Aerospace Engineering Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/2737

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A Time Parallel Approach to Numerical Simulation of Asymptotically Stable Dynamical Systems with Application to CFD Models of Helicopter Rotors
(2023) Silbaugh, Benjamin Scott; Baeder, James D; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Modern High Performance Computing (HPC) machines are distributed memoryclusters, consisting of multi-core compute nodes. Engineering simulation and analysis tools must employ efficient parallel algorithms in order to fully utilize the compute capability of modern HPC machines. The trend in Computational Fluid Dynamcis (CFD) has been to construct parallel solution algorithms based on some form of spatial domain decomposition. This approach has been shown to be a success for many practical applications. However, as one attempts to utlize more compute cores, limitations in strong scalability are inevitably reached due to a diminishing compute workload per compute core and either fixed or increasing communication cost. Furthermore, spatial domain decomposition approaches cannot be easily applied to mid-fidelity structural dynamics or rigid body dynamics models. A significant majority of industrial fluid and structural dynamic models utilize some form of time marching. Thus, if the domain decomposition strategy may be extended to include the temporal dimension, additional opportunity for increased parallelism may be realized. A new form of periodic multiple shooting is proposed that ismatrix-free and may be applied to high-fidelity multiphysics models or other high dimensional systems. The proposed methodology is formulated entirely in the time domain. Therefore, existing time-domain simulation tools may utilize the proposed approach to achieve a high degree of distributed memory parallelism without requiring any reformulation. Furthermore, the proposed methodology may be combined with conventional space domain decomposition techniques and other forms of data parallelism to achieve maximal performance on modern HPC architectures. The proposed algorithm retains the iterative shoot-correct approach of conventational periodic shooting methods. However, the correction stage is formulated using a hierarchical evaluation strategy combined with an Arnoldi subspace approximation to eliminate the need for explicit formulation of Jacobian matricies. The local convergence of the proposed method is formally proven for the case of an asyptotically stable dynamical system. The proposed method is numerically tested for a 2D limit cycle problem, a rigid blade helicoper rotor model with quasi-steady aerodynamics and autopilot trim, and an OVERSET CFD model of a helicopter rotor with prescribed elastic blade motions. The method is observed to be convergent in all test cases and found to exhibit good scalability. The proposed periodic multiple shooting method is a practical means of reducingtime-to-solution for numerical simulations of asymptotically stable periodic systems on distributed memory parallel computers. Furthermore, the proposed method may be used to enhance the parallel scalability of OVERSET CFD models of helicopter rotors in steady periodic flight.
A Time Parallel Approach to Numerical Simulation of Asymptotically Stable Dynamical Systems with Application to CFD Models of Helicopter Rotors
(2023) Silbaugh, Benjamin Scott; Baeder, James; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Modern High Performance Computing (HPC) machines are distributed memoryclusters, consisting of multi-core compute nodes. Engineering simulation and analysis tools must employ efficient parallel algorithms in order to fully utilize the compute capability of modern HPC machines. The trend in Computational Fluid Dynamcis (CFD) has been to construct parallel solution algorithms based on some form of spatial domain decomposition. This approach has been shown to be a success for many practical applications. However, as one attempts to utlize more compute cores, limitations in strong scalability are inevitably reached due to a diminishing compute workload per compute core and either fixed or increasing communication cost. Furthermore, spatial domain decomposition approaches cannot be easily applied to mid-fidelity structural dynamics or rigid body dynamics models. A significant majority of industrial fluid and structural dynamic models utilize some form of time marching. Thus, if the domain decomposition strategy may be extended to include the temporal dimension, additional opportunity for increased parallelism may be realized. A new form of periodic multiple shooting is proposed that ismatrix-free and may be applied to high-fidelity multiphysics models or other high dimensional systems. The proposed methodology is formulated entirely in the time domain. Therefore, existing time-domain simulation tools may utilize the proposed approach to achieve a high degree of distributed memory parallelism without requiring any reformulation. Furthermore, the proposed methodology may be combined with conventional space domain decomposition techniques and other forms of data parallelism to achieve maximal performance on modern HPC architectures. The proposed algorithm retains the iterative shoot-correct approach of conventational periodic shooting methods. However, the correction stage is formulated using a hierarchical evaluation strategy combined with an Arnoldi subspace approximation to eliminate the need for explicit formulation of Jacobian matricies. The local convergence of the proposed method is formally proven for the case of an asyptotically stable dynamical system. The proposed method is numerically tested for a 2D limit cycle problem, a rigid blade helicoper rotor model with quasi-steady aerodynamics and autopilot trim, and an OVERSET CFD model of a helicopter rotor with prescribed elastic blade motions. The method is observed to be convergent in all test cases and found to exhibit good scalability. The proposed periodic multiple shooting method is a practical means of reducingtime-to-solution for numerical simulations of asymptotically stable periodic systems on distributed memory parallel computers. Furthermore, the proposed method may be used to enhance the parallel scalability of OVERSET CFD models of helicopter rotors in steady periodic flight.
INVESTIGATION OF COMPOUND ROTORCRAFT AEROMECHANICS THROUGH WIND-TUNNEL TESTING AND ANALYSIS
(2022) Maurya, Shashank; Datta, Anubhav; Chopra, Inderjit; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The aeromechanics of a slowed-rotor compound rotorcraft is investigated through wind-tunnel testing and comprehensive analysis. The emphasis is on a lift-offset wing compound with a hingeless rotor configuration. A new Maryland Compound Rig is developed and instrumented for wind-tunnel testing and an in-house rotor comprehensive code is modified and expanded for compound rotorcraft analysis. The compound rig consists of a lift compound model and a propeller model. The lift compound model consists of an interchangeable hub (articulated or hingeless), a fuselage, a half-wing of 70% rotor radius on the retreating side. The wing has a dedicated load cell and multiple attachment points relative to the rotor hub (16%R, 24%R, and 32%R and 5%R aft of the hub). The rotor diameter is 5.7-ft. The rotor has four blades with NACA 0012 airfoils with no twist and no taper. The wing incidence angle is variable between 0 to 12 degrees. The wing has a linearly varying thickness with symmetric airfoils NACA 0015 at the tip and NACA 0020 at the root. Sensors can measure rotor hub forces and moments, wing root forces and moments, blade pitch angles, structural loads (flap bending moment, lagbending moment, and torsional moment) at 25%R, pitch link loads, and hub vibratory loads. Wind tunnel tests are conducted up to advance ratio 0.7 for lift compound with half-wing at wing incidence angles of 4 and 8 degrees and compared with an isolated rotor. Hover tests are conducted up to tip Mach number of 0.5 to measure download penalty with the wing at various positions. The University of Maryland Advanced Rotorcraft Code (UMARC) is modified for compound rotorcraft analysis code. Aerodynamic models for the wing and the propeller are integrated. A recently developed Maryland Free Wake model is integrated, which can model the wake interaction between unequal and inharmonic speed rotor, wing, and propeller. The analysis is then validated with the test data. The validated analysis is used to analyze the US Army hypothetical full-scale aircraft. The compound rotorcraft is categorized into multiple configurations in a systematic manner to find the extreme limits of speed and efficiency of each. The key conclusions are: 1) slowing the rotor or compounding the configuration provide no benefit individually; they must be accomplished together, 2) Half-Wing is more beneficial if a lift-offset hingeless rotor is used, 3) hover download penalty is only 3% of net thrust, and this penalty can be predicted satisfactorily by free wake, 4) the main rotor wake interaction is more pronounced on the wing and less on the propeller, 5) the validated analysis indicates a speed of 240 knots may be possible with 20% RPM reduction along with a wing and propeller, if structural weights allow, and 6) the oscillatory and vibratory lag moments and in-plane hub loads may be significantly reduced by compounding.
SURROGATE MODELING AND CHARACTERIZATION OF BLADE-WAKE INTERACTION NOISE FOR HOVERING SUAS ROTORS USING ARTIFICIAL NEURAL NETWORKS
(2022) Thurman, Christopher; Baeder, James; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
This work illustrates the use of artificial neural network modeling to study and characterize broadband blade-wake interaction noise from hovering sUAS rotors subject to varying airfoil geometries, rotor geometries, and operating conditions. Design of Experiments was used to create input feature spaces over 9 input features: the number of rotor blades, rotor size, rotor speed, the amount of blade twist, blade taper ratio, tip chord length, collective pitch, airfoil camber, and airfoil thickness. A high-fidelity strategy was then implemented at the discrete data points defined by the designed input feature spaces to design airfoils and rotor blades, predict the unsteady rotor aerodynamics and aeroacoustics, and isolate the blade-wake interaction noise from the acoustic broadband noise, which was then used for prediction model training and validation. An artificial neural network tool was developed and implemented into NASA's ANOPP2 code and was used to identify an optimal prediction model for the nonlinear functional relationship between the 9 input features and blade-wake interaction noise. This optimal artificial neural network was then validated over test data, and exhibited prediction accuracy over 91% for data previously unseen by the model. First- and second-order sensitivity analyses were then conducted using the developed artificial neural network tool and it was seen that input features which serve to directly modify the thrust coefficient, such as airfoil camber and collective pitch, had a dominant effect over blade-wake interaction noise, followed by second-order interaction effects related to the mean rotor solidity. The optimal prediction model along with aerodynamic simulations were used to further study the effect of varying input features on blade-wake interaction noise and three types of blade-wake interaction noise were identified. Blade-wake interaction noise caused by impingement of the turbulence entrained in a tip vortex on the leading edge of a subsequent rotor blade showed to be the most prominent type of blade-wake interaction noise, exhibiting an acoustic contribution upward of 7 dB. Blade-wake interaction noise caused by a direct impingement of a tip vortex on the leading edge of a subsequent rotor blade had the second largest acoustic significance, exhibiting roughly 6 dB of broadband noise. The third, and least significant type of blade-wake interaction noise was shown to be caused by impingement of a blade-wake sheet on the mid-span of a subsequent rotor. This last type of blade-wake interaction noise was seen to only occur in the turbulent-wake operating state and possibly mild vertical descent conditions, and had approximately a 2.5 dB acoustic contribution.
A Scalable Time-Parallel Solution of Periodic Dynamics for Three-Dimensional Rotorcraft Aeromechanics
(2022) Patil, Mrinalgouda; Datta, Anubhav; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The principal barrier of computational time for rotorcraft trim solution using high-fidelity three-dimensional (3D) structures on real rotor problems was overcome with parallel and scalable algorithms. These algorithms were devised by leveraging the modern supercomputer architecture. The resulting parallel X3D solver was used to investigate advanced coaxial rotors using a notional hingeless rotor test case, Metaltail. This investigation included rotor performance, blade airloads, vibratory hub loads, and three-dimensional stresses. The technical approach consisted of first studying existing algorithms for periodic rotor dynamics --- time marching, finite element in time (FET), and harmonic balance. The feasibility of these algorithms was studied for large-scale rotor structures, and drawbacks were identified. Modifications were then performed on the harmonic balance method to obtain a Modified Harmonic Balance (MHB) method. A parallel algorithm for skyline solver was devised on shared memory to obtain faster solutions to large linear system of equations. The MHB method was implemented on a hybrid distributed--shared memory architecture to allow for parallel computations of harmonics. These developed algorithms were then integrated into the X3D solver to obtain a new parallel X3D. The new parallel X3D was verified and validated in hover and forward flight conditions for both idealized and real rotor test cases. A total of four test cases were studied: 1) uniform beam, 2) Frank Harris rotor, 3) UH-60A-like Black Hawk rotor, and 4) NASA Tilt Rotor Aeroacoustic Model (TRAM). The predictions of tip displacements, airloads, and stress distributions from the MHB algorithm showed good agreement with the test data and time marching predictions. The key conclusion is that the new solver converges to the time marching solution 50-70 times faster and achieves a performance greater than 1 teraFLOPS. The new parallel X3D solver opened the opportunity for modeling advanced rotor configurations. In this work, the coaxial rotor was the selected configuration. Two open access models were developed; 1) a notional hingeless coaxial rotor, and 2) a notional articulated UH-60A-like coaxial rotor. The aerodynamics, structural dynamics, and trim modules of X3D were expanded for coaxial modeling. The coaxial aerodynamics was validated with hover performance data from the U.S. Army model test. The coaxial solver was then used to study rotor aeromechanics in forward flight. The analysis was performed at a low-speed transition flight for which qualitative data is available for the Sikorsky S-97 Raider aircraft for comparison. The UH-60A coaxial airloads showed good agreement with the S-97 data as the twists are likely similar. However, the Metaltail model showed dissimilarities, and the cause was investigated to be its high twist. Vibratory hub loads with advance ratio were studied, and the maximum vibration occurred at the transition flight speed ($\mu = 0.1 - 0.15$), which was consistent with the S-97 data. The effect of the inter-rotor phase was examined for the reduction of vibratory hub loads. Three-dimensional stresses and strains were predicted and visualized for the first time on lift offset coaxial rotors in the blade and the hub.
Measurement and Prediction of the Separated Flow on a Rotor at High Advance Ratio
(2020) Smith, Luke Robert; Jones, Anya R; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Flow separation is prevalent in a number of aerospace applications, but because of complex non-linearities in the governing equations, the resulting aerodynamic forces are challenging to model. This mathematical limitation is particularly impactful in the field of high speed rotorcraft. When a rotor operates at high advance ratio, a regime typical of high speed (and low power) flight, the blades of the rotor are subject to several unsteady motions that incur flow separation, including high pitch inputs and a region of reverse flow that occupies much of the rotor's retreating side. The aerodynamic forces in these regions are dominated by large-scale, coherent vortex structures that are poorly captured by conventional aerodynamics theories. The purpose of this work is to understand the physics of flow separation on high advance ratio rotors, and to leverage this understanding into a low-order, physics-based model for use in rotorcraft design applications. The current work approaches this goal by identifying, understanding, and ultimately modeling the coherent flow structures present on a representative, sub-scale rotor system operating at high advance ratio. Flowfield measurements on this rotor revealed the presence of two distinct vortex structures, a ``sharp-edge'' vortex and a ``blunt-edge'' vortex, believed to dominate unsteady loading in the reverse flow region. The sharp-edge vortex was studied via a high-fidelity numerical simulation, and its growth was found to be dominated by 2-D mechanisms of vorticity transport. The insignificance of 3-D effects was attributed to a mutual cancellation of Coriolis forces and spanwise convection/tilting, a feature unique to reverse flow. Likewise, the blunt-edge vortex was studied in a series of 2-D surging and pitching wing experiments; its formation was found to largely depend on the unsteady, "external" features of the flow, most notably the trailing wake. Together, these observations led to the development of a 2-D discrete vortex model capable of predicting the strength of the sharp-edge vortex and the timing of the blunt-edge vortex. The model has a computation time on the order of seconds, features only a single empirical parameter, and captures the fundamental physical mechanisms at play on a rotor at high advance ratio.
Wind Tunnel Test on Slowed Rotor Aeroechanics at High Advance Ratios
(2020) Wang, Xing; Chopra, Inderjit; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
In forward flight, slowing down a rotor alleviates compressibility effects on the advancing side, extending the cruise speed limit and inducing high advance ratio flight regime. To investigate the aerodynamic phenomena at high advance ratios and provide data for the validation of analysis tools, a series of wind tunnel tests were conducted progressively with a 33.5-in radius, 4-bladed Mach-scaled rotor in the Glenn L. Martin Wind Tunnel. In the first stage of the research, a wind tunnel test was carried out at high advance ratios with highly similar, non-instrumented blades and on-hub control angle measurements, in order to gain a baseline performance and control dataset with minimum error due to blade structural dissimilarity and pitch angle discrepancy. The tests were conducted at advance ratios of 0.3 to 0.9, and a parametric study on shaft tilt was conducted at $0^\circ$ and $\pm 4^\circ$ shaft tilt angles. The test data were then compared with those of previous tests and with the predictions of the in-house comprehensive analysis UMARC. The airload results were investigated using comprehensive analysis to gain insights on the influences of advance ratio and shaft tilt angle on rotor performance and hub vibratory loads. Results indicate that the thrust benefit from backward shaft tilt is dependent on the change in the inflow condition and the induced angle of attack increment, and the reverse flow region at high advance ratios is the major contributor to changes in shaft torque and horizontal force. In the second stage of the research, the rotor blades were instrumented with pressure sensors and strain gauges at 30\% radius, and pressure data were acquired to calculate the sectional airloads by surface integration up to an advance ratio of 0.8. The test results of blade airloads and structural loads were compared with the predictions of comprehensive analysis (UMARC and PrasadUM) and CFD/CSD coupled analysis (PrasadUM/HAMSTR). The focus was on the data correlation between experimental pressure, airload and structural load data and the CFD/CSD predicted results at various collective and shaft tilt settings. Overall, the data correlation was found satisfactory, and the study provided some insights into the aerodynamic mechanisms that affect the rotor airload and performance, in particular the mechanisms of backward shaft tilt, hub/shaft wake and the formation of dynamic stall in the reverse flow region. The next stage focused on hingeless rotor with lift offset. Previous wind tunnel tests have shown that an articulated rotor trimmed to zero hub moment generates limited thrust at high advance ratios, because the advancing side needs to be trimmed against the retreating side with significant reverse flow, in which the rotor is ineffective in generating thrust. Therefore, a hingeless rotor that allows the advancing side to generate more thrust can be rewarding in overall thrust potential. Wind tunnel tests were conducted up to an advance ratio of 0.7 to investigate the behavior of hingeless rotors at high advance ratios with lift offsets. Performance, control angles, hub vibratory loads and blade structural loads were compared with comprehensive analysis predictions from UMARC, plus the wing performance predictions from AVL. The results demonstrate that a hingeless rotor with lift offset is more efficient in generating thrust and exhibits higher lift-to-drag ratio at high advance ratios. The blade structural load level is significantly higher compared to an articulated rotor, especially for 2/rev flap bending moment, which can pose a critical structural constraint on the rotor.
Advancing the Multi-Solver Paradigm for Overset CFD Toward Heterogeneous Architectures
(2019) Jude, Dylan P; Baeder, James; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
A multi-solver, overset, computational fluid dynamics framework is developed for efficient, large-scale simulation of rotorcraft problems. Two primary features distinguish the developed framework from the current state of the art. First, the framework is designed for heterogeneous compute architectures, making use of both traditional codes run on the Central Processing Unit (CPU) as well as codes run on the Graphics Processing Unit (GPU). Second, a framework-level implementation of the Generalized Minimal Residual linear solver is used to consider all meshes from all solvers in a single linear system. The developed GPU flow solver and framework are validated against conventional implementations, achieving a 5.35× speedup for a single GPU compared to 24 CPU cores. Similarly, the overset linear solver is compared to traditional techniques, demonstrating the same convergence order can be achieved using as few as half the number of iterations. Applications of the developed methods are organized into two chapters. First, the heterogeneous, overset framework is applied to a notional helicopter configuration based on the ROBIN wind tunnel experiments. A tail rotor and hub are added to create a challenging case representative of a realistic, full-rotorcraft simulation. Interactional aerodynamics between the different components are reviewed in detail. The second application chapter focuses on performance of the overset linear solver for unsteady applications. The GPU solver is used along with an unstructured code to simulate laminar flow over a sphere as well as laminar coaxial rotors designed for a Mars helicopter. In all results, the overset linear solver out-performs the traditional, de-coupled approach. Conclusions drawn from both the full-rotorcraft and overset linear solver simulations can have a significant impact on improving modeling of complex rotorcraft aerodynamics.
Identification of State-Space Rotor Wake Models with Application to Coaxial Rotorcraft Flight Dynamics and Control
(2019) Hersey, Sean Patrick; Celi, Roberto; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
Modern aerodynamic analysis tools, such as free-vortex wake models and CFD-based techniques, include fewer theoretical limitations and approximations than classical simplified schemes, and represent the state-of-the-art in rotorcraft aerodynamic modeling, including for coaxial and other advanced configurations. However, they are impractical or impossible to apply to many flight dynamics problems because they are not formulated in ordinary differential equation (ODE) form, and they are often computationally intensive. Inflow models, for any configuration type, that couple the accuracy of high-fidelity aerodynamic models with the simplicity and ODE form of dynamic inflow-type theories would be an important contribution to the field of flight dynamics and control. This dissertation presents the methodology for the extraction of linearized ODE models from computed inflow data acquired from detailed aerodynamic free-vortex wake models, using frequency domain system identification. These methods are very general and applicable to any aerodynamic model, and are first demonstrated with a free wake model in hover and forward flight, for a single main rotor, and subsequently for the prediction of induced flow off the rotor as well, at locations such as the tail or fuselage. The methods are then applied to the extraction of first order linearized ODE inflow models for a coaxial rotor in hover. Subsequent analysis concluded that free-vortex wake models show that the behavior of the inflow of a coaxial configuration may be higher-order. Also, tip-path plane motion of a coaxial rotor causes wake distortion which has an impact on the inflow behavior. Therefore, the methodology is expanded to the identification of a second order inflow representation which is shown to better capture from all of the relevant dynamics from free-vortex wake models, including wake distortion. With ODE models of inflow defined for an advanced coaxial configuration, this dissertation then presents a comparison of the fully-coupled aircraft flight dynamics, and the design of an explicit modeling-following feedback controller, with both a free-vortex wake identified model and a momentum theory based approach, concluding that accurate inflow modeling of coaxial rotor inflow is essential for investigation into the flight dynamics and control design of advanced rotor configurations.
An Experimental and Analytical Investigation of Hydrogen Fuel Cells for Electric Vertical Take-Off and Landing (eVTOL) Aircraft
(2019) Ng, Wanyi; Datta, Anubhav; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
The objective of this thesis is a comprehensive investigation of hydrogen fuel cells for electric vertical take-off and landing (eVTOL) aircraft. The primary drawback of battery powered eVTOL aircraft is their poor range and endurance with practical payloads. This work uses simulation and hardware testing to examine the potential of hydrogen fuel cells to overcome this drawback. The thesis develops steady state and transient models of fuel cells and batteries, and validates the models experimentally. An equivalent circuit network model was able to capture the waveforms and magnitudes of voltage as a function of current. Temperature and humidity corrections were also included. Examination of the results revealed that the transient behavior of batteries and fuel stacks are significant primarily shortly after startup of the fuel stack and at the limiting ranges of high and low power; for a nominal operating power and barring faults, steady state models were adequate. This work then demonstrates fuel cell and battery power sharing in regulated and unregulated parallel configurations. It details the development of a regulated architecture, which controls power sharing, to achieve a reduction in power plant weight. Finally, the thesis outlines weight models of motors, batteries, and fuel cells needed for eVTOL sizing, and carries out sizing analysis for on-demand urban air taxi missions of three different distances -- 50, 75, and 150~mi of cruise and 5~min total hover time. This revealed that for ranges within 75 mi, a light weight (5000-6000~lb gross weight) all-electric tilting proprotor configuration achieves a practical payload (500~lb or more) with current levels of battery specific energy (150~Wh/kg) if high burst C-rate batteries are available (4-10~C for 2.5~min). Either a battery-only or battery-fuel cell (B-FC) hybrid power plant is ideal depending on the range of the mission: For inter-city ranges (beyond approximately 50~mi), the mission is impossible with batteries alone, and fuel cells are a key enabling technology; a VTOL aircraft with a B-FC hybrid powerplant, an aircraft with 6200~lb gross take-off weight, 10~lb/ft$^2$ disk loading, and 10~C batteries, could be sized to carry a payload of 500~lb for a range of 75~mi. For this inter-city range, the research priority centers of fuel cells, as they appear to far surpass future projections of Li-ion battery energy levels based on performance numbers (at a component level), high weight fraction of hydrogen storage due to the short duration of eVTOL missions, and lack of a compressor due to low-altitude missions, with the added benefit of ease of re-fueling. However, for an intra-city mission (within approximately 50~mi), the B-FC combination provides no advantage over a battery-only powerplant; a VTOL aircraft with a battery-only powerplant with the same weight and disk loading as before, and 4~C batteries, can carry a payload of 800~lb for a range of 50~mi. For this mission range, improving battery energy density is the priority.

Aerospace Engineering Theses and Dissertations

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