Showing papers in "Journal of Aircraft in 2015"

Overview and Summary of the Third AIAA High Lift Prediction Workshop.

Abstract: The second AIAA CFD High-Lift Prediction Workshop was held in San Diego, California, in June 2013. The goals of the workshop continued in the tradition of the first high-lift workshop: to assess the numerical prediction capability of current-generation computational fluid dynamics (CFD) technology for swept, medium/high-aspect-ratio wings in landing/takeoff (high-lift) configurations. This workshop analyzed the flow over the DLR-F11 model in landing configuration at two different Reynolds numbers. Twenty-six participants submitted a total of 48 data sets of CFD results. A variety of grid systems (both structured and unstructured) were used. Trends due to grid density and Reynolds number were analyzed, and effects of support brackets were also included. This paper analyzes the combined results from all workshop participants. Comparisons with experimental data are made. A statistical summary of the CFD results is also included.

Hybrid-Electric Propulsion for Aircraft

Abstract: Against a background of increasing energy demand and rising fuel prices, hybrid-electric propulsion systems have the potential to significantly reduce fuel consumption in the aviation industry, particularly in the lighter sectors. By taking advantage of both electric motor and internal combustion engine, hybrid-electric propulsion systems provide not only a benefit in fuel saving but also a reduction in takeoff noise and the emission levels. This research considers the design and sizing process of a hybrid-electric propulsion system for a single-seat demonstrator aircraft, the experimental derivation of the internal combustion engine map, and the electric motor parameters. In addition to the experimental data, a novel modeling approach including several linked desktop PC software packages is presented to analyze and optimize hybrid-electric technology for aircraft. Further to the analysis of a parallel hybrid-electric, midscale aircraft, this paper also presents a scaling approach for a 20 kg unmanned aer...

Aerodynamic Shape Optimization of an Adaptive Morphing Trailing-Edge Wing

Abstract: Adaptive morphing trailing-edge wings have the potential to reduce the fuel burn of transport aircraft. However, to take full advantage of this technology and to quantify its benefits, design studies are required. To address this need, the aerodynamic performance benefits of a morphing trailing-edge wing are quantified using aerodynamic design optimization. The aerodynamic model solves the Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with an adjoint method that computes the required derivatives. The baseline geometry is optimized using a multipoint formulation and 192 shape design variables. The average drag coefficient is minimized subject to lift, pitching moment, geometric constraints, and a 2.5g maneuver bending moment constraint. The trailing edge of the wing is optimized based on the multipoint optimized wing. The trailing-edge morphing is parameterized using 90 design variables that are optimized i...

Methodology for Sizing and Performance Assessment of Hybrid Energy Aircraft

Abstract: The Strategic Research and Innovation Agenda and NASA N+3 goals have set new challenges for the aeronautical community via declaration of dramatic efficiency improvements. Because further evolutionary improvements do not appear to be sufficient, envisioning disruptive technologies turn out to be essential to reach the set of future targets. The design of innovative integrated energy–power systems is certainly a major promising element as can be shown by the increasing interest toward hybrid energy and universally electric aircraft. The consideration of these new types of aircraft represents a new challenge for conventional aircraft sizing and performance methods. As an extension of the conventional methods used for fuel-energy aircraft, a sizing and performance methodology for hybrid-energy aircraft is proposed. A design study of a battery and fuel hybrid-energy single-aisle retrofit is conducted to demonstrate the methodology and to analyze the implications of the associated new design variables on the s...

Optimal Topology of Aircraft Rib and Spar Structures Under Aeroelastic Loads

Abstract: Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered, as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings, and can therefore aid in understanding the complex aircraft design process which must eventually consider all these metrics and load cases simultaneously.

Generic Global Aerodynamic Model for Aircraft

Abstract: Multivariate-orthogonal-function modeling was applied to wind-tunnel databases for eight different aircraft to identify a generic global aerodynamic model structure that could be used for any of the aircraft. For each aircraft database and each nondimensional aerodynamic coefficient, global models were identified from multivariate polynomials in the nondimensional states and controls, using an orthogonalization procedure. A predicted-square-error criterion was used to automatically select the model terms. Modeling terms selected in at least half of the analyses, which totaled 45 terms, were retained to form the generic global aerodynamic model structure. Least squares was used to estimate the model parameters and associated uncertainty that best fit the generic global aerodynamic model structure to each database. The result was a single generic aerodynamic model structure that could be used to accurately characterize the global aerodynamics for any of the eight aircraft, simply by changing the values of t...

Fluid/Structure-Interaction Analysis of the Fish-Bone-Active-Camber Morphing Concept

Abstract: A coupled, partitioned fluid/structure-interaction analysis is introduced for calculation of the deformed equilibrium shape, aerodynamic coefficients, and actuation requirements of the fish-bone-active-camber morphing concept. The fish-bone-active-camber concept is a high-authority morphing camber architecture with a broad range of applications, including fixed-wing aircraft, helicopters, wind turbines, and tidal-stream turbines. The low chordwise bending stiffness of the morphing structure, high stiffness of the tendon drive system, and the large changes in aerodynamic loading while morphing necessitate a coupled fluid/structure-interaction analysis for determination of the static equilibrium. An Euler–Bernoulli beam-theory-based analytical model of the structure is introduced and validated. Aerodynamic loads are found using the XFOIL software, which couples a potential-flow panel method with a viscous boundary-layer solver. Finally, the tendons are modeled as linear stiffness elements whose internal str...

Numerical Study of Aerodynamic Performance of a Multirotor Unmanned-Aerial-Vehicle Configuration

Abstract: Numerical investigations into the aerodynamic performance and the mutual aerodynamic interactions between the rotors and a fuselage were conducted for a multirotor unmanned-aerial-vehicle configuration. For this purpose, time-accurate unsteady-flow calculations were performed by using a three-dimensional unstructured-mesh flow solver. The fluid motion was assumed to be governed by the three-dimensional, incompressible, Navier–Stokes equations. To handle the relative motion of the rotor blades, an overset-mesh technique was adopted. Numerical simulations were performed for a quadrotor unmanned aerial vehicle with fuselage in hover and in forward flight. To examine the effect of flow direction in forward flight, both diamond and square formations of the rotors were considered. It was observed that, in the case of hovering flight, the mutual aerodynamic interactions of the rotors induce slightly higher inflow than an isolated single rotor, and produce unsteady fluctuating-thrust variations. When the vehicle ...

Nonlinear Lift on a Triangular Airfoil in Low-Reynolds-Number Compressible Flow

Abstract: Numerical and experimental analyses of the aerodynamic performance of a triangular airfoil in low-Reynolds-number compressible flow are performed. This airfoil is one of the candidates for propeller blades on a possible future Martian air vehicle design. Based on past experimental studies conducted in the Mars Wind Tunnel at Tohoku University, this airfoil is known to exhibit nonlinear lift behavior. In the present study, direct numerical simulations of low-Reynolds-number compressible flow over a spanwise periodic triangular airfoil are conducted to identify the source of nonlinear lift. The numerical results reveal that the source of the nonlinear aerodynamic behavior is the lift enhancement provided by the large leading-edge vortex generated. For compressible low-Reynolds-number flow, the wake structure becomes elongated, causing the nonlinear lift enhancement to appear at higher angles of attack compared to the case of incompressible flow.

Design of a Morphing Wing tip

Abstract: An initial design of a morphing wingtip for a regional jet aircraft is developed and evaluated. The adaptive wingtip concept is based upon a chiral-type internal structure, enabling controlled cant...

Prescribed velocity method for simulation of aerofoil gust responses

Abstract: A new method for modeling the interaction of an aerofoil with a gust using a prescribed velocity approach, called the split velocity method is presented. This approach effectively rearranges the governing equations into a form that allows for more efficient calculation and includes both the effect of the gust on the aerofoil and the effect of the aerofoil on the gust. The convection of gusts, through the domain from the far field, is investigated using the new method for a range of 1-cosine gusts. The results obtained are compared to an existing prescribed velocity approach called the field velocity method, which neglects the effect of the aerofoil on the gust. The two prescribed velocity approaches agree well for longer gusts. For shorter gusts where the gust length is close to the chord of the aerofoil, the new approach produces better results. Details of a linearized version of the split velocity method are also given. The linearized version is shown to agree well with the full method for cases when th...

Effect of Flutter on the Multidisciplinary Design Optimization of Truss-Braced-Wing Aircraft

Abstract: This study highlights the effects of a flutter constraint on the multidisciplinary design optimization (MDO) of a truss-braced-wing transport aircraft for both medium-range and long-range missions. Previous MDO studies for both of these missions were performed without considering the effect of flutter. Hence, the flutter constraint has now been added to the other design constraints in this MDO study. Minimizing the takeoff gross weight and the fuel burn are selected as the objective functions. The results show that, for the medium-range mission, the flutter constraint applied at 1.15 times the dive speed imposes a 1.5% penalty on the takeoff weight and a 5% penalty on the fuel consumption while minimizing these two objective functions. The penalties imposed on the minimum-takeoff-gross-weight and minimum-fuel-burn designs for the long-range mission due to the similar constraint are 3.5 and 7.5%, respectively. Importantly, the resulting truss-braced-wing designs are still superior to equivalent cantilever ...

Optimal Control Based Vertical Trajectory Determination for Continuous Descent Arrival Procedures

Abstract: Continuous descent arrival (CDA) procedures provide time and fuel savings, and reduce the noise impact of aircraft operations near airports. To date, these procedures have been designed to limit the performance envelopes to achieve trajectory commonality. In this paper, the performance bounds of CDA procedure via multiphase optimal vertical trajectory generation problems with respect to two performance indices—flight time and fuel consumption—have been investigated. The optimal CDA vertical profile is first divided into two segments: the cruise segment before the top of descent (TOD) and the descent segment from the TOD. Then, the second segment is further subdivided based on flap setting and speed constraints. Finally, the resulting multiphase optimal control problem is solved using a pseudospectral method. Two different types of aircraft, B737-500 (light) and B767-400 (heavy), are used in a numerical study, and the optimal CDA trajectories of the two types are compared with a typical vertical navigation...

Development and Validation of a Propeller Slipstream Model for Unmanned Aerial Vehicles

Abstract: Recent interest in high-angle-of-attack flight, aerobatic maneuvering, vertical/short takeoff and landing, etc., of small unmanned aerial vehicles necessitates more detailed modeling of the complex aerodynamics associated with these flight regimes. This includes modeling the effect of the propeller slipstream, also called prop wash, which is the main source of airflow that helps maintain lift and control during near-zero forward-speed flight like that encountered during vertical/short takeoff and landing, as well as during high-angle-of-attack flight/aerobatic maneuvering like hovering. Propeller slipstream models based on conventional theories, such as the momentum theory, have been used extensively in the literature to predict the induced air velocity within the slipstream. However, because these conventional theories consider only acceleration of air within the slipstream and not diffusion, their applicability in regions far downstream of the propeller where diffusion is dominant, is questionable. This...

NASA Trapezoidal Wing Computations Including Transition and Advanced Turbulence Modeling

Abstract: Flow about the NASA Trapezoidal Wing is computed with several turbulence models by using grids from the first High Lift Prediction Workshop in an effort to advance understanding of computational fluid dynamics modeling for this type of flowfield. Transition is accounted for in many of the computations. In particular, a recently-developed 4-equation transition model is utilized and works well overall. Accounting for transition tends to increase lift and decrease moment, which improves the agreement with experiment. Upper surface flap separation is reduced, and agreement with experimental surface pressures and velocity profiles is improved. The predicted shape of wakes from upstream elements is strongly influenced by grid resolution in regions above the main and flap elements. Turbulence model enhancements to account for rotation and curvature have the general effect of increasing lift and improving the resolution of the wing tip vortex as it convects downstream. However, none of the models improve the prediction of surface pressures near the wing tip, where more grid resolution is needed.

Time and Energy Management During Descent and Approach: Batch Simulation Study

Abstract: A novel integrated planning and guidance concept has been developed that optimizes aircraft trajectories from top of descent to the runway threshold to achieve a continuous engine-idle descent. The new concept, named time and energy managed operations, aims at reducing noise, gaseous emissions, and fuel burn while maintaining airport landing capacity by means of time management. Time and energy managed operations uses an optimization algorithm to minimize thrust and speed brake use through energy management by exchanging kinetic and potential energy. Sustained deviations during descent are corrected using a strategic or tactical approach. Time and energy managed operations is evaluated in a batch simulation study for various disturbances to test its robustness to disturbances and time constraints. Moreover, two different methods of correcting deviations are compared. Results show that time and energy managed operations allows idle descents while adhering to time constraints and can cope with disturbances ...

Gust Load Alleviation for a Regional Aircraft Through a Static Output Feedback

Abstract: The paper presents the design of a symmetric, active, gust load alleviation system for a regional transport aircraft, based on a static output feedback with a constrained structure. The design is carried out on a comprehensive finite state aeroservoelastic model, including sensor units and actuator transfer functions, and verified by taking into account saturated control positions, rates, and hinge moments. The controller is designed within a quadratic optimal framework, through a second-order Hessian-based optimization algorithm, exploiting block diagonal Schur transformations of the closed-loop state equations and performance weightings. An accurately chosen worst discrete gust and a reference flight condition provide a baseline design, which is significantly effective in alleviating continuous turbulence loads. Such a reference design proves itself robust enough to alleviate atmospheric loads over the complete flight envelope and is eventually further improved and robustified through a simple bilinear ...

Multiphase Optimal Control Framework for Commercial Aircraft Four-Dimensional Flight-Planning Problems

Abstract: The calculation of a flight plan involves the consideration of multiple elements. They can be classified as either continuous or discrete, and they can include nonlinear aircraft performance, atmospheric conditions, wind forecasts, airspace structure, amount of departure fuel, and operational constraints. Moreover, multiple differently characterized flight phases must be considered in flight planning. The flight-planning problem can be regarded as a trajectory optimization problem. A natural way to address a trajectory optimization problem is using optimal control techniques. The multiphase nature of the problem and the nonlinear dynamics of the aircraft lead to the formulation of a multiphase optimal control problem. A Hermite–Simpson collocation method is employed to transcribe the infinite-dimensional optimal control problem into a finite-dimensional optimization one, which is solved using a nonlinear programming solver. An application to the optimal takeoff weight, minimum fuel consumption trajectory ...

Uncertainty Quantification for Airfoil Icing Using Polynomial Chaos Expansions

Abstract: The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncertainty in the shape of the accreted ice may result in a large amount of uncertainty in aerodynamic performance metrics (e.g., the stall angle of attack). The main focus of this work concerns using the techniques of polynomial chaos expansions to quantify icing uncertainty much more quickly than traditional methods (e.g., Monte Carlo). First, we present a brief survey of the literature concerning the physics of wing icing, with the intention of giving a certain amount of intuition for the physical process. Next, we give a brief overview of the background theory of polynomial chaos expansions. Finally, we compare the results of Monte Carlo simulations to polynomial-chaos-expansion-based uncertainty quantification for several different airfoil-icing scenarios. The results are in good agreement and confirm that polynomial chaos expa...

Unsteady High-Angle-of-Attack Aerodynamic Models of a Generic Jet Transport

Abstract: Accurate simulation of flight beyond normal conditions requires models of the aircraft aerodynamics at high angles of attack, for which the flow over the wing and control surfaces may be rapidly changing and massively separated. This study focuses on large-amplitude forced oscillations of a benchmark commercial aircraft configuration. Existing models are modified to describe the unsteady aerodynamic forces on the aircraft up to stall range. Steady-state and periodically forced unsteady Reynolds-averaged Navier–Stokes simulation data are employed to calibrate the model parameters. The results of the reduced-order models are in good overall agreement with those observed in the unsteady Reynolds-averaged Navier–Stokes simulations.

Study of Ditching Characteristics of Transport Aircraft by Global Moving Mesh Method

Abstract: This paper numerically investigates the ditching characteristics of the NACA TN 2929 model. In the simulation method, the Reynolds-averaged Navier–Stokes equation and realizable k-e turbulence model are solved by the finite volume method; the volume-of-fluid method is used to capture the water–air interface; the six-degree-of-freedom model and the global-moving-mesh method are used to deal with the relative motion between the water and the object. Global moving mesh is a new dynamic-mesh method, which is proposed to simulate water-entry problems. In global moving mesh, the whole computational domain and boundaries move together with the object to avoid the high computational expense and low-quality mesh in the traditional mesh-deformation method. This numerical method is applied to simulate the water impact of a two-dimensional cylinder in free fall, and the results show a good agreement with the experimental data. The effect of each aerodynamic part of the NACA TN 2929 model on the ditching behavior is s...

Conceptual Design of Low-Boom Aircraft with Flight Trim Requirement

Abstract: A new low-boom target generation approach is presented which allows the introduction of a trim requirement during the early conceptual design of supersonic aircraft. The formulation provides an approximation of the center of pressure for a presumed aircraft configuration with a reversed equivalent area matching a low-boom equivalent area target. The center of pressure is approximated from a surrogate lift distribution that is based on the lift component of the classical equivalent area. The assumptions of the formulation are verified to be sufficiently accurate for a supersonic aircraft of high fineness ratio through three case studies. The first two quantify and verify the accuracy and the sensitivity of the surrogate center of pressure corresponding to shape deformation of lifting components. The third verification case shows the capability of the approach to achieve a trim state while maintaining the low-boom characteristics of a previously untrimmed configuration. Finally, the new low-boom target generation approach is demonstrated through the early conceptual design of a demonstrator concept that is low-boom feasible, trimmed, and stable in cruise.

Flight Dynamics Investigation of Compound Helicopter Configurations

Abstract: Compounding has often been proposed as a method to increase the maximum speed of the helicopter. There are two common types of compounding known as wing and thrust compounding. Wing compounding offloads the rotor at high speeds, delaying the onset of retreating blade stall, and hence increasing the maximum achievable speed, whereas with thrust compounding, axial thrust provides additional propulsive force. There has been a resurgence of interest in the configuration due to the emergence of new requirements for speeds greater than those of conventional helicopters. The aim of this paper is to investigate the dynamic stability characteristics of compound helicopters and compare the results with a conventional helicopter. The paper discusses the modeling of two compound helicopters, which are named the coaxial compound and hybrid compound helicopters. Their respective trim results are contrasted with a conventional helicopter model. Furthermore, using a numerical differentiation technique, the dynamic stabil...

Bioinspired wing-surface pressure sensing for attitude control of micro air vehicles

Abstract: Fixed-wing micro aerial vehicles experience attitude control difficulties as they operate in highly turbulent environments. Previous research has identified pressure-based control as a potential approach for augmenting the performance of, or replacing, autopilots reliant on inertial sensors. However, implementation requires an in-depth understanding of the correlation that exists between oncoming gusts and wing surface-pressure variations. This paper investigates the variation of correlation along a representative micro aerial vehicle wing chord and wingspan between upstream flow pitch angle variation and wing surface-pressure variation. Atmospheric turbulence was replicated within the controlled environment of a wind tunnel using planar grids that generated a turbulence intensity of 12.6%. Despite the unsteady nature of the pressure field, it was discovered that high correlation is evident in the vicinity of the leading edge. Thus, a few optimally placed sensors can be used for a pressure-based attitude ...

Advances in Aerodynamic Drag Extraction by Far-Field Methods

Abstract: Far-field methods for aerodynamic drag calculation and breakdown around aircraft configurations by Computational Fluid Dynamics are widely adopted. Recent improvements and advances of one of these algorithms are discussed. Because these methods rely for breakdown purposes on the detection of the boundary-layer region around the body, an analysis of possible alternatives to the currently adopted boundary-layer sensor is proposed. Furthermore, a recently published study in the case of inviscid flow on the influence of the accuracy of the numerical solution at far field has been repeated in viscous flow. It shows how a far-field solution influences the computation of near-field drag, in particular, in high-lift conditions. Finally, an application to a complex high-lift three-dimensional configuration of an alternative method for the computation of the lift-induced drag is discussed. The method is based on the integration of the Lamb-vector field.

Transfer of Training on the Vertical Motion Simulator

Abstract: This paper describes a quasi-transfer-of-training study in the NASA Ames Vertical Motion Simulator. Sixty-one general aviation pilots trained on four challenging commercial transport tasks under one of four different motion conditions: no motion, small hexapod, large hexapod, and Vertical Motion Simulator motion. Then, every pilot repeated the tasks in a check with Vertical Motion Simulator motion to determine if training with different motion conditions had an effect on task performance. New objective motion criteria guided the selection of the motion parameters for the small and large hexapod conditions. Considering results that were statistically significant, or marginally significant, the motion condition used in training affected 1) longitudinal and lateral touchdown position, 2) the number of secondary stall warnings in a stall recovery, 3) pilot ratings of motion utility and maximum load factor obtained in an overbanked upset recovery, and 4) pilot ratings of motion utility and pedal input reaction...

Investigation of Broadband Shock Noise from a Jet Near a Planar Surface

Abstract: Many current and future aircraft designs rely on the wing or other aircraft surfaces to shield observers on the ground from the engine noise. However, the available data showing how surfaces interact with a jet to shield and/or enhance the jet noise are currently limited. Therefore, far-field noise data and background-oriented schlieren images were acquired for a round jet, operating in the overexpanded, ideally expanded, and underexpanded supersonic flow regimes, near a planar surface to investigate how airframe surfaces might affect the shock-cell structure in the jet plume and the broadband shock noise produced. These data show that broadband shock noise is produced by the relatively weak shocks far downstream of the nozzle exit; consequently, a surface will be effective at reducing broadband shock noise only if it is long enough to shield the noise produced by shocks. Furthermore, the presence of a surface very near the edge of an underexpanded jet increases the shock-cell spacing, pushing the shock c...

Eulerian Modeling of Supercooled Large Droplet Splashing and Bouncing

Abstract: A conservative Eulerian numerical approach for modeling postimpact Supercooled Large Droplets undergoing splashing and bouncing on aircraft surfaces is presented. The approach introduces the effect of the postimpact droplets by successive solutions of the conservation equations. Two models have been selected to identify the droplet splashing and bouncing conditions, and to provide initial conditions for the reinjected water. The method has been applied to droplet impingement in Supercooled Large Droplet conditions on clean and iced NACA 23012 geometries, as well as the MS(1)-0317 airfoil, and the results have been compared to experimental data. Good agreement is observed for both impingement limits and collection efficiency. Additionally, the method has been applied to a three-element high-lift configuration operating in one of the proposed Appendix O Supercooled Large Droplet environments to demonstrate the danger posed by the re-impingement of splashing and bouncing droplets on complex interacting aerod...

Piloted Evaluation of a Control Allocation Technique to Recover from Pilot-Induced Oscillations

Abstract: This paper describes the maturation of a control allocation technique designed to assist pilots in recovery from pilot-induced oscillations. The control allocation technique to recover from pilot-induced oscillations is designed to enable next-generation high-efficiency aircraft designs. Energy-efficient next-generation aircraft require feedback control strategies that will enable lowering the actuator rate limit requirements for optimal airframe design. A common issue on aircraft with actuator rate limitations is they are susceptible to pilot-induced oscillations caused by the phase lag between the pilot inputs and control surface response. The control allocation technique to recover from pilot-induced oscillations uses real-time optimization for control allocation to eliminate phase lag in the system caused by control surface rate limiting. System impacts of the control allocator were assessed through a piloted simulation evaluation of a nonlinear aircraft model in the NASA Ames Research Center’s Vertic...

Optimization of Aircraft Lifting Surfaces Using a Cellular Division Method

Abstract: The development of a biologically inspired methodology for topology, shape, sizing, and control surface optimization of aircraft lifting surfaces is presented. The methodology is based on the map L-systems modeling of cellular division to generate the substructure topology. This is combined with variables for aerodynamic shape, structural sizing, and control surfaces (number, size, location, and aeroelastic trimmed settings) and constraints on stiffness, strength, local skin panel buckling, static aeroelastic response (roll performance, pitch rate, trimmed angle of attack), and flutter requirements. A dual-objective function is formulated with weight and L/D and is solved with a bilevel optimization algorithm. The map L-system rules that develop the topology are evolved using a genetic algorithm in the outer optimization loop on L/D and weight, which obtains the optimal parameter settings for topology, shape, and control surfaces, whereas the inner loop performs weight minimization with the structural siz...