The following is for traditional bows, only.
There is a difference in the paradox for a given bow, depending on design, speed of the bow, the amount cut past center, point weight, string weight etc. Shooting a longbow with the least amount of center shot would normally take a weaker spine than a faster bow.
I would suggest reading the article by Denny Sturgis Jr. in Traditional Bowhunter, Feb/Mar, pages 78-79. It is about paper tuning, but if you read further, he tells the reader how to adjust for a weak, or stiff spine.
Also read:
http://elitearrows.com/proper-arrow/ Keep in mind that wood arrows are spined at 26" centers and Aluminum and Graphite on 28". Wood arrows generally have a specific spine and tolerance for correction and graphite the greatest. That means, a 50# longbow may only shoot arrows spined for 55-60#, 50-55#, or 45-50 depending the draw wt, draw length and length of shaft. You will find a spine chart, and conversion for the three different shafts, at:
http://oakcreekarchery.com/ocapages/spine/docs/arrow_translation.pdf