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    Crossbow limb's stiffness

    Let's estimate the stiffness of the crossbow limb. Will consider the limb as a bending beam, which is clamped on the one side and free on the other (console beam). The force F is applied orthogonal to the free end.

    crossbow arm stiffness scheme.PNG

    The stiffness of the spring in general is a ratio of applied force to deformation. Say, the spring was loaded with 100 Newton force and it got deformation 1 cm (0.01 meters), then the stiffness is:

    C=FΔ=1000.01=104NmC = \frac{F}{\Delta} = \frac{100}{0.01} = 10^{4}\quad \frac{N}{m}