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At least 1,207 records · Page 67
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Blended Buffet-Load-Alleviation System for Fighter Airplane

The capability of modern fighter airplanes to sustain flight at high angles of attack and/or moderate angles of sideslip often results in immersion of part of such an airplane in unsteady, separated, vortical flow emanating from its forebody or wings. The flows from these surfaces become turbulent and separated during flight under these conditions. These flows contain significant levels of energy over a frequency band coincident with that of low-order structural vibration modes of wings, fins, and control surfaces. The unsteady pressures applied to these lifting surfaces as a result of the turbulent flows are commonly denoted buffet loads, and the resulting vibrations of the affected structures are known as buffeting. Prolonged exposure to buffet loads has resulted in fatigue of structures on several airplanes. Damage to airplanes caused by buffeting has led to redesigns of airplane structures and increased support costs for the United States Air Force and Navy as well as the armed forces of other countries. Time spent inspecting, repairing, and replacing structures adversely affects availability of aircraft for missions. A blend of rudder-control and piezoelectric- actuator engineering concepts was selected as a basis for the design of a vertical-tail buffet-load-alleviation system for the F/A-18 airplane. In this system, the rudder actuator is used to control the response of the first tail vibrational mode (bending at a frequency near 15 Hz), while directional patch piezoelectric actuators are used to control the second tail vibrational mode (tip torsion at a frequency near 45 Hz). This blend of two types of actuator utilizes the most effective features of each. An analytical model of the aeroservoelastic behavior of the airplane equipped with this system was validated by good agreement with measured results from a full-scale ground test, flight-test measurement of buffet response, and an in-flight commanded rudder frequency sweep. The overall performance of the system was found to be characterized by reductions, ranging from 70 to 30 percent, in vertical-tail buffeting under buffet loads ranging from moderate to severe. These reductions were accomplished with a maximum commanded rudder angle of +/-2deg at 15 Hz and about 10 lb (.4.5 kg) of piezoelectric actuators attached to the vertical tail skin and operating at a peak power level of 2 kW. By meeting the design objective, this system would extend the vertical-tail fatigue life beyond two aircraft lifetimes. This system is also adaptable to other aircraft surfaces and other aircraft

Moses, Robert W.↗
NASA NTRS2005

Estimating Aeroheating of a 3D Body Using a 2D Flow Solver

A method for rapidly estimating the aeroheating, shear stress, and other properties of hypersonic flow about a three-dimensional (3D) blunt body has been devised. First, the geometry of the body is specified in Cartesian coordinates. The surface of the body is then described by its derivatives, coordinates, and principal curvatures. Next, previously relatively simple equations are used to find, for each desired combination of angle of attack and meridional angle, a scaling factor and the shape of an equivalent axisymmetric body. These factors and equivalent shapes are entered as inputs into a previously developed computer program that solves the two-dimensional (2D) equations of flow in a non-equilibrium viscous shock layer (VSL) about an axisymmetric body. The coordinates in the output of the VSL code are transformed back to the Cartesian coordinates of the 3D body, so that computed flow quantities can be registered with locations in the 3D flow field of interest. In tests in which the 3D bodies were elliptic paraboloids, the estimates obtained by use of this method were found to agree well with solutions of 3D, finite-rate-chemistry, thin-VSL equations for a catalytic body.

Scott, Carl D.↗
NASA NTRS2013

Trajectory Reconstruction and Uncertainty Analysis Using Mars Science Laboratory Pre-Flight Scale Model Aeroballistic Testing

As part of the Mars Science Laboratory (MSL) trajectory reconstruction effort at NASA Langley Research Center, free-flight aeroballistic experiments of instrumented MSL scale models was conducted at Aberdeen Proving Ground in Maryland. The models carried an inertial measurement unit (IMU) and a flush air data system (FADS) similar to the MSL Entry Atmospheric Data System (MEADS) that provided data types similar to those from the MSL entry. Multiple sources of redundant data were available, including tracking radar and on-board magnetometers. These experimental data enabled the testing and validation of the various tools and methodologies that will be used for MSL trajectory reconstruction. The aerodynamic parameters Mach number, angle of attack, and sideslip angle were estimated using minimum variance with a priori to combine the pressure data and pre-flight computational fluid dynamics (CFD) data. Both linear and non-linear pressure model terms were also estimated for each pressure transducer as a measure of the errors introduced by CFD and transducer calibration. Parameter uncertainties were estimated using a "consider parameters" approach.

Lugo, Rafael A.↗
NASA NTRS2013

Orion MPCV GN and C End-to-End Phasing Tests

End-to-end integration tests are critical risk reduction efforts for any complex vehicle. Phasing tests are an end-to-end integrated test that validates system directional phasing (polarity) from sensor measurement through software algorithms to end effector response. Phasing tests are typically performed on a fully integrated and assembled flight vehicle where sensors are stimulated by moving the vehicle and the effectors are observed for proper polarity. Orion Multi-Purpose Crew Vehicle (MPCV) Pad Abort 1 (PA-1) Phasing Test was conducted from inertial measurement to Launch Abort System (LAS). Orion Exploration Flight Test 1 (EFT-1) has two end-to-end phasing tests planned. The first test from inertial measurement to Crew Module (CM) reaction control system thrusters uses navigation and flight control system software algorithms to process commands. The second test from inertial measurement to CM S-Band Phased Array Antenna (PAA) uses navigation and communication system software algorithms to process commands. Future Orion flights include Ascent Abort Flight Test 2 (AA-2) and Exploration Mission 1 (EM-1). These flights will include additional or updated sensors, software algorithms and effectors. This paper will explore the implementation of end-to-end phasing tests on a flight vehicle which has many constraints, trade-offs and compromises. Orion PA-1 Phasing Test was conducted at White Sands Missile Range (WSMR) from March 4-6, 2010. This test decreased the risk of mission failure by demonstrating proper flight control system polarity. Demonstration was achieved by stimulating the primary navigation sensor, processing sensor data to commands and viewing propulsion response. PA-1 primary navigation sensor was a Space Integrated Inertial Navigation System (INS) and Global Positioning System (GPS) (SIGI) which has onboard processing, INS (3 accelerometers and 3 rate gyros) and no GPS receiver. SIGI data was processed by GN&C software into thrust magnitude and direction commands. The processing changes through three phases of powered flight: pitchover, downrange and reorientation. The primary inputs to GN&C are attitude position, attitude rates, angle of attack (AOA) and angle of sideslip (AOS). Pitch and yaw attitude and attitude rate responses were verified by using a flight spare SIGI mounted to a 2-axis rate table. AOA and AOS responses were verified by using a data recorded from SIGI movements on a robotic arm located at NASA Johnson Space Center. The data was consolidated and used in an open-loop data input to the SIGI. Propulsion was the Launch Abort System (LAS) Attitude Control Motor (ACM) which consisted of a solid motor with 8 nozzles. Each nozzle has active thrust control by varying throat area with a pintle. LAS ACM pintles are observable through optically transparent nozzle covers. SIGI movements on robot arm, SIGI rate table movements and LAS ACM pintle responses were video recorded as test artifacts for analysis and evaluation. The PA-1 Phasing Test design was determined based on test performance requirements, operational restrictions and EGSE capabilities. This development progressed during different stages. For convenience these development stages are initial, working group, tiger team, Engineering Review Team (ERT) and final.

Neumann, Brian C.↗
NASA NTRS2015

CFD Simulations of the Space Launch System Ascent Aerodynamics and Booster Separation

This paper presents details of Computational Fluid Dynamic modeling of the Space Launch System during ascent. The primary focus of the paper is the flow simulation of the vehicle during ascent using the Overflow Navier-Stokes code. Computations of 739 first-stage flight conditions covering a range of Mach numbers, angles of attack, and roll angles were computed. The overset grid system contained 375 million grid points, and over 28 mil- lion CPU hours were used in the simulations. The simulations were run on the Pleiades supercomputer at the NASA Advanced Supercomputer Center at Ames Research Center. The data products from this work include integrated line-loads, surface pressure coefficients, venting pressures, and protuberance air-loads. Detailed comparisons were made of the aerodynamic performance predicted by Overflow and the wind-tunnel derived aero- dynamic database. A small number of the cases were run with two different turbulence models and with two differencing schemes. These results were used to quantify the sensitivity to the choice of the turbulence model and to the differencing scheme. The paper also introduces an effort to use the inviscid, unstructured Cartesian solver Cart3D to compute the aerodynamics during booster separation. Adaptive mesh refinement is being used to enable accurate simulations of sixteen booster-separation-motor plumes. The use of this tool is explored in preparation for building a booster-separation aerodynamic database.

Ascent Aerodynamics↗
NASA NTRS2020

Pterodactyl: The Development and Performance of Guidance Algorithms for a Mechanically Deployed Entry Vehicle

Pterodactyl is a NASA Space Technology Mission Directorate (STMD) project focused on developing a design capability for optimal, scalable, Guidance and Control (G&C) solutions that enable precision targeting for Deployable Entry Vehicles (DEVs). This feasibility study is unique in that it focuses on the rapid integration of targeting performance analysis with structural & packaging analysis, which is especially challenging for new vehicle and mission designs. This paper will detail the guidance development and trajectory design process for a lunar return mission, selected to stress the vehicle designs and encourage future scalability. For the five G&C configurations considered, the Fully Numerical Predictor-Corrector Entry Guidance (FNPEG) was selected for configurations requiring bank angle guidance and FNPEG with Uncoupled Range Control (URC) was developed for configurations requiring angle of attack and sideslip angle guidance. Successful G&C configurations are defined as those that can deliver payloads to the intended descent and landing initiation point, while abiding by trajectory constraints for nominal and dispersed trajectories.

Johnson, Breanna J.↗
NASA NTRS2020

Pterodactyl: Development and Comparison of Control Architectures for a Mechanically Deployed Entry Vehicle

The Pterodactyl project, seeks to advance the current state-of-the-art for entry vehicles by developing novel guidance and control technologies for Deployable Entry Vehicles (DEVs) that can be applied to various entry vehicle configurations. This paper details the efforts on the NASA-funded Pterodactyl project to investigate and implement multiple control techniques for an asymmetric mechanical DEV. We design multiple control architectures for a Pterodactyl Baseline Vehicle (PBV) and evaluate their performance in achieving varying guidance commands during entry. The control architectures studied are (i) propulsive control systems such as reaction control systems and (ii) non-propulsive control systems such as aerodynamic control surfaces and internal moving masses. For each system, state-feedback integral controllers based on linear quadratic regulator (LQR) optimal control methods are designed to track guidance commands of either (i) bank angle or (ii) angle of attack and sideslip angle as determined by the desired guidance trajectory. All control systems are compared for a lunar return reference mission and by providing a comparative analysis of these systems, configurations, and performance, the efforts detailed in this paper and the Pterodactyl project as a whole will help entry vehicle system designers determine suitable control architectures for integration with DEVs and other entry vehicle types.

Okolo, Wendy A.↗
NASA NTRS2020

Pterodactyl: Control Architectures Development for Integrated Control Design of a Mechanically Deployed Entry Vehicle

The need to return high mass payloads is driving the development of a new class of vehicles, Deployable Entry Vehicles (DEV) for which feasible and optimized control architectures have not been developed. The Pterodactyl project, seeks to advance the current state-of-the-art for entry vehicles by developing a design, test, and build capability for DEVs that can be applied to various entry vehicle configurations. This paper details the efforts on the NASA-funded Pterodactyl project to investigate multiple control techniques for the Lifting Nano-ADEPT (LNA) DEV. We design and implement multiple control architectures on the LNA and evaluate their performance in achieving varying guidance commands during entry.First we present an overview of DEVs and the Lifting Nano-ADEPT (LNA), along with the physical LNA configuration that influences the different control designs. Existing state-of-the-art for entry vehicle control is primarily propulsive as reaction control systems (RCS) are widely employed. In this work, we analyze the feasibility of using both propulsive control systems such as RCS to generate moments, and non-propulsive control systems such as aerodynamic control surfaces and internal moving mass actuations to shift the LNA center of gravity and generate moments. For these diverse control systems, we design different multi-input multi-output (MIMO) state-feedback integral controllers based on linear quadratic regulator (LQR) optimal control methods. The control variables calculated by the controllers vary, depending on the control system being utilized and the outputs to track for the controller are either the (i) bank angle or the (ii) angle of attack and sideslip angle as determined by the desired guidance trajectory. The LQR control design technique allows the relative allocation of the control variables through the choice of the weighting matrices in the cost index. Thus, it is easy to (i) specify which and how much of a control variable to use, and (ii) utilize one control design for different control architectures by simply modifying the choice of the weighting matrices.By providing a comparative analysis of multiple control systems, configurations, and performance, this paper and the Pterodactyl project as a whole will help entry vehicle system designers and control systems engineers determine suitable control architectures for integration with DEVs and other entry vehicle types.

Okolo, Wendy A.↗
NASA NTRS2020

Development of a Numeric Predictor-Corrector Aerocapture Guidance for Direct Force Control

Direct force control, where the angle of attack and sideslip angle are modulated, has been proposed as an alternative to bank angle control for aero-assist maneuvers. This paper reimplements the current state-of-the-art aerocapture guidance for bank angle control, Fully Numeric Predictor-corrector Aerocapture Guidance (FNPAG), for direct force control. The optimal control theory underlying the structure of FNPAG is shown to not be applicable to the direct force control approach. Several solution structures for the longitudinal channel are compared by simulating dispersed three-degree-of-freedom trajectories for a reference mission consisting of a low lift-to-drag vehicle and a highly elliptical, 1-sol target orbit around Mars. The equations of motion for the lateral channel are derived, and a controller is designed to target a specified orbital plane. Finally, a Monte Carlo is used to demonstrate the performance of the new guidance.

Matz, Daniel A.↗
NASA NTRSDate not supplied

Assessment of Control Algorithms for Mars Entry Vehicles With Flap-Based Trajectory Control Under Uncertainty

Flap-based steering systems on blunt-body entry vehicles may improve flight performance relative to heritage bank-angle steering systems. Successful implementation of articulating aerodynamic flaps on a hypersonic entry vehicle requires an active control system to map angle of attack and sidelip angle commands to flap deflection commands. Here, a successive-linearization model prective control algorithm, as a linear quadratic regulator, are formulated, designed, and assessed to address this multiple input multiple output control problem. These two control algorithms are assessed under uncertainty in Monte Carlo simulations for various control profiles and vehicle configurations. Results indicate that while both control algorithms provide successful command tracking under uncertainty, the model predictive controller provides a lower mean and integral error, as well as greater robustness, relative to the linear-quadratic regulator.

Daniel L Engel↗
NASA NTRSDate not supplied

Steady-state RANS Pretest CFD Comparisons for the SWiFT NTF Test

The NATO AVT-298 research program has been underway for seven years to improve the understanding of the full-scale aerodynamics for moderately-swept hybrid wing-bodies found on future civil and military configurations and how this differs from what is measured with low Reynolds number wind tunnel testing or predicted with Computational Fluid Dynamics (CFD). Toward this effort, a hybrid wing-body configuration, known as Swept Wing Flow Test (SWiFT), was designed and tested in the Aircraft Research Association (ARA) and NASA Langley National Transonic Facility (NTF) wind tunnels. This presentation summarizes comparisons between the NTF wind tunnel data and a series of pretest CFD computations generated using steady-state Reynolds-averaged Navier-Stokes (RANS) simulations from participants representing seven institutions using nine separate flow solvers. The objective of this research was to assess the effectiveness of state-of-practice CFD methods in predicting the aerodynamics of swept wing aircraft and identify recommended areas of improvement to the methods themselves. Computational force and moment data will be presented for a series of angle-of-attack and sideslip angle sweeps over a range of Reynolds numbers at both low-speed and near-cruise Mach numbers, as tested in the NTF experiment.

National Transonic Facility↗
NASA NTRS2024

Computational Analysis of the X-57 Maxwell Airplane, the Landing Configuration with High-Lift Blowing and Aileron Deflections (Preliminary Fuselage)

The X-57 Maxwell is an all-electric airplane with a distributed electric propulsion system used for a high-lift system at takeoff and landing conditions. The Kestrel and USM3D flow solvers were used at NASA Langley to investigate the performance of the X-57 Maxwell in the development of an aerodynamic database. The configuration investigated in this paper had a 30° flap deflection, and in addition the pilot’s right aileron were deflected and undeflected in different cases. The solutions were computed at an airspeed of 58 KEAS, for an altitude of 6000 feet, and a flight Reynolds number of 0.588e+06 per foot. To evaluate the high-lift distributed electric propulsion system without aileron deflections, the solutions were computed for an angle-of-attack sweep from −2° to 20°, with the high-lift propellers blowing and the cruise propellers excluded from the simulation. To investigate the aileron effectiveness, the solutions were computed at angles of attack of −2° and 14°, for aileron deflections from −25° to 18° with the high-lift propellers blowing and the cruise propellers windmilling at idle-power. The high-lift propellers and the idle-power cruise propellers were modeled with an actuator disk. Results show negligible differences in lift, drag and pitching moment whether the idle-powered cruise propellers were included or excluded from the simulation. In general, the Kestrel and USM3D codes compared well for lift, drag and pitching moment for the landing configuration with no aileron control. The Kestrel code, using the Spalart-Allmaras turbulence model with the rotation corrections terms, predicted an increasing lift coefficient up to maximum lift coefficient of 4.65 at a 15° angle of attack. The USM3D code, using the Spalart-Allmaras turbulence model turbulence model with the Quadratic Constitutive Relation predicted an increasing lift coefficient up to maximum lift coefficient of 4.5 at a 12° angle of attack, with the lift remaining constant through a 14◦ angle of attack. A possible difference in lift coefficient between the codes for high angles of attack may result from the different available options used with the standard Spalart-Allmaras turbulence model. The Kestrel code predicted more drag across the range of angle of attack than the USM3D code. The codes compared well for pitching moment coefficient across the range of angle of attack. The Kestrel and USM3D codes compared well for aileron effectiveness at a 2° angle of attack. The Kestrel code predicts better aileron effectiveness than USM3D at a 14° angle of attack. There is more flow separation in the region outboard of the last high-lift nacelle for the USM3D solutions at a 14° angle of attack, which diminishes the ability of the aileron to be effective.

X-57 Maxwell Airplane↗
NASA NTRS1957

Experimental static aerodynamic forces and moments at high subsonic speeds on a missile model during simulated launching from the midsemispan location of a 45 degree sweptback wing-fuselage-pylon combination

An investigation was made at high subsonic speeds in the Langley high-speed 7- by 10-foot tunnel to determine the static aerodynamic forces and moments on a missile model during simulated launching from the midsemispan location of a 45 degree sweptback wing-fuselage-pylon combination. The results indicated significant variations in all the aerodynamic components with changes in chordwise location of the missile. Increasing the angle of attack caused increases in the induced effects on the missile model because of the wing-fuselage-pylon combination. Increasing the Mach number had little effect on the variations of the missile aerodynamic characteristics with angle of attack except that nonlinearities were incurred at smaller angles of attack for the higher Mach numbers. The effects of finite wing thickness on the missile characteristics, at zero angle of attack, increase with increasing Mach number. The effects of the pylon on the missile characteristics were to causeincreases in the rolling-moment variation with angle of attack and a negative displacement of the pitching-moment curves at zero angle of attack. The effects of skewing the missile in the lateral direction relative to and sideslipping the missile with the wing-fuselage-pylon combination were to cause additional increments in side force at zero angle of attack. For the missile yawing moments the effects of changes in skew or sideslip angles were qualitatively as would be expected from consideration of the isolated missile characteristics, although there existed differences in theyawing-moment magnitudes.

Alford, William J↗
NASA NTRS1989

Analysis of an unswept propfan blade with a semiempirical dynamic stall model

The time history response of a propfan wind tunnel model with dynamic stall is studied analytically. The response obtained from the analysis is compared with available experimental data. The governing equations of motion are formulated in terms of blade normal modes which are calculated using the COSMIC-NASTRAN computer code. The response analysis considered the blade plunging and pitching motions. The lift, drag and moment coefficients for angles of attack below the static stall angle are obtained from a quasi-steady theory. For angles above static stall angles, a semiempirical dynamic stall model based on a correction to angle of attack is used to obtain lift, drag and moment coefficients. Using these coefficients, the aerodynamic forces are calculated at a selected number of strips, and integrated to obtain the total generalized forces. The combined momentum-blade element theory is used to calculate the induced velocity. The semiempirical stall model predicted a limit cycle oscillation near the setting angle at which large vibratory stresses were observed in an experiment. The predicted mode and frequency of oscillation also agreed with those measured in the experiment near the setting angle.

Reddy, T. S. R.↗
NASA NTRS1989

Aeroelastic analysis of prop fan blades with a semiempirical dynamic stall model

The time-history response of a propfan wind-tunnel model with dynamic stall was studied analytically. The response obtained from the analysis was compared with available experimental data. The governing equations of motion were formulated in terms of blade normal modes calculated using the COSMIC-NASTRAN computer code. The response analysis considered the blade plunging and pitching motions. The lift, drag, and moment coefficients for angles of attack below the static stall angle were obtained from a quasi-steady theory. For angles above static stall angles, a semiempirical dynamic stall model based on a correction to the angle of attack was used to obtain lift, drag, and moment coefficients. Using these coefficients, the aerodynamic forces were calculated at a selected number of strips, and integrated to obtain the total generalized forces. The combined momentum-blade element theory was used to calculate the induced velocity. The semiempirical stall model predicted a limit cycle oscillation near the setting angle at which large vibratory stresses were observed in an experiment. The predicted mode and frequency of oscillation also agreed with those measured in the experiment near this setting angle. The results also correlated well with the other published data that used a semiempirical dynamic stall model based on a synthesized procedure.

Reddy, T. S. R.↗
NASA NTRS1969

Heat-Transfer Measurements Obtained on the X-15 Airplane Including Correlations With Wind-Tunnel Results

Heat-transfer measurements were obtained on the X-15 airplane from two flights under quasi-steady conditions at a free-stream Mach number of 5.1 and an angle of attack of 2.0° and a free-stream Mach number of 4.98 and an angle of attack of 16.3°. These measurements were made at corresponding free-stream Reynolds numbers of 2.45 × 10 6 and 1.31 × 10 6 per foot (8.04 × 10 6 and 4.30 × 10 6 per meter). Experimental heat-transfer coefficients derived from temperatures obtained from 200 recording thermocouples on the skin of the airplane are tabulated. Correlations with wind-tunnel results show that the wind-tunnel data are in fair-to-good agreement with the flight data obtained on the wing, ventral tail, and vertical tail at low angles of attack but are generally in poor agreement with the high-angle-of-attack data and the low-angle-of-attack fuselage data.

Robert D Quinn↗
NASA NTRS1995

Effects of Sonic Line Transition on Aerothermodynamics of the Mars Pathfinder Probe

Flow field solutions over the Mars Pathfinder Probe spanning the trajectory through the Martian atmosphere at angles of attack from 0 to 11 degrees are obtained. Aerodynamic coefficients derived from these solutions reveal two regions where the derivative of pitching moment with respect to angle of attack is positive at small angles of attack. The behavior is associated with the transition of the sonic line location between the blunted nose and the windside shoulder of the 70 degree half-angle cone in a gas with a low effective ratio of specific heats. The transition first occurs as the shock layer gas chemistry evolves from highly nonequilibrium to near equilibrium, above approximately 6.5 km/s and 40 km altitude, causing the effective specific heat ratio to decrease. The transition next occurs in an equilibrium flow regime as velocities decrease through 3.5 km/s and the specific heat ratio increases again with decreasing enthalpy. The effects of the expansion over the shoulder into the wake are more strongly felt on the fustrum when the sonic line sits on the shoulder. The transition also produces a counter-intuitive trend in which windside heating levels decrease with increasing angle of attack resulting from an increase in the effective radius of curvature. Six-degree-of-freedom trajectory analyses utilizing the computed aerodynamic coefficients predict a moderate, 3 to 4 degree increase in total angle of attack as the probe, spinning at approximately 2 revolutions per minute, passes through these regions.

Gnoffo, Peter A.↗
NASA NTRS1940

Investigation of the Characteristics of a High-Aspect-Ratio Wing in the Langley 8-Foot High-Speed Tunnel

An investigation of the characteristics of a wing with an aspect ratio of 9.0 and an NACA 65-210 airfoil section has been made at Mach number up to 0.925. The wing tested has a taper ratio of 2.5:1.0, no twist, dihedral, or sweepback, and 20-percent - chord 37.5-percent-semispan plain ailerons. The results showed that serious changes in the normal-force characteristics occurred when the Mach number was increased above 0.74 at angles of attack between 4 deg. and 10 deg. and above 0.80 at 0 deg. angle of attack.Because of small outboard shifts in the lateral center of load, the bending moment at the root for conditions corresponding to a 3g pull-out at an altitude of 35,000 feet increased by approximately 5% when the Much number was increased beyond 0.83 the negative pitching moments for the high angles of attack increased, whereas those for the low angles of attack decreased with a resulting large increase in the negative slope of the pitching-moment curves. A large increase occurred in the values of the drag coefficients for the range of lift coefficients needed for level flight at an altitude of 35,000 feet when the Mach number was increased beyond a value of 0.80. The wakes at a station 2.82 root chords behind the wing quarter-chord line extended approximately a chord above the wing chord line for the angles of attack required to recover from high-speed dives at high Mach numbers.

Whitcomb, Richard T.↗