American Institute of Aeronautics and Astronautics1

Novel Aerodynamic Compensation Pitot - Static Tube forApplication in Subsonic and Supersonic Flight Regimes

A. Latif*, J. Masud†, S. R. Sheikh‡, K. Pervez§, O. A. Qazi** and H. Qureshi††

Department of Aerospace Engineering, College of Aeronautical Engineering, National University of Sciences &Technology, Risalpur 24090, Pakistan

An aerodynamic compensation pitot-static tube has been developed for the flight regimeof modern fighter aircraft (Mach < 2). The pitot-static tube profile has been designed so thatin the subsonic regime it aerodynamically compensates for the position error in pressurecoefficient (Cp) due to presence of the aircraft, while in the supersonic regime it gives thedesired zero compensation. The unique aspect of the proposed design is that it is able toprovide the desired compensation in both subsonic (negative Cp) and supersonic (zero Cp)regimes at same axial location. At this axial location the local Cp gradient is small in thesubsonic regime and is close to zero in the supersonic regime so that in practical applicationthis pitot-static tube would be less sensitive to manufacturing tolerances. The proposeddesign pitot-tube can be used effectively to compensate for Cp position errors of up to +0.1 inthe subsonic regime by non-dimensional “stretching” of the basic profile while maintainingzero Cp in the supersonic regime. Computational Fluid Dynamics tools have been used in thedesign and analysis of the proposed pitot-static tube. The effect of turbulence model and gridsize on computed results has been evaluated. The complete Mach number regime (Mach < 2)has been computationally explored for different profiles resulting form “stretching” of thebasic profile in order to validate the proposed design’s capability to compensate positionerrors in Cp of up to +0.1. In the end a design methodology is also presented where a specificpitot-static tube profile can be extracted from the general non-dimensional profile in orderto aerodynamically compensate a known position error in Cp.

NomenclatureAOA Angle-of-Attackβ Side slip angleCFD Computational Fluid DynamicsCp Pressure Coefficient (P-P∞)/½ρ∞V∞

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Dmax Maximum diameter of compensation regionf Fineness Ratio (Xmax / Dmax)M Free stream Mach numberP Static pressurePt Total pressureP∞ Free stream static pressureSKE Two equation Standard K-є turbulence modelSA One equation Spalart-Allmaras turbulence modelV∞ Free stream velocityρ∞ Free stream density

* Graduate Student, Dept of Aerospace Engg, College of Aeronautical Engg, NUST, Risalpur 24090, Pakistan.† Associate Prof, Dept of Aerospace Engg, College of Aeronautical Engg, NUST, Risalpur 24090, Pakistan.‡ Prof, HoD Dept of Aerospace Engg, College of Aeronautical Engg, NUST, Risalpur 24090, Pakistan.§ Prof, Dean College of Aeronautical Engg, NUST, Risalpur 24090, Pakistan. AIAA Member.** Associate Prof, Dept of Aerospace Engg, College of Aeronautical Engg, NUST, Risalpur 24090, Pakistan.†† Graduate Student, Dept of Aerospace Engg, College of Aeronautical Engg, NUST, Risalpur 24090, Pakistan.

44th AIAA Aerospace Sciences Meeting and Exhibit9 - 12 January 2006, Reno, Nevada

AIAA 2006-1385

Copyright © 2006 by J. Masud. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

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Xmax Maximum length of compensation regionx Axial coordinatey Radial coordinatey+ Non-dimensional length scale associated with turbulence modelYmax Maximum radial thickness of the compensation region (Dmax/2)

I. IntroductionIRCRAFT pitot-static tube (referred subsequently as pitot tube) is one of the important air data sensors and isdesigned to measure correct ambient static and total pressure corresponding to aircraft flight conditions. These

pressure measurements translate into aircraft speed, pressure altitude, Mach number, vertical velocity informationetc that is necessary for multiple aircraft subsystems such as flight control system, avionics / weapons subsystems,engine control subsystem and cockpit flightinstruments etc. The measurement of correctambient (atmospheric) static pressure by the pitottube over the whole Mach number regime(subsonic to supersonic) of the aircraft is the mostcritical aspect in its design1. Generally a pitot tubeis placed ahead of the aircraft where the localstatic pressure in the subsonic regime is higherthan the ambient static pressure i.e. positive Cpvalue1,2. This is referred to as the Cp “positionerror”. In the supersonic regime the local staticpressure ahead of the aircraft equals the ambientstatic pressure i.e. Cp position error value is zero.An “aerodynamic-compensation” pitot tube isdesigned to “compensate” for the position errorby generating “opposite” local Cp by a carefully contoured profile1,3 as shown in Figure 1. This presents multiplechallenges to the designer due to inherently different nature of subsonic and supersonic flows. An ideal pitot tubewould fully compensate for the aircraft presence and thus the static pressure measured by it over the whole flightregime, subsonic thru supersonic, would be the corresponding atmospheric (ambient) pressure.

Older generation supersonic aircraft generallyused a non-compensating pitot tube withassociated static pressure measurement errors inthe subsonic regime1. A common aerodynamiccompensation pitot tube has an ogival shape thatis based on a profile formed by a quadraticpolynomial1,3. This kind of pitot tube is usedextensively on some modern supersonic aircraft.A feature of such a pitot tube is significantgradient of surface Cp in the vicinity of its zerovalue in the supersonic regime as shown in Figure2. Additionally it can be seen that the zero Cppoint also shifts axially with supersonic Machnumber. These features of surface Cp behaviourmake the ogival pitot tube quite sensitive to staticport location as well as manufacturing tolerances.An approximate solution to this undesirablefeature is through pressure averaging by using axially distributed static pressure ports on the surface of the pitottube.

The aim of the present study is to develop a novel compensation region profile (non-dimensional) by CFDanalysis that has better surface Cp characteristics then an ogival pitot tube in the supersonic regime i.e. negligiblegradient in the vicinity of zero Cp value while maintaining adequate subsonic compensation characteristics. Theproposed design pitot tube can then be used for specific aircraft applications by simply “stretching” the non-dimensional profile to achieve the desired level of compensation in the subsonic regime while maintaining near-zerocompensation in the supersonic regime.

A

Figure 1. Aerodynamic compensation pitot-static tubehaving an ogival (quadratic) compensation region profile.

Figure 2. Cp distribution on the surface of a pitot tubehaving an ogival (quadratic) compensation region.

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II. Development Methodology of Proposed Compensation Region ProfileThe development of a new compensation region profile is challenging due to stringent Cp characteristics

requirement in the supersonic regime as we have discussed earlier. We started the proposed compensation regiondevelopment work by first evaluating the characteristics of an ogival pitot tube having a compensation regiondefined by a quadratic polynomial (Figures 1and 2). The compensation region was thensimplified by us by breaking it down into threeconical segments as shown in Figure 3. Wecreated a number of simplified compensationregions by choosing various relative lengthsand half-cone angles of the three conicalsegments.

The surface Cp characteristics of thesimplified pitot tubes with conical segmentcompensation region were computationallyevaluated and the most promising arrangementwas selected for further refinement by us. Thisparticular arrangement of the three conicalsegments is represented to-scale in Figure 3.

The simplified conical segment compensation region refinement process involved better representation of thecompensation region by a higher order polynomial which closely followed the conical segment profile whilesmoothing out the sharp edges created at the junction of the conical segments. Various coefficients of the higherorder polynomial needed adjustment before the required surface Cp characteristics were achieved. The capability ofthis proposed compensation region profile to compensate a wide range of position error was verified by us bystretching the basic non-dimensional profile (having different fineness ratios ‘f’) and computationally evaluating itscharacteristics for a range of subsonic and supersonic Mach numbers.

III. Computational SetupThe geometry of the pitot tube is symmetric about its longitudinal axis, therefore, 2-D axi-symmetric modeling

was done for CFD analysis. This corresponds to zero angle-of-attack (AOA) and zero side-slip angle (β) duringflight. The rear end of the pitot tube, aft of the compensation region, was modeled as a straight axi-symmetriccircular cylinder. The coordinate system and other parameters of the modeled pitot tube is shown in Figure 3.

For CFD analysis, in addition tothe pitot-static tube, the complete flowdomain was modeled as well as shownin Figure 4. The flow domain includedthe free stream far field, the pitot tubeand the symmetry axis. The far fieldboundary was placed 100 times thepitot tube maximum radius away sinceplacing it even 200 times away did notproduce any change in the computedCp on pitot tube surface. Modeling thefar field in this manner simulatesactual flight conditions. Thecylindrical straight end (Figure 3 and4) of pitot-static tube was extended tillthe end of domain to avoid theinfluence of rear shape on computedsurface Cp in the compensation region at subsonic Mach numbers. In all our analysis only the compensation regionprofile was modified while rest of the computational domain was left unchanged for both subsonic and supersoniccomputations.

Mapped quadrilateral elements were used to mesh the computational domain. Elements were graded towards thesurface of pitot tube in order to accurately resolve the flow phenomena in the vicinity of the pitot tube. Thecomputational mesh near the pitot tube compensation region is shown in Figure 5.

Figure 3. Layout of the pitot-static tube.

Figure 4. Layout of the 2-D axi-symmetric computational domain.

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Fluent® finite volume based CFDcode4 along with its preprocessor5

Gambit® were used by us for thepresent study. The compressibleReynolds-Averaged-Navier-Stokessystem of equations with variableproperty air was solved using thecoupled-implicit formulation ofFluent®. No-slip velocity boundarycondition was enforced at the surfaceof pitot tube. Whereas pressure farfield boundary condition6 was used forfree stream far field as indicated inFigure 4. Symmetry boundarycondition6 was specified on thesymmetry axis. Since the thermal problem was not of paramount importance in the present study, therefore the pitottube surface was modeled as thermally insulated4.

A. Turbulence ModelingThe two-equation standard K-ε (SKE) turbulence model with standard wall treatment (law-of-the-wall) was used

for 2D analysis6,7. However, one-equation Spalart-Allmaras (SA) model6 was also used to determine the sensitivityof computed results to turbulence model. For the present study it was found that the surface Cp in the compensationregion did not change beyond 1% with either SKE or SA turbulence models. Therefore all the computed resultspresented in this study are based on the SKE turbulence model.

B. Grid Independence AnalysisNumerically computed results change with the type and density of mesh / grid used for computations. Three

different grids (Grid-1, Grid-2 and Grid-3) were used to compute cases at M=0.6 and 1.4. Grid-1 had 6615 elements(6808 Nodes), Grid-2 had 13230 elements (13468 Nodes) while Grid-3 had 26460 elements (26845 Nodes). Theresults indicate a large difference in computed surface Cp between Grid-1 and Grid-2. However a percentage changeof less than 1% in computed values of surface Cp was found in the compensation region between the results of Grid-2 and Grid-3 for both subsonic and supersonic Mach numbers. The value of computed turbulent law y+ remainsbelow 87 and 104 at subsonic and supersonic speeds, respectively, for both grids 2 & 3. These values of turbulent y+

are within normal range (30-1000) and show reasonable resolution of grid near the walls6,7. Therefore the resultspresented in this study were computed using Grid-2 of 13230 elements (13468 Nodes) or better.

IV. Results and DiscussionIn the present analysis, computations were carried out at Mach numbers of 0.6, 0.8, 0.9, 1.2, 1.6 and 1.8 for all

analyzed pitot tubes in order to adequately cover the flight envelope of a supersonic aircraft. From our pastexperience we found it difficult to correlate computed results to practical situations in the transonic regime thereforecomputations were not attempted between Mach number 0.9 and 1.2.

The basic flow field around the pitot tube for all cases of the present study consists of free stream flow beingmodified by the presence of the tube. The flow adjacent to the pitot tube generally follows its contour while far awayit merges with the free stream flow. There is no separation / circulation region in the pitot tube near flow field,therefore streamlines or vectors plots are not necessary to visualize this simple flow field.

A. Simplified Compensation Region Profile Based on Conical SegmentsThe pressure coefficient “Cp” variation in the vicinity of the pitot tube “compensation” region is shown in

Figures 6 and 7 for free stream Mach numbers of 0.6 and 1.4, respectively. Since the flow in Figure 6 is subsonic(M=0.6), therefore the pressure variations ahead of the pitot tube is evident. Rapid changes in surface Cp in thevicinity of conical segments junctions is also evident. At supersonic speeds the flow reacts to the presence of thepitot tube via a conical shock wave as seen from Figure 7. Large pressure changes in the shock / expansion wavespinned to the sharp corners formed by conical segments are evident. The pressure adjacent to the pitot tube surfaceextends to the surface itself indicating no pressure variation normal to the surface in the viscous boundary layer.Detailed Cp variation along the pitot surface is not evident from Figures 6 and 7 and is discussed next in this paper.

Figure 5. Mapped mesh in the vicinity of the compensation region.

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The computed Cp variation along the surface of the pitot tube with simplified compensation region is shown inFigures 8 and 9 at subsonic and supersonic Mach numbers, respectively. The rapid pressure variation in the vicinityof sharp corners formed at the interface of conical segments (i.e x/Xmax=0.25 and x/Xmax=0.74) are evident fromthese figures. This particular combination of conical segments gives negative Cp value at subsonic Mach numbersaround axial location x/Xmax=0.5 (Figure 8) while at approximately the same axial location it gives nearly zero Cpvalue at supersonic Mach numbers (Figure 9). From practical application aspect a static pressure port located atx/Xmax=0.5 is acceptable since it is not too close to the pitot tube front tip. Another positive aspect of this particularcombination of conical segments seen from Figures 8 and 9 is the small local gradient of Cp at axial location ofinterest (x/Xmax=0.5). This aspect becomes clear once Figures 8 and 9 are compared with Figure 2 that shows thesurface Cp behavior of the ogival pitot tube. Based on this feature of the simplified profile further refinement wasdeemed possible by us.

B. Refined Compensation Region Profile Based on Higher Order PolynomialThe refinement process included smoothing out the sharp edges formed at the conical interfaces so that the

pressure peaks shown in Figures 8 and 9 at x/Xmax=0.25 and x/Xmax=0.74 diffuse out axially with anticipated furtherreduction in subsonic Cp at x/Xmax=0.5. In the supersonic regime this refinement was expected to reduce the localCp gradient further at the desired axial location (x/Xmax=0.5).

Figure 6. Computed subsonic Cp variation in thevicinity of the pitot tube with simplified conicalsegments profile.

Figure 7. Computed supersonic Cp variation inthe vicinity of the pitot tube with simplifiedconical segment profile.

Figure 9. Computed surface Cp variation forsimplified compensation profile pitot tube atsupersonic Mach numbers.

Figure 8. Computed surface Cp variation forsimplified compensation profile pitot tube atsubsonic Mach numbers.

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For smoothing the simplified profile (conical segments) different higher order polynomials were evaluated by us.The final higher-order polynomial fitted compensation region profile is shown in Figure 10. The simplified (conicalsegment) and the ogival (quadratic polynomial) compensation region profiles are also included for comparison.

Adequate smoothing of the sharp edges of the conical segments while retaining the overall shape characteristics isevident for the curve fitted profile. The curvature of the higher order polynomial based profile was also evaluated byus as shown in Figure 11. This was necessary in order to ensure there are no undesirable surface “wiggles” overmost of the compensation region. As can be seen from Figure 11 the curve fitted profile has negative curvatureexcept for small regions at the ends.

The flow field and corresponding pressuredistribution around the proposed design pitot tubewas computed by us for verification of desirable Cpcharacteristics in both subsonic and supersonicregimes. The basic flow field in both subsonic andsupersonic regimes is similar to the simplified(conical segments) pitot tube discussed earlier inthis paper by us. A representative Cp distribution inthe subsonic regime is shown in Figure 12 at M=0.8for the proposed design pitot tube. The rapidpressure changes in the vicinity of conical segmentjunctions as seen earlier in Figure 6 have axiallydiffused out as discussed by us earlier in this paper.Similar trend is observed in the supersonic regimesince the concentrated expansion waves associatedwith conical segment junctions (Figure 7) are alsomore spread out axially for the proposed design.The figure for supersonic Cp distribution in thevicinity of the pitot tube is omitted for brevity.

Detailed analysis of the surface Cp distribution of the proposed design at both subsonic and supersonic Machnumbers is shown in Figure 13 and 14 respectively. Gradual pressure variations on the surface of the pitot tube areapparent. This is in contrast to pressure peaks observed for the simplified compensation region case shown inFigures 8 and 9. For the supersonic case (Figure 14) the surface Cp approaches zero value at x/Xmax=0.56. At thisaxial location the local gradient of surface Cp is near zero as well, which means that within a reasonable range ofx/Xmax (about 0.55-0.57) the supersonic Cp would remain nearly zero. This feature of the proposed design is veryattractive since it affords a significant tolerance in placing the static pressure port on the surface of the pitot tube forpractical application. At subsonic speeds (Figure 13) a consistent negative Cp value is achieved over the surface ofthe compensation region. At x/Xmax=0.56 a Cp value of about -0.06 is achieved, which is typical of medium-to-smallsupersonic fighter aircraft at subsonic speeds some distance ahead of their fuselage where pitot tube is normallyinstalled8. A desirable aspect of the proposed design is that at x/Xmax=0.56 the surface Cp value is not very sensitive

Figure 10. Comparison of various compensationregion profiles.

Figure 11. Profile and curvature of the higherorder polynomial based compensation region.

Figure 12. Cp distribution in the vicinity of theproposed design pitot tube.

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to Mach number as seen from Figure 13, moreover at this axial location the local Cp gradient is not large. Thereforea single static pressure port located at x/Xmax=0.56 would give nearly zero compensation at supersonic speeds(desirable) while maintaining a reasonable level (Cp value of about -0.06) of compensation in the subsonic regime.So far we have discussed the proposed design pitot tube having a fineness ratio f=4.22, at other fineness ratios thesubsonic Cp values at x/Xmax=0.56 is expected to change significantly while in the supersonic regime somevariations may also occur. This aspect is discussed next by us for the practical application of the proposed designpitot tube.

V. Practical Application of Proposed Design Pitot TubeA robust pitot tube design should be capable of compensating a wide range of subsonic Cp position error values

corresponding to various types and sizes of aircraft while at the same time maintain near zero Cp compensation atsupersonic speeds. For this purpose the non-dimensional proposed design profile (Figures 10 and 11) was stretched.This non-dimensional stretching resulted in compensation regions of various fineness ratios (f). We computationallyevaluated the Cp characteristics of these resultant pitot tubes (different fineness ratios) at subsonic and supersonicspeeds. The results of our computations at proposed static port location of x/Xmax=0.56 is shown in Figure 15.Reducing the fineness ratio of the non-dimensional profile results in dimensional increase in profile curvature and

vice versa, therefore surface Cp at subsonic speeds has greater negative value for lower values of f and lessernegative value for higher values of f as seen from Figure 15. At supersonic speeds the effect of fineness ratio onsurface Cp at x/Xmax=0.56 is negligible, which retains the near zero value. Fineness ratio variation from 3 to 5 resultsin subsonic Cp error compensation capability from 0.04 to 0.1 as seen from Figure 15. This capability is deemedsufficient by us for most practical applications.

Figure 13. Subsonic Cp distribution on thesurface of the compensation region of proposeddesign pitot tube.

Figure 14. Supersonic Cp distribution on thesurface of the compensation region of proposeddesign pitot tube.

Figure 15. Cp vs. Mach number behavior forvarious fineness ratios at x/Xmax=0.56.

Figure 16. Modified parameter vs. Mach numberbehavior for various fineness ratios at x/Xmax=0.56.

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A non-dimensional parameter Cp*f is suggested by similarity rules based on linearized compressible flow theorythat should be able to correlate the data presented in Figure 15. However, we found that an alternate parameterCp*f1.4 correlates the data presented in Figure 15 better due to variations between the linearized compressible flowtheory and the corresponding real case. This correlated data is presented in Figure 16. Very good data correlation isobserved at M=0.6 and 0.8. However, at M=0.9 some variations in correlated data is evident for low fineness ratios(f=3.00 and 3.38) probably due to the combination of higher curvature (low value of fineness ratio) and highsubsonic Mach number (transonic effects). Figure 16 can be conveniently used, instead of Figure 15, to apply theresults of the present work to a practical situation. From Figure 16 we get the value of the parameter Cp*f1.4 as:

Cp*f1.4=-0.454 at M=0.6 (1)Cp*f1.4=-0.49 at M=0.8 (2)

For any practical application the required level of subsonic compensation (Cp error value) is known from CFDanalysis or wind tunnel tests. Corresponding to this Cp error value, the fineness ratio ‘f’ can be determined from Eq(1) or Eq (2) for 0.6 ≤ M ≤ 0.8 (interpolate if necessary) or from Figure 15 directly for 0.8 < M ≤ 0.9. Knowing thevalue of ‘f’ we can now refer to Figure 10 or 11 to find the dimensional profile since the pitot tube cylindricalstraight end radius corresponding to y/Ymax=0.84 at x/Xmax=1 is known or can be chosen based on other designconsiderations (structural etc). Thus Ymax, Xmax and dimensional profile details are now known for the value of Cperror that needs to be aerodynamically compensated in the subsonic regime. At supersonic Mach numbers (M<2) thedimensional profile would automatically give the desired near zero compensation (Figure 15).

This methodology has been verified by us to effectively compensate for position error in Cp of up to +0.1 (mostpractical applications) as shown in Figure 15. We may also be able to compensate for higher values of Cp error(greater than 0.1) by this methodology but that requires further verification, however Cp error values lower than0.04 can be compensated by this methodology without further analysis since that requires larger values of finenessratio ‘f’ which makes the flow behavior in the vicinity of the pitot tube more “linearized”.

In addition to the profile information, the physical pitot-static tube needs a pitot (total) pressure port at the pitottube tip as well as static pressure port at x/Xmax=0.56. The physical dimension and shape of these ports and theirazimuthal orientation (static pressure ports only) for non-zero AOA and β can be found from Ref. 1. It has beenverified in an earlier study8 that the presence of correctly dimensioned pitot pressure port at the pitot tube tip doesnot effect the Cp behavior in the compensation region.

VI. ConclusionIn this paper a novel aerodynamic compensation pitot tube design is presented. This design improves upon

certain limitations of ogival pitot tubes. The proposed design pitot tube is able to compensate for position error in Cpof up to +0.1 in the subsonic regime by non-dimensional stretching of the basic profile while maintaining near zeroCp in the supersonic regime (M<2). These compensation characteristics are achieved at a single axial location(x/Xmax=0.56). At this axial location the local Cp gradient is near zero in the supersonic regime and has a low valuein the subsonic regime which makes this pitot tube less susceptible to manufacturing tolerances for practicalapplication. The data of our present analysis is correlated by a parameter (Cp*f1.4) that makes practical application ofthe present work convenient.

AcknowledgmentsA. Latif gratefully acknowledges the MS thesis research grant provided by the National University of Sciences

and Technology while J. Masud would like to acknowledge the discussions that took place with his Chinesecounterparts during his stay in China.

References1Garcy, W., “Measurement of Aircraft Speed and Altitude,” NASA Reference Publication 1046, 1980.2Letko, W., “Investigation of the Fuselage Interference on a Pitot-Static Tube Extending Forward From the Nose of the

Fuselage,” NACA-TN-1496, 1947.3Ritchie, V. S., “Several Methods for Aerodynamic Reduction of Static-Pressure Sensing Errors for Aircraft at Subsonic,

Near-sonic, and Low Supersonic Speeds,” NASA TR R-18, 1959.4FLUENT, Computational Fluid Dynamics Software Package, Ver. 6.2.16, Fluent Inc, Lebanon, NH, 2004.5GAMBIT, Geometry and Mesh Generation Software Package, Ver. 2.2.30, Fluent Inc, Lebanon, NH, 20056FLUENT, Computational Fluid Dynamics Software Package User Guide, Ver. 6.2.16, Fluent Inc, Lebanon, NH, 2004.7White, F. M., Viscous Fluid Flow, 2nd ed., McGraw Hill, New York, 1991, Chaps. 6, 7.8Latif, A., “Design and Integration of Aerodynamic Compensating Pitot-Static Tube for a Supersonic Aircraft” MS Thesis,

Aerospace Engineering Dept., College of Aeronautical Engg, National Univ. of Sci. & Tech., Risalpur, Pakistan, 2005.