becomes displaced and the  ´ship´  will  submerge by 0.6m
(Druck: Pressure, Zug: Tension)
Notice: The  bow and stern of Egyptian riverboats extends far over the water surface.

If the load of 12000 kg is stored in the middle of the boat  a tension develops, which
press the boat´s nose and tail straight upward .The bouyancy forces are evenly
distributet along the boat length.The sum of these forces multiplied by the lever arm of
effort makes  3000 kg. This tension endangers the lower parts of the hull.l (Zug--Zug). .

The same load in a boat with a curved hull submerging also along 10 meters. I.e. the
same 10 m as in the rectangular boat above, but in a curved hull the bouyancy forces 
are not evenly distributed.
The  bouyancy forces along the 10 meters are maximal in the middle of the boat and
decrease continously  to a minimum at  nose (bow) and tail (stern). Due to the unevenly
distributed bouyancy forces the sum of the corresponding lever forces amounts to
2000 kg only
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Besides bending another ingenious technical trick: The  bow and stern of egyptean
riverboats extends far over the water surface. Thereby the weight of the protruding
bow and stern counteract the bending bouyancy forces along the hull.

These ´protruding´ gravidity-forces will increase if parts of the midship load of 12000 kg
are put to the ship´s ends. For instance only 11000 kg in the midst but 2 x 500 kg at
 bow and stern.

The tracting forces of these  protruding parts -pressing downwards- might  be so strong
that the upper half of the hull may disrupt. Therefore a rope had been streched across
the deck from bow to stern  in order to take up  the ´problematic´ tracting forces along
the upper half of the hull. This *clamping rope* has been frequently depicted.

Facit:  The original lever arm of strength of 3000 kg along a ´longboat´s hull´ is reduced
to 2000 kg due to the crescent- shaped form of the typical eygytean river boat. 500 kg 
put on the projecting nose and tail will reduce the tension along the base of the hull by
further 700 kg.

Compared with a * long ship* a crescent-shaped hull combined with a protruding
bow and stern - both loaded with 500 kg - reduce the calculated traction powers
along the hull  from 3000 to 1300 kg. (Factor : 2.3)
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A technical problem:

The wind on a sail presses the mast food down on the base of a ship. Forces develop
in direction  comparable  with a heavy  load in  the center of a ship.  (s.a) To avoid these
dangerous tracting forces the mast was set at the bow head.

                                                        Crete 1700 BC
   
          a b

a ) The Discus of Phaestos. A longship with a sternpost. At top a crossbar.
An old japanese sailing boat.  b) The Phaestos ship. c)  the sternpost with a
square rigged sail.( by me). A sail and oar vessel. For sailing wind behind is needed
It could be that at earlier  times the hull was´t strong enough to withstand the tracting
 forces of a  midsmast (s.0255 a)

                          

Midsmast with wind behind. The arrows show the corresponding thrust forces at the
mast and  the traction between top of mast and stern.
a) A normal sailing boat. The foot of a mast pressing amids against lengthwise timber
along the base of a ship. Consequently the bow dips more deeply into the water thereby
counteracting the ´bending´ forces of the propelling  forces of the wind.( The traction
forces along the hull are compareable to the granitblock above.)
b) The mast at the bow head. No bending forces between mast food and ship´s base (keel.)
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                                             Egypt 1400 -1500 BC
                            with time  the mast ´moved´  from bow head to midship

                     

 a) An egyptian river boat about 1500 BC. Protruding stem and stern. Mastfood close
to  the front region where the bow head diped into the water. (Vertical sail.)
b) More later about 1400 BC the hull meanwhile more stiff allowing a mast in midship
position.(Horizontal sail.)

It is questionable whether these ships were seaworthy. Navigation of a more crescent
shaped sailing boat is possible only if the wind comes from the rear. I.e. only the north
wind prevailing at the Nile allowed a problem-free travel the river upward.

It is not possible to sail close to the wind. A cross-wind or a wave easily push the ship
towards the river bank or even more dangerous in open sea widthwise to wind and
waves. (An old experience :  Only a ´longship´ runs straight (Nur lang laeuft)

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