The use of Dimensional Analysis for aero-engine superchargers seems to have (at least in Britain) been first published on by employees of the Royal Aircraft Establishment at Farnborough, England. (The R.A.E.).
The first paper was written by R. S. Capon. in May 1928:
“Note on dimensional relationships for air compressors“
(Available at the National Archives: DSIR-23/8539)
Here, Capon describes what the purpose of this study was:
“Dimensional relationships are derived by which the performance of a compressor may be deduced at one set of intake conditions from tests at another.”
In other words, with respect to aircraft superchargers, it would be very useful to understand how the compressor might behave when in flight at high altitude, where the inlet temperature and pressure were totally different to the laboratory at sea-level where it had been originally designed and tested. While it is possible to construct a “high altitude test chamber”, where cold air at varying pressures is supplied, such apparatus becomes extremely expensive and complex with large compressors, as the power needed to pump down the pressure, and refrigerate the inlet air of several cubic meters per second become significant.
Therefore being able to work out the performance using only analytical means was seen as extremely useful.
Two more papers were published soon after:
“Tests on the Application of Dimensional Relationships to a Centrifugal Air Compressor” by Taylor, Brooke and Bargman, January 1930.
(Available at the National Archives: AVIA-6/11241)
“The Application of Dimensional Relationships to Air Compressors, with special reference to the Variation of Performance with Inlet Conditions” by Capon and Brooke, June 1930.
(Available at the National Archives: DSIR-23/8651)
When Stanley Hooker joined Rolls-Royce, he set about improving the Merlin supercharger, and eventually designed the two-stage compressor used in the Merlin-60 onwards. One of the things Hooker did was to use the Capon & Brooke papers to assist him.
“Another landmark is 1938, when S.G. (Stanley) Hooker joined the company as an assistant to Ellor. He applied the non-dimensional method of supercharger performance analysis which had been put forward eight years earlier by Capon & Brooke.”*
*See Royal Aeronautical Society Journal: Centenary Edition 1966, pg161, column 2.