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.

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 𝐴𝑗𝜌(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 𝜌𝑉𝑏𝐴𝑗𝑉𝑗(𝑉𝑗 − 𝑉𝑏)

= 2𝜌𝐴𝑗(𝑉𝑗2𝑉𝑏 − 𝑉𝑗𝑉𝑏

2) 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

𝑉𝑏1

𝑉𝑏2

𝐹𝑏𝑥 𝜌𝐻20 ∗ 𝐴𝑗 ∗ 𝑉𝑗

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 (𝑚3

𝑠 )

& Head (𝑚) compared to two hydro-machines

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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PA11&dq=pelton+wheels+in+mountainous+regions&source=bl&ots=mSD8gLZPN8&si

g=9l_Q957Pi495c6HoucMql8EZ7oc&hl=en&sa=X&ei=n-

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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/157-

pelton-waterwheel-collection.

Shortridge, Robert W. "Lester Pelton and His Water Wheel." HydroReview (1989): 22-

26.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

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08-34-48?task=article&id=205