Persistence Characteristics of Wind-Tunnel Pressure Signatures From Two Similar Models

The overlaid outlines, in figure 7, show that the two wing-fuselage planforms were remarkably similar even though the methods used to design them were not. The Mach 2 concept and its wind-tunnel model were designed with the low-boom methods of reference 3. It was an all-wing configuration with a mild camber and twist in its low-thickness surfaces. The forward section had a blunted apex that started the lift quickly but with a low lift gradient, and a highly- swept strake behind it to control the growth of that lift. Aft of the strake, the leading-edge sweep gradually decreased so that the lift would grow more rapidly and reach its peak at the wing-tip trailing edge.

Model C, on the other hand, was a simpler configuration having only a flat delta wing and a fuselage. The fuselage forebody was the forward half of a parabolic body of revolution, while the “wasp-waisted” aft body covered the flat-camber-surfaced delta wing. This forebody developed a small amount of slender-body lift which reached its peak by the time the wing lift began to grow and affect the flow field. The wing continued the lift growth from the forebody, and reached its maximum at the wing tip trailing edge. Although designed neither for low boom, nor with low- boom methods, the Model C configuration generated pressure signatures that were very similar in persistence characteristics, though not identical, to those of the low-boom Mach 2 model which was about 14 times larger in length and span. This will be seen in the following sections.

Model C Pressure Signatures Pressure signatures generated by Model C were measured at three lift conditions and three separation distances. The lift on the model corresponded to lift coefficients of C = 0.0, 0.10, and L 0.20 while the model-probe separation distances corresponded to distance/span ratios, h /b , of 26.0, 52.1, and 104.2.

With C = 0.0, only volume effects from the fuselage and the wing were present in the L pressure signatures. At C = 0.10 (a lift coefficient typical of supersonic-cruise configurations at L beginning-cruise altitude and weight) the flow-field disturbances were generated by both fuselage and wing volume and wing lift effects. At a C = 0.20, the lift contribution was so much L larger than that of the volume, that it completely overshadowed the foreshortened fuselage and wing volume effect. As a result, the pressure signature was an N-wave at all wind-tunnel test section separation distances. Moreover, at a C = 0.20, the model was much farther from the L design C and the design lift/drag ratio of the Mach 2 concept and wind-tunnel model than at a L C = 0.10. So, only the pressure signatures measured at the three wind-tunnel-study separation L distances and at C = 0.0 and 0.10 are presented for comparison purposes. Of these pressure L signatures, only the signatures measured at C = 0.10 are used in the theoretical comparisons.

L These six Model C wind-tunnel pressure signatures are presented in figures 8 through 10.

C = 0 C = 0.1 L L .15 .10 3/4 .05 ∆ p Y p L − .05 − .10 1.0 .5 0 − .5 −1.0 1.0 .5 0 − .5 −1.0 − 1/4 − 1/4 ∆ x Y ∆ x Y L L L L Figure 8. Model C pressure signatures at M = 2.01, h/b = 26.0, C = 0.0 and 0.10.

L C = 0 C = 0.1 L L .15 .10 .05 3/4 ∆ p Y p L − .05 − .10 1.0 .5 0 − .5 −1.0 1.0 .5 0 − .5 −1.0 − 1/4 − 1/4 ∆ x Y ∆ x Y L L L L Figure 9. Model C pressure signatures at M = 2.01, h/b = 52.1, C = 0.0 and 0.10.

L C = 0 C = 0.1 L L .15 .10 .05 3/4 ∆ p Y p L − .05 − .10 1.0 .5 0 − .5 −1.0 1.0 .5 0 − .5 −1.0 − 1/4 − 1/4 ∆ x Y ∆ x Y L L L L Figure 10. Model C pressure signature at M = 2.01, h/b = 104.2, C = 0.0 and 0.10.

L The pressure signatures in figures 8 to 10 were plotted in far-field pressure-ratio and distance- ratio parameters. In this parametric format, trends in the shapes of the pressure signatures to become “N-wave” shapes could be easily seen, and in the far-field, “N-wave” pressure signatures would be identical at all large separation distances.

On the Model C pressure signatures, as on the Mach 2 model pressure signatures, all the measured shocks were rounded instead of being abrupt jumps due to model vibration, finite orifice size, and probe boundary layer. These effects were discussed in reference 4.

Disturbances from the model nose were due mostly to volume effects. These effects produced a nose shock with about the same strength in the first signature peak at C = 0.0 as at C = 0.10.

L L The wing lift effects appeared mainly as the second peak on pressure signatures at the three separation distances when C = 0.10, even though a small amount of lift was generated by the L circular cross section forebody. At both C = 0.0 and 0.10, these pressure signatures were L interesting because their near-field shape characteristics (none of them had a far-field N-wave shape) extend from distance ratios of h/b = 26.0 to h/b = 104.2. This unforeseen but fortuitous characteristic was noted in the reference 29 report of a study done almost ten years before the introduction of the Seebass and George minimization theory of reference 3.

Another way to determine the trend toward far-field characteristics for pressure signatures is to plot “impulse” versus separation distance or separation/span ratio. Measured, or experimental, pressure signature “impulse” can be defined as: p x ∆   I d = = Measured Impulse (1)   EXP

∫

p l mum   maxi The theoretical value of the impulse is expressed as: F y

M l y ( )  

I d = = Theoretical Impulse γ (2)   THEORY

∫

  h l mum maxi l β 2 and is calculated from the concept’s or model’s volume and lift distributions. It can be seen from equation (2) that

F y ( )

h M y   γ I d = = constant (3)   THEORY

∫

mum   maxi l l l β 2 which, in some ways, is a more convenient form of equation (2). This equation is useful for comparisons of the impulse derived from measured and predicted pressure signatures, or from measured pressure signatures and the model’s or concept’s F-function.

When the measured impulse values of the Model C pressure signatures at C = 0.10 were L compared with the theoretical values for a C = 0.10, a poor agreement was found. Changing the L lift coefficient from C = 0.10 to C = 0.133 and recalculating the F-function of the model with L L the new lift distribution brought the measured and predicted values into closer agreement. This comparison of measured and theoretical impulse values was done with equation (3) for the two values of the lift coefficient, and is shown in figure 11.

.0030 .0020 h I l Experiment C = 0.100 .0010 L Theory C = 0.133 L 0 20 80 60 40 100 120 h/b Figure 11. Comparison of measured and theoretical values of impulse with C = 0.10 and 0.133.

L These results strongly suggested that Model C pressure signatures were really measured at C = 0.133 rather than at C = 0.10. So, the pressure signature in figure 10, measured at L L h/b = 104.2 and a C value of 0.10, was compared with pressure signatures predicted with L Whitham Theory methods at h/b = 104.2 and C values of 0.10 and 0.133. This comparison is L shown in figure 12.

Experiment Theory C .004 L 0.100 0.133 .002 ∆ p p − .002 − .004 − .3 − .2 − .1 0 .1 .2 .3 .4 x − β h L Figure 12. Measured and predicted Model C pressure signatures. M = 2.01 and h/b = 104.2. Signatures were predicted at C = 0.10 and 0.133, L = 4.0 inches.

L A much better agreement between the measured and the predicted pressure signatures was achieved with the model at a C = 0.133 rather than at C = 0.10, the text value of reference 29.

L L This result was in agreement with the conclusion reached after the comparison of measured and theoretical values of pressure signature impulse shown in figure 11. A C = 0.10 would be L obtained with the model at an angle of attack of 2.64 degrees, while a value of C = 0.133 would L be obtained at 3.50 degrees. The difference in C values was attributed to the difficulty in accu- L rately setting the angle of attack of the small model by hands-on bending of the sting, and to small flexures along the sting when the model was at lift conditions (see reference 22).

Increasing the lift on a model or a concept usually enhances tendencies for a low-boom- shaped pressure signature, or a pressure signature with near-field features, to change abruptly to an N-wave pressure signature. This shape instability, i.e. likelihood for an abrupt change from a low-boom shaped (or a quasi-low-boom shaped) to an N-wave pressure signature, was not observed in the Model C measured or predicted pressure signatures. So, it was concluded from an analysis of data in figures 8 to 10 and 12, that pressure signatures generated by Model C would not degenerate into N-waves until separation distance/span ratios much greater than 104.2 were reached. The most probable reason for this fortuitous circumstance was that the volume and lift distribution in the Model C geometry was very close to, but not exactly the same as, a low- boom equivalent area distribution.

Results Although the geometry of Model C had not been designed with low-boom minimization methods, nor had its geometry been tailored to generate low-boom pressure signatures, the pressure signature data suggested that such designing and tailoring had fortuitously been done.

The pressure signatures generated at a C = 0.10 showed noticeable shape-persistence L characteristics, i.e. the shape of the pressure signature at h/b = 26.0 looked very much like the pressure signature at h/b = 104.2 when both pressure signatures were plotted in far-field parametric form. Although the “hint” of a small shock was observed between the nose shock and the expansion to the tail shock, the pressure signature measured at the farthest model-survey probe separation distance, h/b = 104.2, had a positive-pressure top that appeared to have tendencies toward becoming almost “flat topped” in appearance.

The Mach 2 wind-tunnel model, without nacelles, had pressure signatures with several small shocks along the positive-pressure part of the signature. As the separation distance increased from 6.0 to 28.0 inches, these small shocks gradually dissipated without moving forward to coalesce with the nose shock, leaving the positive part virtually “flat topped” in shape. This asymptotic trend toward becoming and remaining flat-topped was very similar to the trend toward retaining non-N-wave characteristics seen on Model C pressure signatures measured at h/b = 26.0 to 104.2. Pressure signature shape “freezing” was predicted to occur on the Mach 2 Concept ground pressure signature under the flight path at start of cruise, and the wind-tunnel data from these two models strongly suggested that these effects might be realized in real atmosphere propagation.

Concluding Remarks The Mach 2 wind-tunnel model, with nacelles off, and the Model C wind-tunnel model were simple wing-fuselage configurations with very similar planform shapes. Measured pressure signatures from both models had identifiable signature persistence trends with increasing separation distance below the flight path. The Model C wind-tunnel data at h/b = 26.0, 52.1, and 104.2, and the results of the model’s sonic-boom analysis lead to the conclusion that the pressure signature shape of Model C would persist from cruise altitude to the ground if Model C were to be scaled up to a full-sized supersonic-cruise concept. Since the Model C planform and configuration geometry had shown strong pressure signature persistence characteristics, and the geometry of the Mach 2 model (and concept) was so similar, it was concluded that the pressure signature shapes of the Mach 2 concept and model would also retain their low-boom characteristics from h/b = 4.375 to h /b = 104.2 , and then to the ground. Thus, it was concluded that these observations could be generalized to predict a low-boom signature generated by a suitably-tailored wing-fuselage configuration would persist from cruise altitude to the ground once it had been established in the atmosphere above 36,000 feet.

The analysis in this paper, as well as the report that described and discussed the Model C wind-tunnel data, demonstrated that small wind-tunnel models could still be useful in sonic boom research. However, the goals of the experiment that employed such small models had to be limited in scope, e.g. the determination of shape evolution, attenuation, and persistence, the effect of wing planform on pressure signature shape, or the effects of engine nacelles and/or nacelle shapes on the flow field.

Although the results of this study demonstrated that the wind-tunnel model’s small size was not a serious detriment to obtaining meaningful sonic-boom data in the wind tunnel, they could not be construed as a blanket endorsement of very small models or as an endorsement for the use of small models for out-of-plane-of-symmetry measurements of overpressures. There will always be a need for increased model size when the effects of the vehicle’s components, such as the engine nacelles, on the flow-field of a complete configuration must be studied. As long as the goals of the test are limited to simple identifiable characteristics, then the possibility of using models in the range of three to five inches in length should be considered.

It should be noted, however, that these test results indicate only that, with properly-configured small models, low-boom pressure signature shapes will show persistence characteristics in wind- tunnel test sections and in non-turbulent, calm, standard atmospheres. They do not and cannot predict shape persistence for pressure signatures that pass through an atmosphere filled with turbulence, wind shear, and temperature gradients; common features usually found in the layer of air 3000 to 5000 feet above the ground. The characteristics of this “last mile” of atmosphere were studied over forty years ago with the intention of simulating them in the wind tunnel. No practical method for fully achieving this simulation was ever found, so including these effects are outside the scope of this paper. These areas of unresolved and unanswered questions resurrected and reinforced the conclusion that the measurements of these real atmospheric effects would probably have to be made with a full-scale low-boom-configured aircraft making a large number of flights over extensive microphone arrays, or having an instrumented aircraft make multiple passes back and forth through the flow field around such a research aircraft.

References 1. Whitham, G. B.: The Flow Pattern of a Supersonic Projectile . Communications on Pure and Applied Mathematics vol. V, no. 3, August 1952, pp. 301-348.

2. Walkden, F.: The Shock Pattern of a Wing-Body Combination, Far From the Flight Path .

Aeronautical Quarterly, vol. IX, pt. 2, May 1958, pp. 164-194.

3. Seebass, R.; and George, A. R.: Sonic-Boom Minimization. Journal of the Acoustical Society of America, vol. 51, no. 2, pt. 3, February 1972, pp. 686 - 694.

4. Carlson, Harry W.: Correlation Of Sonic-Boom Theory With Wind-Tunnel And Flight Measurements , NASA TR R-213, December 1964.

5. Carlson, Harry W.; Mack, Robert J.; and Morris, Odell A.: Sonic-Boom Pressure Field Estimation Techniques . Proceedings of the Sonic Boom Symposium, November 3, 1965.

6. Kane, E. J.: Some Effects Of The Nonuniform Atmosphere On The propagation Of Sonic Booms , Proceedings of the Sonic Boom Symposium, November 3, 1965.

7. Carlson, H. W.; and Maglieri, D. J.: Review Of Sonic-Boom Generation And Prediction Methods. Proceedings of the Second Sonic Boom Symposium, November 3, 1970.

8. Hayes, Wallace D.; and Runyan, Harry L.: Sonic-Boom Propagation Through A Stratified Atmosphere. Proceedings of the Second Sonic Boom Symposium, November 3, 1970.

9. Middleton, Wilbur D.; and Carlson, Harry W.: A Numerical Method For Calculating Near- Field Sonic-Boom Pressure Signatures. NASA TN D-3082, 1965.

10. McLean, F. Edward; and Shrout, Barrett L.: Design Methods For Minimization Of Sonic- Boom Pressure-Field Disturbances . Proceedings of the Sonic Boom Symposium, November 3, 1965.

11. Kane, E. J.: Some Effects Of The Nonuniform Atmosphere On The propagation Of Sonic Booms , Proceedings of the Sonic Boom Symposium, November 3, 1965.

12. Harris, Roy V., Jr.: A Numerical Technique for Analysis of Wave Drag at Lifting Conditions . NASA TN D-3586, 1966.

13. Mack, Robert J.: A Numerical Method for Evaluation and Utilization of Supersonic Nacelle-Wing Interference . NASA TN D-5057, 1969.

14. Hayes, Wallace D.; Haefeli, Rudolph C.; and Kulsrud, H. E.: Sonic Boom Propagation In A Stratified Atmosphere, With Computer Program . NASA CR-1299, 1969.

15. Craidon, Charlotte B.: Description Of A Digital Computer Program For Airplane Configuration Plots . NASA TM X-2074, 1970.

16. Carlson, Harry W.; and Mack, Robert J.: Estimation Of Attainable Leading-Edge Thrust For Supersonic Wings Of Arbitrary Planform . NASA TP 1270, October 1978.

17. Carlson, Harry W.; and Mack, Robert J.: Estimation Of Leading-Edge Thrust For Wings At Subsonic And Supersonic Speeds . NASA TP 1500, October 1979.

18. Darden, Christine M.: Sonic Boom Minimization With Nose-Bluntness Relaxation. NASA TP-1348, 1979.

19. Carlson, Harry W.; and Mack, Robert J.: Estimation Of Wing Nonlinear Aerodynamic Characteristics at Supersonic Speeds . NASA TP-1718, 1980.

20. Mack, Robert J.: Some Considerations on the Integration of Engine Nacelles into Low- Boom Aircraft Concepts . High-Speed Research: Sonic Boom, Volume II, NASA Conference Publication 3173, 1992.

21. Carlson, Harry W.; Barger, Raymond L.; and Mack, Robert J.: Application Of Sonic- Boom Minimization Concepts In Supersonic Transport Design . NASA TN D-7218, June 1973.

22. Mack, Robert J.; and Darden, Christine M.: Wind-Tunnel Investigation Of The Validity Of A Sonic-Boom-Minimization Concept. NASA TP 1421, October 1979.

23. Mack, Robert J.; and Needleman, Kathy E.: The Design Of Two Sonic Boom Wind Tunnel Models From Conceptual Aircraft Which Cruise At Mach Numbers Of 2.0 And 3.0 . AIAA-90- th 4026, AIAA 13 Aeroacoustics Conference, October 22-24, 1990.

24. Mack, Robert J.: Low-Boom Aircraft Concept With Aft-Fuselage-Mounted Engine Nacelles . High-Speed Research: Sonic Boom, Volume II, NASA CP-10133, February 1994.

25. Mack, Robert J.: A Supersonic Business-Jet Concept Designed For Low Sonic Boom .

NASA/TM-2003-212435, October 2003.

26. Mack, Robert J.: An Analysis Of Measured Sonic-Boom Pressure Signatures From A Langley Wind-Tunnel Model Of A Supersonic-Cruise Business Jet Concept. NASA/TM-2003- 212447, October 2003.

27. Hicks, Raymond M.; and Mendoza, Joel P.: Prediction of Sonic Boom Characteristics From Experimental Near Field Results . NASA TM X-1477, September 1967.

28. Thomas, Charles L.: Extrapolation Of Wind-Tunnel Sonic Boom Signatures Without Use Of A Whitham F-function . Third Conference on Sonic Boom Research, NASA SP-255, 1971.

29. Morris, Odell A.: A Wind-Tunnel Investigation At A Mach Number Of 2.01 Of The Sonic- Boom Characteristics Of Three Wing-Body Combinations Differing In Wing Longitudinal Location. NASA TN D-1384, September 1962.

Appendix A

Mach 2 Low-Boom Concept Design Data The Mach 2 concept was designed to validate low-boom analysis and design methodology that had been developed prior to the close of the supersonic-cruise aircraft research programs. It was designed to generate ground-level overpressures of about 1.0 psf while cruising at its design Mach number and cruise altitude. No attempts were made to size the concepts for enhanced mission performance or minimum weight. The beginning-cruise weight, used to calculate sonic boom, was estimated from previous high-technology concepts. Wing planform shapes, areas, spans, and dihedrals were selected primarily to match the concept’s equivalent area distribution to a Seebass and George low-boom equivalent area distribution. Features that reduced both sonic boom and aerodynamic drag were kept; those that increased sonic-boom overpressures were bypassed even though they may have reduced aerodynamic drag or empty weight. Therefore, no gross take-off weights, empty weights, fuel weights, etc. are listed in the data below, because they are the results of sizing and shaping the configuration for minimum weight and maximum mission performance.

Mach 2 Concept Span, b , ft 160.0 Length, l , ft 313.0 Wing Lift Length, ft 300.0 Wing Area, S , ft 15,055.0 Aspect Ratio, b /S 1.70 Beginning Cruise Altitude, h , ft 55,000.0 Beginning Cruise Weight, lb 550,000.0 Cruise Mach Number, M 2.0 Cruise C 0.06803 L Number Of Engines 4 Ground-Level Shock Overpressure, psf 1.0 Type Of Low-Boom Signature Shape, reference 3 “Flat-Top”

Appendix B

Model C Design Data and Dimensions The Model C wind-tunnel model was one of three wing-body models used to determine the effects of wing position on the sonic-boom overpressures of a wing-body configuration in supersonic-cruise flight, reference 29. Basic wing and fuselage shapes were the same for all three models, but the wings were placed in three locations. On Model A, the wind apex was almost, but not quite, coincident with the fuselage nose. For Model B, the wing was positioned aft of the nose, about half way along the overall length of the fuselage. On Model C, the model described in this report along with a sample of its pressure signatures, the wing trailing edge was coincident with the aft end of the wind-tunnel model and with the front edge of the model sting.

Model C Span, b , ft 0.48 Overall Length, l , in 1.00 Wind-Tunnel Model Length, L , in 0.85 Wing Area, S , in 0.09977 Aspect Ratio, b /S 2.3 Circular Airfoil Thickness Ratio 0.048 Test Mach Number, M 2.01 Leading-Edge Sweep Angle, deg 60.0 Test C values 0.0, 0.10, 0.20 L Form Approved REPORT DOCUMENTATION PAGE OMB No. 0704-0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED ( From - To) Technical Memorandum 01 - 2004 01- 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Persistence Characteristics of Wind-Tunnel Pressure Signatures From Two Similar Models 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER Mack, Robert J.

5e. TASK NUMBER 5f. WORK UNIT NUMBER 23-706-92-02 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER NASA Langley Research Center Hampton, VA 23681-2199 L-18340 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) National Aeronautics and Space Administration NASA Washington, DC 20546-0001 11. SPONSOR/MONITOR'S REPORT NUMBER(S) NASA/TM-2004-212671 12. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified - Unlimited Subject Category 05 Availability: NASA CASI (301) 621-0390 Distribution: Standard 13. SUPPLEMENTARY NOTES An electronic version can be found at http://techreports.larc.nasa.gov/ltrs/ or http://ntrs.nasa.gov 14. ABSTRACT Pressure signatures generated by two sonic-boom wind-tunnel models and measured at Mach 2 are presented, analyzed, and discussed. The two wind-tunnel models differed in length and span by a factor of fourteen, but were similar in wing-body planform shape. The geometry of the larger model had been low-boom tailored to generate a “flat top” ground pressure signature, and the nacelles-off pressure signatures from this model became more “flattop” in shape as the model-probe separation distances increased from 0.94 to 4.4 span lengths. The geometry of the smaller model had not been low-boom tailored, yet its measured pressure signatures had non-N-wave shapes that persisted as model-probe separation distances increased from 26.0 to 104.2 span lengths. Since the overall planforms of the two wind-tunnel models were so similar, it was concluded that the shape-persistence trends in the pressure signatures of the smaller, non-low-boom tailored model would also be present at very large distances in the pressure signatures of the larger, low-boom-tailored model.

15. SUBJECT TERMS Sonic boom; Wind-tunnel models; Pressure signature persistence; Low-boom characteristics 19a. NAME OF RESPONSIBLE PERSON 18. NUMBER 17. LIMITATION OF 16. SECURITY CLASSIFICATION OF: OF ABSTRACT STI Help Desk (email: help@sti.nasa.gov) a. REPORT c. THIS PAGE b. ABSTRACT PAGES 19b. TELEPHONE NUMBER (Include area code) 23 (301) 621-0390 U U U UU Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. Z39.18