## The System Edit

**Hydro-Motor Simple math**

In a fluid system, this rotary motor is 14” diameter, 8 cylinders, has 2” dia. pistons, with a 7” dia. crank and 0.5” displacement, there are 3 active cylinders. In this example we are using the constants 450-psi cylinder pressure, rotating at 900 rpm. A hydraulic fluid pump with an electric motor drives the above system.

A pump and motor were chosen to give me the ability to control both the flow and the pressure on the input side. Thereby more accurately calculate the torque and speed on the output side.

**This technology is better than existing technologies for the following two reasons**
1) Greater leverage within a more confined space.

2) Reduced mass used in linear to rotary motion translation.

## Investigation Edit

The information herein may be investigated by use of the following technique.

The Scientific method, which is a body of techniques for investigating phenomena and acquiring new knowledge, as well as for correcting and integrating previous knowledge. It is based on observable, empirical, measurable evidence, and subject to laws of reasoning. All such evidence is collectively called scientific evidence and is used as a means of structural cohesion to new information..

FEA Software offers a wide spectrum of powerful tools to help engineers who are familiar with design validation concepts to perform virtual testing and analysis of parts and assemblies. Engineers who need more specific design analysis capabilities can use FEA Software to predict the physical behavior of practically any part or assembly under any loading condition.

FEA Software was used in the concept validation stage and in testing verious loading condition for this model.

## Constants Edit

[1]

Displacement = disp = 0.5 inches = d

Piston diameter = 2”

Active Cylinders = 3

Star-wheel / Crankshaft = 7” diameter

Pressure = PSI = 450 PSI

Speed = N = 900 RPM’s

1 HorsePower = 746 Watts

5252 = constant (33,000 divided by 3.14 x 2 = 5252)

1 HP = 33,000 ft·pound-force·min−1 = exactly 0.74569987158227022 kW

1 Gallon = 231 Cu. In.

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## Math Edit

Fluid Pressure (PSI) = Force (pounds) / Area ( sq. in.).........P = PSI = F/A

Cylinder Area (sq. In.) = 3.1416 × Radius (inch)(sq.)...........A = Pi × R(sq.)

Cylinder Force (pounds) = Pressure (psi) × Area (sq. in.).....F = P × A

Cylinder Speed (ft./sec.) = (231 × gpm) / (12 × 60 × Area)....v = (0.3208 × gpm) / A

Fluid Motor Speed (rpm) = (231 × gpm) / disp. (cu. in.).........n = (231 × gpm) / d

Pump Output Flow (gpm) = (Speed (rpm) × disp. (cu. in.)) / 231 gpm = (n ×d) / 231

Torque = Force applied x lever arm in “ft” or Ta*psi = F lbs.”

1.) PUMP HP=GPM*P / 1714

2.) PUMP HP=GPM*P*.0007

1.) HP=F*N/5252

2.) HP=(C*N / 12/60) * F / 550

Efficiency=work out / work in * 100

Where D is Displacement, L is Lever radius and E is efficiency D/L=E

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## Math applied Edit

A = Cylinder Head Area = pi*(r^2) = 3.14*(1*1) = 3.14159 sq. in.

Ta = Total Area = A*active cylinders = 3.14*3” = 9.42477 sq. in.

P = Pressure = 450psi

N = RPM = 900

C = Circumference of Star wheel = 7 * 3.14159 = 21.99

L = Star-wheel Crankshaft Radius / 12 inches = 3.5/12 = .29 ft

D = Distance in 1 Min = (C*N) /12 = (21.99*900) /12 = 19,791in/12 = 1,649.25 ft

F = Ta*P = 9.42477*450 = 4,241 lbs Force.

T = Torque in ft_lbs = (crankshaft radius / 12)*4241 = (3.5/12) =. 2916*4,2341 = 1,236.95 ft_lbs.

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## System HP Edit

With the above given; the following is 2 different HP formulas representing work out:

1.) HP=F*N*L/5252 = **211.8** HP or = 158,002 Watt

2.) HP=(C*N / 12/60) * F / 550 = **211.85** HP or = 158,040 Watt

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## Pump Math Edit

[Hydraulic Formulas][6]

With the above, we then calculate pump fluid flow & HP

The volume which will pass through pump is equal to :

9.42477*.5=4.72385 in3 for active cylinders in each strok

7*3.1415/.5= 43.981 number of action of cylinders for one rotation

43.981*4.72385=207.7596 in3 volume of displaced oil in one rotation

207.7596*900=186983.6821 in3 volume of diplaced oil in one minute

186983.6821/231=809.4536 gpm volume of displaced oil in one minute

809.4536*450/1714=212.5169 Hp

As we see the power used by pump theoricaly is equal to the power used by motor ( 212.5169 and 211.85 are a little different only because of unit conversions and and diferent fraction and not because of efficency )

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## Pump HP Edit

The following are 2 Pump HP formulas representing power in.

1.) PUMP HP=GPM*P / 1714 = 809.4536* 450 /1,714 =212.5169 HP or = 158536 Watts

An electric motor and pump were chosen for this example to control the input with calculable knowns. If you can calculate forward then you can transpose.

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## System Efficiency Edit

**Efficiency work out / work in * 100 = 211.8HP / 212.5169 HP * 100 = 99.66% ( the efficiency should be less than 100% and here it is , but remember that it is not correct because we have not acounted any loss up to now in these calculation and this is only because of diferent unit convertions and and fractions )**

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## --212.120.196.158 06:55, December 23, 2009 (UTC)maleki4@hotmail.comEdit

## Math references Edit

Math Formulas:

Reference 1 http://www.gulfcoastairandhyd.com/formulas.htm

Reference 2 Courtesy of Sidener Engineering http://www.sidenereng.com/formulas.htm

Reference 3 MacDizzy© http://www.macdizzy.com/formulas.htm

Reference 4 Engineering fundamentals http://www.efunda.com/home.cfm

Reference 5 Pumps formulas http://www.airlinehyd.com/KnowledgeCenter/Hydraulic/Formulas/PumpH.asp

Efficiency formulas:

http://www.airlinehyd.com/KnowledgeCenter/Hydraulic/Formulas/PumpH.asp

http://www.reliance.com/prodserv/motgen/b7087_5/b7087_5_3.htm

http://www.zoeller.com/zep/techbrief/JF1article.htm

Engine Volumetric Efficiency Calculator

http://www.ajdesigner.com/phpengine/engine_equations_volumetric_efficiency.php

HP formulas:

http://en.wikipedia.org/wiki/Horse_power#Mechanical_horsepower

http://www.elec-toolbox.com/Formulas/Motor/mtrform.htm

http://www.iprocessmart.com/techsmart/formulas.htm

http://www.pesquality.com/formulas.aspx#frm5

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## Published REFERENCES Edit

1. Dale, T.W.,"Spherical Piston Radial Action Engine", U.S. Patent #5,419,288, May 30, 1995.

2. Avallone, E.A. and Baumeister, T. III,"Marks' Standard Handbook for Mechanical Engineers", Ninth edition, McGraw-Hill, New York, 1987.

3. Richards, T.D.,"The Hanes Engine", informational report, copyright 1994, available from the author at P.O. Box 21147, Carson City, NV, 89721.

4. Ashley, S.,"A New Spin on the Rotary Engine", Mechanical Engineering, April 1995, p80-82.

5. Bloch, H.P.,"A Practical Guide to Compressor Technology", McGraw-Hill, New York, 1996.

6. Anon.,"GAUSS Volume I, System and Graphics Manual", Aptech Systems, Inc., Maple Valley, WA, July 18, 1994.

7. Heywood, J.B.,"Internal Combustion Engine Fundamentals", Mcgraw-Hill, New York, 1988.

8. Sliney, H.E. and Dellocorte, C.," The Friction and Wear of Ceramic/Ceramic and Ceramic/Metal Combinations in Sliding Contact", NASA TM-106348, DOE/NASA/50306-3, N94-15769, October 1993.

9. Wikipedia, ,"Scientific Method, Scientific Evidence, & Mechanical Advantage"

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## Quotes by Richard Feynman Nobel Prize Winner Edit

Science is the belief in the ignorance of experts…

No government has the right to decide on the truth of scientific principles, nor to prescribe in any way the character of the questions investigated.

I learned very early the difference between knowing the name of something and knowing something.

What I cannot create, I do not understand.

[12]

[13]

## [By Willie A. Green Jr][14][15] Edit

"The more you know the more you know you don't know"

"If I understand it, I can create it"

Patent # 6,526,925

will2green@gmail.com

Forum:[[16]]

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## Summary Edit

By an increase in mechanical advantage and decrease in volumetric mass with the area of force remaining the same the efficiency in any system is increased, there is a direct relationship within any given fluid dynamic or applied mechanics system.

D/L=E

In the above system, no new energy is being created, rather or more amply put this system better utilizes the energy available.

**Todate I have 6 each, new prime mover devices, created and realized out of the above math.**

[First law of thermodynamics][18]

The increase in the internal energy of a thermodynamic system is equal to the amount of heat energy added to the system minus the work done by the system on the surroundings.

[Second law of thermodynamics][19]

Heat cannot of itself pass from a colder to a hotter body. This is equivalent to this scientific statement:
The entropy of an isolated system not at equilibrium will tend to increase over time, approaching a maximum value.

[Third law of thermodynamics][20]

As a system approaches absolute zero of temperature all processes cease and the entropy of the system approaches a minimum value.

[Zeroth law of thermodynamics][21]

If two thermodynamic systems are in thermal equilibrium with a third, they are also in thermal equilibrium with each other.

Will Green laws of dynamic systems

1"All dynamic systems are a balancing act."

2"Once a system is out of balance there is movement."

3"Movement will continue in a system until a balance is reached in that system"

4"An out of balance movement will pass from one system into another"

5"We can never realize the complete potential from dynamic energy"

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## Other High efficiency devices Edit

Rotary motors/pumps, some of which could utilize the above principle...

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Copyright by Will Green 2006