This forum occasionally ponders the application of science to corporal punishment. Some regular contributors are very good at explaining the physics involved and I would be pleased if they would comment on impedance matching, a term familiar in electronics.
The principle in electronics is to maximise the transfer of power from the source to the destination and minimise reflection of energy back to the source. I believe the same principle applies in mechanics. Certainly if you strike a cane on a hard surface, you feel a shock reflected back into your arm
Canes come in a range of flexibilities from very supple to relatively stiff. The elasticity of the bottom varies between individuals and according to the degree to which they are bending over. How might we determine which is the best combination of flexibility of cane and elasticity of target to give the best transfer of energy?
Off-topic: If "Your Local Council", my former colleague at the Bletchley Biscuit Company and onetime school pupil in North West London cares to e-mail me, I have something that may be of interest to you.