EQUIVALENT AIR DEPTH
DEFINE the Equivalent Air Depth EAD(d,r) for a mix with r% nitrogen at a depth d as the depth at which an air mixture would have the same nitrogen partial pressure as does the mix in question at the depth d.
Recall that the partial pressure of nitrogen in our mix will be P(r,d) = [1 + d/33] * r.
Similarly, the partial pressure of nitrogen in an air mix at the EAD will be P(.79,EAD) = [1 + EAD/33] * 0.79.
Using the definition for EAD, we note that the EAD occurs when these two terms are equal:
[1 + EAD/33] * 0.79 = [1 + d/33] * r
We can simplify this as follows:
[1 + EAD/33] = r/0.79 * [1 + d/33]
EAD/33 = {r/0.79 * [1 + d/33]} -1
EAD = 33 *({r/0.79 * [1 + d/33]} -1)
or, EAD = [r/0.79 * (d + 33)] - 33
(The last expression is the same as that on page 80 of your manual.)