Take-off Trajectory Research Articles

Noise Study Auralization of an Open-Rotor Engine

Based on the performance and acoustic data files of reduced-size open-rotor engines in low-speed wind tunnels, the static sound pressure level was derived by converting the 1-foot lossless spectral density into sound-pressure-level data, the background noise was removed, and the results were corrected according to the environmental parameters of the low-speed wind tunnels. In accordance with the requirements of Annex 16 of the Convention on International Civil Aviation Organization and Part 36 of the Civil Aviation Regulations of China on noise measurement procedures, the takeoff trajectory was physically modeled; the static noise source was mapped onto the takeoff trajectory to simulate the propagation process of the noise during takeoff; and the 24 one-third-octave center frequencies that corresponded to the SPL data were corrected for geometrical dispersion, atmospheric absorption, and Doppler effects, so that the takeoff noise could be corrected to represent a real environment. In addition, the audible processing of noise data with a 110° source pointing angle was achieved, which can be useful for enabling practical observers to analyze the noise characteristics.

Simultaneous optimization of design and takeoff trajectory for an eVTOL aircraft

When designing a vertical takeoff and landing (VTOL) aircraft, it is crucial to consider various operating conditions, including hover, wing-borne cruise, and transition. Takeoff transition and climb phases are critical for vehicle conceptual design because they drive the motor and battery sizing. However, these flight phases are often ignored or simplified in the conceptual design literature due to the complexity of transition dynamics. To address this limitation, we propose simultaneous optimization of VTOL aircraft conceptual design and takeoff trajectory. Simultaneous optimization incorporates the takeoff transition and climb flight dynamics into VTOL design optimization in a fully coupled manner. This paper presents the design-trajectory optimization of lift-plus-cruise and tailsitter UAVs for delivery missions. As a result, simultaneous optimization reduces total energy consumption by 7.4% compared to uncoupled optimization and by 4.8% from iterative sequential optimization in the lift-plus-cruise configuration. It also achieves a 29% energy reduction from uncoupled optimization in the tailsitter configuration. Incorporating takeoff trajectory optimization in UAV sizing enables accurate estimation of takeoff and climb energy, which avoids undersizing or oversizing the battery. Furthermore, simultaneous optimization trades the vehicle weight penalty for a more energy-efficient climb with early transition. These system-level trade-offs can only be captured by simultaneous optimization; they cannot be captured by uncoupled or iterative sequential optimization.

Surrogate-Based Multidisciplinary Optimization for the Takeoff Trajectory Design of Electric Drones

Electric vertical takeoff and landing (eVTOL) aircraft attract attention due to their unique characteristics of reduced noise, moderate pollutant emission, and lowered operating cost. However, the benefits of electric vehicles, including eVTOL aircraft, are critically challenged by the energy density of batteries, which prohibit long-distance tasks and broader applications. Since the takeoff process of eVTOL aircraft demands excessive energy and couples multiple subsystems (such as aerodynamics and propulsion), multidisciplinary analysis and optimization (MDAO) become essential. Conventional MDAO, however, iteratively evaluates high-fidelity simulation models, making the whole process computationally intensive. Surrogates, in lieu of simulation models, empower efficient MDAO with the premise of sufficient accuracy, but naive surrogate modeling could result in an enormous training cost. Thus, this work develops a twin-generator generative adversarial network (twinGAN) model to intelligently parameterize takeoff power and wing angle profiles of an eVTOL aircraft. The twinGAN-enabled surrogate-based takeoff trajectory design framework was demonstrated on the Airbus A3 Vahana aircraft. The twinGAN provisioned two-fold dimensionality reductions. First, twinGAN generated only realistic trajectory profiles of power and wing angle, which implicitly reduced the design space. Second, twinGAN with three variables represented the takeoff trajectory profiles originally parameterized using 40 B-spline control points, which explicitly reduced the design space while maintaining sufficient variability, as verified by fitting optimization. Moreover, surrogate modeling with respect to the three twinGAN variables, total takeoff time, mass, and power efficiency, reached around 99% accuracy for all the quantities of interest (such as vertical displacement). Surrogate-based, derivative-free optimizations obtained over 95% accuracy and reduced the required computational time by around 26 times compared with simulation-based, gradient-based optimization. Thus, the novelty of this work lies in the fact that the twinGAN model intelligently parameterized trajectory designs, which achieved implicit and explicit dimensionality reductions. Additionally, twinGAN-enabled surrogate modeling enabled the efficient takeoff trajectory design with high accuracy and computational cost reduction.

Transfer-Learning-Enhanced Regression Generative Adversarial Networks for Optimal eVTOL Takeoff Trajectory Prediction

Electric vertical takeoff and landing (eVTOL) aircraft represent a crucial aviation technology to transform future transportation systems. The unique characteristics of eVTOL aircraft include reduced noise, low pollutant emission, efficient operating cost, and flexible maneuverability, which in the meantime pose critical challenges to advanced power retention techniques. Thus, optimal takeoff trajectory design is essential due to immense power demands during eVTOL takeoffs. Conventional design optimizations, however, adopt high-fidelity simulation models in an iterative manner resulting in a computationally intensive mechanism. In this work, we implement a surrogate-enabled inverse mapping optimization architecture, i.e., directly predicting optimal designs from design requirements (including flight conditions and design constraints). A trained inverse mapping surrogate performs real-time optimal eVTOL takeoff trajectory predictions with no need for running optimizations; however, one training sample requires one design optimization in this inverse mapping setup. The excessive training cost of inverse mapping and the characteristics of optimal eVTOL takeoff trajectories necessitate the development of the regression generative adversarial network (regGAN) surrogate. We propose to further enhance regGAN predictive performance through the transfer learning (TL) technique, creating a scheme termed regGAN-TL. In particular, the proposed regGAN-TL scheme leverages the generative adversarial network (GAN) architecture consisting of a generator network and a discriminator network, with a combined loss of the mean squared error (MSE) and binary cross-entropy (BC) losses, for regression tasks. In this work, the generator employs design requirements as input and produces optimal takeoff trajectory profiles, while the discriminator differentiates the generated profiles and real optimal profiles in the training set. The combined loss facilitates the generator training in the dual aspects: the MSE loss targets minimum differences between generated profiles and training counterparts, while the BC loss drives the generated profiles to share analogous patterns with the training set. We demonstrated the utility of regGAN-TL on optimal takeoff trajectory designs for the Airbus A3 Vahana and compared its performance against representative surrogates, including the multi-output Gaussian process, the conditional GAN, and the vanilla regGAN. Results showed that regGAN-TL reached the 99.5% generalization accuracy threshold with only 200 training samples while the best reference surrogate required 400 samples. The 50% reduction in training expense and reduced standard deviations of generalization accuracy achieved by regGAN-TL confirmed its outstanding predictive performance and broad engineering application potential.

Optimal Tilt-Wing eVTOL Takeoff Trajectory Prediction Using Regression Generative Adversarial Networks

Electric vertical takeoff and landing (eVTOL) aircraft have attracted tremendous attention nowadays due to their flexible maneuverability, precise control, cost efficiency, and low noise. The optimal takeoff trajectory design is a key component of cost-effective and passenger-friendly eVTOL systems. However, conventional design optimization is typically computationally prohibitive due to the adoption of high-fidelity simulation models in an iterative manner. Machine learning (ML) allows rapid decision making; however, new ML surrogate modeling architectures and strategies are still desired to address large-scale problems. Therefore, we showcase a novel regression generative adversarial network (regGAN) surrogate for fast interactive optimal takeoff trajectory predictions of eVTOL aircraft. The regGAN leverages generative adversarial network architectures for regression tasks with a combined loss function of a mean squared error (MSE) loss and an adversarial binary cross-entropy (BC) loss. Moreover, we introduce a surrogate-based inverse mapping concept into eVTOL optimal trajectory designs for the first time. In particular, an inverse-mapping surrogate takes design requirements (including design constraints and flight condition parameters) as input and directly predicts optimal trajectory designs, with no need to run design optimizations once trained. We demonstrated the regGAN on optimal takeoff trajectory designs for the Airbus A3 Vahana. The results revealed that regGAN outperformed reference surrogate strategies, including multi-output Gaussian processes and conditional generative adversarial network surrogates, by matching simulation-based ground truth with 99.6% relative testing accuracy using 1000 training samples. A parametric study showed that a regGAN surrogate with an MSE weight of one and a BC weight of 0.01 consistently achieved over 99.5% accuracy (denoting negligible predictive errors) using 400 training samples, while other regGAN models require at least 800 samples.

3D High-Resolution Modeling of Aircraft-Induced NO x Emission Dispersion in CAEPport Configuration Using Landing and Take-Off Trajectory Tracking.

Pollutant emissions from aircraft operations contribute to the degradation of air quality in and around airports. Meeting the ICAO’s environmental certification standards regarding both gaseous and particulate aircraft engine emissions is one of the main challenges for air-transportation development over the coming years. To increase the accuracy of airport air pollution monitoring and prediction, advanced decision-making tools need to be developed. In this context, the present study aimed at demonstrating the modeling capabilities of an innovative methodology that accounts for the microscale evolution of aircraft emissions, both spatially and temporally. For this purpose, 3D high-resolution CFD simulations were carried out in the CAEPport configuration (medium-size mock airport) as defined by the Committee on Aviation Environmental Protection (CAEP/8) for local air-quality assessment. The modeled domain extends up to 8 km around the airport. A spatial resolution down to 1 m was used around buildings to refine the prediction of pollutant-emission concentrations. The model accounts for ambient meteorological conditions along with the background chemical composition. NOx emissions from main engines and auxiliary power units (APUs) were individually tracked along LTO trajectories with a time resolution down to 1 s. The impact of atmospheric stability was investigated in three cases, i.e., stable, neutral, and unstable. The results show NO2 dominating in apron areas due to the low power setting of main engines along APU contribution during extended parking. Conversely, a domination of NO emissions was observed at the runway threshold due to the high power setting of the main engines. Stable atmospheric conditions promoted higher NO and NO2 concentrations as compared to both neutral and unstable cases. The use of APUs contributed to higher concentrations of both NO and NO2 emissions and especially of NO2 in terminal areas.

Entrepreneurial university icon: Stanford and Silicon Valley as innovation and natural ecosystem

The author explicates the cultural DNA and take-off trajectory of an exemplary entrepreneurial university and its emerging focus on sustainability. Entrepreneurial initiatives, emanating from the engineering school in the late 19th century, spread to the physical sciences in the 1930s and to the biological sciences and medicine by the 1970s. A concerted and compressed academic development strategy sought researchers with related interests across disciplines, assuming that teaching could be diversified from these critical cores. A multi-pronged financial strategy included attracting federal research funds, leasing university land, technology transfer income and endowment from gifts and equity in university-originated firms in varying past and future proportions. Bottom-up initiatives proliferated, filling technology transfer and start-up support gaps in the entrepreneurial ecosystem. Recently, some innovation initiatives have been shuttered as the Administration has tacked towards addressing climate change though a microscopic initiative. Given an institutionalized and legitimated culture and infrastructure of entrepreneurship and innovation, these dual institutional logics operate in tandem symbiosis, mutually fructifying each other.

Wing coupling mechanism in the butterfly Pieris rapae (Lepidoptera, Pieridae) and its role in taking off

The small white cabbage butterfly (Pieris rapae) flaps its fore- and hindwings in synchrony as the wings are coupled using a wing “coupling mechanism”. The coupling mechanism of butterflies includes an enlarged humeral area located at the anterior of the hindwing base and a corresponding basal posterior part of the forewing, of which the former component dorsally contacts the ventral side of the latter one. The coupling mechanism allows for the fore- and hindwings sliding in contact along the span and chord. It is of interest that butterflies still take off successfully and fly, when their wing couplings are clipped, but they are unable to properly synchronize the fore- and hindwing motions. Compared with the regular takeoff trajectory of intact butterflies that always first fly backwards and then forwards, the coupling-clipped butterflies took off in a random trajectory. Due to the clipping of the coupling mechanism, the initiation of the hindwing flapping and the abdomen rotation from upward to downward during takeoff was postponed. The coupling-clipped butterflies changed their stroke plane in upstroke to a more vertical position and strengthened the abdominal undulation. We believe our work, which for the first time investigates the influence of coupling mechanism removal on insect flight, extends our understanding on the working principle of wing coupling in insects and its significance on the flapping flight.

Development of the Energy Method and Study of Algorithms for Predicting the Takeoff Trajectory of Aircraft

The article is devoted to the development and research of the method of predicting the events on the trajectory of takeoff, climb and overcome highrise obstacles on the course. The prediction method is based on the energy approach to flight control, created by us in previous works. The mathematical formulation of the method is the energy balance equation describing the mutual influence of all acting forces in the aircraft-engine-environment" system. In this article, the equation is extended to ground modes of movement along the runway. For this, a term is added to the equation that takes into account the action of braking forces from the chassis. The balance equation allows us to directly obtain an algorithm for calculating the length of the forward trajectory required for the accumulation of the required amount of terminal energy. Takeoff trajectory includes ground and air segments. Therefore, the possibility of overcoming the obstacle is fixed by the algorithm at the point of a possible decision to takeoff, taking into account the next air segment. This point is reached before the decision-making airspeed prescribed by the flight manual is reached. This advance warning of the possibility of takeoff improves situational awareness of the pilot, which reduces stress and reduces the risk of erroneous actions. A computer stand was developed for the research. Single launches and series of statistical tests are possible. Takeoff scenarios are generated in the stand operator window, as well as initial runway conditions, atmospheric disturbances, aircraft configuration, and obstacle coordinates are specified. The parameters of random errors in the takeoff weight and centering are assigned, as well as the noise of longitudinal overload measurements are set. A large volume of deterministic and statistical tests of algorithms for predicting events on the takeoff trajectory was performed at the stand. Using the statistical analysis module, the characteristics of the range prediction errors to the take-off decision point and the nose wheel separation point were calculated. Probability densities and histograms of error distribution over five characteristic zones of deviations from the mean are constructed. The confidence intervals for calculating the mathematical expectation are obtained. A prototype of an electronic indicator of the takeoff trajectory with marks of predictive characteristic coordinates has been developed.

Take-Off Trajectory Optimization of Tilt-rotor Aircraft Based on Direct Allocation Method

During the take-off stage, the tilt-rotor aircraft’s actuator is redundant and difficult to control. In order to take off more quickly and safety reach horizontal flight state with less power consumption, the take-off trajectory is necessary to be optimized. this paper introduces the direct allocation method to optimize the take-off trajectory of tilt-rotor aircraft. Firstly, the dynamic model of the take-off stage of the tilt-rotor aircraft is established. According to the actual flight conditions, the constraints and the optimization objective function of the take-off process are established. Then, the entire take-off process is divided into several segments according to time, and the continuous optimal control problem is discretized into a nonlinear programming problem by using the direct allocation method. The state and control variables at each segment point and midpoint are taken for optimization. and then the optimized variables are fitted by the third-order Simpson method. Finally, GPOPS toolbox in MATLAB was used to solve the nonlinear programming problem. The simulation results show that the optimized take-off trajectory can well meet the boundary constraints, and its solutions are stable.

Takeoff Simulation of Air Taxi by Using Navier–Stokes Equations

Takeoff trajectory computations are made for a typical small transport aircraft suitable for an urban air taxi. The selected wing–body model consists of lifting and pushing propellers. Flow is modeled using the Navier–Stokes equations. A procedure is developed to embed the trajectory motion equations in an overset grid topology along with rotating blades. Results are validated with lifting line theory computations. A typical takeoff scenario is demonstrated by time-accurately integrating trajectory equations with the flow equations. The present work extends the capabilities of the current Navier–Stokes solvers to simulate trajectory motions of urban air taxi configurations.

3D Trajectory Reconstruction From Monocular Vision Based on Prior Spatial Knowledge

This paper proposed a monocular vision system to reconstruct 3D plane take-off trajectory. This system is designed for airport dynamic surveillance under low visibility conditions. The main purpose of our system is to help traffic controllers to monitor flights taking off in multi-view.

Kinematics that differentiate the beach flags start between elite and non-elite sprinters.

This study differentiated the kinematics of the beach flags sprint start between five elite (three males, two females; age = 21.2 ± 2.6 years; height = 1.71 ± 0.04 m; mass = 66.2 ± 5.9 kg) and five non-elite (three males, two females; age = 20.4 ± 1.7 years; height = 1.69 ± 0.08 meters [m]; mass = 61.6 ± 5.7 kilograms) sprinters. A high-speed camera filmed the start. Timing gates recorded the 0-2, 0-5, and 0-20 m intervals. Data included body position during the start and at take-off; start time; first step length; and sprint times. A Mann-Whitney U-test determined significant (p < 0.05) between-group differences; effect sizes (ES) were also calculated. Elite sprinters had a greater take-off trajectory angle (p = 0.01; ES = 2.57), and were faster over the 0-2 (p = 0.02; ES = 1.77), 0-5 (p = 0.05; ES = 1.20), and 0-20 m (p = 0.02; ES = 1.83) intervals. Large effects were found for: greater take-off swing leg hip flexion (ES = 1.13) and trunk lean (ES = 1.37); longer duration start time (ES = 1.33); and longer first step length (ES = 1.23) in elite sprinters. A longer start time assists with force generation, which in conjunction with increased hip flexion, could translate to a longer first step. Increased trunk lean shifts the take-off trajectory angle towards the horizontal. A greater trajectory angle at start take-off, which could be advantageous for force production during sprint performance, is likely necessary for beach flags.

Application of Online Iterative Learning Tracking Control for Quadrotor UAVs

Quadrotor unmanned aerial vehicles (UAVs) have attracted considerable interest for various applications including search and rescue, environmental monitoring, and surveillance because of their agilities and small sizes. This paper proposes trajectory tracking control of UAVs utilizing online iterative learning control (ILC) methods that are known to be powerful for tasks performed repeatedly. PD online ILC and switching gain PD online ILC are used to perform a variety of manoeuvring such as take-off, smooth translation, and various circular trajectory motions in two and three dimensions. Simulation results prove the ability and effectiveness of the online ILCs to perform successfully certain missions in the presence of disturbances and uncertainties. It also demonstrates that the switching gain PD ILC is much effective than the PD online ILC in terms of fast convergence rates and smaller tracking errors.

Safety Considerations for Helicopter Roll On Takeoffs

A six-degree-of-freedom simulation of helicopter roll on takeoff is used for evaluation of a twin-engine helicopter continued takeoff trajectory, following one engine failure. For this study, an AH-64A Apache was used. The simulation is used for the determination of the required runway length that will enable safe continued takeoff using the remaining engine’s power.Apreliminary optimizationwas carried out for thedefinition of the liftoff airspeed and critical decision point height that minimize the required runway length.

Tabletop Jumping: Engineering Analysis of Trajectory and Landing Impact

Abstract This study is an engineering analysis of skiers and snowboarders jumping what is known as a mid-sized tabletop feature at a ski resort. The analysis specifically looks at the trajectories and landing impacts of individuals while jumping mid-sized tabletop features (deck lengths 20 to 30 ft) at a ski resort. For the trajectory analysis, out of a total of 117 jumps by skiers and snowboarders that were observed, 57 jumps were analyzed using a radar gun to determine actual speed on the ramp, digital photography to document flight paths and landing points as well as jumper body position at the moment of take-off. For the impact analysis, a total of 31 jumps by an instrumented subject were videotaped; the landing impacts for 21 of these jumps were measured with triaxial accelerometers to measure the impact resulting from the landing at the boot top, chest, and head levels. With respect to trajectory analysis, the study concludes that simply knowing the ramp angle and take-off speed is not a sufficient dataset to predict where the jumper will land; alternatively, knowing the ramp angle and the landing point is an insufficient dataset to predict the take-off speed. The specific actions of the jumper with regard to raising or lowering the jumper’s center of mass while on the last part of the take-off ramp can significantly alter the effective take-off angle and subsequent flight trajectory. For the jumps observed in this study, the jumpers were able to routinely add or subtract as much as 15° to the actual take-off ramp angle, resulting in effective take-off angles much larger or smaller than the measured take-off angle. With respect to impact analysis, the study concluded that for jumps similar to the those observed in the trajectory analysis, when the jumper lands in an upright controlled manner, the resulting impact (measured in G units) at the boot level ranged from 50 to 100 Gs, with a mean of 75 Gs, it averaged 4.7 Gs at the chest and only 2.5 Gs at the head.

Control of landing flight by laying hens: implications for the design of extensive housing systems

1. Ten domestic hens (Lohmann Brown) were video-recorded while moving between perches at a horizontal distance of 0·6, 0·8 or 1·15 m apart. The take-off perch was either 0·2 m above or below the landing perch. 2. Weight and wing area of the hens were measured at the end of the experiment. The same measures where taken from 10 jungle fowls. 3. Clumsy or missed landings were observed on some downward flights over 0·8 and 1·15 m. 4. Hens’ trajectories on take-off were closely related to the position of the target perch, and variation in take-off trajectory decreased as the distance between perches increased. 5. The standard deviation of the horizontal distance between head and perch, at the point when the feet first contacted the perch, did not vary with flight distance, suggesting that timing of foot extension was equally accurate at all distances. 6. The standard deviation of the vertical distance between head and perch, at the point when the feet first contacted the perch, did increase with distance, suggesting increasing difficulty in controlling the height of the flight trajectory above the landing perch. 7. Wing loading of the hens (mean 213 N/m2) was approximately twice that of the jungle fowl (mean 111 N/m2). 8. Loss of accuracy in hens’ landings at greater distances can be attributed specifically to the effects of high wing loading on the ability to generate and control lift.

Head orientation is aligned with take-off trajectory as chicks jump.

Chicks of up to one week of age were video recorded while jumping across gaps of different widths and depths. The orientation of the head in the sagittal plane was measured at the point where jumps began. As the gap became wider, or the far side of it was raised, chicks' heads rotated upwards, but this change in head orientation did not keep the far edge of the gap fixated at a particular elevation in the visual field. Except with narrow gaps, which chicks often stepped over, there was a consistent relationship between head orientation and the initial trajectory of a jump. Each 1 degree change in trajectory was accompanied by an approximately 1 degree change in head orientation. It is proposed that the visual control of head orientation and position in relation to the dimensions of a gap contributes to adjusting a chick's posture and, therefore, its trajectory at take-off.

On the calculation of the maximum sound pressure spectrum from stationary and mobile jets

The calculation of the maximum sound pressure spectrum from turbojets of aeroplanes on their take-off trajectory is based on the generalized expression of acoustical power emitted by the fixed or moving axisymmetric jets; it takes account of the laws of spatial distribution of the sound energy and of the generalized characteristics of the linear maximum sound pressure spectrum at a given distance of reference (30 m). The numerical solutions of the equation obtained are facilitated by the use of diagrams and require knowledge of the geometrical and aerodynamic parameters of the jets and also the aeroplane speed.