William John Macquorn RankineFRSEFRS (/ˈræŋkɪn/; 5 July 1820 – 24 December 1872) was a Scottish mathematician and physicist. He was a founding contributor, withRudolf Clausius andWilliam Thomson (Lord Kelvin), to the science ofthermodynamics, particularly focusing on its First Law. He developed theRankine scale, a Fahrenheit-based equivalent to the Celsius-basedKelvin scale of temperature.
Rankine developed a complete theory of thesteam engine and indeed of all heat engines. His manuals of engineering science and practice were used for many decades after their publication in the 1850s and 1860s. He published several hundred papers and notes on science and engineering topics, from 1840 onwards, and his interests were extremely varied, including, in his youth,botany,music theory andnumber theory, and, in his mature years, most major branches of science, mathematics and engineering.
He was also a singer, pianist and cellist as well as a rifleman.[1][2]
Rankine was born inEdinburgh to Lt David Rankin (sic), a civil engineer from a military background, who later worked on theEdinburgh and Dalkeith Railway (locally known as the Innocent Railway).[2][3] His mother was Barbara Grahame, of a prominent legal and banking family.
His father moved around Scotland on various projects and the family moved with him. William was initially educated at home, due to his poor health,[4] but he later attendedAyr Academy (1828–29) and then theHigh School of Glasgow (1830). Around 1830 the family moved to Edinburgh when the father got a post as Manager of the Edinburgh to Dalkeith Railway. The family then lived at 2 Arniston Place.[5]
In 1834 he was sent to theScottish Naval and Military Academy on Lothian Road in Edinburgh[6] with the mathematician George Lee. By that year William was already highly proficient in mathematics and received, as a gift from his uncle,Isaac Newton'sPrincipia (1687) in the original Latin.
In 1836, Rankine began to study a spectrum of scientific topics at theUniversity of Edinburgh, includingnatural history underRobert Jameson andnatural philosophy underJames David Forbes. Under Forbes he was awarded prizes for essays on methods of physical inquiry and on theundulatory (or wave) theory of light. During vacations, he assisted his father who, from 1830, was manager and, later, effective treasurer and engineer of theEdinburgh and Dalkeith Railway which brought coal into the growing city. He left the University of Edinburgh in 1838 without a degree (which was not then unusual) and, perhaps because of straitened family finances, became anapprentice to SirJohn Benjamin Macneill, who was at the time surveyor to theIrish Railway Commission. During his pupilage he developed a technique, later known asRankine's method, for laying out railway curves, fully exploiting thetheodolite and making a substantial improvement inaccuracy and productivity over existing methods. In fact, the technique was simultaneously in use by other engineers – and in the 1860s there was a minor dispute about Rankine's priority.
The year 1842 also marked Rankine's first attempt to reduce the phenomena ofheat to amathematical form but he was frustrated by his lack of experimental data. At the time of Queen Victoria's visit to Scotland, later that year, he organised a largebonfire situated onArthur's Seat, constructed with radiating air passages under the fuel. The bonfire served as a beacon to initiate a chain of other bonfires across Scotland.
From 1855 he was Professor of Civil Engineering and Mechanics atGlasgow University.[3]
He died at 8 Albion Crescent (now called Dowanside Road), Dowanhill, Glasgow at 11:45pm on Christmas Eve, 24 December 1872, aged only 52.[7] He was unmarried and had no children. His death was registered by his uncle, Alex Grahame (his late mother's brother in law).
Rankine studied the mechanics of theheat engine. Though his theory of circulating streams of elastic vortices whose volumes spontaneously adapted to their environment sounds fanciful to scientists formed on a modern account, by 1849, he had succeeded in finding the relationship betweensaturated vapour pressure andtemperature. The following year, he used his theory to establish relationships between the temperature,pressure anddensity ofgases, and expressions for thelatent heat ofevaporation of aliquid. He accurately predicted the surprising fact that the apparentspecific heat ofsaturated steam would be negative.[8]
Emboldened by his success, in 1851 he set out to calculate the efficiency of heat engines and used his theory as a basis to deduce the principle, that the maximum efficiency possible for any heat engine is a function only of the two temperatures between which it operates. Though a similar result had already been derived byRudolf Clausius andWilliam Thomson, Rankine claimed that his result rested upon his hypothesis of molecular vortices alone, rather than upon Carnot's theory or some other additional assumption. The work marked the first step on Rankine's journey to develop a more complete theory of heat. In 1853, he coined the termpotential energy.[9]
Rankine later recast the results of his molecular theories in terms of a macroscopic account ofenergy and its transformations. He defined and distinguished betweenactual energy which was lost in dynamic processes andpotential energy by which it was replaced. He assumed the sum of the two energies to be constant, an idea already, although surely not for very long, familiar in the law ofconservation of energy. From 1854, he made wide use of histhermodynamic function which he later realised was identical to theentropy of Clausius. By 1855, Rankine had formulated ascience ofenergetics which gave an account of dynamics in terms of energy and its transformations rather thanforce andmotion.[10] This article presents the first published definition of energy in terms of capacity for performing work,[11] which quickly became the standard general definition of energy.[12] The theory was very influential in the 1890s. In 1859 he proposed theRankine scale of temperature, an absolute or thermodynamic scale whose degree is equal to aFahrenheit degree. In 1862, Rankine expanded Lord Kelvin's theory of universalheat death and, along with Kelvin himself, formulated theheat death paradox, which disproves the possibility of an infinitely old universe.[13]
Energetics offered Rankine an alternative, and rather more mainstream, approach, to his science and, from the mid-1850s, he made rather less use of his molecular vortices. Yet he still claimed that Maxwell's work on electromagnetics was effectively an extension of his model. And, in 1864, he contended that the microscopic theories of heat proposed by Clausius andJames Clerk Maxwell, based on linear atomic motion, were inadequate. It was only in 1869 that Rankine admitted the success of these rival theories. By that time, his own model of the atom had become almost identical with that of Thomson.
As was his constant aim, especially as a teacher of engineering, he used his own theories to develop a number of practical results and to elucidate their physical principles including:
TheRankine cycle, an analysis of an ideal heat-engine with a condensor. Like other thermodynamic cycles, the maximum efficiency of the Rankine cycle is given by calculating the maximum efficiency of theCarnot cycle;
Properties of steam, gases and vapours.
The history ofrotordynamics is replete with the interplay of theory and practice. Rankine first performed an analysis of aspinning shaft in 1869, but his model was not adequate and he predicted that supercritical speeds could not be attained.
Rankine was one of the first engineers to recognise thatfatigue failures of railway axles was caused by the initiation and growth of brittle cracks. In the early 1840s he examined many broken axles, especially after theVersailles train crash of 1842 when a locomotive axle suddenly fractured and led to the death of over 50 passengers. He showed that the axles had failed by progressive growth of a brittle crack from a shoulder or otherstress concentration source on the shaft, such as akeyway. He was supported by similar direct analysis of failed axles byJoseph Glynn, where the axles failed by slow growth of a brittle crack in a process now known asmetal fatigue. It was likely that the front axle of one of the locomotives involved in theVersailles train crash failed in a similar way. Rankine presented his conclusions in a paper delivered to the Institution of Civil Engineers. His work was ignored however, by many engineers who persisted in believing that stress could cause "re-crystallisation" of the metal, a myth which has persisted even to recent times. The theory of recrystallisation was quite wrong, and inhibited worthwhile research until the work ofWilliam Fairbairn a few years later, which showed the weakening effect of repeated flexure on large beams. Nevertheless, fatigue remained a serious and poorly understood phenomenon, and was the root cause of many accidents on the railways and elsewhere. It is still a serious problem, but at least is much better understood today, and so can be prevented by careful design.
Rankine was instrumental in the formation of the forerunner ofGlasgow University Officer Training Corps, the 2nd Lanarkshire Rifle Volunteer Corps at Glasgow University in July 1859, becoming Major in 1860 after it was formed into the first company of the 2nd Battalion, 1st Lanarkshire Rifle Volunteer Corps; he served until 1864, when he resigned due to pressure of work – much of it associated with Naval Architecture.
Rankine worked closely with Clyde shipbuilders, especially his friend and lifelong collaboratorJames Robert Napier, to make naval architecture into an engineering science. He was a founding member, and first President[14] of theInstitution of Engineers & Shipbuilders in Scotland in 1857. He was an early member of theRoyal Institution of Naval Architects (founded 1860) and attended many of its annual meetings. With William Thomson and others, Rankine was a member of the board of enquiry into the controversial sinking ofHMSCaptain.
^ Complete List of the Members & Officers of the Manchester Literary & Philosophical Society.From its institution on February 28th 1781 to April, 1896.
