Pelton Wheel
Cive 401: Hydraulic Engineering
Melissa James, Robert Jaquet, Scott Kemper
11/19/2014
History of the Pelton Wheel
During the 1850s, the hurdy-gurdy wheels were the main water turbines used in the gold
and silver fields of California and Nevada and were considered to be the primitive design that
developed into the Pelton Wheel (“Pelton Waterwheel Collection”). The hurdy-gurdy wheels
(given the name after the musical instrument the wheels sounded like when in operation) were
made of “blocks of wood about four inches thick...cut so that...each one formed a tooth like that
of a circular ripsaw” (Shortridge, 22). The wheel moved as a water jet hit the teeth tangentially
with heads of 40 to 50 feet. This contraption mostly powered small quartz mills and had a low
maximum efficiency of 40 percent, which was assumed to be due to the flat surface of the
buckets or teeth (Shortridge, 22-23). In order to increase efficiency, the first major alteration to
the wheel system transformed the wooden teeth of the hurdy-gurdy into a cup-shaped bucket that
discharged water to the side and middle when hit by a rectangular jet of water formed by a slit
nozzle.
Lester Pelton, known to some as “the Father of Hydroelectric Power”, encountered the
hurdy-gurdy wheels in the gold fields when he worked as a gold miner and millwright and began
experimenting on around 40 different types of wheel designs to improve efficiency. He began
his work in California at age 20 and continued until his death at age 79 (Csanyi). Many
hydroelectric ideas stemmed from the initial designs created by Pelton in the 19th century.
Figure 1 below shows a common image of Lester Pelton.
Figure 1. Lester Pelton
Source: (Csanyi)
Pelton’s first successful wheel design was built in Camptonville, California in 1878
(“Pelton Waterwheel Collection”). In the fall of 1880, Pelton received his first patent on the
design shown in Figure 2 below.
Figure 2. Pelton’s First Patent Design Sketches
Source: (Shortridge, 24)
Coincidentally, a similar design had been patented in 1873 by Nicholas J. Coleman.
However, Coleman’s patent was misplaced during Pelton’s submission and was not discovered
again until a few years later by a vengeful foreman, W.G. Dodd, of Rankine, Brayton &
Company in San Francisco after a misunderstanding resulted in Dodd losing his spot in the
Pelton Water Wheel Company. The misunderstanding was later resolved by the Pelton Water
Wheel Company buying up the rights for Coleman’s patent. The Pelton Water Wheel Company
was cofounded by Brayton of Rankine, Brayton & Company and Pelton himself as a
manufacturing company for the new successful wheel turbine design (Shortridge, 24). The
Pelton Water Wheel Company quickly jumped up in the ranks as a famous wheel turbine
manufacturing company.
Improvements to Pelton’s original design were made by many contributors, the final
major one being made by Pelton Water Wheel Company’s competitor, William Doble. Doble
noticed how the buckets in the Pelton design were worn down quickly due to the scouring of the
sand of the water jet in turbulent flows hitting the buckets. Doble fixed this by essentially
creating a double bucket design with the addition of a water splitter, which divides the jet of
water in half and minimizes the turbulence and abrasion of the water in the buckets. Doble’s
revision of the design led to “a second stage in the development of Pelton turbines” (“Pelton
Waterwheel Collection”).
How does a Pelton wheel work?
A Pelton wheel is typically a set of 20 buckets (blades) attached to a wheel that can vary
in diameter; however, they are usually 10 meters. The buckets receive the jet(s) of water from a
typically large head source which is then converted into high velocities at the exit nozzle(s) that
then strike the blade.
𝑉𝑏 1
𝐹𝑏𝑥
𝜌𝐻2 0 ∗ 𝐴𝑗 ∗ 𝑉𝑗
𝑉𝑏 2
Figure 4: Force Diagram. Created by Robert Jaquet
The force felt by this blade can be found using the momentum equation and applying it to
the control volume in equation one through three found below (Julien, 2014).
𝐹𝐵𝑥 = −𝜌(𝑉𝑗 − 𝑉𝑏 )𝐴𝑗 [(𝑉𝑗 − 𝑉𝑏 )1 − (𝑉𝑗 − 𝑉𝑏 )2 ]
Eq 1
This can be simplified base on the reasonable assumption that the x component (𝑉𝑗 -𝑉𝑏 ) 2
is the maximum when theta is equal to 180 degrees. This creates a change in sign and the
resulting simplification has been made equation 2).
𝐹𝑏 = 2 𝜌𝐴𝑗 (𝑉𝑗 − 𝑉𝑏𝑥1 )(𝑉𝑗 − 𝑉𝑏𝑥2 )
Eq 2
However, since there is a loss from the consecutive blade pushing a cylinder of water
forward and is partially deflected until the full stream is within the blades edges. The resulting
total force is shown in equation 3.
𝐹𝑏 = 2𝑉𝑗 𝐴𝑗 𝜌(𝑉𝑗 − 𝑉𝑏 )
Eq 3
Using the force on the blade multiplied with the velocity of the jet the product is the
power developed by the blade is shown in equation four.
𝑃𝑜𝑤𝑒𝑟 = 𝑃 = 𝑉𝑏 ∗ 𝐹𝑏 = 2 𝜌𝑉𝑏 𝐴𝑗 𝑉𝑗 (𝑉𝑗 − 𝑉𝑏 )
= 2𝜌𝐴𝑗 (𝑉𝑗2 𝑉𝑏 − 𝑉𝑗 𝑉𝑏2 )
Eq 4
A Pelton Wheel assembly can extract the energy from the impulse of the water from the
cupped blades at a high hydraulic efficiency of 95 percent. The reason for this is that the velocity
of the incoming jet is deflected at approximately 175 degrees between two curved blades shown
in figures 4 and 5. Five degrees on either side allows the water jets to separate from the
consecutive blade moving into the previously occupied space. Separation decreases the
resistance from the influx of water which would impede the angular velocity of the wheel.
Optimal power is reached when the velocity of the blade, relative to the jet, is one half, proven
by differentiating equation four and setting it equal to zero (Julien, 2014).
Figure 5:
Six Nozzle Pelton Wheel
Vertical Crank Shaft
(Advanced Design)
Source: Swiss National Computing Centre
Considering efficeny, the more advanced six jet pelton wheel system portrayed in figure
5 has amoung the highest hydralic efficency at 98 % (SNSC, 2011). An efficency that has the
associated complexity and cost can be beneficial if the design life is much longer than a single or
double jet acting on the wheel. A design life analysis must be conducted for a numeric estimate
to choose the most economical design. The six jet design will have higher outputs of power than
the single/double jet for the same discharge and head which over a period of time will make
more money. Another aspect that is considered in the design of a hydro-electric powersource is
the footprint of the structure that encloses the generator and all the esentails for operations. The
vertical shaft has a smaller footprint than a horizontal shaft, however the vertical shaft requires a
higher level off the ground for the generator and other euquiptment used in power generation
(Atthanayake, 2009).
Once the hydraulic energy has been transformed to mechanical shaft work, this enters the
generator which will produce the electrical energy needed at peak hours of the day, or
continuously throughout the day depending on the regional situation. The most efficiency
developed from this process is nearly 90 percent which is from hydraulic energy to mechanical
energy to electricity.
Gilkes, one of the leading global manufacturers of Pelton wheels, has typical design
values shown in figure 6 below. In addition to design values of Pelton wheels, this figure shows
how this type of turbine compares with two other types, the Turgo and the Francis. The Pelton
wheel is suited for high head and lower discharges, while the Francis can use lower head sources
with more discharge. The power will not be sacrificed in either case, the turbine must fit the site
where it will be in service.
Figure 6:
Gilkes Pelton Wheel Power Generated (MW) Versus Discharge (
& Head (𝑚) compared to two hydro-machines
𝑚3
𝑠
)
Uses of the Pelton Wheel
Since the Pelton wheel works best with high head and low discharge, mountainous areas
potentially benefit the most from using them. An advantage of Pelton wheels over other power
generators is that the Pelton wheel is able to generate a good amount of energy from just a small
brook, provided the head is large enough. This allows for electricity generating ability in hard to
reach areas and third world countries. Due to the compact shape of the Pelton wheel, installation
of these systems is much easier, making them more desirable for implementation. An example of
a good setup could be the Hongping power station of China, shown in Figure 7 below, using a
nearby stream and diverting some flow for use in hydropower.
Figure 7. Hongping power station
Due to the Pelton wheel’s convenient system, the Pelton Water Wheel company says, “It
is no exaggeration to say that, in this way, a small trout brook with a high head will often furnish
as much power as a large stream under a low head, in a much more convertible form and at
probably not more that one-fourth the outlay” (1909). As opposed to other methods of
hydropower, the Pelton wheel avoids many common difficulties that a hydropower plant may
experience. The Pelton Water Wheel company also says:
All mountainous regions, particularly those in tropical countries, such as Mexico, Central and
South America, present conditions which offer the most serious objections to the turbine
wheel. The streams furnishing power in such locations are subject to sudden freshets from
excess of rainfall, and carry, at such times, grit and sand sufficient to destroy any turbine in a
very short time. They also carry roots, leaves and other trash that fill the vanes and choke the
wheels to such an extent as to often prevent their running until the obstructions are removed,
involving a degree of unreliability that discredits the many advantages such a power ought
always to afford. The Pelton Wheel, on the contrary is constructed with a perfectly free
discharge, and the buckets will not choke up by anything that may be thrown upon them, thus
making it absolutely reliable (1909).
For a more hands-on approach, a model of a Pelton wheel was created using a milk jug,
some spoons, a long plastic tube (for use as the penstock), a garden hose and a tree. Figure 8
shows what the experiment looked like.
Figure 8. Pelton Model
By hooking the plastic tube and garden hose together on the tree, the water was then
allowed to flow down and cause the wheel to rotate. This was to show how a small amount of
water with a high head could be used to make electricity. The following link gives a video of the
model in action. https://vid.me/XGdQ
During the 15 second video, the wheel makes 32 rotations, so the wheel makes about 2.1
rotations per second or 13.2 rad/s. The average diameter of the wheel was 0.14m. This means the
velocity of the bucket was then 0.924 m/s. Under ideal conditions, a jet velocity will be twice
that of the bucket’s velocity. In this case, the wheel was under minimal resistance since it was
not being operated as a generator. Since there is lower resistance, the velocity of the jet will be
assumed to be 1.2 times greater than that of the bucket, or 1.1 m/s. The diameter of the jet was
about 0.01m and thus gave an area of 7.85 x10-5 m2.
Using these variables and plugging them into equation four from above gives about 0.03
watts of power. Since this example uses a tree at about 4.6 meters high with a garden hose at a
low discharge, this low amount of power generation makes sense.
References
Atthanayake, U. I. (2009). International Journal of Engineering IJET-IJENS Vol:09 No:09.
Retrieved from http://www.ijens.org/1929091%20ijet.pdf
Csanyi, Edvard. "Lester Allan Pelton – The Father of Hydroelectric Power." EEP Electrical
Engineering Portal RSS. N.p., 8 June 2012. Web. 01 Nov. 2014. Retrieved from
http://electrical-engineering-portal.com/lester-allan-pelton-father-hydroelectric-power.
Gilkes. (2014). Pelton Turbine Manufacturers - Gilkes Product Range. Retrieved from
http://www.gilkes.com/Pelton-Turbines
Julien, Pierre Y. (10/6/2014). Turbines and Hydro-machinery Handout. CIVE 401. Lecture
conducted from Colorado State University, Fort Collins, CO.
Pelton Water Wheel Company. “The Pelton Water Wheel: The Pelton System of Power.” 1909.
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"Pelton Waterwheel Collection." Landmarks. ASME, n.d. Web. 01 Nov. 2014. Retrieved from
https://www.asme.org/about-asme/who-we-are/engineering-history/landmarks/157pelton-waterwheel-collection.
Shortridge, Robert W. "Lester Pelton and His Water Wheel." HydroReview (1989): 2226.HydroWorld. HydroWorld. Web. 1 Nov. 2014. Retrieved from
http://www.hydroworld.com/content/dam/hydroworld/downloads/Q%26Aturbine4.pdf.
Swiss National Supercomputing Centre. (2011). PRACE Supercomputers, Software and
Applications (Image). Retrieved from http://scc.acad.bg/ncsa/index.php/en/2011-06-29
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