Cabin Altitude & Differential Pressure Equation?

[PA32]

Some of the Aircraft Flight Manuals I have contain a "Cabin Altitude for Various Airplane Altitudes" graph in them. Typically, the Aircraft Altitude is on the y-axis, going from 0 to about 50,000 feet; and the Cabin Altitude is on the x-axis. Then there are a series of diagonal lines on the graph which are labeled 0 Diff Press (delta p), 1 PSI Diff Press, 2 PSI Diff Press, on up through about 10 PSI delta p. (Which is about as good as the best pressurization system gets on the fanciest bizjets.) The 0 delta p line is perfectly linear (of course), and the other delta p lines, below about 5 PSI delta p, are "close to" linear at the lower altitude ranges (below about 25,000 feet). Above this, the lines get progressively more non-linear.

Can anyone tell me what the equation is that determines the values on this chart? i.e., if I did not have the chart handy, and if I knew my current aircraft altitude (in feet), and my current cabin differential pressure (in PSI), and wanted to calculate my predicted cabin altitude (in feet) based on these factors, what equation would I use?

 

[mfb]

The 0 delta p line is perfectly linear (of course)

This is not trivial, it depends on the scaling of the axes.

Can anyone tell me what the equation is that determines the values on this chart? i.e., if I did not have the chart handy, and if I knew my current aircraft altitude (in feet), and my current cabin differential pressure (in PSI), and wanted to calculate my predicted cabin altitude (in feet) based on these factors, what equation would I use?

Pressure outside roughly follows an exponential function, see Wikipedia for an introduction.