Environmental Engineering Reference
In-Depth Information
the elevation of the center shaft, were no more efficient
than well-designed undershots, and high-breast machines
approached the outputs of overshot wheels. Traditional
overshots (fig. 7.5) exploited heads greater than 2-2.5
m (their diameters was equal to about 75% of the head)
and hence were either confined to hilly or mountainous
areas or needed a carefully regulated water supply, which
often required construction of ponds and long races.
Smooth downstream races were also needed in order to
prevent any backing up of discharged water and excessive
channel silting. Water was usually fed through troughs
or flumes into buckets at rates between
<
100 kg/s and
>
1000 kg/s, resulting in 4-12 rpm. The kinetic energy
of the water was relatively unimportant because the grav-
itational energy of the descending mass generated the
bulk of the rotary motion.
Overshots became the favorite wheel for many applica-
tions besides efficient grain milling. Eventually they pow-
ered scores of previously manual tasks with relatively high
efficiency, from sawing and wood turning to oil pressing,
wire pulling, and majolica glazing. In England overshots
were also used in mines for winding (Woodall 1982) and,
particularly in the Northeast, for draining. Some were
deployed in groups of three to draw water from a depth
of nearly 80 m (Clavering 1995). Until the early decades
of the eighteenth century it was widely believed that they
were less efficient than undershots, but between 1752
and 1754 experiments by Antoine de Parcieux and John
Smeaton, and calculations by Johann Albrecht Euler,
proved the very opposite (T. S. Reynolds 1979). Smea-
ton then began promoting overshots, and within a few
generations undershots had largely disappeared from En-
gland as the more efficient waterwheels delayed the diffu-
sion of steam engines.
Smeaton's (1759) classic experiments indicate an
average overshot efficiency of about 66% (52%-76%)
and the best undershot performance at 32%. Smeaton
also correctly concluded that a wheel's power is a func-
tion of the cubed velocity of the water. M. Denny's
(2004) simplified theoretical analysis of the efficiency of
waterwheels ended up with figures very close to Smea-
ton's experimental values: 71% for overshots, 30% for
undershots, and about 50% for Poncelets. Properly
designed twentieth-century overshot wheels operating
within optimum parameters had efficiencies of 85% and
shaft efficiencies close to 90% (Muller and Kauppert
2004), but 60%-70% was a common performance of the
best preindustrial machines. In contrast, traditional, low-
rpm undershots had efficiencies just around 20%, and the
nineteenth-century wheels converted up to 35%-45% of
water's kinetic energy into rotary power. However, the
best German undershot designs of the 1930s reached
efficiencies as high as 76% (M¨ller 1939).
Waterwheels were the most efficient preindustrial en-
ergy converters. They opened up new productive possi-
bilities, particularly in mining and metallurgy. Animate
energies could never generate kinetic energy at such
high continuous rates. Waterwheels were a key ingredi-
ent of Europe's emerging technical superiority, and they
were also a leading prime mover during the early stages
of European and North American industrialization.
Power of the simplest small machines was limited, but
even they made a great difference. Two hard-working
slaves in 1 h (useful input of 200 W) could grind 7 kg of
flour with hand querns; a donkey-driven mill (300-400
W) produced about 12 kg; and a set of waterwheel-
driven millstones (2.2-2.5 kW) typically produced 80-
100 kg. If flour were to supply half of an average person's
