Phi geometry: impeller & propeller design for fluids handling

Oct. 1, 1999
More thrust, less heat, less vibration, no cavitation
Recessive spiral prototype designs have been tested in fluids up to 6,000 rpm and show promise of higher marine and aircraft speeds from smaller power plants.
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Now revolutionary ideas are leading us to rethink the physics behind impellers, propellers, and fans. Many present technologies have scarcely changed since the Archimedes screw, invented in 2,300 BC, or the piston pumps and centrifugal impellers used by Egyptians 4,000 years ago.

While the principle of using jet pumps for propulsion had been known for hundreds of years, marine jet pumps have changed little since they were developed by English and Swedish engineers in the 1920s. Aircraft jet engines have become much more efficient and quieter, but the basic principle of generating thrust is the same as 50 years ago, and a new Boeing 777 or its equivalent doesn't fly much faster than the oldest DC8.

An aircraft propeller is still only an updated variant of the wooden blades used by the Wright brothers at Kitty Hawk and the engines that drive them operate on the same principle as the internal combustion engine of that same era. Although some experimental ship propellers are as high as 77% efficient, most ship propellers operate at efficiencies of about 56%. Ship propellers continue to suffer pitting due to the implosive pressure of cavitation bubbles. Pumps and compressors of all kinds still experience many limitations and inefficiencies not found in natural liquid and gas flows. It's time for a technological revolution capable of leading fluids handling and propulsion into the next century.

Inside a seashell

New impeller designs draw from a common geometry found in nature, from galaxies to particle decay.
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Australian naturalist and marine designer Jayden Harman has drawn observations from the natural world that may alter the way we build marine craft, aircraft, pumps, and fans. Older and more fundamental than Archimedes or the Egyptians, nature has demonstrated high efficiency propulsion, pumping, and cooling for approximately 14 billion years, but nature's systems are not based on the pump, propeller, or fan concepts used in industrial technology. The key difference is that technologists try to suppress turbulence, while nature leverages turbulence to accelerate or decelerate fluids, increase or decrease heat, and vary pressures.

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To illustrate this, ask yourself: What is the shortest distance between two points? Any student knows that the answer is - a straight line. But, is a straight line the most efficient way to move matter or energy between two points? For years, Harman has been impressed by the fact that the most efficient line of travel in nature is never in a straight line, but rather in a logarithmic spiral called the Phi ratio. Variations of this ratio and its related Phi geometry are found throughout our world and space.

This same pattern is found in galaxies, hurricanes, eddy currents, and the trajectory of subatomic particles. It's the flow path that water takes in a stream, smoke in the air, sap in a tree, and blood in our veins. A good example of the logarithmic spiral is the inside of an abalone shell. The interior structure describes the spiraling Phi geometry of extraordinary fluid efficiency.

Progress to infinity

Harman has spent many years studying the variations of this geometric pattern, a three-dimensional, equiangular, logarithmic curve that progresses to infinity, also known historically as the Golden Mean. He has developed mechanisms that exactly replicate this dynamic pattern in various fluid flow situations.

Early in his career he noticed that most seaweeds and fan corals, while extremely fragile, remain attached to rocks and structures in even the worst storms and surges. They do this by changing their shapes to present the least possible resistance to waves and currents. Ongoing observation over several years led him to develop an understanding of which flow designs to replicate for varying conditions.

He initially started with part of the inside of a shell epoxied to a shaft. In a series of experiments, a pump impeller of this configuration demonstrated considerably more efficiency than off-the-shelf pumps. The efficiency results because the impeller replicates nature's method of moving fluids along the path of least resistance. This consumes the least amount of necessary energy.

These impellers turn recessively, yet the action is centripetal, not centrifugal. Centripetal action engages the fluids at the outer extremities of the spiral and then moves them in towards the center. Operating in this way the impellers produce virtually no cavitation or separation, simply high-speed laminar flow. Similarly designed impellers have been tested at speeds up to 6,000 rpm with consistent results.

Dropping temperature

Interestingly, fluids moved along this flow path experience temperature drops, rather than increases, though this can be reversed for particular applications. The rotor design expands from inlet to outlet, so clogging is not a problem. What goes in, must come out. Variations of the rotors can produce powerful, focused jets of liquid or gas without the use of nozzles, pipes, or chambers.

In short, rotors designed in this way can produce more thrust while giving off less noise, heat and friction. Harman is adapting his patented Phi geometry principle to a rapidly increasing range of industrial applications and believes that almost any fluids-handling situation could benefit by the application of natural geometry (Jayden Harman may be reached at paxresearch @

About the authors

William McLarty is President of McLarty Engineering, which specialized in engineering and fabrication for the Australian offshore oil fields and marine industry in the 1970s and 1980s.

John Petersen is the President of the Arlington Institute; a Washington DC-based think tank that specializes in identifying future trends.

Implications of the Phi ratio

Proportional Spiral.
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Each number in a Phi ratio sequence is the sum of the previous two numbers - A:B = B:A+B. For example, starting with the seed numbers of 0 and 1, the sequence would be: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ...

This is known as the Fibonacci sequence and is extremely common in plant and animal forms including the number of petals on flow ers, seeds on a sunflower, or number of bees in a hive. Other starting numbers may be used, resulting in different final shapes. The Phi spiral allows for smooth, rapid growth in plants, animals, and natural liquid and solid forms. Each stage of growth shares the same proportions.

The effectiveness of Phi ratio designs is based on more than just applying the Phi spiral shape onto a basic propeller or impeller. A design deals with three dimensions, angles of pitch, expansion rates, etc.

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