The hen's EGG: Shell forces at impact and quasi‐static compression

1. An equation is derived which relates the maximum force, P_m , exerted on an egg shell to the relative velocity, v₀ , of the egg and a body on which it impacts and to their masses, M₁ and M₂ , and stiffnesses, S₁ and S₂ ; it is

2. Another equation is derived which relates the maximum force exerted by the egg to the reciprocals, R_a and R_e , of its average and first principal curvatures at the point of impact, to the shell thickness, T_ε , that is effective in respect of tensile strength, and to the ultimate strength of shell material, St_u ; it is P_m = kStuT_εR^χ _α(Ra/Re)y in which k, χ and y are constants.

3. These equations are shown to be concordant with published data on egg shell fracture under both quasi‐static and dynamic conditions when x and y have the values — 1 and 0 respectively.

4. The equations provide a theoretical structure that can be used to identify the factors likely to affect egg shell fracture under specified conditions.