A general unified solution of the plane Couette–Poiseuille–Stokes–Womersley incompressible linear fluid flow in a slit in the presence of oscillatory pressure gradients with periodic synchronous vibrating boundaries is presented. Oscillatory flow remains stable and laminar with no-slip boundary conditions applied. Eigenfunction expansion method is used to obtain the exact analytical solution of the general linear inhomogeneous boundary value problem. Fourier expansion of arbitrary harmonic pressure gradient and non-harmonic wall oscillations was used to calculate arbitrary driving of the fluid. In-house developed optimized computational fluid dynamics marching-in-time finite-volume method was used to test and verify all analytical results. A number of particular transients, steady-state and combined flows were obtained from the general analytical result. Generalized Stokes and Womersley flows were solved using the analytical computations and numerical experiments. The combined effects of periodic non-harmonic wall movements with oscillatory pressure gradients offers rich and interesting flow patterns even for a linear Newtonian fluid and may be particularly interesting for pumping-assist microfluidic devices. The main motivation for developing a unified solution of the unsteady laminar planar Couette–Stokes–Poiseuille–Womersley flow originates in a need for, but is not limited to, in-depth exploration of flow patterns in hemodynamic and microfluidic pumping applications.

A mathematical model of free balloon launches in windy conditions is based on the conservation of the linear momentum in horizontal and vertical axes. Linear momentum conservation equations are represented by a set of four nonlinear first-order ODEs. Some ODEs were solved analytically, while the nonlinear Riccati ODE with variable coefficients for the vertical acceleration was solved using numerical ODE solvers. Transient aerodynamic lift and horizontal drag are caused by the slip flow over the balloon envelope. It takes free balloon ten half times to reach 90.9% of the wind velocity in a step function response. A launch condition was developed in terms of the minimum required envelope temperature for which the net aerostatic lift overcomes inert weight of a balloon. Perturbation analysis was used to explore changes in the net aerostatic lift. Simulations were performed to cases with and without envelope distortion and enhanced cooling due to forced convection. Since all balloon takeoffs are performed downwind, obstacle clearance becomes an issue due to rapid loss of aerodynamic lift. Balloons may stop climbing and even start descending shortly after liftoff despite intense heating representing real hazard.

One of the most difficult steps in estimating the cruise performance characteristics of high-subsonic transport-category turbofan-powered airplanes is the estimation of the transonic wave drag. Modern jet airplanes cruise most efficiently in the vicinity of the drag-divergence or drag-rise Mach numbers. In the initial design phase and later when the preliminary wind-tunnel and/or CFD computations and drag polars are known with increased accuracy, a method of estimating cruise performance is needed. In this study, a new semi-empirical transonic wave drag model using modified Lock’s equation was developed. For maximum range cruise estimations, an optimization criterion based on maximizing specific air range was used. The resulting nonlinear equations are of 12th- and 13th-order. Numerical Newton–Raphson nonlinear solvers were used to find real positive roots of such polynomials. The NR method was first tested for accuracy and convergence using known analytical solutions. A methodology for an initial guess was developed starting with the maximum-range cruise Mach without the wave-drag included. This guess resulted in fast quadratic convergence in all computations. Other novel features of this article include a new semi-empirical fuel-flow law, which was also extensively tested. Additionally, a semi-empirical turbofan thrust model usable for a wide range of bypass ratios and the entire flight envelope was developed. Such physics-based semi-empirical model can be used for a wide range of turbofans. The algorithm can be utilized to identify most beneficial input parameter values and combinations for the cruise flight phase. The model represents a powerful tool to estimate important cruise performance airspeeds located in the transonic regime. An intended application is in the conceptual development stages for early design optimizations of future airplanes. It is possible with additional effort to extend existing model capabilities to deal with supersonic transports optimal cruise parameters.

Vertical flight performance of Lighter-than-Air free hot-air balloons is derived and discussed. Novel mathematical model using lumped-parameters has been used to model balloon flight dynamics and steady-state performance in particular. Thermal model was not treated as the super-heat is under the control of aeronauts/pilots. Buoyancy or gross lift, net or effective lift, specific lift, and excess specific lift were derived for a general single envelope balloon and can be applied to hot-air, gas and hybrid balloons. Rate-of-climb, absolute ceiling, rate-of-descent, and the maximum rate-of-descent or the uncontrolled terminal descent have all been modeled and sample computations performed for AX8 or AX9 FAI-class hot-air balloons. Lifting index or the specific net/effective lift have been computed treating ambient and hot air as ideal gases at various pressure altitudes and representative envelope temperatures. Drag coefficient in upward and downward vertical flights have been chosen based on best available data. Experimental scale and full-scale flight tests are suggested for more accurate estimates of external aerodynamics in vertical balloon flights. CFD computations of coupled inner- and external-flows are also recommended in future efforts. Knowledge of free balloon’s vertical performance is essential in flight planning and operational safety of flight.

The basic thermodynamic theories of terrestrial dry and moist air are summarized. Atmospheric water vapor-liquid, vapor-ice and liquid-ice phase transitions using Clapeyron and Clausius-Clapeyron equations are presented in a coherent and clear way. Basic theory and several practical expressions to compute dew points and/or relative humidity are presented. Density altitude corrected for humidity can be easily computed from presented moist air thermodynamic relationships. Understanding thermodynamics and dynamics of atmospheric moist air and phase transitions is of fundamental importance for safety and economy of flight operations. Moist air plays significant role not only in atmospheric and cloud physics, but also for aircraft performance computations, human life support and environmental control systems.

Knowledge of and the ability to predict lifting condensation levels (LCL) is important ingredient in weather predictions, cloud formation, planetary albedo and Earth's energy balance. It is also essential topic in aviation safety and flight operations. In this article, we derive a new model of LCL and compare it to some older commonly-used models. This includes also the recently published Romps' (2017) model. The new model presented here includes dependence, however weak, of the surface atmospheric pressure and the specific humidity on the LCL height and temperature. Such is not the case with widely used models and expressions by Espy and FAA among others, which neglect the effect of atmospheric pressure and specific humidity. We also present an iterative successive-approximations numerical method on computations of the LCL temperature and compare it with closed-form Bolton's model. All these LCL models assume constant atmospheric lapse rate, which is the result of isentropic lifting including adiabatic cooling of moist air. Air pressure at LCL height is computed using Poisson's equation. Our model predictions come close to the exact solution of LCL parameters in terms of Lambert's special functions by Romps', but more efforts are required to understand all the differences.

We have derived and summarized and most important atmospheric temperature lapse rates. ALRs essentially govern vertical atmospheric air stability and creation of some cloud types. The sensitivity analysis of various atmospheric lapse rates and their dependence on actual ideal-gas air properties and gravitational attraction was conducted for the first time to the best of our knowledge. SALR, which has DALR as the upper asymptote, showed steepest decrease at around 9 degrees Celsius then flattening out and apparently approaching another asymptotic solution which has not been investigated as it falls outside of the terrestrial temperature range. ISA lapse rates are adopted atmospheric standards and hence do not depend on actual conditions. We have also analyzed the dependence of DPLR on air temperatures and moisture content. Understanding thermodynamics and dynamics of atmospheric moist air and phase transitions is of fundamental importance for safety and economy of flight operations and aircraft performance.

A proposed novel DC-Link VSCF AC-DC-AC electrical power system converter for Embraer 190/195 transport category airplane is presented. The proposed converter could replace the existing conventional system based on the CSCF IDGs. Several contemporary production airplanes already have VSCF as a major or backup source of electrical power. Problems existed with the older VSCF systems in the past; however, the switched power electronics and digital controllers have matured and can be now, in our opinion, safely integrated and replace existing constant-speed hydraulic transmissions powering CSCF AC generators. IGBT power transistors for medium-level power conversion and relatively fast efficient switching are used. Electric power generation, conversion, distribution, protection, and load management utilizing VSCF offers flexibility, redundancy, and reliability not available with a conventional CSCF IDG systems. The proposed DC-Link VSCF system for E190/195 delivers several levels of 3-ϕ AC and DC power, namely 330/270/28 VDC and 200/ 115/26 VAC utilizing 12-pulse rectifiers, Buck converters, and 3-ϕ 12-step inverters with D-Y, Y-Y, and Y-D 3-ϕ transformers. Conventional bipolar double-edge carrier-based pulse-width-modulation using three reference AC phase signals and up to 100 kHz triangular carriers are used in a manner to remove all even and many odd super-harmonics. Passive low-pass filters are used to remove higher harmonics. The RL AC loads are active in connection with the synchronous and induction AC motors and also include passive AC loads. The overall power factor exceeded 85%. Total harmonic distortions for voltages and currents are below 5%, thus satisfying the MIL-STD-704F and the IEEE Std. 519 power-quality standards, while avoiding the need for active filters. Several PI and PID controllers that regulate synchronous generator DC excitation and inverter banks were designed and tuned using the continuous–cycle tuning method to offer required performance and stability of the feedback loop. Mathworks’s SimulinkTM software was used for simulation of electrical components and circuits. Several critical scenarios of aircraft operations were simulated, such as go-around, to evaluate the transient behavior of the VSCF system.

Global range air navigation implies non-stop flight between any two airports on Earth. Such effort would require airplanes with the operational air range of at least 12,500 NM which is about 40-60% longer than anything existing in commercial air transport today. Air transportation economy requires flying shortest distance, which in the case of spherical Earth are Orthodrome arcs. Rhumb-line navigation has little practical use in long-range flights, but has been presented for historical reasons and for comparison. Database of about 50 major international airports from every corner of the world has been designed and used in testing and route validation. Great Circle routes between many major international airports have been generated and waypoints designed for both GC and rhumb-line routes. Some global-range flights including to polar crossings and/or long flights over open water with not many alternate landing sites available may be ETOPS limited. Additionally, we summarized short-lines navigation theory with particular emphasis on Polar Regions and very short distances elsewhere on the Earth. Working equations and algorithms have been coded into several high-level programming languages, such as, Fortran 90/95/2003/2008, Matlab, and True Basic. Considerable testing of programs have been conducted and compared with the publicly-available geodesic computations over the surface of the terrestrial reference ellipsoid. Distance computations usually were no more than 0.3% in error, while the angles and courses discrepancies were mostly within few angular minutes. Further development will include computations of gliding distances from any altitude under arbitrary winds depending on the type of aircraft and the calculations of PET and PNR for every segment of the route and arbitrary wind conditions.

A valveless shear-driven micro-fluidic pump design (SDMFP) for hemodynamic applications is presented in this work. One of the possible medical and biomedical applications is in-vivo hemodynamic (human blood circulation) support/assist. One or more SDMFPs can be inserted/implanted into vascular lumens in a form of a stent/duct in series and/or in parallel (bypass duct) to support blood circulation in-vivo. A comprehensive review of various micro-pump designs up to about mid 2000’s is given in [1,2]. Many of micropump designs considered are not suitable for in-vivo or even in-vitro medical/biomedical applications. Operating principles, design, and SDMFP features are given in [3]. A particular design used in cardiovascular applications has no moving valves. SDMFP with Gourney-flap type valves to support high-pressure applications are developed for other applications. SDMFP could be fully bi-directional and can control its operation on the run using embedded microcontrollers and sensors. Estimated efficiency is high with low leakage resulting in low power consumption. Proprietary “fish-scale” surface coating ShearQ™ designs are implemented to improve unidirectional flow pumping efficiency. Bi-directional feature may be especially critical when clogging of blood vessels is detected. By automatically and temporarily switching into the reverse-mode operation and retrogressive flow, while inducing suction-head for a short time periods it is hoped that possibly blood conduits can be cleared/unclogged and the normal forward-flow operation resumed. Such may be an important feature if SDMFP is used in-vivo, such as, in coronary arteries which are prone to clogging leading to cardiac-arrest.

Transport-category or FAR/CS 25 certified airplanes may occasionally become braking energy capacity limited. Such limitation may exist when heavy airplanes are departing airports at high-density altitudes, on relatively long runways, and/or possibly with some tailwind component. A maximum braking energy VMBE speed exists which may limit the maximum allowable takeoff decision/action speed V1. The ever-existing possibility of high-speed rejected takeoff in such conditions may also limit the airplane gross weight for declared available distances. To gain deeper insights and acquire better understanding of the topic, a theoretical model of the maximum braking energy and the related VMBE speed for T-category airplanes was developed. The total kinetic energy of an airplane includes translational and rotary kinetic energy and the potential height-energy component for sloped runways. Time-dependent airplanes' mechanical power expression has been derived. Weight transfer during dynamic braking has been implemented in the full nonlinear model. Added mass due to rotary inertia of spinning components has been incorporated and assumed constant. The brakes thermal model is based on a lumped-parameter analysis of ventilated brake rotors and stators; the thermal model is based on a small Biot-number approximation and sufficiently well describes the physics of friction braking. The nonlinear differential equations of motion and the differential thermal model are coupled. A nonlinear model incorporating a set of ordinary differential equations with tire slip can be solved numerically. This model enables determination of the entire history of translational and angular accelerations and speeds, longitudinal distance, forces, torque, and disc temperature during braking. A simpler model assuming constant physical and thermodynamic parameters is solved analytically for constant negative acceleration. This linear analytical model has been used as a workhorse method in our calculations. A new semi-empirical expression of temperature-dependent friction coefficient on brake rotor-stator pairs has been proposed. A theoretical model of maximum braking energy speed VMBE, which includes density-altitude, runway slope, and wind effects as parameters, has been developed for the first time to the best of our knowledge. A comparison of the theoretical VMBE model showed good agreement with measured and approved data for the B737-400 airplane at different density altitudes with and without, individual and combined, runway slope and tailwind effects. Results for new and fully worn brakes were obtained showing the effect of elevated temperatures on brake fade and consequently braking time and distance.

For the past ten years' efforts have been made to introduce environmentally-friendly "green" electric-taxi and maneuvering airplane systems. The stated purpose of e-taxi systems is to reduce the taxiing fuel expenses, expedite pushback procedures, reduce gate congestion, reduce ground crew involvement, and reduce noise and air pollution levels at large airports. Airplane-based autonomous traction electric motors receive power from airplane's APU(s) possibly supplemented by onboard batteries. Using additional battery energy storages ads significant inert weight. Systems utilizing nose-gear traction alone are often tractionlimited posing serious dispatch problems that could disrupt airport operations. Existing APU capacities are insufficient to deliver power for tractive taxiing while also providing for power off-takes. In order to perform comparative and objective analysis of taxi tractive requirements a "standard" taxiing cycle has been proposed. An analysis of reasonably expected tractive resistances has to account for steepest taxiway and runway slopes, taxiing into strong headwind, minimum required coasting speeds, and minimum acceptable acceleration requirements due to runway incursions issues. A mathematical model of tractive resistances was developed and was tested using six different production airplanes all at the maximum taxi/ramp weights. The model estimates the tractive force, energy, average and peak power requirements. It has been estimated that required maximum net tractive force should be 10% to 15% of the taxi weight for safe and expeditious airport movements. Hence, airplanes can be dispatched to move independently if the operational tractive taxi coefficient is 0.1 or higher.

An emergency descent maneuver initiated by pilots shortly after the onset of the decompression recognition was developed for subsonic, supersonic and hypersonic cruisers. Among other findings, the times when a passenger cabin is exposed to altitudes above 25,000 and 40,000 ft and the maximum cabin altitude reached are estimated. An airplane descent aerodynamic model was incorporated for high-speed and low-speed high-drag emergency descents. Airplane cabin atmosphere is assumed to be isothermal. The environmental atmosphere is simulated using the NLPAM nonlinear atmospheric model valid up to 47 geopotential kilometers. Rapid and slow decompressions at several discrete cruising altitudes ranging from 12 to 40 km and varying pilot reaction times in initiating the emergency descent were simulated. The main motivation for this work was to estimate times and altitudes a cabin reaches during depressurization for various flight conditions. This model can be utilized in optimizing the emergency-descent piloting techniques, calculating oxygen supplies, evaluating aeromedical factors, estimating harmful exposures to low pressures, and for other important high-altitude aircraft operations.

Unbalanced field length exists when ASDA and TODA are not equal. Airport authority may add less expensive substitutes to runway full-strength pavement in the form of stopways and/or clearways to basic TORA to increase operational takeoff weights. Here developed Takeoff Performance Tool is a physics-based total-energy model used to simulate FAR/CS 25 regulated airplane takeoffs. Any aircraft, runway, and environmental conditions can be simulated, while complying with the applicable regulations and maximizing performance takeoff weights. The mathematical model was translated into Matlab, Fortran 95/2003/2008, Basic, and MS Excel computer codes. All existing FAR/CS 25 takeoff regulations are implemented. Average forces are calculated for takeoff accelerate-go and accelerate-stop scenarios with all-engine-operating and one-engine-inoperative conditions. Special attention was paid to simulating increase in FLLTOW as the clearways and/or stopways are added in varying ratios. From the limited parametric study it appears that clearway-to-stopway ratio addition of 4:1 gives good overall performance increase while keeping decision/action speed constant. The critical clearway length exists for which both TORA and TODA are equally limiting. Corrections for effective runway slopes and wind were derived. The presented takeoff performance model provides a platform for more in-depth optimization studies and economic analysis of runway-airplane-engines synergy.