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NASA NTRS2009

High-Temperature Modal Survey of a Hot-Structure Control Surface

NASA Dryden is directing a program to test a Carbon-Silicon Carbide (C/SiC) Ruddervator Subcomponent Test Article (RSTA). The RSTA is a truncated version of the full-scale X-37 hot-structure control surface incorporating all major features including the metallic spindle and five major C/SiC quasi isotropic lay-up components secured with C/SiC fasteners. As part of NASA's Aeronautics Research Mission Directorate Hypersonics program, the RSTA will undergo thermal-structural testing to develop an extensive database for future structural design and analysis methodology validation. Ground Vibration Tests (GVTs) are routinely conducted for model validation in supporting flutter analysis for subsonic and supersonic vehicles; however, for hypersonic vehicle applications, GVT techniques are not well-established. New fabrication technologies, high-temperature materials systems, and sensors offer new opportunities to develop techniques for performing GVTs at elevated temperatures. The RSTA is comprised of materials whose stiffness both increases and decreases with increasing temperature. The impact of this type of material system interaction must be understood as it will ultimately affect hypersonic flutter analysis. The test objectives are to perform room-temperature GVTs, develop the capability to conduct high-temperature GVTs and to compare and generate an understanding of the modal characteristics which capture RSTA's material interaction when subjected to temperature varying conditions.

Spivey, Natalie D.↗

NASA NTRS1987

Flap-lag-torsion aeroelastic stability of a circulation control rotor in forward flight

The aeroelastic stability of a circulation control rotor blade undergoing three degrees of motion (flap, lag, and torsion) is investigated in forward flight. Quasi-steady strip theory is used to evaluate the aerodynamics forces; and the airfoil characteristics are from data tables. The propulsive and the auxiliary power trims are calculated from vehicle and rotor equilibrium equations through the numerical integration of element forces in azimuth as well as in radial directions. The nonlinear time dependent periodic blade response is calculated using an iterative procedure based on Floquet theory. The periodic perturbation equations are solved for stability using Floquet transition matrix theory. The effects of several parameters on blade stability are examined, including advance ratio, collective pitch, thrust level, shaft tilt, structural stiffnesses variation, and propulsive and auxiliary power trims.

Chopra, Inderjit↗

NASA NTRS1998

Mechanics of Granular Materials (MGM) Microgravity Experiment

The second series of MGM experiment was conducted during the STS-89 mission in January 1998. The experiment was previously flow on Atlantis's STS-79 mission in September 1996. Six displacement-controlled, drained triaxial compression experiments were performed at very low effective confining stresses. The confining stresses were in the ranges 0.05, 0.52 and 1.30 kPa. Three experiments were subjected to monotonic loading and unloading cycles while the other three experiments were subjected to cyclic loading. The results show very high peak strength friction angles in the range of 47.6 to 70.0 degrees, which are mainly due to overconsolidation and grain interlocking effects. It was observed that the residual strength levels in the monotonic loading experiments were in the same range as that observed at higher confining stress levels. The dilatancy angles were unusually high in the range of 30 to 31 degrees. All specimens display substantial initial stiffnesses and elastic moduli during unloading and reloading events, which are nearly an order of magnitude higher than conventional theories predict. A periodic instability phenomenon which appears to result from buckling of multiple internal arches and columnar systems, augmented by stick-slips was observed in the experiments. Computed Tomography (CT) measurements revealed valuable data about the internal fabric and the specimens deformation patterns. Uniform diffuse bifurcation with multiple radial shear bands was observed in the specimens tested in a microgravity environment. In the axial direction, two major conical surfaces were developed. Spatial nonsymmetrical deformations were observed in specimens tested in terrestrial laboratory.

Alshibli, Khalid A.↗

NASA NTRS2026

Mechanical Design and Operation of a Novel Lunar Environment Structural Test Rig (LESTR)

The Lunar Environment Structural Test Rig (LESTR) was developed to address a critical gap in mechanical property data for metal alloy wire materials under lunar-relevant conditions down to 40 K. Conventional aerospace material databases provide thermophysical properties for bulk metals over a wide temperature range, but validated mechanical and physical property data below 77 K, particularly for small-diameter wires, remain limited and are generally the exception rather than the rule. These conditions are essential for Artemis mission hardware such as shape memory alloy (SMA) rover tires. LESTR’s design requirements were to combine a high-stiffness electrodynamic load frame with closed- cycle cryogenic cooling, high-vacuum capability (10–6 torr), and noncontact optical strain measurement to enable tensile, four-point bend, and fatigue testing of wires or other materials and geometries at temperatures from 40 to 125 K. These considerable requirements were merged with the need to lower the barrier of testing for the end user as measured in terms of cost-per-test cycle, safety improvement, and reduction in upkeep costs associated with state-of-the-art solutions associated with cryomechanical material characterization. The system incorporates modular gripping and alignment fixtures; precision thermal management using cryocoolers and embedded heaters; and integrated instrumentation for displacement, load, temperature, and vacuum control. Calibration procedures establish correlations between tooling and specimen temperature, ensuring accurate thermal conditions across the design envelope unbound by cryofluid conditions in heritage immersion-based test systems. Initial validation tests using Inconel (Special Metals Corp.) wire demonstrated accurate ultimate strength and post-yield behavior. The load frame operation was also verified under representative service conditions, including thermal cycling and prolonged fatigue loading. By generating mechanical property data at ultralow temperatures, LESTR fills a critical gap in existing materials databases and provides a scalable platform for iterative alloy development and durability assessment for planetary hardware. This capability supports NASA’s long-term objectives for surface exploration by enabling design confidence for components operating in extreme cryogenic environments.

LESTR↗

NASA NTRS2001

Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows

Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.

Sjoegreen, B.↗

NASA NTRS2018

Implementation of a Matrix Crack Spacing Parameter in a Continuum Damage Mechanics Finite Element Model

Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed.

Hyder, Imran↗

NASA NTRS1986

Large-scale Advanced Prop-fan (LAP) hub/blade retention design report

The Large-scale Advanced Prop-fan (LAP) hub assembly forms a semi-rigid link between the blades, which provide the thrust, and the engine shaft, which provides the torque. The hub and tailshaft is a one piece partially forged part which is carburized, heat treated and machined. A single row ball bearing restrains each of the eight blades in the hub, while the tailshaft secures the propeller to the engine shaft with two cone seats that are preloaded against each other by the Prop-fan retaining nut. The hub also forms the support for the pitch change actuator system, the control and the spinner. The retention transmits the loads from the blades to the hub while allowing the changes in blade pitch. The single row ball bearing retention provides ease of maintenance by allowing individual blade replacement without dissassembly of the hub. It has a through hardened inner race which seats against the aluminum blade shank and an outer race which is integral with the barrel. The outer race area is carburized to achieve the hardness necessary to support the ball loads. The balls are kept from contact with each other by a separator. The rotational speed of the propeller keeps the retention submerged in the oil which is contained in the hub by a seal. Stress and strain analysis, material hardness requirements, weight predictions, and stiffness characteristics are discussed.

Soule, Matthew↗

NASA NTRS1995

Expendable launch vehicle studies

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Bainum, Peter M.↗

NASA NTRS1999

Constitutive and Stability Behavior of Granular Materials Under Very Low Effective Stresses

The study of the behavior of granular materials such as sand is of great importance to the understanding of the response of foundations resting on surface and near-surface soil deposits. A clear understanding of the behavior of such materials can also provide insights into other related issues where low effective stresses are encountered such as liquefaction. The main sources of the constitutive and stability properties of cohesionless granular materials is interparticle friction, which in turn under low confinement stress levels is strongly affected by gravitational body forces under terrestrial (1 gravity) conditions. Under moderate-to-high stress levels, the influence of gravity on the behavior of experiments may not be pronounced and therefore the test results in a terrestrial environment may be acceptable for engineering purposes. However, the conduct of experiments on granular materials under very low stress levels and under quasi-static conditions can only be performed in a microgravity environment. A series of displacement-controlled cyclic triaxial compression experiments were performed in a SPACEHAB module on the Space Shuttle during the STS-79 mission to Mir in September, 1996, and the STS-89 mission in January, 1998. The experiments were conducted on six right cylindrical specimens 75 mm in diameter and 150 mm long at effective confining pressures of 0.05, 0.52 and 1.30 kPa. The results show very high peak strength friction angles in the range of 47.6 to 70.0 degrees, which are mainly due to overconsolidation and grain interlocking effects. It was observed that the residual strength levels were in the same range as that observed at higher confining stress levels. The dilatancy angles were unusually high in the range of 30 to 31 degrees. All specimens display substantial initial stiffnesses and elastic moduli during unloading and reloading events, which are nearly an order of magnitude higher than conventional theories predict. A periodic instability phenomenon which appears to result from buckling of multiple internal arches and columnar systems, augmented by stick-slips was observed in the experiments. Computed Tomography (CT) measurements revealed valuable data about the internal fabric and the specimens deformation patterns. Uniform diffuse bifurcation with multiple radial shear bands was observed in the specimens tested in a microgravity environment. In the axial direction, two major conical surfaces were developed. Spatial nonsymmetrical deformations were observed in specimens tested in terrestrial laboratory.

Alshibli, Khalid A.↗

NASA NTRS2000

Rudder/Fin Seal Investigations for the X-38 Re-Entry Vehicle

NASA is currently developing the X-38 vehicle that will be used to demonstrate the technologies required for a crew return vehicle (CRV) for the International Space Station. The X-38 control surfaces require high temperature seals to limit hot gas ingestion and transfer of heat to underlying low-temperature structures to prevent over-temperature of these structures and possible loss of the vehicle. This paper presents results for thermal analyses and flow and compression tests conducted on as-received and thermally exposed seals for the rudder/fin location of the X-38. A thermal analysis of the rudder/fin dual seal assembly based on representative heating rates on the windward surface of the rudder/fin area predicted a peak seal temperature of 1900 F. The temperature-exposed seals were heated in a compressed state at 1900 F corresponding to the predicted peak temperature. Room temperature compression tests were performed to determine load versus linear compression, preload, contact area, stiffness, and resiliency characteristics for the as-received and temperature-exposed seals. Temperature exposure resulted in permanent set and loss of resiliency in these seals. Unit loads and contact pressures for the seals were below the 5 lb/in. and 10 psi limits set to limit the loads on the Shuttle thermal tiles that the seals seal against in the rudder/fin location. Measured seal flow rates for a double seal were about 4.5 times higher than the preliminary seal flow goal. The seal designs examined in this study are expected to be able to endure the high temperatures that they will be exposed to for a single-use life. Tests performed herein combined with future analyses, arc jet tests, and scrubbing tests will be used to select the final seal design for this application.

Dunlap, Patrick H., Jr.↗

NASA NTRS2000

Rudder/Fin Seal Investigations for the X-38 Re-Entry Vehicle

NASA is currently developing the X-38 vehicle that will be used to demonstrate the technologies required for a crew return vehicle (CRV) for the International Space Station. The X-38 control surfaces require high temperature seals to limit hot gas ingestion and transfer of heat to underlying low-temperature structures to prevent over-temperature of these structures and possible loss of the vehicle. This paper presents results for thermal analyses and flow and compression tests conducted on as-received and thermally exposed seals for the rudder/fin location of the X-38. A thermal analysis of the rudder/fin dual seal assembly based on representative heating rates on the windward surface of the rudder/fin area predicted a peak seal temperature of 1900 F. The temperature-exposed seals were heated in a compressed state at 1900 F corresponding to the predicted peak temperature. Room temperature compression tests were performed to determine load versus linear compression, preload, contact area, stiffness, and resiliency characteristics for the as-received and temperature-exposed seals. Temperature exposure resulted in permanent set and loss of resiliency in these seals. Unit loads and contact pressures for the seals were below the five pounds/inch and ten psi limits set to limit the loads on the Shuttle thermal tiles that the seals seal against in the rudder/fin location. Measured seal flow rates for a double seal were about 4.5 times higher than the preliminary seal flow goal. The seal designs examined in this study are expected to be able to endure the high temperatures that they will be exposed to for a single-use life. Tests performed herein combined with future analyses, arc jet tests, and scrubbing tests will be used to select the final seal design for this application.

Dunlap, Patrick H., Jr.↗

NASA NTRS1996

Optimization of Residual Stresses in MMC's through Process Parameter Control and the use of Heterogeneous Compensating/Compliant Interfacial Layers. OPTCOMP2 User's Guide

A user's guide for the computer program OPTCOMP2 is presented in this report. This program provides a capability to optimize the fabrication or service-induced residual stresses in unidirectional metal matrix composites subjected to combined thermomechanical axisymmetric loading by altering the processing history, as well as through the microstructural design of interfacial fiber coatings. The user specifies the initial architecture of the composite and the load history, with the constituent materials being elastic, plastic, viscoplastic, or as defined by the 'user-defined' constitutive model, in addition to the objective function and constraints, through a user-friendly data input interface. The optimization procedure is based on an efficient solution methodology for the inelastic response of a fiber/interface layer(s)/matrix concentric cylinder model where the interface layers can be either homogeneous or heterogeneous. The response of heterogeneous layers is modeled using Aboudi's three-dimensional method of cells micromechanics model. The commercial optimization package DOT is used for the nonlinear optimization problem. The solution methodology for the arbitrarily layered cylinder is based on the local-global stiffness matrix formulation and Mendelson's iterative technique of successive elastic solutions developed for elastoplastic boundary-value problems. The optimization algorithm employed in DOT is based on the method of feasible directions.

Pindera, Marek-Jerzy↗

NASA NTRS1984

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Pratt, D. T.↗

NASA NTRS1995

Characterization of Two-Dimensionally Braided Composites Subject to Static and Fatigue Loading

This paper presents a characterization of damage processes in four different two-dimensionally braided architectures consisting of graphite fibers in an epoxy matrix, subjected to both static and fatigue loading. Both notched and unnotched specimens were tested from each architecture. Damage mechanisms in static compression testing were found to range from matrix cracking in an architecture controlled by shearing characteristics of the matrix to axial fiber bundle kinking and splitting in architectures controlled by unidirectional fiber bundles. In both static tension and tension-tension fatigue testing, it was found that all architectures sustained the same basic damage types and progression sequences. The first types of damage to occur were splits in the braider bundles and cracks in the resin rich areas. Once a sufficient density of this type of damage had occurred, the axial bundles began to disbond from the surrounding constituents, and continued to do so until ultimate failure. One architecture sustained an additional mode of failure, which involved splitting of the axial bundles along their length. Varied degrees of notch sensitivity were found among the different architectures. In one architecture, this was attributed to differences found in the stacking of the individual plys of the braided architecture. As the density of axial bundles adjacent to the notch increased, the rate of stiffness loss increased and the life decreased.

Burr, Scott T.↗

NASA NTRSDate not supplied

Aeroelastic Analysis of an Urban Air Mobility Rotor in Forward Edgewise Flight

Urban Air Mobility vehicle concepts represent a new type of vertical lift machine. From the use of multirotor configurations to the use of variable RPM for thrust control of rigid, propeller-style rotors, many of the UAM concepts observed in industry have departed significantly from traditional VTOL designs. While such novel vehicle types may provide beneficial mission capability and efficiency, they have not been as thoroughly studied as more traditional configurations, and new aeromechanics analysis must be conducted. Operating states such as low-tip-speed rotors in edgewise flight may prove to yield unusual aeroelastic behavior and must be investigated. In the present work, a rotorcraft comprehensive analysis is used to analyze the aeroelastic characteristics of a fixed-pitch, variable RPM rotor in edgewise flight. The rotor model, a three-bladed, fixed pitch propeller, was developed in a previous work. Floquet theory analysis is used to capture the periodic nature of the dynamics. Parameters such as rotor rotational speed, forward flight speed, and blade torsion stiffness are varied and their impact on performance and stability are assessed. A value of torsion stiffness is identified to yield stable flight from 0-100 kts with a wide range of RPM values. The results may be used to provide insight into the aeroelastic characteristics of certain UAM-type rotors.

Aeroelastic Analysis↗

NASA NTRS2004

Modeling and Evaluation of Canted Coil Springs as High Temperature Seal Preloading Devices

Future reusable launch vehicles will require advanced structural seals. This includes propulsion seals along edges and hinge lines in hypersonic engines, and control surface seals for movable flaps and elevons on proposed reentry vehicles. Seals must remain in sealing engagement with opposing surfaces, for multiple missions, even though the seal gap may be opening and closing due to thermal and structural loads. To meet this requirement either the seals themselves must be resilient or there must be a resilient structural element behind the seals. Case Western Reserve University is working with NASA s Glenn Research Center to develop more resilient high temperature seal components and preloading devices. Results are presented for a finite element analysis of a canted coil spring that is being considered as a high temperature seal preloading device. This type of spring is a leading candidate due to its ability to provide nearly constant force over a large deflection. The finite element analyses were verified by comparing them to experimental results of canted coil springs of three different stiffnesses, measured at Glenn Research Center. Once validated the parameterized model was combined with a scripting algorithm to assess the effects of key spring design variables (wire diameter, coils per inch, cant amplitude, eccentricity, and spring width) on spring stiffness and maximum Von Mises stress to aid in subsequent design.

Oswald, Jay J.↗

NASA NTRS1961

Aerodynamic Effects of Some Configuration Variables on the Aeroelastic Characteristics of Lifting Surfaces at Mach Numbers from 0.7 to 6.86

Results of flutter tests on some simple all-movable-control-type models are given. One set of models, which had a square planform with double-wedge airfoils with four different values of leading- and trailing-edge radii from 0 to 6 percent chord and airfoil thicknesses of 9, 11, 14, and 20 percent chord, was tested at Mach numbers from 0.7 to 6.86. The bending-to-torsion frequency ratio was about 0.33. The other set of models, which had a tapered planform with single-wedge and double-wedge airfoils with thicknesses of 3, 6, 9, and 12 percent chord, was tested at Mach numbers from 0.7 to 3.98 and a frequency ratio of about 0.42. The tests indicate that, in general, increasing thickness has a destabilizing effect at the higher Mach numbers but is stabilizing at subsonic and transonic Mach numbers. Double-wedge airfoils are more prone to flutter than single-wedge airfoils at comparable stiffness levels. Increasing airfoil bluntness has a stabilizing effect on the flutter boundary at supersonic speeds but has a negligible effect at subsonic speeds. However, increasing bluntness may also lead to divergence at supersonic speeds. Results of calculations using second-order piston-theory aerodynamics in conjunction with a coupled-mode analysis and an uncoupled-mode analysis are compared with the experimental results for the sharp-edge airfoils at supersonic speeds. The uncoupled-mode analysis more accurately predicted the flutter characteristics of the tapered-planform models, whereas the coupled-mode analysis was somewhat better for the square-planform models. For both the uncoupled- and coupled-mode analyses, agreement with the experimental results improved with increasing Mach number. In general, both methods of analysis gave unconservative results with respect to the experimental flutter boundaries.

Hanson, Perry W.↗

NASA NTRS2000

Model Refinement Using Eigensystem Assignment

IA novel approach for the refinement of finite-element-based analytical models of flexible structures is presented. The proposed approach models the possible refinements in the mass, damping, and stiffness matrices of the finite element model in the form of a constant gain feedback with acceleration, velocity, and displacement measurements, respectively. Once the free elements of the structural matrices have been defined, the problem of model refinement reduces to obtaining position, velocity, and acceleration gain matrices with appropriate sparsity that reassign a desired subset of the eigenvalues of the model, along with partial mode shapes, from their baseline values to those obtained from system identification test data. A sequential procedure is used to assign one conjugate pair of eigenvalues at each step using symmetric output feedback gain matrices, and the eigenvectors are partially assigned, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The procedure can also impose that gain matrices be dissipative to guarantee the stability of the refined model. A numerical example, involving finite element model refinement for a structural testbed at NASA Langley Research Center (Controls-Structures-Interaction Evolutionary model) is presented to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗