Murphy was the first airman on the RAAF's strength when it formed in 1921, and rose to the rank of temporary air commodore during World War II, commanding No.

Having been employed at various engineering firms, Murphy joined the Australian Army's Aviation Instructional Staff at Central Flying School Point Cook in 1914 to train as an air mechanic.

[6][7] On 12 August, he and his observer were selected to join Colonel T. E. Lawrence and his irregular Arab army in the Hejaz near Daraa, providing air cover and reconnaissance.

[8] Credited with bringing down two enemy aircraft while supporting Lawrence's troops, Murphy was awarded the Distinguished Flying Cross for his "keenness, reliability and boldness".

[2] Later that year he took part in the first transcontinental flight across Australia, from Melbourne to Darwin, Northern Territory, accompanying pilot and former schoolmate, Captain Henry Wrigley.

The pair departed Point Cook on 16 November and arrived in Darwin on 12 December, having travelled 4,500 kilometres (2,800 mi) in forty-seven flying hours.

They flew in a single-engined Royal Aircraft Factory B.E.2 with no radio, over unmapped and often hazardous terrain, and surveyed seventeen potential landing grounds along the journey.

[4][11] Such was the perceived danger of the expedition that while making preparations for the return flight they received a telegram from the Defence Department ordering them to desist, arrange for the B.E.2 to be dismantled and shipped back, and themselves to travel southwards by steamer.

[5] Murphy married Alicia Shoebridge at Erskine Presbyterian Church in South Carlton, Melbourne, on 17 October 1922; the couple had two sons and a daughter.

3 Squadron under Flight Lieutenant Frank Lukis, when it became the first flying unit to be based at the recently opened RAAF Station Richmond, New South Wales.

[14] Promoted to flight lieutenant, Murphy was posted to the RAAF Experimental Section under Wing Commander (later Sir) Lawrence Wackett in November 1926.

Towards the end of 1935, he was responsible for specially modifying a Westland Wapiti and a de Havilland Gipsy Moth for Antarctic conditions, to enable an Air Force team led by Flight Lieutenant (later Group Captain) Eric Douglas and Flying Officer (later Air Marshal Sir) Alister Murdoch to rescue explorer Lincoln Ellsworth, who was presumed lost on a journey across the continent.

Murphy was, according to Winneke, "a product of the old school of airmen who could not only fly a plane but also pull it apart and put it together again", generally "amiable" but who "could act gruffly when the occasion demanded".