An Overview of the Mechanics of Oscillating Mechanisms

Transcription

1 Aerican Journal of echanical Engineering, 3, Vol., No. 3, Available online at Science Education Publishing DOI:.69/aje--3- An Overview of the echanics of Oscillating echaniss Christopher G. Provatidis * Departent of echanical Engineering, National Technical University of Athens, Greece *Corresponding author: cprovat@central.ntua.gr Received Deceber 3, ; Revised April 6, 3; Accepted ay 9, 3 Abstract This paper extends a previous study on the echanics of oscillating echaniss in which otion of an object is produced by attached rotating eccentric asses. In addition to the well known twin contra-rotating pair (Dean drive), the single eccentric echanis is studied. In contrast to the contra-rotating systes where the initially still object oves along a vertical track, this study shows that in case of a single eccentric ass the track of the sae object is extended in both the horizontal vertical directions. In both configurations, the path is ainly influenced by the initial linear angular oentu of the eccentrics. While contra-rotation requires a otor to ensure constant angular velocity, in single systes the latter event is conditionally achieved per se. In order to deonstrate the significance of the initial angular oentu in the otion of the object, the two types of eccentrics were applied for the conditions of the eleentary Rutherford-Bohr s odel of a hydrogen ato also of a virtual hydrogen olecule. It was found that, if interolecular forces suddenly disappear at a specific synchronization, the virtual olecule or ato is predicted to reach the incredible altitude of 7k. Keywords: Two-body otion, synchronization, inertial propulsion, dean drive, hydrogen ato. Introduction Inertial propulsion appears in nature, ainly for navigation in diptera [], in industrial applications like shakers in obile phones, wash-achines any others []. The possibility to convert rotary otion into unidirectional otion has been presented by Dean [3] in id-fifties but only recently details have been reported for the particular case of twin contra-rotating eccentrics attached to the object we wish to ove [4,5]. The ain conclusion was that otion is controlled ainly by the initial position of the rotating asses when the object is left to fall down into the air, also by the agnitude of the luped asses as well as by the angular velocity ω the radius r (the product ωr constitutes the angular oentu of the propulsion syste). When the otor keeps on working, the angular velocity ay be controlled to be preserved at a constant value, while when it is switched off the conservation of echanical energy des the periodical variation of the angular velocity [5]. In addition to the aboveentioned twin eccentrics, there are any cases where only one eccentric ass is attached to an object. Typical exaples are: twin echaniss suddenly broken, shakers in obiles where the friction plays a significant role, athletes who rotate their ars during long jup, electrons that rotate around protons in atos, any others. This paper ais at studying priarily the single eccentric echanis also to copare it with the twin one.. Inertial Propulsion echaniss.. Contra-rotation (Twin Eccentricity)... General Forulation The particular case of contra-rotating synchronized eccentric asses has been previously investigated [4,5]. We consider the particular echanis that consists of a horizontal object (rigid plate) characterized by a large ass, on which two rigid rods of equal length (radius r) are syetrically articulated at their one end while a saller ass is attached to their other ends, as shown in Figure. Details are given elsewhere [5], but for reasons of copleteness we ust ake clear that: The object of ass is rigid has a unifor shape in the horizontal x-direction. The eccentric asses (No. No.) rotate at equal opposite angular velocities, t t : contrarotation. Both asses (No. No. ) possess the sae vertical z-level. The object is left free to fall down when the orientation of the rods for an angle with the horizontal line, as shown in Figure. Obviously, the above ideal syetric conditions lead to an ideal upward translational otion of the echanis. The analysis below is based on the use of Lagrange equations.

2 Aerican Journal of echanical Engineering 59 Figure. A typical Dean drive, in which the centroid of the object (of ass ) oves upwards fro the initial position G to the current G The position of the ass in the echanis is described by the altitude z, whereas the position of each ass (No. No.) is deterined by z. According to Figure, the relationship between the is: z z r sin () By virtue of (), at every tie instance the velocity coponents of the i-th eccentric ass will be: z, i z r sini z ri cos i, i, () x, i x r cosi x ri sin i, i, (3) Obviously, the object does not ove horizontally, that is: x (4) Therefore, due to the syetric arrangeent of the two rotating asses so as, with respect to the inertial reference frae (fixed to the ground), both velocities have the sae easure given by x z v, the kinetic energy of the entire echanis will be: Ekin z v z x z z r sin z r cos while the potential energy of the syste will be: E pot z z r sin g gz gr sin (5) (6) Using (5) (6), we can write the Lagrangian L of the dynaic syste as follows: L T V E E kin pot sin x z x r sin cos x r z r gz gr sin (7) The two generalized coordinates of the dynaic syste ay be chosen as follows: q x t, q z t (8) By virtue of (8) considering t while all four quantities (, g, r, ) are constants, (7) becoes: L q q q r q r sin q r cos q, q, q, q sin (9) gq gr sin Following Reference [6], the equation of otion is: d L L for i, q i qi For i =, Eq() iplies that: () q, () which eans that the object does not accelerate therefore preserves its initial (zero) horizontal velocity, i.e. x t, as anticipated due to the syetry. For i =, after anipulation, Eq() becoes: z r sin g () Considering that at the initial tie t = the angular velocity the angular position are, respectively, the exact solution of Eq() is obtained as follows: where cos z t z v t gt t sin sin (3) z t v gt cos cos (4) r (5) It should becoe clear that equations ()-(4) are valid either the angular velocity is variable or constant. We note that Eq(3) consists of the usual ter that appears in the accelerated otion, plus the ter cos t, which is proportional to tie, accopanied by a inor sinusoidal ter. Equating the su of initial kinetic potential energy, Eq(5) Eq(6), with the potential energy at the upper point, that is gzax, we can approxiately write that zax cos (6) g Also, the tie required for the echanis to reach the aboveentioned upper point is obtained by setting the object velocity equal to zero. Thus, ignoring the ter cos in Eq(4), we can approxiately write that tax (7) cos g

3 6 Aerican Journal of echanical Engineering In other words, it is like as if the object perfored a straight line otion with constant acceleration, -g, upward initial velocity v cos. This eans that the critical quantity to deterine the upper point of object s orbit is the initial polar angle. Then, the altitude becoes axiu when the eccentric asses are initially on the sae horizontal line with the centroid of the object ( cos ), at the sae tie no external (support) forces exist.... Energy Conservation Let us suppose that the otor stops feeding the rotation of the rods, at the sae tie, the object is left to fall. After considerable anipulation, the condition that the su of kinetic potential energy given by equations (5) (6) is preserved to be constant, leads to the following relationship for the variation of the angular velocity: t sin sin t (8) Considering that t t, Eq(8) can be nuerically solved using, for exaple, the Runge-Kutta ethod, as ipleented by ode45 in ATLAB...3. Internal Forces oents If we consider half of the echanis, we can calculate the force oent transitted by one half to the other one...3. Forces Concerning forces, it is easily found that the two coponents of the force exerted fro the left to the right half will be: Fint, X x x (9) r sin cos Fint, Z z z g () The sign of Fint, X refers to the positive or negative direction of the force coponent is not related whether tension or copression occurs. In fact, a positive F corresponds to copression whereas a negative to int, X tension...3. oents Concerning oents, the bending oent in the iddle of the ass is obtained considering the eleentary equation that the total oent of external forces with respect to the center of ass for the half echanis equals to the rate of total angular oentu, that is b dl. In ore details, with respect to the center of ass C for the half echanis the angular oentu is given in ters of the position vectors for the center of ass C of half the object ass (i.e. /) the corresponding eccentric ass, by: L r v r v () rel, rel, whence (see Figure ) dl b drrel, dv v rrel, drrel, dv v rrel, () Substituting in Eq() the relative vectors by rrel, r rc r rel, r r, that is in ters of the C position vectors ( r r ) with respect to the axis origin O (along the vertical axis of syetry), considering that the position r C of the center of ass for the right half echanis is given by the well known expression rc r r, after anipulation the bending oent is finally given by the forula: b r r a a (3) Since the vector r r in Eq(3) equals to ( EC ), it becoes obvious that it depends not only on the position L of the center C but also on the position L of the attachent point P of the rod on the object. Figure. The free body diagra for the right half of Dean drive, to deterine internal loads.. Single eccentricity... General Conditions In case that the syste consists of only one eccentric ass (attached to point E), which is connected to the object through the rigid rod EP (Figure 3), echanics becoes quite different. The otion depends ainly on (i) whether the point P coincides with the center of ass of the object or not, also on (ii) the type of joint at P. In general, the syste of the rigid rod EP associated with the asses (,) is a closed syste except of the gravitational forces. Therefore, with respect to its center of ass (C) to which the oent of gravity forces vanishes, the angular oentu is preserved. Obviously, the aforeentioned center of ass ay be firly connected to the rod EP (when P is the centroid of the object) or ay also vary (when P is not the previously entioned centroid).

4 Aerican Journal of echanical Engineering 6 Figure 3. A single eccentric ass attached to the center of ass of the object (of ass ) oves horizontally vertically fro the initial position P to the current P' In the particular case that (a) the point P actually coincides with the center of ass of the object (b) considering a proper (e.g. ball or hinge) joint between the object the connecting rod, the internal torque between the object the connecting rod EP vanishes at P ( y = ), therefore the free diagra of the object ( L I ) leads to the fact that the object aintains its initial angular oentu. Without loss of generality, we assue that initially the object P does not rotate (ω = ) therefore it continues not rotating. Under these conditions, the rigid rod EP rotates as if two luped asses were attached to the points E P. In ore details, the center of ass C of the two-body syste (, ) lies always along the segent EP at a distance r E (CE) r P (CP), given by: re r, rp r (4) Considering again the entire syste (,), the total angular oentu wrt C is given by the forula: where L total I C C, (5) C P E I r r (6) Substituting Eq(4) into Eq(6), one obtains: I C... Equations of otion r (7) Although the previous subsection (..) could be the starting point to derive the equations of otion, in order to be consistent with subsection. we follow the Lagrangian forulation as well. Therefore, in case of an object with ass an eccentric ass, the kinetic energy of the syste will be: z Ekin x x z x z x r sin z r cos while the potential energy of the syste will be: E pot z z r sin g gz gr sin (8) (9) Taking the sae generalized variables as in Eq(8), Lagrange equations (Eq()) lead to the following syste of decoupled ODEs: x r cos (3) z r sin g (3) Since the angular velocity ω is a constant, the above ODEs are easily integrated in tie t, progressively obtaining for the horizontal otion: ˆ sin sin x t u, (3) ˆ sin ˆ cos cos x t x u t t (33) while for the vertical otion: where ˆ cos cos z t v gt, (34) t.. z t z v t gt ˆ sin sin ˆ cos t ˆ..3. Energy Conservation r, (35) (36) Based on the closed for expressions of the four velocity coponents ( xp, zp, xe, z e ), after anipulation the total echanical energy is found always to be constant therefore equal to its initial value: Etotal er r g sin 3. Nuerical Results (37) 3.. Exaple : Twin Eccentrics Following [5], we consider a contra-rotating echanis with the following data: Rotating ass : = kg (wrt. Eq()-(5)) ass of the object B : = 5 kg Radius of rigid rod : r =

5 b [N] Zax [] FintX [N] Zdot [/s] z [] Z [] 6 Aerican Journal of echanical Engineering Angular velocity : ω = 34 6 s - (3 rp) Initial polar angle of the rods: deg Acceleration of gravity: g = 9 8/s In this particular case where the anti-clockwise angular velocity is ensured to be constant by the aid of a otor, the result of the kineatical siulation is shown in Figure 4. The graph reinds the vertical shoot of a projectile, well known fro lyceu physics. As it has been previously shown [5], the axiu altitude of the object is achieved when the object is left free to fall at the tie where the two rigid rods have taken an ideally horizontal position, that is. 6 4 Object Altitude It is clarified that here the rotating ass was obtained equal to kg, which equals to the total ass of both asses used in Exaple. Therefore, Equations (3,3) are valid for = kg, while Eq () is valid for = kg. Again for anti-clockwise rotation, the results are shown in Figure 6, where one can notice that the track of the object highly depends on the initial value of the polar angle, as it was also the case in Exaple. In ore details, when 8 deg (equivalently 8 36 deg), the object oves fro the left to the right, whereas when 8 deg it oves fro the right to the left (not shown in the graph)..5 deg OBJECT TRACKS -.55 deg -45 deg deg Object Velocity -9 deg deg Tie (s) Figure 4. The calculated otion of the object (top: the altitude versus tie, botto: the object velocity) oreover, the variation of forces oents in the iddle of the syetric object (at the axis of syetry) is shown, for the first tie, in Figure 5. x 4 Horizontal Force deg deg -35 deg x [] Figure 6. The track followed by the center of ass of the object, for the sae anti-clockwise angular velocity several initial polar angles 8,, degrees. oreover, as shown in Figure 7, the axiu altitude is obtained when, is identical with that of the contra-rotating echanis (cf. Eq ((3) with Eq (35)) Bending oent Tie (s) Figure 5. The calculated loads in the iddle of the object (top: axial force, botto: bending oent) UPPER POINT Initial angle f [deg] 3.. Exaple : Single Eccentric ass We select very siilar data with those in Exaple : Rotating ass : = kg (wrt. Eq(36)) ass of the object B : = 5 kg Radius of rigid rod : r = Angular velocity : ω = 34 6 s - (3 rp) Initial polar angle of the rods:,,36 deg Acceleration of gravity: g = 9 8/s Figure 7. The axiu altitude of the object achieved for the sae anti-clockwise angular velocity several initial polar angles 8,, degrees Finally, in Figure 8 we copare all possible cases concerning Exaple Exaple. For alost 5 periods in rotation of the eccentric asses, the nuerical solutions for both constant (achieved by the otor in Exaple, without any otor in Exaple ) as well as variable angular velocities are very close one another.

6 Z [] Aerican Journal of echanical Engineering 63 In other words, either the otor is switched on ( controlled so as to preserve the angular velocity of the eccentrics) or the otor is switched off ( the echanical energy is preserved thus deing a variable angular velocity, cf. Eq (8)), the axiu possible altitude the object can reach is the sae. Again, the only difference between contra-rotation single eccentric ass echaniss is only the horizontal otion of the object, which is possible only for the single echanis, of course under the conditions illustrated in Figure OBJECT ALTITUDE Constant Angular Velocity (Exaples & ) Variable Angular Velocity Tie (s) Figure 8. Coparison between Exaple- Exaple- concerning the track followed in three cases 3.3. Exaple 3: Siplified Hydrogen olecule or Hydrogen Ato This exaple is of rather acadeic (educational) iportance, in the sense that it only depicts the great role of the initial angular oentu in the otion of the object, the latter taken to be the proton of a hydrogen ato (836 ties heavier than the rotating electron [8]). It has been chosen because the two previous exaples (Exaple- Exaple-) have already prepared the reader to underst the role of one or two eccentric asses, which could correspond to the hydrogen olecule (two rotating electrons) or hydrogen ato (one rotating electron), respectively. For purposes of copleteness, we reind that when two hydrogen olecules approach, the forces consist of three parts: exchange, quadrupole, dispersion (van der Waals) forces [7]. These interolecular forces are very iportant because they achieve to keep the olecules in close distance fro their neighboring ones not escape; otherwise, under certain individual circustances, incredible phenoena could happen Virtual Hydrogen olecule In order to create siilar conditions with those in Exaple, we assue that the interolecular forces suddenly vanish exactly when both atos in the olecule are on their horizontal position (Figure 9, botto). In order to estiate the axiu altitude which the hydrogen ato or olecule can reach, it becoes necessary to calculate the ass ratio (i.e. the unknown radius r) also the angular velocity. The easiest way to achieve it is to consider the old Rutherford Bohr odel of hydrogen ato. The tangential velocity, v r, is calculated in ters of classical echanics by equating the centripetal force with the Coulob force, that is: e kee v r, (38) r where e is the electron's ass, e is the charge of the electron, ke 4 is Coulob's constant ( is the perittivity constant). This equation deterines the electron's speed at any radius r: ke e v (39) r e In addition, we consider the quantu rule, according to which the angular oentu L = e vr is an integer ultiple of ħ (=h/π) [8]: vr n, n,,3, (4) e Substituting (39) into (4) gives an equation for r in ters of n: kee er n (4) so that the allowed orbit radius at any n is: n rn kee e (4) The sallest possible value of r in the hydrogen ato, for n =, is called the Bohr radius. For the purposes of this paper we assue that the otion of every electron takes place on the vertical plane the distance between the two protons (nuclei) in the virtual hydrogen olecule is constant, thus the two nuclei copose the object of ass for which our theory (section.) has been developed. As previously was explained, each electron corresponds to the eccentric ass. According to Eq(4) the distance between every electron its corresponding proton (nucleus) is constant transfers axial forces. Figure 9. A virtual set up of a synchronized hydrogen olecule oving upwards (botto figure refers to the initial position, t =, where both electrons are assued at the horizontal level)

7 64 Aerican Journal of echanical Engineering We consider the following well established data: [joule.sec] 8.85 [farad/], k e 4 9 e.6 [Coulob] [kg] e 7 p.67 [kg] g = 9.8 [/s ] Then the Bohr radius is equal to: r 5.9 kee e (43) oreover, Eq (39) iplies that the electron velocity is calculated equal to: 6 v.869 / s, whereas its angular velocity ( vr) is: s. Also, Eq (6) Eq (7) iply that: z k, ax 4 tax.39 s. Although there is no otor to aintain a constant angular velocity (as happened in Exaple ), we assue for instance that the latter is practically constant then we intend to coe back to check the validity of this assuption. Under this assuption, the nuber of revolutions until the olecule reaches the upper point is estiated by: t ax revolutions Since the olecule oves upward, a part of the kinetic energy is transfored into gravitational potential energy gz, a fact that soehow reduces the angular ax p e velocity. Actually, for the current Rutherford Bohr odel the initial kinetic energy K e v equals to Joules, while the potential energy at the altitude of 7k is only.37 - Joules. As the latter corresponds to a very sall relative variation of the kinetic energy, only.5% with respect to K, the angular velocity of the electron does not practically change. Applying the above odel for ore haronics, n, the results are shown in Table. Table. axiu altitude for several haronics (Initial condition: ) Haronic ( n ) axiu Altitude z ax (k ) Rise tie t ax (s) In all cases, the variation of the angular velocity is less than.3 percent with respect to its initial value. Obviously, for any different initial condition,, the results of Table ust be properly ultiplied by either cos or cos, according to Eq(6) or Eq(7), respectively Virtual Hydrogen Ato If now the hydrogen ato is isolated fro its olecule, the theory of Section. (single eccentricity) the closely related Exaple are applicable. Due to identitity between Eq(3) Eq(35), the axiu altitude for hydrogen ato is the sae with that the hydrogen olecule can reach. Therefore, the results of Table are applicable to the hydrogen ato as well, for the additional reason that the angular velocity is preserved per se. Concerning the horizontal otion, except of the case 8 degrees, in all other cases it is endless (cf. Figure 6). 4. Discussion Concerning the twin contra-rotating echanis, the graphs of internal force (alternating between tension copression) alternating internal bending oent was presented for the first tie. The shear forces along the axis of syetry of the object were found to be zero, a fact that is theoretically supported by the perfect syetry in echanis in both shape external loading. Concerning the echanis based on one single eccentric ass only, it was ade clear that the ain reason that the angular velocity is constant is the lack of external oent on the object. This study was restricted to the case that the point of attachent coincides with the center of ass C of the object. If the latter does not hold, the oent of object s weight with respect to C will induce an additional angular oentu that has to be taken into account in the foration of odified equations, which are not included in this work. A possible application of this theory is the bioechanics of long jup. Concerning the hydrogen olecule odel, it is a calculation of classical otion of a hydrogen olecule when the interolecular force between it nearby hydrogen olecules suddenly disappears. The calculation assues an unlikely initial configuration for the electrons around the two nuclei: as far away as possible fro each other in a Bohr orbital with opposite angular oentu so that each velocity is upward. The paper continues to ake assuptions that are ore based on convenience than the physics of the situation: a Bohr odel of each electron around the proton (but still bound as a hydrogen olecule), a constant angular velocity of the electrons even though the initial oentu of the electron is what propels the olecule upward. On the other point of view, the Bohr odel is only useful for one-electron atos. In the Hydrogen olecule, there are two electrons interacting experiencing a nonspherical potential fro the two protons. Despite these weaknesses, in the light of Section. (single eccentric

8 Aerican Journal of echanical Engineering 65 ass), for any certain value of the initial polar angle both the olecule or the ato achieve to reach the sae axiu altitude z ax. Despite possible reservations fro the point of view of odern physicists, despite the probability that all restrictions ade siultaneously occur is practically zero, the educational value of this study is obvious. In the case we studied, the ass of the proton is uch larger, that is about 836 ties the ass of the electron [8]. Nevertheless, the treendous angular velocity of the electron ( /s = rp) is capable of producing the otion of the olecule due to its initial oentu. A secondary shortcoing of our approach is that relevant analysis was based on the assuption of a constant angular velocity. Of course, based on energy conservation, accurate nuerical analysis is possible but then the elegance of closed for solution is lost. The fact that the assuption of a constant angular velocity leads to a variation of total energy by.5% (i.e. initial kinetic energy: K = Joules; final gravitational potential energy: E pot =.37 - Joules) supports that the analysis of this paper is adequately correct. Based on the above analytical solution, the linear velocity fro /s decreases to only /s, so the variation is only.7% with respect to the initial value. Since the radius r reains unaltered, the sae percentage holds for the angular velocity as well. Another reark is that at the altitude of 7k, which corresponds to the saller (Bohr s) radius, the gravitational acceleration reduces fro 9.8 to 9.59/s, but this is only a variation of approxiately. percent. In other words, the fully analytical odel used in this paper is adequately accurate, at least for the purposes of this work. It is worth-entioning that, obviously, the virtual case of an isolated hydrogen olecule is equivalent to the virtual case in which all olecules have the sae orientation also the sae initial condition, i.e. at a certain tie, t =, all electrons are on their horizontal level with respect to the center of their associated protons. In such perfect synchronization at t =, all vectors of the centrifugal forces lie on the horizontal plane thus no external vertical force is needed to support the. The topic of the echanics of contra-rotating oscillating echaniss has been previously covered in the fraework of rigid body dynaics [4,5], whereas alternative figure-eight shaped echaniss have been proposed (instead of the circuference used in this study) on which the rotating asses ove [9]. However, even within the context of contra-rotation, very recent studies have extended the theory by considering elastic waves transitted through the rigid rods EP that connect the rotating asses with the heavy object []. Also a very recent study deals with an electroagnetic equivalent ( Tesla drive), in which no echanical rotation is necessary []. The latter has been said to be proising for the future of aeronautics astronautics []. 5. Conclusion It was found that initial angular oentu of eccentric asses, which rotate around heavy objects, force the latter to travel in long distances. The track followed by the objects is priarily proportional to the angular oentu. However, for a specific initial angular oentu, the distance travelled is highly influenced by the initial polar angle at which the echanis is left free to fall down. In both cases studied, that is (i) contra-rotated (ii) single ass echaniss, the object ay be initially entirely still but otion is afterwards induced by the oentu of the rotating sall asses. In all cases, the otion of the center of ass follows a track siilar to that of the well known vertical or oblique shoot for a given initial velocity. The theory was also applied to the hydrogen ato the hydrogen olecule where interolecular forces were assued to vanish, despite possible concerns fro the point of view of odern physics, calculations predicted incredibly large range such as 7k. References [] Thopson, R.A., Wehling,.F. Evers, J.E., Evaluation of the haltere as a biologically-inspired inertial rate sensor, AIAA Guidance, Navigation, Control Conference, Aug. 8, AFRL-RW-EG-TP [] Blekhan, I.I., Synchronization in Science Technology, ASE Press, NY, 988 (in English, translated fro Russian 98). [3] Dean, N.L., Syste for converting rotary otion into unidirectional otion, US Patent,886,976, ay 9, 959. [4] Provatidis, C.G., Soe issues on inertia propulsion echaniss using two contra-rotating asses, Theory of echaniss achines, 8 () [5] Provatidis, C.G., A study of the echanics of an oscillating echanis, International Journal of echanics, 5 (4) [6] Goldstein, H., Classical echanics, nd edn. Addison-Wesley, Reading, 98. [7] argenau, H., The Forces between Hydrogen olecules, Physical Review, 64 (5-6) [8] Halliday, D. Resnick, R., Physics, Parts I II, Cobined edition, Wiley International Edition, New York, 966, [9] Provatidis, C.G., A device that can produce net ipulse using rotating asses, Engineering, (8) [] Provatidis, C.G., Influence of rotation speed on natural frequency: A short introduction presentation of an iaginary 'antigravity' world, arxiv: physics.gen-ph/ Apr.. [] Provatidis, C.G. Gable.A., Support forces in a synchronized rotating spring-ass syste its electroagnetic equivalent, International Journal of Applied Electroagnetics echanics, 4 (3) [] anning, J. Space, Propulsion & Energy Sciences International Foru: A Journalist s Notes, Infinite Energy, ay/june.