The importance of matching arrow to bow is illustrated by the photographs below, taken by a slow motion camera during the Warbow trials at The Defence Academy.
The arrow has to pass around the bow, clearing it so that it's flight is not affected by hitting the riser, and then straighten up quickly, helped by the spinning action induced by the fletchings. The arrow is therefore 'spined' to match the bow. With wide bows (e.g. the English longbow) the arrow is usually more flexible (ie of lower spine) than for bows which have a cut away on the riser.
At full draw the arrow is already slightly bent against the bow, induced by the rolling of the fingers on the string.
At the moment of release, pictured left, the arrow bends around the bow.
The arrow must clear the bow, and then straighten sufficiently early to head for the target without 'gadding' from side to side (too whippy a spine) or, for a right handed archer, flying to the left (too stiff).
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