A compressor map in the standard format with pressure ratio over corrected flow cannot be used directly in a performance calculation program. It is not always possible to read efficiency from such a map with given speed N/sqrt(T1) and flow W*sqrt(T1)/P1 because in a part of the map the speed lines can be vertical. It is also not possible to read the map with given speed N/sqrt(T1) and pressure ratio P2/P1 because it might be, that there are two values for corrected flow at a given pressure ratio P2/P1.
The solution to the problem is to introduce auxiliary coordinates (here called beta lines) which intersect the speed lines. This mathematical trick allows reading the map independent from the shape of the lines with given beta and speed N/sqrt(T1).
From principle the beta grid can be selected arbitrarily as long as there are unambiguous intersections of the beta lines with the speed lines. In Smooth C the beta-