Piston Driven Rotary Engine by Willie Green Jr.

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Message 1

In a fluid embodiment, this motor is 14" diameter, 8 cylinders, has 2" dia. pistons, with a 7" dia. crank shaft and 0.5" stroke, there are 3 active cylinders. In this example we are using the constants 450 psi cylinder pressure, rotating at 900 rpm. The above system is driven by a hydraulic fluid pump with an electric motor.

Constants

Fluid Pressure (PSI) = Force ( pounds) / Area ( sq. in.)           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 
Hydraulic Horsepower = Pressure (psi) × gpm / 1714      HP = (psi × gpm) / 1714
Fluid Motor Torque (in. lbs.) = Pressure (psi) × disp. (cu.in./ rev.) / 6.2822  T = (P ×d) / (2 ×3.1416) d = disp. rev (cu. in. / rev.)
Fluid Motor Speed (rpm) = (231 × gpm) / disp.   (cu. in.) n = (231 × gpm) /d
Fluid Motor Horsepower = Torque (in. lbs.) × rpm / 63025     HP = TN /63025 
Pump Output Flow (gpm) = (Speed (rpm) × disp. (cu. in.)) / 231      gpm = (n ×d) / 231     
Pump Input Horsepower = gpm × Pressure (psi) / 1714 × eff.          HP = (Q ×P) / 1714 × E 
Displacement = 1/2" inch
Pistons = 2" diameter
Active Cylinders = 3
Starwheel Crankshaft = 7" diameter
Pressure = 450 PSI
Speed = 900 RPM’s

A = Cylinder Area = pi*(r^2) = 3.14*(1*1) = 3.14"
Ta = Total Area = A*active cylinders = 3.14*3" = 9.42"
P = Pressure = 450psi
F = Force in Foot Pounds = ft lbs = (crankshaft radius / 12)*4239 = (3.5/12) =.2916 * 4,239 = 1,236 ft lbs
T = Ta*P = 9.42*450 = 4,239 in lbs.
C = Circumference of Star wheel = 7 * 3.14159 = 21.99
N = RPM = 900
D = Distance in 1 Min = (C*N) /12 = (21.99*900) /12 = 19,791in/12 = 1,649.25 ft
L = Starwheel Crankshaft Radius / 12 inches = 3.5/12 = .29 ft
With the above given; the following is 3 different HP formulas for work out:
1.) HP=F*N/5252 = 211.8 HP or = 158,002 W
2.) HP=(C*N / 12/60) * T / 550 =211.85 HP or = 158,040 W
3.) Fluid Motor HP =T*N/63025 or   4,239 * 900 / 63025 = 60.53 HP or = 45,155 W

With the above, we then calculate pump fluid flow & HP based on a volume of 12.56 cu in per rev @ 900 rpm then convert that into gal per min, and use the above pressure at 450 psi

The total displacement per cylinder = Cylinder Area* Displacement = 3.14*.5=1.57 cubic inches
The total displacement per rev = Cubic Inches* 8 Cylinders = 3.14*0.5*8 = 12.56 displacement per rev.
Total Displacement at speed = Displacement per rev* RPM = 12.56 * 900 rpm = 11,304 total displaced cubic inches
GPM = Total Displacement Cubic Inches / GPM Constant = 11304 Cu In / 231 = 48.93 GPM
With 48.93 GPM and a pressure of 450 psi we can compute pump HP work in.
The following are 2 Hydro HP formulas representing work in.
1.) PUMP HP=GPM*P / 1714 = 48.93 * 450 /1,714 =12.84HP or = 9,578.64 W
2.) HP=GPM*P*.0007 = 48.93 * 450 * .0007 = 15.41 HP or = 11,495.86 W

Efficiency work out / work in * 100 = 211.8HP / 15.41 HP * 100 = 1,374.43%
Fluid Motor/Pump  work out /  work in * 100 = 60.53HP / 12.84 HP *100 = 471.42%
The efficiency of a machine, which is defined as the ratio of the work output to the work input, is always less than one, since some of the input is invariably wasted in overcoming friction. The element of time does not enter into the computation of work; the time rate of doing work is called power.

US Patent #6,526,925

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