text: Compressor performance changes, day to day, with changes in the ambient pressure and temperature. Woolenweber shows the change in performance of a turbocharger compressor when the inlet temperature varies between 70 and 100 deg F. In the case of aircraft compressors, inlet pressure and temperature also change with altitude and airspeed. The presentation of different performance for every combination of inlet temperature and pressure would be unmanageable but it is possible to collapse it all onto a single map, which is applicable to a wide range of inlet conditions, using dimensional analysis. In dimensional analysis individual quantities such as rotor speed, mass flow and delivery pressure are each grouped with other relevant quantities in such a way that the groups have no dimensions but still have a physical meaning. For example rotor speed , inlet temperature , compressor diameter  and gas properties  and  are grouped together as dimensionless  which is equivalent to the blade mach number.
  Parameter groups which are used as the basis for gas turbine engine compressor maps are total-pressure ratio (P/P), <math>w
  \sqrt{\gamma \ R \ T}/{AP} and efficiency. , for example, is simplified below while still being representative of mach number. Maps for other applications use head or discharge pressure and volume flow.
  For a particular compressor and gas the flow and speed groups are simplified, by deleting the terms which are constant for a particular compressor and application, namely compressor dimensions and gas properties , ,  and . They are named pseudo-non-dimensional parameters  and .
  A final step is to give the pseudo-non-dimensional parameters standard units for mass flow and speed and more recognizable numerical values by applying pressure and temperature ratio correction factors, also derived as part of the dimensional analysis.
  The corrected parameters are  and . They have the same units as the original observed values and are corrected to agreed standard conditions, the International Standard Atmosphere at sea level (ISA SL). Alternatively they may be shown relative to the design value where the design value is specified as either 100% or 1.0.
  The fuel burned in a gas turbine engine sets the compressor running line and also has to be used in non-dimensional form to show its effect on engine operation. It is used as a ratio with combustor pressure when shown on a compressor map. Corrected fuel flow is shown as      . Although both air and fuel are flows of fluid their non-dimensional parameters are different,  and  , because non-dimensional airflow is a form of fluid Mach number while fuel is flow of an incompressible energy source. The dimensions of airflow are M/t and those of fuel-flow are ML/t, where M, L and t are mass, length and time.
  Fuel flow is also shown on a compressor map, but in the form of its effect, ie turbine inlet temperature. This effect is shown, again non-dimensionally, as the ratio of turbine inlet temperature to compressor inlet temperature, and known as engine temperature ratio. Grandcoing shows the constant temperature lines crossed as a helicopter compressor goes from no-load to full-load with increasing fuel flow.