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At least 361 records · Page 20

Concept Development of a Mach 2.4 High-Speed Civil Transport

In support of the NASA High-Speed Research Program, a Mach 2.4 high-speed civil transport concept was developed to serve as a baseline for studies to assess advanced technologies required for a feasible year 2005 entry-into-service vehicle. The configuration was designed to carry 251 passengers at Mach 2.4 cruise with a 6500-n.mi. range and operate in the existing world airport structure. The details of the configuration development, aerodynamic design, propulsion system and integration, mass properties, sizing, and mission performance are presented. The baseline configuration has a wing area of 9l00 sq ft and a takeoff gross weight of 614300 lb. The four advanced turbine bypass engines have 39 000 lb thrust with a weight of 9950 lb each, yielding a vehicle takeoff thrust-to-weight ratio of 0.254 and a takeoff wing loading of 67.5 lb/sq ft. The configuration was sized by the 11000-ft takeoff field length requirement and the usable fuel volume limit, which results in a rotation speed of 179 knots and an end-of-mission landing approach velocity of 134 knots.

Fenbert, James W.↗

Trajectory Dispersed Vehicle Process for Space Launch System

The Space Launch System (SLS) vehicle is part of NASA's deep space exploration plans that includes manned missions to Mars. Manufacturing uncertainties in design parameters are key considerations throughout SLS development as they have significant effects on focus parameters such as lift-off-thrust-to-weight, vehicle payload, maximum dynamic pressure, and compression loads. This presentation discusses how the SLS program captures these uncertainties by utilizing a 3 degree of freedom (DOF) process called Trajectory Dispersed (TD) analysis. This analysis biases nominal trajectories to identify extremes in the design parameters for various potential SLS configurations and missions. This process utilizes a Design of Experiments (DOE) and response surface methodologies (RSM) to statistically sample uncertainties, and develop resulting vehicles using a Maximum Likelihood Estimate (MLE) process for targeting uncertainties bias. These vehicles represent various missions and configurations which are used as key inputs into a variety of analyses in the SLS design process, including 6 DOF dispersions, separation clearances, and engine out failure studies.

Statham, Tamara↗

NDARC NASA Design and Analysis of Rotorcraft - Input, Appendix 4

The NDARC code performs design and analysis tasks. The design task involves sizing the rotorcraft to satisfy specified design conditions and missions. The analysis tasks can include off-design mission performance analysis, flight performance calculation for point operating conditions, and generation of subsystem or component performance maps. The principal tasks (sizing, mission analysis, flight performance analysis) are shown in the figure as boxes with heavy borders. Heavy arrows show control of subordinate tasks. The aircraft description consists of all the information, input and derived, that denes the aircraft. The aircraft consists of a set of components, including fuselage, rotors, wings, tails, and propulsion. This information can be the result of the sizing task; can come entirely from input, for a fixed model; or can come from the sizing task in a previous case or previous job. The aircraft description information is available to all tasks and all solutions. The sizing task determines the dimensions, power, and weight of a rotorcraft that can perform a specified set of design conditions and missions. The aircraft size is characterized by parameters such as design gross weight, weight empty, rotor radius, and engine power available. The relations between dimensions, power, and weight generally require an iterative solution. From the design flight conditions and missions, the task can determine the total engine power or the rotor radius (or both power and radius can be fixed), as well as the design gross weight, maximum takeoff weight, drive system torque limit, and fuel tank capacity. For each propulsion group, the engine power or the rotor radius can be sized. Missions are defined for the sizing task, and for the mission performance analysis. A mission consists of a number of mission segments, for which time, distance, and fuel burn are evaluated. For the sizing task, certain missions are designated to be used for design gross weight calculations; for transmission sizing; and for fuel tank sizing. The mission parameters include mission takeoff gross weight and useful load. For specified takeoff fuel weight with adjustable segments, the mission time or distance is adjusted so the fuel required for the mission equals the takeoff fuel weight. The mission iteration is on fuel weight or energy. Flight conditions are specified for the sizing task, and for the flight performance analysis. For the sizing task, certain flight conditions are designated to be used for design gross weight calculations; for transmission sizing; for maximum takeoff weight calculations; and for anti-torque or auxiliary thrust rotor sizing. The flight condition parameters include gross weight and useful load. For flight conditions and mission takeoff, the gross weight can be maximized, such that the power required equals the power available. A flight state is defined for each mission segment and each flight condition. The aircraft performance can be analyzed for the specified state, or a maximum effort performance can be identified. The maximum effort is specified in terms of a quantity such as best endurance or best range, and a variable such as speed, rate of climb, or altitude.

Rotorcraft Input↗

NDARC - NASA Design and Analysis of Rotorcraft: Input and Data Structures - Vol 2

The NDARC code performs design and analysis tasks. The design task involves sizing the rotorcraft to satisfy specified design conditions and missions. The analysis tasks can include off-design mission performance analysis, flight performance calculation for point operating conditions, and generation of subsystem or component performance maps. Figure 1-1 illustrates the tasks. The principal tasks (sizing, mission analysis, flight performance analysis) are shown in the figure as boxes with heavy borders. Heavy arrows show control of subordinate tasks. The aircraft description (figure 1-1) consists of all the information, input and derived, that defines the aircraft. The aircraft consists of a set of components, including fuselage, rotors, wings, tails, and propulsion. This information can be the result of the sizing task; can come entirely from input, for a fixed model; or can come from the sizing task in a previous case or previous job. The aircraft description information is available to all tasks and all solutions (indicated by light arrows). The sizing task determines the dimensions, power, and weight of a rotorcraft that can perform a specified set of design conditions and missions. The aircraft size is characterized by parameters such as design gross weight, weight empty, rotor radius, and engine power available. The relations between dimensions, power, and weight generally require an iterative solution. From the design flight conditions and missions, the task can determine the total engine power or the rotor radius (or both power and radius can be fixed), as well as the design gross weight, maximum takeoff weight, drive system torque limit, and fuel tank capacity. For each propulsion group, the engine power or the rotor radius can be sized. Missions are defined for the sizing task, and for the mission performance analysis. A mission consists of a number of mission segments, for which time, distance, and fuel burn are evaluated. For the sizing task, certain missions are designated to be used for design gross weight calculations; for transmission sizing; and for fuel tank sizing. The mission parameters include mission takeoff gross weight and useful load. For specified takeoff fuel weight with adjustable segments, the mission time or distance is adjusted so the fuel required for the mission (burned plus reserve) equals the takeoff fuel weight. The mission iteration is on fuel weight or energy. Flight conditions are specified for the sizing task, and for the flight performance analysis. For the sizing task, certain flight conditions are designated to be used for design gross weight calculations; for transmission sizing; for maximum takeoff weight calculations; and for antitorque or auxiliary thrust rotor sizing. The flight condition parameters include gross weight and useful load. For flight conditions and mission takeoff, the gross weight can be maximized, such that the power required equals the power available. A flight state is defined for each mission segment and each flight condition. The aircraft performance can be analyzed for the specified state, or a maximum effort performance can be identified. The maximum effort is specified in terms of a quantity such as best endurance or best range, and a variable such as speed, rate of climb, or altitude. The aircraft must be trimmed, by solving for the controls and motion that produce equilibrium in the specified flight state. Different trim solution definitions are required for various flight states. Evaluating the rotor hub forces may require solution of the blade flap equations of motion.

NDARC↗

NDARC - NASA Design and Analysis of Rotorcraft: Input - Vol 3

The NDARC code performs design and analysis tasks. The design task involves sizing the rotorcraft to satisfy specified design conditions and missions. The analysis tasks can include off-design mission performance analysis, flight performance calculation for point operating conditions, and generation of subsystem or component performance maps. Figure 1-1 illustrates the tasks. The principal tasks (sizing, mission analysis, flight performance analysis) are shown in the figure as boxes with heavy borders. Heavy arrows show control of subordinate tasks. The aircraft description (figure 1-1) consists of all the information, input and derived, that defines the aircraft. The aircraft consists of a set of components, including fuselage, rotors, wings, tails, and propulsion. This information can be the result of the sizing task; can come entirely from input, for a fixed model; or can come from the sizing task in a previous case or previous job. The aircraft description information is available to all tasks and all solutions (indicated by light arrows). The sizing task determines the dimensions, power, and weight of a rotorcraft that can perform a specified set of design conditions and missions. The aircraft size is characterized by parameters such as design gross weight, weight empty, rotor radius, and engine power available. The relations between dimensions, power, and weight generally require an iterative solution. From the design flight conditions and missions, the task can determine the total engine power or the rotor radius (or both power and radius can be fixed), as well as the design gross weight, maximum takeoff weight, drive system torque limit, and fuel tank capacity. For each propulsion group, the engine power or the rotor radius can be sized. Missions are defined for the sizing task, and for the mission performance analysis. A mission consists of a number of mission segments, for which time, distance, and fuel burn are evaluated. For the sizing task, certain missions are designated to be used for design gross weight calculations; for transmission sizing; and for fuel tank sizing. The mission parameters include mission takeoff gross weight and useful load. For specified takeoff fuel weight with adjustable segments, the mission time or distance is adjusted so the fuel required for the mission (burned plus reserve) equals the takeoff fuel weight. The mission iteration is on fuel weight or energy. Flight conditions are specified for the sizing task, and for the flight performance analysis. For the sizing task, certain flight conditions are designated to be used for design gross weight calculations; for transmission sizing; for maximum takeoff weight calculations; and for antitorque or auxiliary thrust rotor sizing. The flight condition parameters include gross weight and useful load. For flight conditions and mission takeoff, the gross weight can be maximized, such that the power required equals the power available. A flight state is defined for each mission segment and each flight condition. The aircraft performance can be analyzed for the specified state, or a maximum effort performance can be identified. The maximum effort is specified in terms of a quantity such as best endurance or best range, and a variable such as speed, rate of climb, or altitude. The aircraft must be trimmed, by solving for the controls and motion that produce equilibrium in the specified flight state. Different trim solution definitions are required for various flight states. Evaluating the rotor hub forces may require solution of the blade flap equations of motion.

NDARC↗

NDARC - NASA Design and Analysis of Rotorcraft: Input - Appendix 3

The NDARC code performs design and analysis tasks. The design task involves sizing the rotorcraft to satisfy specified design conditions and missions. The analysis tasks can include off-design mission performance analysis, flight performance calculation for point operating conditions, and generation of subsystem or component performance maps. Figure 1-1 illustrates the tasks. The principal tasks (sizing, mission analysis, flight performance analysis) are shown in the figure as boxes with heavy borders. Heavy arrows show control of subordinate tasks. The aircraft description (figure 1-1) consists of all the information, input and derived, that defines the aircraft. The aircraft consists of a set of components, including fuselage, rotors, wings, tails, and propulsion. This information can be the result of the sizing task; can come entirely from input, for a fixed model; or can come from the sizing task in a previous case or previous job. The aircraft description information is available to all tasks and all solutions (indicated by light arrows). The sizing task determines the dimensions, power, and weight of a rotorcraft that can perform a specified set of design conditions and missions. The aircraft size is characterized by parameters such as design gross weight, weight empty, rotor radius, and engine power available. The relations between dimensions, power, and weight generally require an iterative solution. From the design flight conditions and missions, the task can determine the total engine power or the rotor radius (or both power and radius can be fixed), as well as the design gross weight, maximum takeoff weight, drive system torque limit, and fuel tank capacity. For each propulsion group, the engine power or the rotor radius can be sized. Missions are defined for the sizing task, and for the mission performance analysis. A mission consists of a number of mission segments, for which time, distance, and fuel burn are evaluated. For the sizing task, certain missions are designated to be used for design gross weight calculations; for transmission sizing; and for fuel tank sizing. The mission parameters include mission takeoff gross weight and useful load. For specified takeoff fuel weight with adjustable segments, the mission time or distance is adjusted so the fuel required for the mission (burned plus reserve) equals the takeoff fuel weight. The mission iteration is on fuel weight or energy. Flight conditions are specified for the sizing task, and for the flight performance analysis. For the sizing task, certain flight conditions are designated to be used for design gross weight calculations; for transmission sizing; for maximum takeoff weight calculations; and for antitorque or auxiliary thrust rotor sizing. The flight condition parameters include gross weight and useful load. For flight conditions and mission takeoff, the gross weight can be maximized, such that the power required equals the power available. A flight state is defined for each mission segment and each flight condition. The aircraft performance can be analyzed for the specified state, or a maximum effort performance can be identified. The maximum effort is specified in terms of a quantity such as best endurance or best range, and a variable such as speed, rate of climb, or altitude. The aircraft must be trimmed, by solving for the controls and motion that produce equilibrium in the specified flight state. Different trim solution definitions are required for various flight states. Evaluating the rotor hub forces may require solution of the blade flap equations of motion.

NDARC↗

Analysis of the gas-lubricated flat-sector-pad thrust bearing

A flat sector-shaped pad geometry for a gas-lubricated thrust bearing is analyzed considering both the pitch and roll of the pad. It is shown that maximum load capacity is achieved when the pad is tilted so as to create uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves, and a comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

Etsion, I.↗

Wind tunnel test results of a 1/8-scale fan-in-wing model

A 1/8-scale model of a fan-in-wing concept considered for development by Grumman Aerospace Corporation for the U.S. Army was tested in the Langley 14- by 22-Foot Subsonic Tunnel. Hover testing, which included height above a pressure-instrumented ground plane, angle of pitch, and angle of roll for a range of fan thrust, was conducted in a model preparation area near the tunnel. The air loads and surface pressures on the model were measured for several configurations in the model preparation area and in the tunnel. The major hover configuration change was varying the angles of the vanes attached to the exit of the fans for producing propulsive force. As the model height above the ground was decreased, there was a significant variation of thrust-removed normal force with constant fan speed. The greatest variation was generally for the height-to-fan exit diameter ratio of less than 2.5; the variation was reduced by deflecting fan exit flow outboard with the vanes. In the tunnel angles of pitch and sideslip, height above the tunnel floor, and wind speed were varied for a range of fan thrust and different vane angle configurations. Other configuration features such as flap deflections and tail incidence were evaluated as well. Though the V-tail empennage provided an increase in static longitudinal stability, the total model configuration remained unstable.

Wilson, John C.↗

Separation of Lift-Generated Vortex Wakes Into Two Diverging Parts

As part of an ongoing study of the spreading rate of lift-generated vortex wakes, the present investigation considers possible reasons as to why segments of lift-generated wakes sometimes depart from the main part of the wake to move rapidly in either an upward or downward direction. It is assumed that deficiencies or enhancements of the lift carry over across the fuselage-shrouded wing are the driving mechanism for departures of wake-segments. The computations presented first indicate that upwardly departing wake segments that were observed and photographed could have been produced by a deficiency in lift carryover across the fuselage-shrouded part of the wing. Computations made of idealized vortex wakes indicate that upward departure of a wake segment requires a centerline reduction in the span loading of 70% or more, whether the engines are at idle or robust thrust. Similarly, it was found that downward departure of wake segments is produced when the lift over the center part of the wing is enhanced. However, it was also found that downward departures do not occur without the presence of robust engine-exhaust streams (i.e., engines must NOT be at idle). In those cases, downward departures of a wake segment occurs when the centerline value of the loading is enhanced by any amount between about 10% to 100%. Observations of condensation trails indicate that downward departure of wake segments is rare. Upward departures of wake segments appears to be more common but still rare. A study to determine the part of the aircraft that causes wake departures has not been carried out. However, even though departures of wake segments rarely occur, some aircraft do regularly shed these wake structures. If aircraft safety is to be assured to a high degree of reliability, and a solution for eliminating them is not implemented, existing guidelines for the avoidance of vortex wakes [1,3] may need to be broadened to include possible increases in wake sizes caused by vertical departures of wake segments. Further study may indicate that it is not possible to modify existing aircraft enough to prevent wake departures. Wake-avoidance guidelines must then be adjusted to provide the desired degree of safety. It appears that steps to avoid upwardly moving wake segments have already been incorporated into the avoidance procedures used for aircraft on approach to runways at the Frankfurt Airport [6,7]. The uncertainty in the prospects for compromises in flight safety caused by rapidly upwardly or downwardly moving wake segments suggest that it be specified that aircraft do not fly above or below each other during operations in the airport vicinity where aircraft are likely to be closely spaced [20].

Rossow, Vernon J.↗

Rocket ascent G-limited moment-balanced optimization program (RAGMOP)

This document describes the RAGMOP (Rocket Ascent G-limited Momentbalanced Optimization Program) computer program for parametric ascent trajectory optimization. RAGMOP computes optimum polynomial-form attitude control histories, launch azimuth, engine burn-time, and gross liftoff weight for space shuttle type vehicles using a search-accelerated, gradient projection parameter optimization technique. The trajectory model available in RAGMOP includes a rotating oblate earth model, the option of input wind tables, discrete and/or continuous throttling for the purposes of limiting the thrust acceleration and/or the maximum dynamic pressure, limitation of the structural load indicators (the product of dynamic pressure with angle-of-attack and sideslip angle), and a wide selection of intermediate and terminal equality constraints.

Lyons, J. T.↗

Prediction methods for jet V/STOL propulsion aerodynamics

The current status of prediction methods for propulsive flows and propulsion-induced effects which occur on jet V/STOL aircraft is reviewed. Among the major topics studied are flows in propulsive ducts, propulsion-induced ground and thermal effects, aerodynamic loads induced during V/STOL and transition flight, flow vectoring devices, and thrust augmented ejector and lift-fan studies. The current predictive capability in jet V/STOL propulsion aerodynamics is assessed. Future research needs are identified, with particular reference to activities that can improve the usefulness of prediction methods for jet V/STOL aircraft.

Platzer, M. F.↗

Mechanisms of UK radiometers flown on Nimbus 5 and 6 with particular reference to bearings, pivots and lubrication

The mechanisms incorporated in the vertical sounding infrared radiometry experiments which were launched on Nimbus 5 in 1972 and on Nimbus 6 in 1975 are discussed. Both use dry lubricants. The Nimbus 5 radiometer includes a rotating chopper driven via a carbon fiber-acetal resin gearwheel. The driving motor runs at 2000 rpm and has completed over 7 x 10 to the 9th power revolutions. Four gear driven filter wheels powered by stepper motors have each completed 2 x 10 to the 8th power changes. The input calibration mirror mechanism and its field of view compensation mechanisms are also described. All 25 ball races used in the experiment are of the film transfer type. The Nimbus 6 radiometer includes two cells. Each contains a piston supported on diaphragm springs and driven electromagnetically. The pistons are 6 cm in diameter with a stroke of 1 cm and are driven at their mechanical resonant frequency of approx. 15 Hz. The calibrating mirrors rotate periodically to view a target. The support pivots are synthetic sapphire ring stones with separate end thrust stones. The problems of mounting these stones to withstand vibration loads is described.

Hadley, H.↗

Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary Lagrangian-eulerian Approach

Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.

Melis, Matthew E.↗

SMART Rotor Wind Tunnel Test Report

The Boeing Company, Mesa Arizona, has been developing smart material actuated rotor technology (SMART) under in-house, DARPA (Defense Advanced Research Projects Agency), NASA and Army funding. A whirl tower test of the SMART active flap rotor system was successfully conducted at the remote test facility (RTF) in Mesa, Arizona, in 2003. Under DARPA and NASA funding, the SMART rotor system was tested in the NASA Ames National Full Scale Aerodynamic Complex (NFAC) 40- by 80-Foot Wind Tunnel in 2008. The DARPA program objectives were to demonstrate the active flap impact on rotor acoustics in forward flight and establish a validation database for noise prediction tools. Under NASA funding, additional wind tunnel tests were conducted, with the objective to demonstrate and quantify vibration, noise, and performance improvements.Wind tunnel testing was successfully and safely concluded, meeting all high priority objectives. The authority, effectiveness, and reliability of the flap actuation system were demonstrated in 65 hours of testing at up to 155 knots and 7,700 pound thrust. Validation data was successfully acquired for four test conditions; blade loads were too high for the high speed condition. The effectiveness of the flap for noise and vibration control was demonstrated conclusively, with results showing significant reductions in BVI (Blade-Vortex Interaction) and in-plane noise as well as vibratory hub loads. The impact of the flap on control power and rotor smoothing was also demonstrated. Data evaluating any benefits in aerodynamic performance and impact on flight controls were acquired, but will need more detailed evaluation. Both open loop control and closed loop feedback control, using continuous time and higher harmonic controllers, were applied.The purpose of the Test Report is to provide a comprehensive document that describes the preparation for and conduct of the wind tunnel test and summarizes the processing and evaluation of wind tunnel test data for the DARPA and the NASA portion of the test. An overview of the wind tunnel test and results can be found in Reference 1. Details on the testing and results for BVI noise, in-plane noise, and vibrations can be found in References 2-4, respectively. These references are four papers, presented at the American Helicopter Society Annual Forum in 2009. A brief description of the delivered electronic data is provided in Reference 5.

Rotor↗

Effect of yaw angle on steering forces for the lunar roving vehicle wheel

A series of tests was conducted with a Lunar Roving Vehicle (LRV) wheel operating at yaw angles ranging from -5 to +90 deg. The load was varied from 42 to 82 lb (187 to 365 N), and the speed was varied from 3.5 to 10.0 ft/sec (1.07 to 3.05 m/sec). It was noted that speed had an effect on side thrust and rut depth. Side thrust, rut depth, and skid generally increased as the yaw angle increased. For the range of loads used, the effect of load on performance was not significant.

Green, A. J.↗

Effects of solid-propellant temperature gradients on the internal ballistics of the Space Shuttle

The internal ballistic effects of combined radial and circumferential grain temperature gradients are evaluated theoretically for the Space Shuttle solid rocket motors (SRMs). A simplified approach is devised for representing with closed-form mathematical expressions the temperature distribution resulting from the anticipated thermal history prior to launch. The internal ballistic effects of the gradients are established by use of a mathematical model which permits the propellant burning rate to vary circumferentially. Comparative results are presented for uniform and axisymmetric temperature distributions and the anticipated gradients based on an earlier two-dimensional analysis of the center SRM segment. The thrust imbalance potential of the booster stage is also assessed based on the difference in the thermal loading of the individual SRMs of the motor pair which may be encountered in both summer and winter environments at the launch site. Results indicate that grain temperature gradients could cause the thrust imbalance to be approximately 10% higher in the Space Shuttle than the imbalance caused by SRM manufacturing and propellant physical property variability alone.

Sforzini, R. H.↗

The Chevron Foil Thrust Bearing: Improved Performance Through Passive Thermal Management and Effective Lubricant Mixing

An improved foil thrust bearing is described that eliminates or reduces the need for forced cooling of the bearing foils while at the same time improves the load capacity of the bearing, enhances damping, provides overload tolerance, and eliminates the high speed load capacity drop-off that plagues the current state of the art. The performance improvement demonstrated by the chevron foil thrust bearing stems from a novel trailing edge shape that splays the hot lubricant in the thin film radially, thus preventing hot lubricant carry-over into the ensuing bearing sector. Additionally, the chevron shaped trailing edge induces vortical mixing of the hot lubricant with the gas that is naturally resident within the inter-pad region of a foil thrust bearing. The elimination of hot gas carry-over in combination with the enhanced mixing has enabled a completely passive thermally managed foil bearing design. Laboratory testing at NASA has confirmed the original analysis and reduced this concept to practice.

foil bearing↗

An accurate solution of the gas lubricated, flat sector thrust bearing

A flat sector shaped pad geometry for gas lubricated thrust bearings is analyzed considering both pitch and roll angles of the pad and the true film thickness distribution. Maximum load capacity is achieved when the pad is tilted so as to create a uniform minimum film thickness along the pad trailing edge. Performance characteristics for various geometries and operating conditions of gas thrust bearings are presented in the form of design curves. A comparison is made with the rectangular slider approximation. It is found that this approximation is unsafe for practical design, since it always overestimates load capacity.

Etsion, I.↗