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At least 145 records · Page 8

Geometry control in prestressed adaptive space trusses

In this work the actuator placement problem for the precision control in prestressed adaptive space trusses is studied. These structures cannot be statically determinate, implying that the length-adjusting actuators have to work against the existing prestressing forces, and also against the stresses caused by the actuation. This type of difficulties does not exist in statically determinate adaptive trusses where, except for overcoming the friction, the actuators operate under zero axial force, and require almost no energy. The actuator placement problem in statically inderterminate trusses is, therefore, governed seriously by the energy and the strength requirements. The paper provides various methodologies for the actuator placement problem in prestressed space trusses.

Sener, Murat↗

A Baseline Load Schedule for the Manual Calibration of a Force Balance

A baseline load schedule for the manual calibration of a force balance is defined that takes current capabilities at the NASA Ames Balance Calibration Laboratory into account. The chosen load schedule consists of 18 load series with a total of 194 data points. It was designed to satisfy six requirements: (i) positive and negative loadings should be applied for each load component; (ii) at least three loadings should be applied between 0 % and 100 % load capacity; (iii) normal and side force loadings should be applied at the forward gage location, aft gage location, and the balance moment center; (iv) the balance should be used in "up" and "down" orientation to get positive and negative axial force loadings; (v) the constant normal and side force approaches should be used to get the rolling moment loadings; (vi) rolling moment loadings should be obtained for 0, 90, 180, and 270 degrees balance orientation. In addition, three different approaches are discussed in the paper that may be used to independently estimate the natural zeros, i.e., the gage outputs of the absolute load datum of the balance. These three approaches provide gage output differences that can be used to estimate the weight of both the metric and non-metric part of the balance. Data from the calibration of a six-component force balance will be used in the final manuscript of the paper to illustrate characteristics of the proposed baseline load schedule.

Ulbrich, N.↗

Experimental investigation and analysis of two sources of nozzle-thrust misalignment

Asymmetry of nozzle's throat produces oscillatory type net side-force axial profile. Using mean values of localized static pressure and Mach number, scaling laws for flat-plate supersonic flow over protrusion are applied to nozzle expansion cone irregularities to give approximate indication of perturbed-pressure profiles and induced side forces.

Dowdy, M. W.↗

Flight Test of a 40-Foot Nominal Diameter Disk-Gap-Band Parachute Deployed at a Mach Number of 2.72 and a Dynamic Pressure of 9.7 Pounds per Square Foot

A 40-foot-nominal-diameter (12.2 meter) disk-gap-band parachute was flight tested as part of the NASA Supersonic Planetary Entry Decelerator (SPED-I) Program. The test parachute was deployed from an instrumented payload by means of a deployment mortar when the payload was at an altitude of 158,500 feet (48.2 kilometers), a Mach number of 2.72, and a free-stream dynamic pressure of 9.7 pounds per foot(exp 2) (465 newtons per meter(exp 2)). Suspension line stretch occurred 0.46 second after mortar firing and the resulting snatch force loading was -8.lg. The maximum acceleration experienced by the payload due to parachute opening was -27.2g at 0.50 second after the snatch force peak for a total elapsed time from mortar firing of 0.96 second. Canopy-shape variations occurred during the higher Mach number portion of the flight test (M greater than 1.4) and the payload was subjected to large amplitude oscillatory loads. A calculated average nominal axial-force coefficient ranged from about 0.25 immediately after the first canopy opening to about 0.50 as the canopy attained a steady inflated shape. One gore of the test parachute was damaged when the deployment bag with mortar lid passed through it from behind approximately 2 seconds after deployment was initiated. Although the canopy damage caused by the deployment bag penetration had no apparent effect on the functional capability of the test parachute, it may have affected parachute performance since the average effective drag coefficient of 0.48 was 9 percent less than that of a previously tested parachute of the same configuration.

EXPERIMENTS↗

Some anomalies observed in wind-tunnel tests of a blunt body at transonic and supersonic speeds

An investigation of anomalies observed in wind tunnel force tests of a blunt body configuration was conducted at Mach numbers from 0.20 to 1.35 in the Langley 8-foot transonic pressure tunnel and at Mach numbers of 1.50, 1,80, and 2.16 in the Langley Unitary Plan wind tunnel. At a Mach number of 1.35, large variations occurred in axial force coefficient at a given angle of attack. At transonic and low supersonic speeds, the total drag measured in the wind tunnel was much lower than that measured during earlier ballistic range tests. Accurate measurements of total drag for blunt bodies will require the use of models smaller than those tested thus far; however, it appears that accurate forebody drag results can be obtained by using relatively large models. Shock standoff distance is presented from experimental data over the Mach number range from 1.05 to 4.34. Theory accurately predicts the shock standoff distance at Mach numbers up to 1.75.

Brooks, J. D.↗

Experiments in Aligning Threaded Parts Using a Robot Hand

Techniques for determining and correcting threaded part alignment using force and angular position data are developed to augment currently limited techniques for align- ing threaded parts. These new techniques are based on backspinning a nut with respect to a bolt and measuring the force change that occurs when the bolt "falls" into the nut. Kinematic models that describe the relationship between threaded parts during backspinning are introduced and are used to show how angular alignment may be determined. The models indicate how to distinguish between the aligned and misaligned cases of a bolt and a nut connection by using axial force data only. In addition, by tracking the in-plane relative attitude of the bolt during spinning, data can be obtained on the direction of the angular misalignment which, in turn, is used to correct the misalignment. Results from experiments using a bolt held in a specialized fixture and a three fingers Stanford/JPL hand are presented.

Diftler, M. A.↗

Flight Test of a 40-Foot Nominal-Diameter Disk-Gap-Band Parachute Deployed at a Mach Number of 1.91 and a Dynamic Pressure of 11.6 Pounds per Square Foot

A 40-foot (12.2 meter) nominal-diameter disk-gap-band parachute was flight tested as part of the NASA Supersonic Planetary Entry Decelerator Program (SPED-I). The test parachute was ejected by a deployment mortar from an instrumented payload at an altitude of 140,000 feet (42.5 kilometers). The payload was at a Mach number of 1.91 and the dynamic pressure was 11.6 pounds per square foot (555 newtons per square meter) at the time the parachute deployment mortar was fired. The parachute reached suspension line stretch in 0.43 second with a resultant snatch force loading of 1990 pounds (8850 newtons). The maximum parachute opening load of 6500 pounds (28,910 newtons) came 0.61 second later at a total elapsed time from mortar firing of 1.04 seconds. The first full inflation occurred at 1.12 seconds and stable inflation was achieved at approximately 1.60 seconds. The parachute had an average axial-force coefficient of 0.53 during the deceleration period. During the steady-state descent portion of the flight test, the average effective drag coefficient was also 0.53 and pitch-yaw oscillations of the canopy averaged less than 10 degrees in the altitude region above 100,000 feet (30.5 meters).

EXPERIMENTS↗

Modeling Interplanetary Expansion and Deformation of CMEs With ANTEATR-PARADE: Relative Contribution of Different Forces

Coronal Mass Ejections (CMEs) are key drivers of space weather activity but most predictions have been limited to the expected arrival time of a CME, rather than the internal properties that affect the severity of an impact. Many properties, such as the magnetic field density and mass density, follow conservation laws and vary systematically with changes in the size of a CME. We present ANTEATR-PARADE, the newest version of the ANTEATR arrival time model, which now includes physics-driven changes in the size and shape of both the CME's central axis and its cross section. Internal magnetic and thermal and external drag forces affect the acceleration of the CME in different directions, inducing asymmetries between the radial and perpendicular directions. These improvements should lead to more realistic CME velocities, both bulk and expansion, sizes and shapes, and internal properties. We present the model details, an initial illustration of the general behavior, and a study of the relative importance of the different forces. The model shows a pancaking of both the cross section and central axis of the CME so that their radial extent becomes smaller than their extent in the perpendicular direction. We find that the initial velocities, drag, any form of cross section expansion, and the precise form of thermal expansion have strong effects. The results are less sensitive to axial forces and the specific form of the cross section expansion.

C. Kay↗

Cryogenic strain gage techniques used in force balance design for the National Transonic Facility

A force balance is a strain gage transducer used in wind tunnels to measure the forces and moments on aerodynamic models. Techniques have been established for temperature-compensation of force balances to allow their use over the operating temperature range of a cryogenic wind tunnel (-190C to 60C) without thermal control. This was accomplished by using a patented strain gage matching process to minimize inherent thermal differences, and a thermal compensation procedure to reduce the remaining thermally-induced outputs to acceptable levels. A method of compensating for mechanical movement of the axial force measuring beam caused by thermally-induced stresses under transient temperatures was also included.

Ferris, A. T.↗

The Determination of Forces and Moments on a Gimballed SRM Nozzle Using a Cold Flow Model

The Solid Rocket Motor Air Flow Facility (SAF) at NASA Marshall Space Flight Center was used to characterize the flow in the critical aft end and nozzle of a solid propellant rocket motor (SRM) as part of the design phase of development. The SAF is a high pressure, blowdown facility which supplies a controlled flow of air to a subscale model of the internal port and nozzle of a SRM to enable measurement and evaluation of the flow field and surface pressure distributions. The ASRM Aft Section/Nozzle Model is an 8 percent scale model of the 19 second burn time aft port geometry and nozzle of the Advanced Solid Rocket Motor, the now canceled new generation space Shuttle Booster. It has the capability to simulate fixed nozzle gimbal angles of 0, 4, and 8 degrees. The model was tested at full scale motor Reynolds Numbers with extensive surface pressure instrumentation to enable detailed mapping of the surface pressure distributions over the nozzle interior surface, the exterior surface of the nozzle nose and the surface of the simulated propellant grain in the aft motor port. A mathematical analysis and associated numerical procedure were developed to integrate the measured surface pressure distributions to determine the lateral and axial forces on the moveable section of the nozzle, the effective model thrust and the effective aerodynamic thrust vector (as opposed to the geometric nozzle gimbal angle). The nozzle lateral and axial aerodynamic loads and moments about the pivot point are required for design purposes and require complex, three dimensional flow analyses. The alignment of the thrust vector with the nozzle geometric centerline is also a design requirement requiring three dimensional analyses which were supported by this experimental program. The model was tested with all three gimbal angles at three pressure levels to determine Reynolds number effects and reproducibility. This program was successful in demonstrating that a measured surface pressure distribution could be integrated to determine the lateral and axial loads, moments and thrust vector alignment for the scaled model of a large space booster nozzle. Numerical results were provided which are scaleable to the full scale rocket motor and can be used as benchmark data for 3-D CFD analyses.

Whitesides, R. Harold↗

Flight Test of a 30-Foot Nominal Diameter Cross Parachute Deployed at a Mach Number of 1.57 and a Dynamic Pressure of 9.7 Pounds per Square Foot

A 30-foot (9.1-meter) nominal-diameter cross-type parachute with a cloth area (reference area) of 709 square feet (65.9 square meters) was flight tested in the rocket-launched portion of the NASA Planetary Entry Parachute Program (PEPP). The test parachute was ejected from an instrumented payload by means of a mortar when the system was at a Mach number of 1.57 and a dynamic pressure of 9.7 psf. The parachute deployed to suspension-line stretch in 0.44 second with a resulting snatch-force loading of 1100 pounds (4900 newtons), Canopy inflation began at 0.58 second and a first full inflation was achieved at approximately 0.77 second. The maximum opening load occurred at 0.81 second and was 4255 pounds (18,930 newtons). Thereafter, the test item exhibited a canopy-shape instability in that the four panel arms experienced fluctuations, a "scissoring" type of motion predominating throughout the test period. Calculated values of axial-force coefficient during the deceleration portion of the test varied between 0.35 and 1.05, with an average value of 0.69. During descent, canopy-shape variations had reduced to small amplitudes and resultant pitch-yaw angles of the payload with respect to the local vertical averaged less than 10 degrees. The effective drag coefficient, based on the vertical components of velocity and acceleration during system descent, was 0.78.

TESTS↗

PipeSight: A High-Performance Computing Platform for Pipeline Integrity Management

The Phase I feasibility study completed as part of this project has led to a number of innovative technologies being developed and has laid the foundation for a successful Phase II effort to commercialize a platform for managing the integrity of pipelines for the damage mechanisms of the new, hybrid-energy based economy. To ground the development efforts and direction of the project, an extensive market research and customer discovery effort was undertaken early in Phase I. Through this effort, a number of pipeline owners and operators were interviewed, and the following key findings were discovered about the pipeline industry: • Small pipeline operators do not have the central engineering groups necessary to perform their own independent analysis of inspection data, but instead rely on summarized tally sheets provided to them by inspection service providers. • The time it takes to go from an inspection to a completed engineering assessment, even for small segments of pipeline, can take anywhere from 30-120 days. During this delay, critical threats can (and have been known to) cause failures. • Uncertainty is often not accounted for in the assessment of pipeline integrity. The tally sheets provided by third-party service providers are almost always deterministic in nature, identifying threats that present a concern only to the current (not the future) integrity of the pipeline. • It is uncommon to apply the latest technologies to perform advanced assessments of damaged pipelines. There is a desire to use more advanced analysis capabilities to assess threats. Many pipeline operators indicated that they would often excavate a pipeline to perform an inspection and find that the damage was not as bad as they anticipated, thus using limited resources unnecessarily. Companies are not consistent in their use of inspection data to determine corrosion rates, and those that do only calculate deterministic corrosion rates. • The industry has prominently relied on time-based inspections but has recently started to transition to risk-based inspections. However, there appears to be no uniform guidance on how to do so while properly accounting for all sources of uncertainty. • Companies are not storing inspection data in a manner that allows for the ready determination of temporal trends. • Predictive maintenance principles and practices are beginning to be used by early adopters • Some pipelines are being re-purposed to transport different process fluids than they were designed for, e.g., H 2 and CO 2 rich process streams to serve the new hybrid-energy based economy, which are presenting new integrity concerns for the existing pipeline network that crisscrosses the United States. As a result of these discoveries, we were able to target the development efforts in Phase I to best serve the needs of the industry. In Phase I, we developed a way to correlate multiple large-scale scans of the pipeline to determine a probabilistic corrosion rate that accounts for all sources of error and uncertainty in the inspection process. This probabilistic corrosion rate can be used to predict the future thickness distribution of the pipe wall. We demonstrate how this analysis may be performed in an analytical fashion and has been implemented in such a manner that it can be readily distributed using GPU computing through integration of the Kokkos programming model. We also make a very novel extension of the analytical corrosion rate model to Bayesian Networks (an explainable AI technique) that can account for non-parametric distributions of corrosion rates. With the predictions made above for the probabilistic corrosion rate and corresponding future distribution of the pipe wall thickness, we can assess the integrity of the pipeline through the use of a probabilistic engineering assessment. We developed a novel screening data analysis approach that can rapidly identify ‘hotspots’ (local thin areas) where the integrity of the pipeline is a concern. Once more, we implemented this screening approach in C++ to leverage GPU computing via the Kokkos programming model. After the critical hotspots are identified, we developed a program that can automatically generate an advanced finite element model of the damaged regions. Since the number of damaged regions that require advanced analysis can number in the thousands, we integrated an open-source container-native workflow engine for orchestrating parallel jobs on the cloud. Initially, these advanced numerical models were only designed to account for loading due to internal pressure. However, in a slight pivot from the initial Phase I proposal, we developed a complete pipe stress analysis program (called Simflex) which can simulate the complete pipeline and its response to thermal expansion, pressure, thermal bowing, weight, wind, earthquake, support displacement, support friction and external forces. This pipe stress analysis program was written generically, to handle any piping system, but contains the features needed to model long pipelines (i.e., it incorporates a model for soil mechanics and can account for the nonlinear boundary conditions necessary to simulate long underground pipelines). This pipe stress analysis program can simulate any segment of the pipeline (simple or complex) under any set of conditions and loads, to determine the supplemental loads (axial forces and bending moments) at the location of damage. This enables the most accurate state of stress to be accounted for in the pipeline, which can prove critical when evaluating the integrity of a damaged region. In the process of developing the technologies to perform the integrity assessment of the pipeline, we also extended one of the industry standard approaches for performing the assessment of local thin areas that extend more in the circumferential direction than the longitudinal direction of the pipeline. This approach was presented to the API 579-1/AS ME FFS-1 steering committee in November 2021 for consideration in the next edition of the industry standard for Fitness-For-Service (expected to be released in 2023). To help pipeline operators make decisions with the results on any integrity assessment, we developed a new approach to the life-cycle management of pipelines which uses a Bayesian Decision Network. The network is designed to help pipeline operators plan and prioritize inspection activities and ultimately make smarter, more cost-effective decisions. The Bayesian approach accounts for all sources of uncertainty and carries them through to the final optimal decisions, providing a probabilistic framework for optimizing inspection intervals. The proof-of-concept networks developed in the feasibility study are complete, verified, and are focused on a subset of the pipeline. To expand this novel approach to the scale necessary for an entire network of pipelines in Phase II, we will leverage the DOE-funded Bengi solver for industrial-scale decision making with Bayesian Networks [22]. Once implemented, we will be able to provide the pipeline industry with a much-needed tool for optimal inspection planning using truly explainable artificial intelligence (XAI). To handle all of these advanced capabilities into a cloud-based platform, the architecture of the Equity Engineering Cloud (EEC) was extended to include Argo Workflows, a framework capable of distributing and managing a massive number of jobs that consume their own resources, such that thousands of serial finite element simulations can be run in parallel. As part of this substantial undertaking, we also integrated Argo Continuous Delivery (CD) into the EEC, to aid with the rapid prototyping and iterations that will be imperative to the success of the PipeSight platform’s Agile development process in Phase II. As part of the pipe stress analysis program, we also developed a custom visualizer that leverages the DOE-funded VTK visualization library. We added custom contouring capabilities and a means for interacting visually with both the inputs and outputs of the pipe stress analysis program. We also developed routines for automating the post-processing of the finite element simulations to determine if any failure criteria are met and to visualize the deformations, stresses and strains in ParaView using the exodus II file format (a subset of netCDF).

24 POWER TRANSMISSION AND DISTRIBUTION↗

Fan and wing force data from wind tunnel investigation of a 0.38 meter (15 inch) diameter VTOL model lift fan installed in a two dimensional wing

Test data are presented for a 38-cm (15-in.) diameter, 1.28 pressure ratio model VTOL lift fan installed in a two-dimensional wing and tested in a 2.74-by 4.58-meter (9-by 15-ft)V/STOL wind tunnel. Tests were run with and without exit louvers over a wide range of crossflow velocities and wing angle of attack. Tests were also performed with annular-inlet vanes, inlet bell-mouth surface disconuities, and fences to induce fan windmilling. Data are presented on the axial force of the fan assembly and overall wing forces and moments as measured on force balances for various static and crossflow test conditions. Midspan wing surface pressure coefficient data are also given.

Yuska, J. A.↗

High Altitude Flight Test of a 40-Foot Diameter (12.2 meter) Ringsail Parachute at Deployment Mach Number of 2.95

A 40-foot-nominal-diameter (12.2-meter) modified ringsail parachute was flight tested as part of the NASA Supersonic High Altitude Parachute Experiment (SHAPE) program. The 41-pound (18.6-kg) test parachute system was deployed from a 239.5-pound (108.6-kg) instrumented payload by means of a deployment mortar when the payload was at an altitude of 171,400 feet (52.3 km), a Mach number of 2.95, and a free-stream dynamic pressure of 9.2 lb/sq ft (440 N/m(exp 2)). The parachute deployed properly, suspension line stretch occurring 0.54 second after mortar firing with a resulting snatch-force loading of 932 pounds (4146 newtons). The maximum loading due to parachute opening was 5162 pounds (22 962 newtons) at 1.29 seconds after mortar firing. The first near full inflation of the canopy at 1.25 seconds after mortar firing was followed immediately by a partial collapse and subsequent oscillations of frontal area until the system had decelerated to a Mach number of about 1.5. The parachute then attained a shape that provided full drag area. During the supersonic part of the test, the average axial-force coefficient varied from a minimum of about 0.24 at a Mach number of 2.7 to a maximum of 0.54 at a Mach number of 1.1. During descent under subsonic conditions, the average effective drag coefficient was 0.62 and parachute-payload oscillation angles averaged about &loo with excursions to +/-20 degrees. The recovered parachute was found to have slight damage in the vent area caused by the attached deployment bag and mortar lid.

TESTS↗

Flight Reynolds Number Testing of the Orion Launch Abort Vehicle in the NASA Langley National Transonic Facility

A 6%-scale unpowered model of the Orion Launch Abort Vehicle (LAV) ALAS-11-rev3c configuration was tested in the NASA Langley National Transonic Facility to obtain static aerodynamic data at flight Reynolds numbers. Subsonic and transonic data were obtained for Mach numbers between 0.3 and 0.95 for angles of attack from -4 to +22 degrees and angles of sideslip from -10 to +10 degrees. Data were also obtained at various intermediate Reynolds numbers between 2.5 million and 45 million depending on Mach number in order to examine the effects of Reynolds number on the vehicle. Force and moment data were obtained using a 6-component strain gauge balance that operated both at warm temperatures (+120 . F) and cryogenic temperatures (-250 . F). Surface pressure data were obtained with electronically scanned pressure units housed in heated enclosures designed to survive cryogenic temperatures. Data obtained during the 3-week test entry were used to support development of the LAV aerodynamic database and to support computational fluid dynamics code validation. Furthermore, one of the outcomes of the test was the reduction of database uncertainty on axial force coefficient for the static unpowered LAV. This was accomplished as a result of good data repeatability throughout the test and because of decreased uncertainty on scaling wind tunnel data to flight.

Chan, David T.↗

Longitudinal Force and Moment Data at Mach Numbers from 0.60 to 1.40 for a Family of Elliptic Cones with Various Semiapex Angles

An investigation has been made to determine the aerodynamic characteristics of four elliptic cones having plan-form semiapex angles ranging from about 9 to 31 deg., and also for one of these cones modified on the upper surface to reduce the base area by about one half. The tests were made for angles of attack from about -2 to +21 deg., at Mach numbers from 0.60 to 1.40, and for a constant Reynolds number of 1.4 million, based on the length of the models. For each model, lift, pitching-moment, and drag coefficients, and lift-drag ratios are presented for the forebody, and axial-force coefficients are presented for the base. Calculated lift and pitching- moment curves for the elliptic cones, and lift-curve slopes for each model at supersonic Mach numbers are shown for comparison with the corresponding experimental values. Lift-drag ratios are also given for the forebody and base combined. These data are presented without discussion.

Stivers, Louis S., Jr.↗

A Factorial Data Rate and Dwell Time Experiment in the National Transonic Facility

This report is an introductory tutorial on the application of formal experiment design methods to wind tunnel testing, for the benefit of aeronautical engineers with little formal experiment design training. It also describes the results of a Study to determine whether increases in the sample rate and dwell time of the National Transonic Facility data system Would result in significant changes in force and moment data. Increases in sample rate from 10 samples per second to 50 samples per second were examined, as were changes in dwell time from one second per data point to two seconds. These changes were examined for a representative aircraft model in a range of tunnel operating conditions defined by angles of attack from 0 deg to 3.8 degrees, total pressure from 15.0 psi to 24.1 psi, and Mach numbers from 0.52 to 0.82. No statistically significant effect was associated with the change in sample rate. The change in dwell time from one second to two seconds affected axial force measurements, and to a lesser degree normal force measurements. This dwell effect comprises a "rectification error" caused by incomplete cancellation of the positive and negative elements of certain low frequency dynamic components that are not rejected by the one-Hz low-pass filters of the data system. These low frequency effects may be due to tunnel circuit phenomena and other sources. The magnitude of the dwell effect depends on dynamic pressure, with angle of attack and Mach number influencing the strength of this dependence. An analysis is presented which suggests that the magnitude of the rectification error depends on the ratio of measurement dwell time to the period of the low-frequency dynamics, as well as the amplitude of the dynamics The essential conclusion of this analysis is that extending the dwell time (or, equivalently, replicating short-dwell data points) reduces the rectification error.

DeLoach, R.↗

Flight-Test-Determined Aerodynamic Force and Moment Characteristics of the X-43A at Mach 7.0

The second flight of the Hyper-X program afforded a unique opportunity to determine the aerodynamic force and moment characteristics of an airframe-integrated scramjet-powered aircraft in hypersonic flight. These data were gathered via a repeated series of pitch, yaw, and roll doublets; frequency sweeps; and pushover-pullup maneuvers performed throughout the X-43A cowl-closed descent. Maneuvers were conducted at Mach numbers of 6.80 to 0.95 and altitudes from 92,000 ft msl to sea level. The dynamic pressure varied from 1300 psf to 400 psf with the angle of attack ranging from 0 deg to 14 deg. The flight-extracted aerodynamics were compared with preflight predictions based on wind-tunnel-test data. The X-43A flight-derived axial force was found to be 10 percent to 15 percent higher than prediction. Under-predictions of similar magnitude were observed for the normal force. For Mach numbers above 4.0, the flight-derived stability and control characteristics resulted in larger-than-predicted static margins, with the largest discrepancy approximately 5 in. forward along the x-axis center of gravity at Mach 6.0. This condition would result in less static margin in pitch. The predicted lateral-directional stability and control characteristics matched well with flight data when allowance was made for the high uncertainty in angle of sideslip.

Davis. Marl C.↗