William John Macquorn Rankine, (born July 5, 1820, Edinburgh, Scot.—died Dec. 24, 1872, Glasgow), Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. Trained as a civil engineer under Sir John Benjamin MacNeill, Rankine was appointed to the Queen Victoria chair of civil engineering and mechanics at the University of Glasgow (1855). One of Rankine’s first scientific works, a paper on fatigue in metals of railway axles (1843), led to new methods of construction. His Manual of Applied Mechanics (1858) was of considerable help to designing engineers and architects. His classic Manual of the Steam Engine and Other Prime Movers (1859) was the first attempt at a systematic treatment of steam-engine theory. Rankine worked out a thermodynamic cycle of events (the so-called Rankine cycle) used as a standard for the performance of steam-power installations in which a condensable vapour provides the working fluid.

1. William John Maquorn Rankine
(1820 - 1872)
Used with permission from the Institution of Civil Engineers, London
The Man
One can only wonder if the brilliance of William John Maquorn Rankine was hereditary or if
he was merely a prodigy of his time. In a lecture delivered before the British Geotechnical
Society at the University of Glasgow on December 13, 1972, Hugh B. Sutherland, Cormack
Professor of Civil Engineering from the University of Glasgow said of him:
‘Rankine was no ordinary man.’
He humbly described his task of telling of Rankine’s life and times by saying:
‘It has left me with the feeling that anything I can say is a tribute to a giant of
the past from a tiny mortal of the present."
On ending his lecture, he stated:
‘Rankine was the most wonderful combination of the man of genius and of
humor. How much more pleasant and effective is the contribution, scientific or
otherwise, when you know behind it lies a man capable of having a twinkle in
his eye.’
William John Maquorn Rankine is a name engraved in scientific annals throughout the world.
Rankine is best known for his accomplishments in thermodynamics (description of the
operational cycle of an ideal engine using steam or another vapor) and soil mechanics (earth
pressure theory). Yet another stellar attribute of this great man was his pioneering role as an
engineering educator. He was born in Edinburgh, Scotland, on July 5, 1820. His learning
consisted of a primary education taught mostly by his father and private tutors, and two
extraordinary years of schooling at the University of Edinburgh. Leaving without a degree,
Rankine set out to become a civil engineer. He apprenticed under Sir John Benjamin MacNeill,
a notable civil engineer of his time who had been Thomas Telford’s chief assistant. He
practiced the civil engineering profession until the late 1840’s, switching without hesitation to
practice mathematical physics. From 1848 to 1855, Rankine spent a great amount of his time
in researches on theoretical physics, thermodynamics and applied mechanics. On December 3,
1855, at the age of 35, Rankine was appointed by the Queen’s Commission to the Chair of
Civil Engineering and Mechanics at Glasgow - a Regius Chair established by royal decree. His
ensuing years, leading up to the time of his death, were spent as a professor and author. Rankine
imparted an immense knowledge of learned theory and practice to eager students. Authoring
111 papers and writing numerous textbooks, his respective scientific findings remain a
foundation in soil mechanics and thermodynamics today.
Civil Engineer
Very little is known today of Rankine’s work as a practicing civil engineer. However, it is
apparent he was introduced during his second year of college to the profession by his father,
David Rankine. The elder Mr. Rankine, a civil engineer, was a superintendent for the
Edinburgh and Dalkeith Railway. Young Rankine spent a year assisting his father and then he

2. left for Ireland, where he worked on railroad, hydraulic, and various other projects. After four
years in Ireland, he returned to Scotland and worked with railway companies and consultants
until about 1848.
Educator
"Pioneer with a determination" best describes William John Maquorn Rankine as an educator.
Separate from his great contribution as an author, Rankine introduced and vigorously sought
at Glasgow, a degreed program in engineering. Engineering courses in Rankine’s time were
not recognized in fulfilling any degree requirements. Rankine first pushed for an award of
Diploma in Engineering Science, but was turned down by Scotland University Commissioners.
On a second effort, Rankine endeavored for the award and got approval. Lastly to Rankine’s
effort were his success at establishing a BSc in science. Once again, Rankine’s incessant efforts
aside from his respected knowledge gained him praise throughout the world for pioneering the
engineering education.
Author
In his teaching, Rankine taught from practice and theory. His writing was no different. Rankine
authored a very successful collection of engineering textbooks. Through his books, he was able
to deliver systematic instruction in engineering. Some of his more renowned texts are A Manual
of Applied Mechanics, A Manual of the Steam Engine and Other Prime Movers, A Manual of
Civil Engineering, and A Manual of Machinery and Millwork. Without textbooks, some of
Rankine’s great works may have gone unknown--this learned from other noted historians who
have studied and documented his life. On the lighter side Rankine wrote the nontechnical
books, Songs and Fables, A Memoir of John Elder, and Engineer and Shipbuilder.
References
red before the British
Geotechnical Society at the University of Glasgow on 13 December 1972 to mark the centenary
of the death on 24 December 1872 of William John Macquorn Rankine. London: 1973.
c Biography. 1975 ed., Vol. XI,
pp. 291-295.
pp.1216-1217.
acquorn." New Encyclopedia Britannica. 1997 ed., Vol. 9, p.
939.
Prepared by Mark Brown, Dec. 1997

3. William John Macquorn Rankine, (born July 5, 1820, Edinburgh, Scot.—died Dec. 24,
1872, Glasgow), Scottish engineer and physicist and one of the founders of
the science of thermodynamics, particularly in reference to steam-engine theory.
Trained as a civil engineer under Sir John Benjamin MacNeill, Rankine was appointed to the
Queen Victoria chair of civil engineering and mechanics at the University of Glasgow (1855).
One of Rankine’s first scientific works, a paper on fatigue in metals of railway axles (1843),
led to new methods of construction. His Manual of Applied Mechanics (1858) was of
considerable help to designing engineers and architects. His classic Manual of the Steam
Engine and Other Prime Movers (1859) was the first attempt at a systematic treatment of
steam-engine theory. Rankine worked out a thermodynamic cycle of events (the so-
called Rankine cycle) used as a standard for the performance of steam-power installations in
which a condensable vapour provides the working fluid.
In soil mechanics his work on earth pressures and the stability of retaining walls was a notable
advance, particularly his paper “On the Thermodynamic Theory of Waves of Finite
Longitudinal Disturbance.”
LEARN MORE in these related Britannica articles:

dam: The 19th century
In the 1850s, William John Macquorn Rankine, professor of civil engineering at the
University of Glasgow in Scotland, successfully demonstrated how applied science could help
the practical engineer. Rankine’s work on the stability of loose earth, for example, provided a
better understanding of the principles of dam design…

soil mechanics
Soil mechanics, the study of the physical properties and utilization of soils, especially used in
planning foundations for structures and subgrades for highways.
The first scientific study of soil mechanics was undertaken by French physicist Charles-
Augustin de Coulomb, who published a theory of earth pressure in 1773. Coulomb’s work and
a theory of earth masses published by Scottish engineer William Rankine in 1857 are still

4. primary tools used to quantify earth stresses. These theories have been amended in the 20th
century to take into account the influence of cohesion, a more recently discovered property of
soils that causes them to behave somewhat differently under stress than Rankine and Coulomb
predicted.
Soil is a natural aggregate of mineral particles, sometimes including organic constituents; it has
solid, liquid, and gaseous phases. How the soil of a given site will support the stresses put upon
it by the weight of structures, or how it will respond to movement in the course of construction,
depends upon six properties—internal friction (the resistance of a soil mass to sliding, inversely
related to the amount of moisture in the soil and thus greater in sands and gravel than clays)
and cohesion (molecular attraction between soil particles, much higher in clays than sands or
silt), both of which lessen the tendency of soils to shear, or slide along
planes; compressibility (the degree to which soil may be made denser by various means
including tamping and vibration, and thus able to support greater loads); elasticity (the ability
of soil to reexpand after being compressed); permeability (the degree to which a soil will
conduct a flow of water); and capillarity (the degree to which water is drawn upward from the
normal water table).
…published by Scottish engineer William Rankine in 1857 are still primary tools used to
quantify earth stresses. These theories have been amended in the 20th century to take into
account the influence of cohesion, a more recently discovered property of soils that causes
them to behave somewhat differently under stress…

thermodynamics
Thermodynamics, science of the relationship between heat, work, temperature, and energy. In
broad terms, thermodynamics deals with the transfer of energy from one place to another and
from one form to another. The key concept is that heat is a form of energy corresponding to a
definite amount of mechanical…

Rankine cycle
Rankine cycle, in heat engines, ideal cyclical sequence of changes of pressure and temperature
of a fluid, such as water, used in an engine, such as a steam engine. It is used as a
thermodynamic standard for rating the performance of steam power plants. The cycle was
described in 1859…
Rankine cycle
PHYSICS
WRITTEN BY:

5.  The Editors of Encyclopaedia Britannica
See Article History
Rankine cycle, in heat engines, ideal cyclical sequence of changes
of pressure and temperature of a fluid, such as water, used in an engine, such as a steam engine.
It is used as a thermodynamic standard for rating the performance of steam power plants. The
cycle was described in 1859 by the Scottish engineer William J.M. Rankine.
In the Rankine cycle the working substance of the engine undergoes four successive changes:
heating at constant pressure, converting the liquid to vapour; reversible adiabatic expansion,
performing work (as by driving a turbine); cooling at constant pressure, condensing the vapour
to liquid; and reversible adiabatic compression, pumping the liquid back to the boiler.
Rankine theory
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Rankine's theory (maximum-normal stress theory), developed in 1857 by William John
Macquorn Rankine,[1] is a stress field solution that predicts active and passive earth pressure.
It assumes that the soil is cohesionless, the wall is frictionless, the soil-wall interface is vertical,
the failure surface on which the soil moves is planar, and the resultant force is angled parallel
to the backfill surface. The equations for active and passive lateral earth pressure coefficients
are given below. Note that φ' is the angle of shearing resistance of the soil and the backfill is
inclined at angle β to the horizontal.
For the case where β is 0, the above equations simplify to
Active and passive soil pressures[edit]
This theory, which considers the soil to be in a state of plastic equilibrium, makes the
assumptions that the soil is homogeneous, isotropic and has internal friction. The pressure
exerted by soil against the wall is referred to as active pressure. The resistance offered by the
soil to an object pushing against it is referred to as "passive pressure". Rankine's theory is

6. applicable to incompressible soils. The equation for cohesionless active earth pressure is
expressed as:
where:
and:
Ka = Coefficient of active pressure
w = weight density of soil
h = depth of the section (below top soil) where the pressure is being evaluated.
β = angle that the top surface of soil makes with the horizontal.
φ = angle of internal friction of soil.
The expression for passive pressure is:
where:
Or in the case of β=0, then the two coefficients are inversely proportional, such that:
The primary difference between Rankine and Coulomb earth pressure theories is that
Coulomb's considers a frictional retaining wall. In other words, the interface between the soil
and the retaining wall is not assumed frictionless (as it is in Rankine theory).
That being said, it is typically considered that Rankine underpredicts the true orientation of
the failure surface, whereas Coulomb overpredicts the orientation. In that sense, you could
use both methods, and use the two solutions to bound what will likely occur.