Thursday, 8 December 2016

An Overview of Dr. Paul Zarda’s Professional Career at Lockheed Martin

Dr. Paul Zarda is a skilled professional serving as the Manager of Engineering Methods Group at Lockheed Martin. He joined this organization in the year 1980. He has both practical and theoretical experience of almost four decades in the area of MCAE (Mechanical Computer Aided Engineering) and KBE (Knowledge Based Engineering). He has been in charge of a Mechanical Designing team at corporate and local level.

Dr. Paul Zarda has reviewed engineering processes at Lockheed Martin Missiles and Fire Control facility in the area of preliminary and conceptual design of missile and fire control systems, which led to a developed methodology and architecture to capture that knowledge. The Engineering Method Groups offer Interactive Missile Design (IMD) and Interactive Gimbal Design (IGD) systems for conceptual designs of fire control and missile systems, respectively. This effort has made a significant impact in multi-disciplinary design processes that has led to over $5 million of savings. The Interactive Missile Design has been singled out by Lockheed’s Air Force customer as a key discriminator in successful proposal wins.

At Lockheed Martin, Dr. Paul Zarda is handling a wide range of responsibilities: Member of Technical Staff assigned to Research and Technology in Technical Operations, Manager of the Engineering Methods Group, Program Manager of Supersonic Hypersonic Vehicle Design contract with WPAFB, Program Manager of the WBDE (Web-based Design Environment contract with the Wright-Patterson Air Force Base). He is also a professor at UCF, where he holds the title of Research Professor of Mechanical Engineering in Mechanical Engineering Department, And Aerospace Engineering.

Paul Zarda of Sanford, Florida has a high academic profile: he acquired his Bachelor of Arts in Physics and Mathematics, from Jacksonville University. He took received his Bachelors of Science in Civil Engineering from Columbia University, N.Y. Thereafter, he received his Masters in Engineering Mechanics from the same University. In his free time, he likes to enjoy and celebrate along with his whole family, playing tennis, and doing wood working in his home shop.

Wednesday, 30 November 2016

Paul Zarda Has Diligently Worked On IBM And VAX Systems

Dr. Paul Zarda is an Orlando based professional serving as the Manager of the Engineering Methods Group at Lockheed Martin Group. In 1980, he acquired MSC/NASTRAN for structural analysis on the IBM 3084 system. Until this time, Martin Orlando was using in-house structural analysis codes that were 10-15 years old, unsupported and poorly documented. This significantly changed the way structural analysis was to be performed over the next 19 years.  In direct contrast to this until 1990, Lockheed Martin Denver had continued their use of in-house codes at a significant reduction in productivity and capability.

Thereafter, in the year 1982, Dr. Zarda acquired SUPERTAB, a pre- and post- processor, on the IBM 3084.  This significantly increased the productivity of all analysts at Martin. This software has been the workhorse for all analysis software that is geometry driven, and its longevity (Master Series, now available on the workstations) has proven its worth.

In addition, Dr. Paul Zarda participated in the solicitation and acquisition of the 1st VAX 11/780 that was acquired by Martin.  He was instrumental in moving the engineering analyst from IBM TSO to this system.  He was responsible for the acquisition of MSC/NASTRAN, SDRC's SUPERTAB, and the solid modeler GEOMOD for the VAX system.  It is estimated that this move probably affected engineering analysis productivity by a factor of 10.  Today the CAE analysis software, I-DEAS, NASTRAN, PATRAN, FEM/SINDA, etc., represent over 50 percent of the TCC's usage.

Dr. Paul Zarda solicited and helped in acquiring a suitable communication link between our IBM 3090 systems and VAX systems so the analyst could have some alternatives in performing his job.  This resulted in the acquisition of INTERLINK, a software/ hardware communication package that finally coupled our IBM and VAX worlds.  This took place despite significant resistance by Martin Marietta Data Systems. This software/hardware is the foundation today between our IBM and DEC mainframes and our 

Thursday, 3 November 2016

Paul Zarda Is a Mechanical Engineer Based In Orlando

Paul Zarda is a highly skilled professional with many areas of expertise. By profession, he is a mechanical engineer and has both theoretical & practical expertise in the area of Mechanical Computer Aided Engineering (MCAE) and Knowledge Based Engineering (KBE). Currently, he is serving as a Distinguished Member, Technical Staff, and Manager of the Engineering Methods Group at Lockheed Martin Missiles and Fire Control. He is also an Adjunct Professor at UCF, where he holds the title of research professor of mechanical engineering in the department of mechanical, material and aerospace engineering.

As Manager of the Engineering Methods Group, Paul Zarda is responsible for helping provide direct support of the engineering community in the areas of mechanical design and analysis, systems engineering and optical design. He has been involved in the capture of the design process of missile & fire control systems. This further led to the development of the Interactive Missile Design (IMD) system for missile systems & to the development of the Interactive Gimbal Design (IGD) system for fire control.

Paul Zarda
is also the inventor of a tennis racquet –The “Zarda-Top-Spin-Racquet”, also known as the Z-TSR. It provides top-spin to the ball (and under-spin if the ball is appropriately struck) through a different design compared to the spaghetti tennis racquet and other racquets on the market.

Wednesday, 26 October 2016

Paul Zarda, The “Zarda-Top-Spin-Racquet” Inventor Is A Mechanical Engineer by Profession

Paul Zarda, who is the inventor of a tennis racquet called the Zarda-Top-Spin-Racquet, or the Z-TSR, is a Mechanical Engineer by profession. The invention is designed in such a way that it provides top-spin to the ball by using a different design compared to the spaghetti and to other racquets on the market. The design causes a ball’s top spin and under spin that is 30% to 50% (or more) greater than conventional rackets.

The Z-TSR has an inner frame that contains strings under tension that make contact with the ball. This inner frame is connected to the outer frame through an isolation system that allows movement of the inner frame relative to the outer frame upon impact of the ball on the outer frame.  The movement between the inner and outer frame results in an additional spin to the struck ball when compared to the same swing with a traditional racket.

Paul Zarda’s Z-TSR also has the ability to modify the isolation system to affect the play of a racquet. It is possible to adjust, replace, or supplement the isolating system according to how one wants the racquet to perform. These adjustments could take place during a match or after matches and may not require adjusting the string pattern.

Monday, 24 October 2016

Elliptical shaped tennis racquet only carries axial load

Preface: Paul Zarda notes that an elliptical shaped tennis racquet, with a dual loading condition of main string tensions and cross string tensions, will be shown to carry only a low-stress-level compressive load and not the expected high-stress-level bending moment. This 2-D loading condition applied to a tennis racquet is analogous to the historical 1-D loading of a parabolic arch (carrying only axial load) that is well documented in mechanical engineering and engineering mechanics. As far as the author is aware of, this is the first ever documentation and corresponding proof that an elliptical shaped tennis racquet head, loaded using a derived formula for the main and cross string tensions, will be shown to carry only a low-stress axial compressive load.  In order to minimize stress-levels in a tennis racquet due to stringing, these in-racquet-derived-formula-string tensions should be a targeted final-string-tension level for the stringing of any elliptical or nearly-elliptical tennis racquet.  

                                                            Figure 101

Figure 101 shows the head of a tennis racquet that is subjected to tensioned strings that cause loads in the cross string direction (x-direction) and the main string direction (y-direction). As shown in Figure 101, Wx corresponds to a loading per unit length for the cross string tensions, and Wy corresponds to a loading per unit length for the main string tensions.

Paul Zarda of Sanford notes the insert shown in Figure 101 exposes the internal forces that can develop in the frame caused by the string tensions. M is the bending moment on the x-section, V is the shear force on the x-section, and N is the axial force on the x-section. It will be shown that if the in-plane x-y shape of the tennis frame is elliptical, then the bending moment and shear force will be identically zero. This will be shown to only occur for a specific ratio of Wy/Wx.

                                                                      Figure 102

Figure 102 shown a free body diagram of the right half of the tennis frame. As shown in Figure 102, the symmetry plane cut at x=0 only exposes normal forces Fx (and from symmetry about the y=0 plane, Fx is the same for the top x-sectional cut and the bottom x-sectional cut shown in Figure 102).

 Sum of forces in the X-direction = 0:      
                                                                                                                 Equation 101                                                                                                           
                                                                                                                               Equation 102
Figure 103 is a free body diagram of the top half of the tennis frame. The x-sectional cut on the symmetry plane y=0 exposes the axial force Fy (as shown in the Figure). Fy is the same axial force for the left cut and the right cut of the frame since x=0 is also a symmetry plane.

                                                                        Figure 103

From Figure 103, using sum of forces in the Y-direction = 0:

                                                                                                                            Equation 103
                                                                                                                            Equation 104
                                                         
Figure 104 is a free body diagram of the tennis frame in the 1st quadrant. It shows the frame with x-sectional cuts both on the symmetry plane y=0 and also a cut at the (x,y) position shown in the Figure. The x-sectional cut at position (x,y) exposes the axial force N acting an angle θ as shown in Figure 104. 

                                                                                Figure 104

From Figure 104, with the assumption that M and V are 0 at the x-sectional cut at the position (x, y), then the sum of forces in the x-direction = 0 gives
  
                                                                                                                             Equation 105
From Figure 104, sum of forces in the y-direction = 0 gives

                                                                                                                             Equation 106
From Figure 104, sum of moments (counterclockwise) about point A = 0 gives
                                                                                                                              Equation 107
Substituting Ncosθ from Equation 105 and Nsinθ from Equation 106 into Equation 107, one gets

                                                                                                                             Equation 108 
Combining similar terms
                                                                                                                               Equation 109
                                         
 Simplifying, and substituting in for from Equation 104
                                                                                                              Equation 110
                                                                                       
Expanding 
                                                                                                                               Equation 111 
With the orange terms canceling, and rearranging

                                                                                                                                Equation 112
 And dividing by the right hand side  

                                                                                                                                Equation 113
 Re-adjusting the first term
                                                                                                                                Equation 114
Re-writing Equation 114
                                                                                                                                Equation 115                                                     
If the term in { brackets } in Equation 115 is unity, Equation 115 is the equation of an ellipse, centered at (0, 0), with minor/major axis of 2a/2b, respectively, as shown in Figure 101. Hence, setting the bracket term to unity
                                                                                                                               Equation 116
Or
                                                                                                                              Equation 117
Statement: Equation 117, in conjunction with Equation 115, says that if the cross string tensions per unit length, Wx, is a fraction (a/b)2 of the main string tension per unit length, Wy, then, with a racquet head in the form of an ellipse per Equation 115, the frame will only develop a low-stress-level compressive force N. It is the author’s opinion that this is the first time in history that this revealing statement and corresponding proof has been publically offered.

                                                            Figure 105
Paul Zarda of Orlando notes the observations made in the above statement have impact both on stringing a tennis racquet and the performance of a tennis racquet. Figure 105 shows an elliptical shape head of a tennis racquet with several definitions provided associated with the stringing of a tennis racquet. If we define, as shown in Figure 105, that Tx is the cross string tension, Ty is the main string tension, nx is the number of cross strings, and ny is the number of main strings, then Wx, the cross string loading per unit length, is approximated by (using an average spacing)
                                                                                                                           Equation 118
Similarly, Wy, the main string loading per unit length, is approximated by (using an average spacing)

                                                                                                                           Equation 119
Substituting Equations 118 and 119 into Equation 117

                                                                                                                           Equation 120
Simplifying
                                                                                                                           Equation 121
To somewhat quantify this formula, let’s do the calculation where the head width 2a of a racquet is 10 inches and the head height 2b is 13 inches, and the string pattern is 16 x 19 (ny = 16 main strings, nx = 19 cross strings, a somewhat typical racquet). Using a reference main string tension of Ty = 60 lbs, the above formula produces a cross string tension Tx of 38.9 lbs. This cross string tension of 38.9 lbs assumes equal spacing of main and cross strings (an approximation), and is relative to the main string tension of 60 lbs. This set of tensions ( Tx ,Ty ) = (38.9, 60), in an elliptical shaped head (or nearly elliptical) of 10 inches x 13 inches, will produce a low-stress-level axial compressive load (see Equations 102 and 104 for representative axial compressive loads; using these formulas, at 12 o-clock Fx = 370 lbs and at 3 o’clock Fy = 480 lbs).

Paul Zarda of Orlando and Sanford notes it is important to point out that Equation 121 provides the final cross string tension Tx in a frame relative to the final main string tension Ty. These tensions are not necessarily (or even likely) the tensions pulled when stringing a racquet in a stringing machine. This observation is due to the fact that, during the stringing process, a racquet’s frame can deform, and that deformation will cause the pulled tensions to change. This deformation is related to the flexibility of the stringing machine and its support of the tennis racquet, the flexibility of the tennis racquet and the stiffness of the strings themselves. There are stringing machines that adequately support a racquet by not allowing a tennis frame to deform during stringing; in this case the pulled tensions are representative of the final, in-place tensions. For flexible conditions, determining what tensions to pull that would result in the recommended final tensions of Equation 121 is the subject of future investigation.

In a number of stringing machines that support a frame at 2-6 points, it is a recommended practice to pull both the main and cross string tensions at the same level (say 60 lbs). What is interesting is that the measured final tensions in such a strung frame are closer to the Tx/Ty tensions predicted above. This is due to racquet deformation (and stringing machine deformation) and it represents the racquet trying to reach, via deformations as best as it can, the low strain energy state implied by equation 121.

One final observation: a ball can rebound in an unexpected direction from a string-bed whose string tensions are not-uniform. This effect has never been quantified and perhaps is handled by a player in his/her swing, or perhaps it results in a ball’s trajectory that is not completely player controllable. This is also a topic for future investigation.

Elliptical shaped tennis racquet only carries axial load

Preface: Paul Zarda notes that an elliptical shaped tennis racquet, with a dual loading condition of main string tensions and cross string tensions, will be shown to carry only a low-stress-level compressive load and not the expected high-stress-level bending moment. This 2-D loading condition applied to a tennis racquet is analogous to the historical 1-D loading of a parabolic arch (carrying only axial load) that is well documented in mechanical engineering and engineering mechanics. As far as the author is aware of, this is the first ever documentation and corresponding proof that an elliptical shaped tennis racquet head, loaded using a derived formula for the main and cross string tensions, will be shown to carry only a low-stress axial compressive load.  In order to minimize stress-levels in a tennis racquet due to stringing, these in-racquet-derived-formula-string tensions should be a targeted final-string-tension level for the stringing of any elliptical or nearly-elliptical tennis racquet.  

                                                            Figure 101

Figure 101 shows the head of a tennis racquet that is subjected to tensioned strings that cause loads in the cross string direction (x-direction) and the main string direction (y-direction). As shown in Figure 101, Wx corresponds to a loading per unit length for the cross string tensions, and Wy corresponds to a loading per unit length for the main string tensions.

Paul Zarda of Sanford notes the insert shown in Figure 101 exposes the internal forces that can develop in the frame caused by the string tensions. M is the bending moment on the x-section, V is the shear force on the x-section, and N is the axial force on the x-section. It will be shown that if the in-plane x-y shape of the tennis frame is elliptical, then the bending moment and shear force will be identically zero. This will be shown to only occur for a specific ratio of Wy/Wx.

                                                                      Figure 102

Figure 102 shown a free body diagram of the right half of the tennis frame. As shown in Figure 102, the symmetry plane cut at x=0 only exposes normal forces Fx (and from symmetry about the y=0 plane, Fx is the same for the top x-sectional cut and the bottom x-sectional cut shown in Figure 102).

 Sum of forces in the X-direction = 0:      
                                                                                                                 Equation 101                                                                                                           
                                                                                                                               Equation 102
Figure 103 is a free body diagram of the top half of the tennis frame. The x-sectional cut on the symmetry plane y=0 exposes the axial force Fy (as shown in the Figure). Fy is the same axial force for the left cut and the right cut of the frame since x=0 is also a symmetry plane.

                                                                        Figure 103

From Figure 103, using sum of forces in the Y-direction = 0:

                                                                                                                            Equation 103
                                                                                                                            Equation 104
                                                         
Figure 104 is a free body diagram of the tennis frame in the 1st quadrant. It shows the frame with x-sectional cuts both on the symmetry plane y=0 and also a cut at the (x,y) position shown in the Figure. The x-sectional cut at position (x,y) exposes the axial force N acting an angle θ as shown in Figure 104. 

                                                                                Figure 104

From Figure 104, with the assumption that M and V are 0 at the x-sectional cut at the position (x, y), then the sum of forces in the x-direction = 0 gives
  
                                                                                                                             Equation 105
From Figure 104, sum of forces in the y-direction = 0 gives

                                                                                                                             Equation 106
From Figure 104, sum of moments (counterclockwise) about point A = 0 gives
                                                                                                                              Equation 107
Substituting Ncosθ from Equation 105 and Nsinθ from Equation 106 into Equation 107, one gets

                                                                                                                             Equation 108 
Combining similar terms
                                                                                                                               Equation 109
                                         
 Simplifying, and substituting in for from Equation 104
                                                                                                              Equation 110
                                                                                       
Expanding 
                                                                                                                               Equation 111 
With the orange terms canceling, and rearranging

                                                                                                                                Equation 112
 And dividing by the right hand side  

                                                                                                                                Equation 113
 Re-adjusting the first term
                                                                                                                                Equation 114
Re-writing Equation 114
                                                                                                                                Equation 115                                                     
If the term in { brackets } in Equation 115 is unity, Equation 115 is the equation of an ellipse, centered at (0, 0), with minor/major axis of 2a/2b, respectively, as shown in Figure 101. Hence, setting the bracket term to unity
                                                                                                                               Equation 116
Or
                                                                                                                              Equation 117
Statement: Equation 117, in conjunction with Equation 115, says that if the cross string tensions per unit length, Wx, is a fraction (a/b)2 of the main string tension per unit length, Wy, then, with a racquet head in the form of an ellipse per Equation 115, the frame will only develop a low-stress-level compressive force N. It is the author’s opinion that this is the first time in history that this revealing statement and corresponding proof has been publically offered.

                                                            Figure 105
Paul Zarda of Orlando notes the observations made in the above statement have impact both on stringing a tennis racquet and the performance of a tennis racquet. Figure 105 shows an elliptical shape head of a tennis racquet with several definitions provided associated with the stringing of a tennis racquet. If we define, as shown in Figure 105, that Tx is the cross string tension, Ty is the main string tension, nx is the number of cross strings, and ny is the number of main strings, then Wx, the cross string loading per unit length, is approximated by (using an average spacing)
                                                                                                                           Equation 118
Similarly, Wy, the main string loading per unit length, is approximated by (using an average spacing)

                                                                                                                           Equation 119Substituting Equations 118 and 119 into Equation 117

                                                                                                                           Equation 120
Simplifying
                                                                                                                           Equation 121
To somewhat quantify this formula, let’s do the calculation where the head width 2a of a racquet is 10 inches and the head height 2b is 13 inches, and the string pattern is 16 x 19 (ny = 16 main strings, nx = 19 cross strings, a somewhat typical racquet). Using a reference main string tension of Ty = 60 lbs, the above formula produces a cross string tension Tx of 38.9 lbs. This cross string tension of 38.9 lbs assumes equal spacing of main and cross strings (an approximation), and is relative to the main string tension of 60 lbs. This set of tensions ( Tx ,Ty ) = (38.9, 60), in an elliptical shaped head (or nearly elliptical) of 10 inches x 13 inches, will produce a low-stress-level axial compressive load (see Equations 102 and 104 for representative axial compressive loads; using these formulas, at 12 o-clock Fx = 370 lbs and at 3 o’clock Fy = 480 lbs).

Paul Zarda of Orlando and Sanford notes it is important to point out that Equation 121 provides the final cross string tension Tx in a frame relative to the final main string tension Ty. These tensions are not necessarily (or even likely) the tensions pulled when stringing a racquet in a stringing machine. This observation is due to the fact that, during the stringing process, a racquet’s frame can deform, and that deformation will cause the pulled tensions to change. This deformation is related to the flexibility of the stringing machine and its support of the tennis racquet, the flexibility of the tennis racquet and the stiffness of the strings themselves. There are stringing machines that adequately support a racquet by not allowing a tennis frame to deform during stringing; in this case the pulled tensions are representative of the final, in-place tensions. For flexible conditions, determining what tensions to pull that would result in the recommended final tensions of Equation 121 is the subject of future investigation.

In a number of stringing machines that support a frame at 2-6 points, it is a recommended practice to pull both the main and cross string tensions at the same level (say 60 lbs). What is interesting is that the measured final tensions in such a strung frame are closer to the Tx/Ty tensions predicted above. This is due to racquet deformation (and stringing machine deformation) and it represents the racquet trying to reach, via deformations as best as it can, the low strain energy state implied by equation 121.

One final observation: a ball can rebound in an unexpected direction from a string-bed whose string tensions are not-uniform. This effect has never been quantified and perhaps is handled by a player in his/her swing, or perhaps it results in a ball’s trajectory that is not completely player controllable. This is also a topic for future investigation.