The modulus of elasticity of a wood fixes the relation between curvature, thickness and stress. Any given wood has a certain modulus of elasticity.

For any given draw:—

Bow length limits curvature.

Limb curvature limits thickness (for any given wood).

Thickness determines stress (for any given wood).

Thickness then practically determines the cast of the bow (for any given wood).

Width fixes power of bow.

The algebraic interrelationship between these factors

When

R is the radius of curvature in inches at any point;

T the thickness in inches at that point;

E is the modulus of elasticity of the material;

(I use 1,000,000[1] for yew and over 1,200,000 for Osage)

S is the fiber stress in pounds per square inch;

(I use 10,000 for yew and not over 15,000 for Osage)

As E and S are inherent in the wood, the relationship between R and T is fixed and the bow must conform to it. For example, with yew, R/T should exceed 50.