Hankinson’s equation describes the compressive strength of wood, as a function of the angle, relative to the grain of the wood, at which that stress is applied.

Suppose that σ0 is the compressive strength of wood when the stress is applied parallel to the wood grain, and σ90 < σ0 is the compressive strength when the stress is applied at right angle to the grain.

Let σ(α) denote the compressive strength when the stress is applied at angle α to the grain. Then, Hankinson’s equation says

σ(α) =

σ0σ90

σ0 sin2 α + σ90 cos2 α

.

a. Calculate σ when α = 0 and when α = π/2. Do your values make sense?

b. Calculate σ if σ0 = σ90. Does your answer make sense?

c. Calculate σ

0

(α).

d. Where are the maxima and minima of σ? What are the maxima and minima?

e. Is it possible to find a value for α such that σ(α) is not between σ0 and σ90?

f. Google values for σ0 and σ90 and plot σ. Choose your domain so as to illustrate your answers to

(d) and

(e) above.

A rod is a photoreceptor, which is a type of cell in the retina that detects light. They are discussed in slightly more detail at the beginning of this chapter, on page 337. Salamander rods are not identical to human rods, but there are still many similarities.