Design Factors
If a limb is 'straight' its effective length remains the same as the bow is drawn. That is, the string goes directly to the nock in the strung (braced) position. When the limb is recurved (tip of limb away from the archer), the string touches the limb before it gets to the nock. The effective length of the limb, as the draw commences, is therefore shorter. However, as the bow is drawn, the recurve 'unwinds', the limb becomes effectively longer, and the mechanical advantage of the archer increases. Counter to this, stresses are building up in the materials of the limb. The belly of the bow (nearest the archer) is in compression, the back (furthest away from the archer) is in tension, and the line between is in shear.
The materials must withstand these stresses, store the energy, and rapidly give back that energy efficiently. The amount of energy stored is determined by the stresses withstood and the shape of the limb, from the unstrung position to strung (consider as pre-stressed), then de-formed further to full draw as the recurve unwinds. These basic principles of changing mechanical advantage, to efficiently store more energy, and deliver it to accelerate the arrow, were clearly understood in antiquity, as shown by the examples that follow.
Read more about this topic: Bow Shape
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