Section 2


Invention No. 1:

           A New Isentropic Air Motor and Clean Energy Source


Abstract   A new air motor is described which uses isentropic linear acceleration to enormously increase the power of an air flow from a vacuum pump source plus a new  reaction rotor to efficiently extract the power for useful work. The fuel  used is ordinary air - no heat is supplied. The exhaust is clean air.  The invention is described in excerpts from the Patent Application. The process can be made to be quasi-self-sustaining if desired, that is to say, a species of ‘Perpetual Motion’ can be achieved.




2.1  Extracting Flow Energy and Flow Power : Turbo-machines

2.2  Calculating the Power Curve of Air Flows and of Power Take-off  Rotors

2.3  A New Method and Apparatus for Greatly Increasing and Extracting Power from an Air Flow

2.4  Invention No. 1: Excerpts from a  U.S. Patent Application



                                                    Perpetual Motion Operating Mode

                                                    Design Steps


                                                    Design Safety  Considerations

                                           2.5 Conclusions





2.1  Extracting Flow Energy and Flow Power : Turbo-machines


Turbines are used to extract energy from fluid flow. Those that involve rotors  (and usually blades ) are often  called turbo-machines. Examples are steam turbines, gas turbines, jet engines  and so.  Rotary lawn sprinklers are an example of simple reaction turbines.


Windmill propellers are flow turbines which extract power from the wind flow by slowing it down. This extraction of flow  kinetic energy by inserting a windmill or ducted fan into a wind flow is  governed by what is called the Betz Limit which states that only  59.3% of the total flow  kinetic energy  available in the air approaching the propeller can be extracted. [ 1].

Here, we describe a new invention which first, greatly increases the power of an air flow, and then extracts a portion of the increased power without at the same time reducing the flow power.  It does so by a reaction force method . 


2.2  Calculating the Power Curve of Air Flows and of Power Take-off  Rotors     


In Section 1.4 above we calculated  the power of an air flow in terms of the mass flow and the velocity squared (  P = ½ m-dot x V2 ).  The power can also be calculated in other equivalent  ways.

For example, we can  take the product of the pressure drop  −Δp over the  flow path,   multiplied by the volume flow rate VA,  since energy per unit volume multiplied by volume per second gives energy per second or power in watts. Thus, we have  

P = Δp  x  VA =  ( force x velocity = energy per second =  joules per second = watts ).



This relation between air flow  VA (  m3 /s)  and pressure drop  ( Pascals, Pa) is  shown in Figure 1.


Figure 1. Power output in air watts for a vacuum source drawing in a linear flow  of air, expressed in terms of pressure drop and flow rate.


Here we note that the maximum power available in any flow system comes at neither the maximum flow rate nor at the  maximum pressure drop point,  but rather at some intermediate values which give the  maximum product of the  two flow variables.

In the case of rotating turbo-machinery, the power can be calculated as the product of the torque To and the rotation rate ω. This yields the power formula: 

P = Torque x Rate of rotation = To ω ( watts)

This is  plotted in Fig. 2 and is seen to be similar in form to that calculated from air flow and pressure drop (Fig. 1). 



Fig. 4.  Power  Curve of a Rotor in terms of Torque and Rate of Rotation


We may note here that at maximum torque the rotation rate is zero and so the power output  is zero. At maximum rotation the torque becomes zero and again there is no power.  It is at the intermediate rotation and torque that the maximum in rotational power output is reached.

[We also note that the maximum power transferred to the rotor by the flow thrust is only one half the nozzle thrust power. This is because as the rotor speeds up, its thrust  speed measured relative to the rotor itself   decreases. Consequently, only one half of the  nozzle power can be extracted by the rotor power take-off means. However, because the power amplification by the acceleration of the flow in the nozzle throat  is so great, the net power produced  by the invention is still very much larger than any prior art. ]

Now that we have outlined the principles of flow acceleration, power increase and power curve calculation, we turn to a new  practical method and apparatus for implementing these principles to produce clean, renewable, economical  energy



2.3  A New Method and Apparatus for Greatly Increasing and Extracting Power from an Air Flow



In the course of experimental investigation into methods of accelerating air flow to achieve increased power, a new method of extracting the increased power was also discovered  (Fig. 3)  and is now described.


 First a basic mass flow rate of air is set up, say by a vacuum pump source. Then,  the new method involves inducing the desired acceleration of the air flow by passing the air flow through  a set of concentric, converging  nozzles in a cylindrical rotor;  the flow is accelerated  through the nozzles to increase the flow power, and at the same time the nozzle thrust imparts reaction rotation to the rotor so that power can efficiently be taken off to do useful work.



Fig. 3.   Flow-Accelerator/ Power Take-off Rotor Means  



The thrust  from the accelerated flow through the nozzles induces a rotation of the rotor in the reverse or reaction sense to the thrust direction. The invention both greatly increases the power of a basic mass flow air through the rotor while  at the same time inducing  rotation energy to the rotor  for easy and efficient take- off of power for doing useful work.  This new  method and apparatus are described in  detail in a recent patent application from which the following excerpts are taken.  


2.4 Invention No. 1:  A Method  for efficiently generating and extracting power from an air flowfor useful work “ . Inventor:  Bernard A. Power. Opened-to public inspection by Canadian Intellectual Property Office on 2011/06/07 at :





( 1).  A method of efficiently generating and extracting power from a flow of air for useful work comprising the steps of::

: (a) inducing a chosen mass flow of air or other  compressible fluid,  preferably ambient atmospheric air by a vacuum pump;


b) conducting said chosen mass flow of air into and through a set of two or more conical internally  converging nozzles formed within a cylindrical rotor disc, said rotor rotating freely on a central shaft or axle, said rotor having its rotation axis aligned  at right angles to the longitudinal axes of said conical nozzles;  said chosen mass  flow of air  thus becoming partitioned into a set ot equal portions of said mass flow of air among said set of conical converging nozzles;


(c) arranging said conical nozzles circumferentially and symmetrically  in said rotor, with their flow entrance ports situated on the outside  rim  of said rotor, said nozzles leading through said rotor into an inner central circular air chamber  of designed radius inside said rotor, each of said nozzles having its  longitudinal axis aligned at right angles to the rotation axis of said rotor, each of said nozzles being also aligned so as to be essentially tangent at its  exit port  to said  inner air chamber at said designed radius  so that  the air flow through each said converging nozzle exits tangentially into said inner chamber at  said designed radius  from said inner air chamber’s longitudinal axis;


 (d) constructing each  said converging nozzle to have a minimum throat cross- sectional area so as to pass through each said throat an equal portion of the total said chosen mass  flow of air at near sonic speed;  said chosen mass air flow  thus undergoing a quasi-isentropic acceleration to near sonic speed through said converging nozzles, and with the total of all of the  partial flow of air  through  all said nozzles taken together  being equal to the total of said chosen mass flow of air; 


 (e) accelerating  said chosen  mass  flow of air  through said converging nozzles and  thus exerting a reverse thrust on said rotor as said  sonic flow passes out from said  nozzles and into the said inner air chamber, said thrust direction  being offset  from the centre of rotation at said designed radius from the central rotation axis of said rotor and thus also exerting a torque on said rotor;  said torque causing said rotor to rotate in the opposite direction to the direction of the nozzle exit flow into said inner air chamber, said rotor  thereby acquiring by reaction force a  rotational  energy from the thrust force of the nozzles’  accelerated  air flow;


 (f) said inner air chamber having a downstream  exit port of cross- sectional area equal to the combined throat area of the said nozzles taken together, said mass air flow then exiting from said inner chamber through said  downstream exit port  into a flow  diffuser or diverging  duct; said flow diffuser decelerating said air flow  and leading it towards  a flow exit port and back into the ambient atmosphere.



(2)  An air motor apparatus, consisting of  a substantially cylindrical rotor, said rotor being mounted on a central shaft or axis, said rotor having two or more converging nozzles molded, cast, machined or otherwise formed into said rotor and situated symmetrically in said rotor so as to conduct a chosen mass air flow drawn in by a vacuum pump source  through said converging nozzles from said nozzles  entrance openings on the said rotor‘s circumference or rim, said nozzles having their smaller  inner exit opening in an inner circular air chamber within said rotor, said nozzle  exit openings in said inner circular air chamber being  situated at  a designed radial distance from the axial centre of said inner air chamber,  said accelerated chosen mass flow of air thereby exerting a  thrust when said air flow  leaves said nozzle’s exit ports  and enters  said rotor’s inner air   chamber;  said thrust then in turn exerting a torque on said  rotor so as to  rotate said rotor in the opposite sense to the direction of the exiting flow thrust,  said  flow then passing through said inner air chamber and exiting through  a chamber exit port of approximately the same area as  the sum total area  of the nozzles exit port areas;  said inner chamber’s exit port leading said air flow into a  flow diffuser connected to a vacuum pump  that provides and sustains  said chosen mass air flow through  said air motor; said rotor thereby acquiring power from the reaction force accompanying said accelerating air flow  produced by said converging air flow  nozzles; said rotor power at its maximum being one half of the  air power of the flow when accelerated through the nozzles to sonic speed;  said power in said rotating rotor being then exportable to the exterior as shaft power by coupling to any rotary power transfer means such as belt, gear, hydraulic, magnetic or other means. .







Figure 1

0007 Figure 1 shows an air flow source 1, such as a vacuum pump, drawing a mass flow of air in through a cylindrical rotor 2 via a set of air nozzles 3  which accelerate the mass flow through them to near sonic speed without any heat being added or extracted,  that is to say the change is isentropic. The accelerated air flow exerts a thrust and torque on the rotor and causes it to rotate. The mass flow then is decelerated efficiently through a flow diffuser 8  to the vacuum pump source and exhausted to the atmosphere out  through the pump  exit. The acceleration of the air flow adds great  air power to the flow; the resulting  thrust and  torque is transmitted reactively to  the rotor for exaction via a power take-off means.


(Figures   2  to 4 not reproduced here) show details of a inner air chamber 5  in the rotor into which the nozzles pass the accelerated air flow and in  which  the thrust and torque are produced; Figure 3  shows the chamber exit plug   6  which forms one side of the said inner air chamber, The exit plug  6 and diffuser tube  8  efficiently slow down the accelerated air flow coming from the nozzles and inner air chamber with minimum loss and delivers it to the vacuum source for exhaustion back to the ambient atmosphere.

0009 In one preferred  embodiment of my invention, shown in Figures  1 to 4.   I first produce (see Figure 1)   from a vacuum source 1  a  flow of air having a fixed mass flow rate  m-dot = ρVA.  I then accelerate said mass flow by passing it through  a set of  two or more converging nozzles   3   in a substantially cylindrical rotor  2 , said rotor being mounted on an  axle or shaft 10,  said nozzles being  molded , cast , machined or otherwise  formed into the material of which the said rotor is made  and being situated circumferentially and symmetrically in said rotor so as to conduct an air flow in through said rotor entrance openings 3 on the said rotor ‘s circumference or rim, said nozzles  having their smaller  inner exits  4  ( see Figure 2) opening into an inner  annular  air chamber 5 within said rotor; said nozzles 3 being positioned circumferentially and symmetrically so that their exit openings 4  into said inner circular air chamber  5 are situated at  a designed radial distance  from the axial  centre of said inner air chamber  5, said converging  nozzles 3 accelerating said air flow through them and said acceleration thereby exerting a  thrust when said accelerated  air flow  leaves said nozzles’ exit ports 4 and enters  said inner rotor  chamber 5 at the said designed radial distance from the centre of said inner  air chamber; said thrust then in turn exerting a torque on said  rotor so as to  rotate said rotor in the opposite sense to the direction of the exiting flow thrust,  said exiting  or thrust flow then passing through said inner air chamber 5;, said air chamber  having an tapered exit plug 6 (see Figure 3), said tapered exit plug being of such a diameter as to fit inside said inner  air chamber 5 leaving a resulting annular clearance space between said exit plug 6  and said inner air chamber 5 through which the nozzle exit flow can exit at approximately the same total cross-  sectional flow area as the sum total  of the nozzle exit areas, so as to maintain the near sonic flow velocity that supplies the thrust; said tapered exit plug 6 moreover having a shaped groove 7 in  its larger end  (see  Figure 3 )  into which the nozzle thrust flow discharges  before then  exiting through the said annular clearance space; said exit plug 6 in turn fitting inside a flow  diffuser tube 8  with the resulting   clearance space  between said exit plug 6  and said diffuser tube 8 (see Figure 4) forming thereby a diverging flow duct for the air flow from the inner air chamber 5, said resulting annular flow duct initially  having approximately the same cross sectional area as the sum total of the  exit areas of the  rotor nozzle exits combined  so as not to slow down such air flow suddenly and inefficiently,  said duct area formed annularly between said tapered exit plug and said diffuser tube then gradually  increasing in area along said tapered plug  6 of diminishing cross sectional area  inside said diffuser tube 8  so as to gradually and smoothly increase the  effective annular  flow duct’s cross-sectional area  thus  allowing the said diverging air flow to slow down efficiently and  match  the design intake flow velocity of the vacuum pump 1;  said diffuser being connected to the intake port of said vacuum pump 1, which sustains the said mass air flow through said air motor system and delivers the final exhaust flow to the apparatus air flow exit port 9, said tapered exit plug 6  being positioned  so as to fit at its larger end  centrally into said inner air chamber 5 and at its tapered portion  to be centrally positioned inside said diffuser tube 8  by being securely  attached to said diffuser tube 8 by two or more smoothly shaped mounting and centering pins  11 or similar mounting brackets.


My invention thus passes the flow through the nozzles, causing an isentropic acceleration of the flow in the nozzles up to sonic or near sonic speed at the nozzle throat or exit so as to generate the desired maximum thrust at the exit from the nozzles and exert a desired  torque on the rotor causing it to rotate and take up the power being generated by the torque. The rotor turns in the direction opposite to that of the thrust flow as required by the law of conservation of momentum or Newton’s Law of Action and Reaction. 


Thus, the torque generated by the reaction force opposite to the  flow thrust through the nozzles transfers power  to the rotor without in any way impeding the mass  flow itself, which simply passes out through the nozzle exits  4, into the air chamber exit channel 7 , then into the diffuser   8  and on to the vacuum system flow exit  9.  In this manner, rotational energy is transferred by the thrust/ torque reaction force  to the rotor 2  automatically, and  so  it becomes readily available as shaft turning power  to be  extracted economically and efficiently from the said rotor by any suitable coupling or rotary power transfer means  ( not diagrammed)   to do useful work, for example by a belt or chain power takeoff, a cog or gear take off, a hydraulic take off or other suitable power take-of means.


The present invention is thus a novel isentropic method of  efficiently accelerating a linear air flow through a converging nozzle or nozzles situated in or on a freely turning  rotor,  while simultaneously and efficiently  transforming said flow’s increased linear kinetic energy into flow  thrust and torque  and into rotational  energy of the rotor which then becomes readily available to produce  work. It is indeed startling in its economy, its simplicity and its improvement on any existing energy source or method for the generation and supply of clean, economical energy.


The “fuel” or energy source for the present invention is typically air, and so, for continuous operation of the method, a continuous flow of air is required.  In the embodiment just described the source of the said mass flow of air is a vacuum pump. In another embodiment the air flow source is a compressor or compressed air supply reservoir. In yet another embodiment the air flow is the relative air flow moving past the air motor when it is mounted on a moving vehicular  platform such as on an automobile, a truck, train, ship, airplane, rocket  or the like. In another embodiment the air flow is supplied by the wind with suitable ducting to conduct the air to the cylindrical rotor of the invention. The source of the air flow may also be a convective up-current of warmer or less dense air, a hot gas rising through a chimney, or a natural convective up-current in the atmosphere, and so on.


It is pointed out that, while the present disclosure and application deals specifically with air, the invention disclosed applies equally to any compressible fluid.


In any actual device there will frequently be some inefficiency so that the flow may be actually quasi- isentropic, but the disclosed  invention covers these situations as well as  isentropic devices and means.


Perpetual Motion Operating Mode


As to efficiency, for example, a certain vacuum device which produces a mass flow rate of 0.074 kg/s can  only produce a maximum suction  power of about 625 watts, but requires an input power of 1690 watts, so that the device  is only about 37% efficient with respect to the  transformation of internal air energy into linear flow energy.  In the present invention, however, the same mass rate of air flow of 0.074 kg/s  at 100% efficiency results in an air flow  power output of 3625 watts  and a rotor take-off useable  power output of 1812 watts for the same power input of 1690 watts. The present invention  thus appears to be  uniquely “self sustaining” in that it apparently can, if desired, be configured, by feeding back sufficient generated rotary power to the vacuum pump, to provide a unique Perpetual Motion ( Perpetuum Mobile) achievement. It is repeated, however, that it is not a heat engine system and so such self-sustaining operation does not involve violation of the second law of thermodynamics [1,2,3]. 


It is also pointed out that if there are substantial flow losses , that is if  the efficiency is less than 100%, the method may not then be self sustaining , but it will still be very  much more efficient than prior  art flow devices.. For example, at 76% efficiency a flow of 0.074 kg/s becomes 0.056 kg/s which will  produce 2743 watts or air flow power and  1371 watts of useable take off rotor power. for the same input power of 1690 watts. While this would not be self sustaining,  it will still be several hundred per cent more efficient than existing prior art flow devices.


In the self sustaining mode of operation, once the base mass flow is initiated, the atmospheric air is the only  ‘fuel’ or energy input needed, while the exhaust is the same air that entered the nozzles from the atmosphere substantially unaltered. .



                                              Design Steps

To illustrate the elements of the method as clearly as possible, we may consider the following design steps:

(1)    The mass flow rate selected or available m  -dot = ρVA, from the vacuum or pressure source, will determine a maximum design air  power output, Pair  to be   obtained at the sonic velocity flow limit, under the condition of  no flow  velocity losses, ( that is, under 100 %  efficiency of flow), which is given by

Pair = ½ m-dot Vsonic2  =  ½ m-dot x (313)2  watts

For example, under this condition of 100 % assumed flow efficiency ( no flow velocity losses), a chosen  flow of 0.74 kg/s, for example,  will produce a  maximum air power at the sonic limit of Pair = ½ x 0.074 x (313)2 = 3625 watts.


(2)  The  design throat area A*  of the nozzle, needed to accelerate a selected design mass flow rate m-dot to the sonic flow speed  ( 313 m/s), is given by

A* = m-dot /ρ*V*.

(2a) For example, for a mass flow rate of m-dot = 0.074 kg/s, and no flow losses,  the nozzle throat area  A* must be 0.074/ 1.2 x 063394 x 313 = 3.11 x 10-4 m2  to pass the mass flow at sonic speed of 313 m/s through the throat area A* to produce the designed air power of 3625 watts.

(2b) If  there are  flow losses  (which is the usual case) then they must be calculated or estimated. For example  if the flow velocity losses are estimated to be, say, 24%,  then the design mass flow rate in the case above will be  m-dot =  [0.074  – 0.24 x 0.074]  =  .056 kg/s. In this reduced  mass flow case the throat area A*  must be designed to be 2.35 x 10-4 m2 . At this area the maximum designed air power will be 2743 watts.


(3) The Thrust Fthr. produced in the rotor at the nozzle exit by the throat  flow of 313 m/s speed will be

Fthr. = m-dot x Vexit  = m-dot x 313   Newtons

For example, a flow of 0.074 kg/s will produce a sonic nozzle thrust of Fthr. = 0.074 x 313 = 23.16 Newtons, whereas a flow rate of 0.056 kg/s will produce a thrust of 17.53 Newtons.


(4) The Torque To that will be produced in the rotor by the thrust Fthrust  of a nozzle flow exiting at a radial offset distance of   r meters from the centre of  the rotor , will then be  

To = Fthrust x r (Newton .meters)

For example, a thrust of 17.53 Newtons, exiting tangentially from the rotor nozzles at a nozzle exit radius of  0.04 meters from the rotor centre, will produce a torque of To  = 17.53 x .04 = 0.72 N. m.


(5) This torque To will then produce a  rotor power  Protor given by   Protor  = To x ω where ω is the rotation speed in radians per second. (  ω in radians/sec = (ω/2π) x 60 in rpm).


For example, at a rotation speed of ω = 1000 radians per second (9549 rpm)  and a  torque of 0.72Newtons   we will have Protor  = 0.72 x 1000 = 720 watts. The rotor power will go up as the rotation rate ω is increased to some maximum value and then diminish to zero, To determine this maximum rotor power we need to take into account the fact that there is a reduction in thrust and torque  that occurs as the rotor speeds up. In the case of air power Pair   we need only use the gas exit velocity from the nozzle relative to the nozzle. However, in the case of the rotor power, the appropriate velocity is the net velocity  difference between the gas exit velocity from the nozzles and the rotor turning speed.  This is because as the rotor  speeds up it gradually overtakes  the exiting gas flow and at some ultimate rotation speed it reduces the power to zero since there is then no net thrust. The rotor power formulae are  as follows:

Protor = To x ω = (Torque) x (rotation)

Protor = (Vnet x m-dot x r)  x ω

Protor = [Vexit -Vrotor ] x m-dot x r x ω

Furthermore, since {Vexit  - Vrotor]  = V­net = r  ω , then when Vrotor =  Vexit /2  =   313/2 = r  ω , we have the important result

Protor =   [Vexit/2 x Vexit /2 ]  m-dot = 1/4 m-dot Vexit 2 = 1/2 P­air

 that is to say,  at a rotor speed of one-half the sonic speed [ 313/2 = 156.5. m/s ], the rotor power is one-half the maximum or sonic  air power.                             

This can clearly be seen if we look at the rotor power curve data in Table 1.for one particular design example:

Design Specifications

Mass flow m-dot = 0.074 kg/s

Input vacuum power needed  to supply 0.074 kg/s flow  = 1690 watts

Nozzle exit radial offset distance r = 0.04 m

Nozzle exit flow speed = Vexit  = sonic = 313 m/s

Rotor speed at radius r  =   Vrotor = r ω

Rotor rotation ω  = Vrotor /r

Maximum air power at sonic throat flow : P air.max  = ½ 0.074  Vexit2 = ½ x0.074 x 3132 = 3624 watts

Table 1

Rotor Power  Data


Vexit         Vrotor        [Vexit – Vrotor]     ω    Torque To    Protor = [Vexit – Vrotor] x 0.074x r x ω

m/s       m/s                  m/s          rad/s       N.m                  watts

313       0                      0               0          0.074                 0

313       100                213           2500      0 .63                  1576

313       120                193           3000       0.57                  1714

313       150                163           3750       0.48                  1809

313       156.5             156.5        3912.5    0.463                1812.4 watts (peak rotor power point)          

313       170                143           4250       0.42                  1798

313       313                 0              7825         0                     0

Notes:  (a) At maximum rotor velocity ( 313 m/s and ω = 7825 radians/s) the rotor power is zero because the net flow absolute velocity measured relative  to the test bed , developed thrust and  torque have all  fallen to zero. (b) The maximum power ( 1812.4 watts) occurs at some lower rotor speed; that is to say at Vrotor = 156.5  m/s and ω = 3912.5 rad./s. i.e. at a rotor velocity  half the nozzle exit velocity of 313 m/s.. The maximum rotor power 1812.4 watts is thus  seen to be one-half the rated sonic air power ( i.e. one half of 3624 watts air power).   (c) In the case of the vacuum source specification of the cited test,  the maximum rotor power ( assuming 100% efficiency) also exceeds the  vacuum source input   power of 1690 watts by 122.4 watts – clearly a Perpetual Motion possibility.  However, since the invention is an isentropic system and does not involve heat injection or rejection, it accomplishes this without at the same time infringing the second law of thermodynamics  [5].  (d) In the laboratory test case cited  here, the level of net power output is small ( 122.4 watts)  but the invention can be readily scaled –up by those skilled in the art  to the level of much higher net  power output. (e)Even when operated at less than maximum rotor power, the present invention can produce power at far higher efficiency than any previous air motor system. If practiced on a moving platform or in the atmospheric wind  flow to provide the basic air flow, the economics obviously become even more attractive since there is much lower cost in  providing the base flow of air  than with a vacuum pump or compressor motor.


(6) The  rotor power can also be expressed in terms of the moment of inertia I of the rotor and the angular acceleration of the rotor  ∂ω/∂t . First we have

Protor  = To  x ω

and since  To  = I  x ∂ω/dt, then also

Protor = = I x ∂ω/dt x ω


(7) The design  Moment of Inertia I  is calculable from the mass of the rotor, plus  its shape and dimensions from standard formulae of rotational  mechanics [1,2,3,6]. With the moment of inertia, we can then go on to calculate the design angular acceleration ∂ω/∂t  from the torque To and the moment of inertia I as follows

 I x ∂ω/∂t = To , so

 ∂ω/∂t = To/I

(8)   Testing: Finally, once the design values are calculated, and the rotor assembled, the system can be operationally tested. First, the mass flow can be measured at the exit port and compared with the design value. Second, the power produced can be verified  by measuring the angular acceleration ∂ω/∂t at various values of rotation ω, and comparing the observed results with the design values through the equation  Protor = = I x ∂ω/dt x ω.  Similarly the maximum rotor power produced can be observed by running the rotor at its peak power rotation speed. (In this final test the safety concerns for high rotation speeds must be kept in mind).


If the measured mass flow  in the test matches the design mass flow, then clearly any losses are not greater than the design value chosen and the design will then produce the expected sonic throat flow speed and the design air power to be delivered to the rotor. If, on the other hand, the measured mass flow in the test is less than the design mass flow, the power will decline markedly. This is so because the air power equation is P = ½ m-dot x V2 , so that the deficiency in mass flow lowers the power linearly, but the accompanying lower flow velocity at the throat also comes into the power equation as an additional quadratic loss. We can then either attempt to reduce the large losses and so raise the mass flow to its design value, or we can redesign the rotor nozzles to accommodate the reduced flow at sonic speed and accept a lower power output.


The basic mass flow, m-dot = ρVA , which sets the scale of the whole design and the power output,  can be furnished  by either an air flow  “push” or  by a “pull”, that is to say, either by a compressive air flow source or by a vacuum air flow source. It can also be set up by a natural “push” flow source such as the wind.    Each case will require a different configuration of the elements of the invention such as the rotor orientation, but the claimed method will be the same in all. In the vacuum or “pull’ case, the rotor will typically be orientated with its axis of rotation parallel to the general air flow through the vacuum source, that is to say the rotor itself will rotate in a plane of rotation at right angles to this said general flow.   In the compressive air flow source case, the rotor  axis of rotation may conveniently be at right angles to the general flow from the  pressurized flow source, but  various  other  orientation options are also possible. If the source of the mass flow of air is either the wind or the relative air flow past a moving vehicle, then the general category will be the compressive or “ push” type source flow.            


When the rotor, rotating with rotational kinetic energy (Iω2) of the accelerated  flow is  then coupled to a power transfer system it completely eliminates the need for inserting any supplementary turbine means, propeller means, or the like, to extract the flow power to do useful work. The rotor means is directly able to produce the desired rotational power and to couple it   to any exterior motor, generator, or other mechanical machine desired to accomplish useful work.  The method of the present invention is thus one of truly remarkable simplicity, efficiency and economy.


If the rotor nozzles are to produce the designed maximum thrust and torque, their exit flow velocity immediately downstream from their exit throat must be as near as possible to the desired sonic speed of 313 m/s. and the flow direction  must also be a linear as possible. This requires that any inefficient premature deceleration and back pressure rise must be avoided as the air from the rotor passes through a   diverging cone or diffuser cone linking the properly decelerating flow from the rotor to the vacuum suction source which sustains the basic mass flow rate.


(f) Design Safety Considerations. With sonic nozzle flow speeds, the rotor typically revolves at very high speeds ( e.g. 20,000 to 40,000  rpm or higher) It therefore develops extremely high centrifugal stresses at its rim which can cause bursting and disintegration of the entire rotor if critical rotation speeds are reached or exceeded.

One  working formula for this bursting limit in a solid rotor is [6]

Vburst = [ 10 x s ]1/2

This formula gives the  rim speed burst limit in feet per second for a material having tensile strength s (in lbs. per square inch). For example, any solid cylindrical rotor made of aluminum with a tensile strength of 36000 lbs./in2  of any radius will have the same limiting  rim speed from the formula of 600 ft per second. Perforated rotors with the nozzles cast or machined into them would have a lower burst speed and therefore a lower safe operating speed. Such safety concerns require state of the art knowledge and input from mechanical safety experts.


Figure 4. Example of shrapnel from catastrophic rupture of rotor  ( acrylic) run at greater than maximum design speed ( 14,500 rpm; 1518 rad/sec) This design flaw  caused serious  injury to operator.





At sonic speed the  flow  can also produce a high pitched piercing noise that may require use of ear protectors to avoid hearing damage.


2.5 Conclusion  


 In Sections I and II we have disclosed flow amplification, flow energy increase and a new power take-off means. The new air motor that has been described uses a vacuum or compressor source for the basic mass flow of air needed to start the process.


It is also possible, however, to use the wind or the relative air flow past a moving vehicle to provide  the basic mass air flow, and  this will now be discussed in Section III,  where a new invention for producing large amounts of clean, economical  energy from the wind and moving vehicles by using conical ducts is disclosed in detail.




1. Standard Handbook for Mechanical Engineers.  T. Baumeister,  Ed. Seventh edition ,  McGraw-Hill Book Company, New York,1958.     

2. Shapiro, A. H.,  The Dynamics and Thermodyn2amics of Compressible Fluid Flow. 2  vols.  Wiley and Sons, New York, 1953.

3. Munson, Bruce, R., Donald F. Young, and Theodore H. Okiishi, Fundamentals of Fluid Mechanics,  Wiley and Sons, New York, 1990.

4. Power, Bernard A.,   Tornado- genesis by an Isentropic Energy Transformation. Posted June 21, 2008 on Website

5.  Perpetual Motion”.  Encyl. Britannica. Vol. 17, p.528, 1959.

6. Machinery’s Handbook.  27th Edition..  Industrial Press Inc,. New York, 2004.



Figure 5. Acrylic Experimental Rotor with 4 Symmetrical Inlet Nozzles.
















Figure 6.  Aluminum Experimental Rotor With 4 Symmetrical Nozzles


Fig. 7. Isentropic Air Motor Showing  ( left to right)  the Rotor, Vacuum Line Coupler and  Vacuum Pump Mass Flow Source


       Copyright: Bernard A. Power 2011  



Section Links:


Section 1:  Linear  ( streamline) Flow and Flow Power Amplification


Section 3:  To be posted in near future


Section 4:  Flow Acceleration and Centrifugal Force as a Possible Cause of the  Observed Temperature Rise Anomaly in the Ranque-Hilsch Vortex Tube


Section 5:  A Note on Isentropic Flow ‘Potential Motion’



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