Ground-generation airborne wind energy design space exploration

Abstract. While some Airborne Wind Energy System (AWES) companies aim at small-scale, temporary or remote off-grid markets, others aim to integrate utility-scale, multi-megawatt AWES into the electricity grid. This study investigates the scaling effects of single-wing, ground-generation AWESs from small to large-scale systems, subject to realistic 10-minute, onshore and offshore wind conditions derived from the numerical mesoscale weather research and forecasting (WRF) model. To reduce computa5 tional cost, wind velocity profiles are grouped into k=10 clusters using k-means clustering. Three representative profiles from each cluster are implemented into a nonlinear AWES optimal control model, to determine power-optimal trajectories, system dynamics, as well as instantaneous and cycle-average power. We compare the performance of three different aircraft masses and two sets of nonlinear aerodynamic coefficients for each aircraft size, with wing areas ranging from 10 m to 150 m. We predict size and weight-dependent, optimal AWES power curves, annual energy production (AEP) and capacity factor 10 (cf).Tether impacts, such as power losses associated with tether drag and the tether contribution to total system mass are quantified. Furthermore, we estimate a minimum average cycle-average lift to weight ratio, above which ground-generation AWES can operate, to explore the viable AWES mass budget.

One of the biggest companies working on this concept is Ampyx Power (Ampyx). Ground-generation AWES generate power during the reel-out phase while the wing generates large lift forces and pulls the tether from a drum. During the following reelin phase a fraction of the energy is consumed to return the aircraft back to its initial position and restart the cycle (Luchsinger, 2013). As a result, the power generated by such systems is inherently oscillating which could be offset using multiple devices in a wind farm setup or buffering the energy before feeding it into the grid (Malz et al., 2018). 30 Over last years two main AWES applications emerged. The first makes use of the mobile nature of the technology which allows the deployment in inaccessible or remote places such as temporary mines or remote off-grid communities as these locations often rely on expensive diesel generators. Second is the grid-scale integration of AWES, which requires upscaling the systems to compete with fossil and renewable energy sources in the energy market. One example is Ampyx Power (Ampyx) which aims to re-power decommissioned offshore wind farms or deploy floating platforms, expecting higher energy yield due 35 to better wind conditions, which in combination with design choices lead to lower levelized cost of electricity. Additionally, setting up AWES offshore allows for safer operation and is likely to be socially more accepted (Ellis and Ferraro, 2016). We therefore investigate the scalability and design space of small to large-scale AWES, both offshore and onshore. Depending on the aircraft's wing surface area, aerodynamic coefficients and the tether diameter, rated power ranges from P rated = 145 kW to 199 kW for A wing = 10 m 2 and P rated = 2010 kW to 3430 kW for A wing = 150 m 2 . We compare the optimal system 40 performance subject to various wing mass for representative onshore and offshore wind conditions.
In comparison to the commonly used logarithmic wind speed profile, this WRF-derived set of wind data includes the wind direction rotation with height and the complex range of profile shapes emerging from atmospheric stability. This includes almost constant wind velocity profiles associated with unsteady stratification, high sheer wind velocity profiles resulting from stable conditions, as well as non-monotonic wind velocity profiles including low level jets (LLJs). The power output of an AWES 45 not only depends on the wing size, but also the prevalent wind velocity profile shape and magnitude which result in distinct trajectories and operating altitudes. Therefore, a representative wind data set up to mid-altitudes, here defined as heights above 100 m and below 1500 m, is necessary to determine realistic AWES performance. This study relies on mesoscale numerical weather prediction models such as the Weather Research and Forecasting (WRF) model, which is well known for conventional WT siting applications (Salvação and Guedes Soares, 2018;Dörenkämper et al., 2020), as measuring wind conditions 50 at mid-altitudes is difficult due to reduced data availability aloft (Sommerfeld et al., 2019a). To reduce the computational cost, 10-minute average wind speed profiles were clustered using the k-means clustering method described in (Sommerfeld, 2020).
We compare AWES performance for an onshore location in northern Germany near Pritzwalk (Sommerfeld et al., 2019b) and an offshore location at the FINO3 research platform in the North Sea. These wind clustered wind conditions were implemented into the awebox (Leuthold et al., 2020) optimization framework which computes periodic flight trajectories that maximize 55 average mechanical power output.
In comparison to our previous studies, which derived onshore and offshore AWES power curves, this paper explores the AWES design space from small to to utility-scale. We aim at setting up-scaling design and mass targets, instead of a detailed system design. While other studies rely on simplified logarithmic wind speed profiles or reanalysis data sets, we optimize supports decision-making regarding location-specific design, power estimation and scaling limitations.
Section 2 summarizes the onshore and offshore wind resource as well as the clustering results. For a detailed description of the WRF model and clustering algorithm see (Sommerfeld, 2020). Section 3 briefly introduces the AWES model and optimization method as well as the implemented constraints and initialization. Section 4 compares the results for six AWES sizes with three different mass scaling assumptions and two sets of non-linear aerodynamic coefficients. We present, inter alia, trajectories, power curves and annual energy production estimates for for a representative onshore and offshore location.
Finally, Section 5 concludes the article with an outlook and motivation for future work to continue to advance AWES towards commercial reality.
Both horizontal velocity components of the resulting mesoscale wind data set are clustered using a k-means clustering algorithm (Pedregosa et al., 2011). According to previous investigations (Sommerfeld, 2020), a small number of clusters with few representative profiles per cluster yield good power and AEP estimates at reasonable computational cost. Therefore, the 75 wind velocity profiles were grouped into k=10 clusters from which the 5th, 50th and 95th percentile (sorted by wind speed at 200 m) were implemented into the optimization algorithm as design points to cover the entire annual wind regime.
The resulting average wind velocity profiles for each of the ten clusters, also known as centroids, are shown in the top row of figure 2. For presentation purposes, only each centroid's wind speed magnitude, colored according to average wind speed up to 500 m, is shown. The complete set of clustered profiles profiles are shown in grey. The cluster average wind profile 80 shapes show wind shears typically associated with unstable and stable conditions. They follow expected location-specific trends with lower wind shear and higher wind speeds offshore (right) in comparison to onshore (left). The associated, color-coded annual centroid frequency is shown in the center. The bottom subfigures summarize the wind speed probability distribution at a reference height of 100 ≤ z ≤ 400 m. We chose this reference height as a proxy for wind speed at operating altitude, because an a priori estimation is impossible, and onshore and offshore power curves are almost identical using this reference 85 wind speed. For a detailed description of the WRF model and setup, the clustering process as well as the correlation between clusters and stability conditions see (Sommerfeld, 2020).

AWES trajectory optimization model
The investigation of the scaling potential of AWESs not only requires understanding of wind conditions at higher altitudes, but also of AWES power production, which is intrinsically linked to the aircraft's flight dynamics, as the AWES never reaches a steady state over the course of a power cycle. Hence power output estimation based on steady-state simplifications are generally not suited for describing the effects of realistic wind profiles or varying system parameters on the power output over the entire operational window. Therefore we make use of optimal control methods to compute power-optimal, dynamically feasible flight trajectories that satisfy operation constraints such as flight envelope and structural system limits.

Model overview 95
We compute ground-generation AWES power cycles by solving a periodic optimal control problem which maximizes the cycle-average AWES power output P . In periodic optimal control, the system state at the initial and final time of the trajectory must be equal, but are chosen freely by the optimizer. This methodology, implemented in the open-source software framework awebox (Leuthold et al., 2020), is used to generate power-optimal trajectories for single-wing ground-generation AWES sizes with various wing area, mass and aerodynamic performance. Table 1 summarizes the imposed constraints for each system 100 design.
The AWES model considers a 6 degree of freedom rigid-wing aircraft model with pre-computed quadratic lift, drag and pitch moment coefficients, which is controlled via aileron, elevator and rudder deflection rates. For this scaling study, the Ampyx 5 https://doi.org/10.5194/wes-2020-123 Preprint. Discussion started: 20 November 2020 c Author(s) 2020. CC BY 4.0 License.
AP2 reference model (Ampyx;Malz et al., 2019) serves as a base from which the aircraft size and mass as well as aerodynamic coefficients were scaled (see sections 3.3 and 3.4).

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While the ground station dynamics are not explicitly modeled, constraints on tether speed, acceleration and jerk are implemented to ensure a realistic operating envelope. For this study a reel-out to reel-in ratio of 2 3 ( vout vin = 10 ms −1 15 ms −1 ) was chosen. Tether accelerationl max = 10 ms −2 and tether jerkl max = 100 ms −3 were limited to simulate generator torque constraints.

Wind profile implementation
The 2D horizontal wind velocity profiles were clustered into k=10 clusters. Three representative profiles from each cluster as well as each cluster's centroid, rotated such that the main wind direction u points in positive x direction and the deviation v from it points in positive y direction, were implemented. This assumes omnidirectional AWES operation, which simplifies the comparison of results. We interpolate the u and v components using Lagrange polynomials to obtain a twice continuously 115 differentiable function representation of the wind velocity profiles, which is necessary formulate an optimal control problem that can be solved with the gradient-based nonlinear programming (NLP) solver IPOPT (Wächter and Biegler, 2006).

System scaling
Aircraft mass m and inertia J are scaled relative to the Ampyx AP2 reference model (Malz et al., 2019;Ampyx) according to simplified geometric scaling laws relative to wing span b (see equation 1). The mass scaling exponent κ ranges from 2.7 to 3.3. 120 An exponent of 3 represents pure geometric scaling, while κ = 2.7 implies positive scaling effects and weight savings with size, while κ = 3.3 assumes negative scaling. Based on the wing area, maximum tether force and diameter are scaled while tether speed and acceleration constraints are kept constant.
Makani's openly published technical reports describe their "M600 SN6" as well as their MX2 (Oktoberkite) design, which redesigned the M600 air frame to overcome some of its shortcomings and produce P MX2 = 600 kW at a wind speed of 125 U MX2−ref = 11 ms −1 at operating height (Echeverri et al., 2020). Note that Makani's on-board-generation concept is inherently heavier than the ground-generation concept considered here, because of propellers, generators and supporting structures. The intended M600 design specified a mass of 919 kg, which corresponds to an AP2 mass scaling exponent of κ = 2.72. The asbuilt M600 had a wing area of A wing = 32.9 m 2 and a mass m M600 = 1730.8 kg. If we scale the AP2 reference aircraft to the same wing area and mass, the corresponding mass scaling exponent is κ = 3.23. The air frame of the improved MX2 design 130 aimed at m MX2 = 1852 kg for a wing area of A MX2 = 54 m 2 , equivalent to κ = 2.72 relative to the AP2 reference. Similarly, WT mass scales with an exponent slightly below 3 based on rotor diameter (Fingersh et al., 2006).
(1)  (HL) (orange). Aerodynamic efficiency metrics: lift over drag, lift to drag ratio and c 3 L /c 2 D according to Loyd (Loyd, 1980). HL is derived by modifying the AP2 reference model, in accordance with the theoretical, as if high-lift devices, e.g. flaps and slats were attached.

Tether model
The tether is modeled as a single solid rod which can not support compressive forces. This is a good assumption when tether tension is high during the power production phase of the power cycle. Total tether drag is proportional to tether diameter d tether and tether length l tether . Both scale with tether tension, assuming a constant tensile strength, and therefore aircraft 150 size and wind speed (see subsection 4.6). The tether drag is approximated by dividing the tether into multiple elements (here n tether = 15 ) and calculating the apparent wind speed at each element individually, assuming a constant tether drag coefficient of c tether D = 1. Each elements tether drag is then equally divided between the two endpoints and finally transferred to either the aircraft or ground station. However, this leads to an underestimation of total tether drag at the aircraft (Leuthold et al., 2018).
Similarly, the total tether weight W tether , calculated with a constant material density of ρ tether = 970 kgm −3 , is distributed 155 evenly between the aircraft and ground station.
Tether force constraints are chosen such that the system's rated power is achieved for a logarithmic wind speed profile with U sizing (z = 200 m) ≈ 10ms −1 (U sizing (100 ≤ z ≤ 400 m) ≈ 10 ms −1 ), similar to wind at hub height for conventional wind turbines. The tether diameter is calculated assuming a maximum allowable tether stress σ tether = 3.6 · 10 9 Pa and a safety factor SF tether = 3.

Constraints
As previously mentioned, the AWES model solves an optimal control problem to maximize average cycle-power. These constraints include system dynamics, material properties, aircraft and ground station hardware constraints as well as flight envelope limitations. These limitations contain a minimum operating height (z min operation ) as well as a maximum tether length to maintain safe operation. Additionally, an apparent flight speed constraint of v app ≤ 80 ms −1 for all aircraft sizes was imposed to reduce 165 the mechanical wing load. The maximum tether stress and force, from which the tether diameter is calculated, together with the periodicity constraint are some of the most important path constraints. Ground station hardware limitations such as torque and acceleration dynamics are not explicitly modeled, but implemented as tether speed, acceleration constraints. A fixed angle of attack α and side slip angle β range ensures operation within realistic bounds. However, neither angular constraint is active during flight, because the optimizer tries to achieve an angle of attack close to the maximum of c L , c D and c m (see figure 3).

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Due to weight and drag effects, actual angle of attack is closer to α ≈ 10 • during reel-out for the majority of wind speeds.
Table 1 summarizes constraints and system sizes.

Initialization
The AWES dynamics are highly non-linear and therefore result in a non-convex optimal control problem which possibly has multiple local optima. Therefore, the particular results generated by a numerical optimization solver can only guarantee local 175 optimality, and usually depend on the chosen initialization The optimization is initialized with a circular trajectory based on a fixed number of n loop = 5 loops at a 30 • elevation angle and an estimated aircraft speed of v init = 10 ms −1 . Previous analyses showed that the convergence of large AWES highly depends on initial tether length. Larger systems become less sensitive to tether drag and hence can drag along a longer tether, because lift to tether drag ratio scales linearly with wing span. Therefore, initial tether length is increased linearly with aircraft wing area (see table 2).

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In order to solve the highly nonlinear optimization problem, an appropriate initial guess is generated using a homotopy method similar to those detailed in (Gros et al., 2013;Malz et al., 2020). This technique gradually relaxes the problem from simple tracking of circular loops to the original nonlinear path optimization problem where the previous result serves as an initial guess for the following problem. The resulting problem is formulated in the symbolic modeling framework CasADi for linear solver MA57 (HSL) . We compare 6 AWES sizes with three different mass properties and two sets of nonlinear aerodynamic coefficients each to investigate the AWES design space and upscaling potential. Furthermore, we contrast AWES performance at representative onshore (Pritzwalk in northern Germany) and offshore locations (FINO3 research platform in the North Sea) based on one year 190 of WRF simulated and k-means clustered wind data. To that end, we show representative optimized trajectories (subsection 4.1) and compare typical operating altitudes and tether lengths (subsection 4.2). We estimate reaction forces and bending moments based on the assumption of an elliptical lift distribution (subsection 4.3). Subsection 4.4 analyses AWES power curves for each design and determines an AWES power coefficient based on swept area and wing chord. From this we derive the annual energy production (AEP) in subsection 4.5 for each location and system configuration. We examine the predicted power losses 195 (subsection 4.7) due to tether drag. Finally, we establish an upper limit of the weight to lift ratio and compare tether drag forces in subsection 4.6.

Flight trajectory and time series results
Due to the high level of model and problem non-linearity, the solution of the optimization algorithm can only guarantee local optimality. However, the generated trajectories, shown in figures 4 and A1 (center) for a representative AWES with a wing 200 area of A wing = 50 m 2 and κ = 3 and seem reasonable, are within the set constraints, and are consistent with other studies (De Schutter et al., 2019;Sommerfeld, 2020). It is striking that higher wind speed trajectories above rated power often deviate from the expected trajectory, which occur at lower wind speeds. The system tries to de-power by moving out of the wind window, either upwards or perpendicular to the main wind direction, to stay with in the tether force, tether speed and flight speed constraints, while still maximizing average power. Subsection 4.2 further analyzes the trend towards longer tethers and 205 higher operating altitude with increasing wind speed, which can be seen here as distance from the origin. The four sub-figures on the right display the lift force F L , tether speed v tether , the apparent, constrained wind speed v app and the instantaneous power p current time series for the corresponding trajectories. Both the production (reel-out) and recovery phase (reel-in) are clearly distinguishable by the transition to negative tether speed and power. Total cycle time seems independent of wind speed and solely determined by the number of loops and tether length used to initialize the optimization. However, 215 previous investigations showed that AWES power output seems to be insensitive to both number of loops (here n loop = 5 for all setups) and flight time.
Looking at the periodic nature of the lift force gives an insight into the load cycles AWES need to withstand during longterm operation. During the production phase the aerodynamic loads oscillate about a constant base load with a periodicity of approximately 8 to 15 seconds depending on aircraft size and wind speed which is comparable to the rotational speed of 220 a conventional wind turbine. Additionally, aerodynamic loads drop to almost zero during the recovery phase as the aircraft returns to it's initial position and the tether is reeled in. Subsection 4.3 further investigates the resulting wing peak loads.
During the production phase tether speed repeatedly drops to zero for an extended period of time, especially at lower wind speeds. This is caused by insufficient lift during the ascent of the aircraft as the system can not produce enough aerodynamic force to pull the tether and overcome gravity. Simultaneously as a consequence power drops to zero and ramps up again, 225 following the flight cycle. To alleviate this inherent intermittency, buffering the energy or coupling multiple, phase-shifted AWES in a wind farm setup would be beneficial (Malz et al., 2018). The reel-out speed only remains positive during the entire production phase at higher wind speeds or for aircraft with higher aerodynamic lift. During the recovery phase tether speed quickly reaches it's minimum of v tether = 15 ms −1 to keep this phase as short as possible and reduce power loss. The angle of attack remains moderate to stay close to optimal c 3 L /c 2 D . However, the angle of attack is generally higher than the theoretical 230 optimum to offset the weight and drag of the entire system.

Tether length and operating altitude
One of the major value propositions of AWESs is that they can tap into wind resources beyond the reach of conventional wind turbines. However, the choice of optimal operating height highly dependents on the wind speed profile and system design. Two opposing effects influence the optimal operating height. On the one hand, an increase in altitude is generally associated with an 235 increase in wind speed and therefore produced power. On the other hand, higher altitudes require a longer tether which result in higher drag losses and also increase the elevation angle which increase gravity-caused "cosine" losses . Figure 5 shows a trend towards longer average tether lengths l tether (top) and higher average operating altitudes z operating (center) with increasing system size for a representative scaling exponent of κ = 3 (see equation 1) and wind speed. We chose U ref to be the average wind speed between 100 m ≤ z ≤ 400 m as we previously found that this range is a good proxy for 240 conditions at operating height (Sommerfeld, 2020). Lighter aircraft and higher lift wings results in slightly higher operating altitudes, a longer tether and higher elevation angle (compare figure A2 in the appendix).  Outliers, e.g. for high wind speed profiles (compare figure 2), are likely local optima of the highly nonlinear trajectory optimization problem described in section 3.
As wind speed increases beyond rated power (U ref ≈ 10 ms −1 , see figures 7 and A3), the aircraft moves out of the wind 245 window to de-power. This is seen as rising average elevation angles ε (bottom) above U ref = 10 ms −1 . Results for both offshore (right) and onshore (left) follow the same trends, but operating heights below rated wind speed are lower offshore because of lower wind shear and higher wind speeds.
It is important to keep in mind that even though the operating height exceeds 500 m for wind speeds of more than U ref ≈ 15 ms −1 such wind speeds occur only about 10 % of the time (see figure 2). Between 5 and 15 ms −1 , the most likely wind speed 250 range, operating heights both onshore and offshore are between 200 to 300 m. For smaller system sizes these heights are even lower. While this is slightly above the hub-height of current conventional wind turbines, it rebuts the argument of harvesting wind energy beyond this altitude. These findings are consistent with current offshore WT trends, whose rotor diameter increased significantly while hub height only increased marginally over the last years. However, it is likely that offshore hub heights will

Reaction forces and moments
We analyze wing loads since detailed design of the aircraft and wing box is beyond the scope of this paper. Weight is neglected as it is an order of magnitude smaller than the aerodynamic lift force. We assume an elliptic lift distribution ( Plotting the cycle-average power P , derived from 3 representative profiles from each of the 10 wind velocity clusters, over reference wind speed produces typical wind power curves as seen in figure 7 (top). As of now, no standard reference wind 280 speed U ref , equivalent to wind speed at hub height for conventional WT, has been agreed upon for AWES. Furthermore, using this altitude range results in comparable power curve trends onshore and offshore.  Missing data in figure 7 originate from an infeasible combination of constraints and boundary conditions, mostly related to a heavy aircraft and insufficient wind speeds. This results in a minimal cut-in wind speed for each system. However, instead of a gradual increasing from zero, the optimizer finds a feasible solution above cut-in wind speed with power closer to rated power 290 (see A wing = 80, 100 m 2 in figure A4 or A wing = 150 m 2 in figure 7). Higher system mass does not seem to affect rated power, which is determined by tether tension and tether speed constraints (i.e. no direct generator constraint) only cut-in wind speed.
No cut-out wind speed limitations were implemented. Therefore, wind power is only limited by each location's maximum wind speed, which is significantly higher offshore (compare figure 2). All system sizes reach rated power at about U ref = 10 ms −1 , because the tether diameter of each AWES configuration was sized for this reference wind speed (see subsection 3.5). We 295 defined the same tether diameter for both onshore and offshore location. However, offshore AWES design could benefit from a larger tether diameter as wind speeds are generally higher (see figure 2). This would result in higher rated power and a higher AEP (see subsection 4.5). Higher lift coefficients result in higher rated power and a steeper power increase up to rated power.
Power variations are caused by local optima mostly occurring above rated wind speed as the system de-powers to stay within tether force and flight speed constraints (see subsection 3.6).

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In contrast to (Sommerfeld, 2020) the flight path length l path (figure 7 second from top) remains almost constant with wind speed. In comparison to this previous study overall path length is lower, which is probably due to the lower mass scaling exponent of κ = 2.3. Path length increases with system size and mass due to higher inertia, longer tether length and an increased minimal turning radius. We estimate AWES power coefficients c AWES p to simplify the AWES power estimation and to compare AWES performance.
We derive the power coefficient (see equation 3) from the cycle average power P , the swept area A swept (wing span b wing multiplied by path length l path ) and reference wind speed U ref , similar to conventional WTs. Since determining the wind speed along the flight path before deployment is impossible, we use average wind speeds between 100 m and 400 m as a proxy. The resulting trends shown in figure 7 (third from top) decrease non-linearly with wind speed, which can be attributed to different trajectories and increased losses associated with a longer tether, i.e. tether drag and weight. The AWES power coefficients 310 seem to converge for wing areas larger than A wing ≥ 50 m 2 , while c AWES p of the smallest two aircraft sizes A wing = 10, 20 m are significantly lower. A possible explanation is that smaller wings have a higher tether drag to lift force ratio, which might reduce the power coefficient. As expected, aerodynamic efficiency highly affects AWES power coefficients, with HL values almost doubling in comparison to the AP2 reference (compare figure 7 with A3 in the appendix).
Scaling the power coefficients with each system's wing chord c wing collapses results onto a single curve (bottom). A possible 315 explanation for this is that the mechanical power of a ground-generation AWES, which is the product of tether force and tether speed, scales with both wing area and path length. Path length increases with system size, but total cycle times remain almost constant, which results in an increased average flight speed (see subsection 4.1).

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We estimate the annual energy production (AEP) and capacity factor cf (equation 4) from the previously described power curve P (subsection 4.4) and annual wind speed probability distribution f , derived from the histogram of annual wind speeds seen in the bottom subfigure of figure 2.
Rated power P rated is defined from optimization results, as the a priori estimation of nonlinear, trajectory dependent losses is difficult. Figure 8 compares the impact of aerodynamic efficiency by contrasting the previously described power curve (top) for AWESs with a wing area of A wing = 50 m 2 and a mass scaling exponent of κ = 2.7. Data for high lift aerodynamic coefficients are highlighted by a circle while AP2 reference data is marked by a square. Wind conditions are the p5, p50, p95 percentile onshore (blue) and offshore (orange) wind velocity profiles for each of the k=10 clusters. The center sub-figure summarizes the 330 wind speed probability distribution between 100 ≤ z ≤ 400 m which stands in as a proxy for wind at operating altitude (see section 2). As expected, higher wind speeds are more likely to occur offshore (FINO3) than onshore (Pritzwalk). However, very high wind speeds above U ref > 18 − 20 ms −1 , beyond the cut-off speed of realistic wind energy converters, have a very low chance occurrence at both locations. The resulting annual average energy production distribution E (bottom) reveal a clear difference between the offshore and onshore energy potential. Better wind conditions offshore lead result in higher AEP and cf.
Higher aerodynamic efficiency increases rated power and power up to rated wind speed. Therefore, AEP and cf almost doubles for HL in comparison to the AP2 reference, highlighting the importance of exploring high lift configurations.  Figure 9 compares the AEP and cf estimates for all system sizes scaled with a mass scaling exponent of κ = 2.7. AEP increases almost linearly with wing area (top), because power, which is the product of tether force and tether speed, scales with wing area. Tether force scales linearly with wing area and maximum tether speed is kept constant throughout all optimization 340 runs. As expected HL aerodynamic coefficients (circle) outperform the AP2 reference (square). Offshore (orange) AEP and cf is generally higher than onshore (blue) because higher wind speeds are more likely. Overall cf (bottom) remains almost unchanged for wing sizes up to A wing = 100 m and sharply declines for A wing = 150 m, due to the high number of infeasible solutions at lower wind speeds, equivalent to not being able to fly due to weight (see figure 7). The relatively high cf values are caused by the relativity low rated wind speed of U rated = 10 ms −1 . This leads to a design trade-off between generator size 345 relative to wing area and tether diameter, similar to conventional WT.
Onshore AEP and cf seems to outperform offshore for wing areas larger than 100 m 2 . This is likely caused by outliers, or wind velocity profile specific local minima, in the power curve (compare to power curve figure A5 in appendix) before rated wind speed (v rated = 10 ms −1 ), where the system seemingly overperforms.  offshore. Heavy configurations with no feasible trajectory at any wind speed result in missing data. While smaller systems seem almost unaffected by aircraft weight, mass scaling effects lead to significant reduction in AEP for larger AWES. This is particularly true for wings with aerodynamic reference coefficients (AP2, square) and onshore wind conditions. Combining results from both figure 9, which already shows diminishing returns in AEP and cf with increasing wing area for the lightest, idealized aircraft mass scaling, and figure 10, which predicts that AEP will only decline for heavier mass scaling, conveys that 355 upscaling AWES is only beneficial with significant weight reduction. These results hint at the existence of an upper limit of AWES weight relative to AWES size or lift (see subsection 4.6), which is plausible since mass scales with aircraft volume and lift scales with aircraft area. Therefore and for compensating power fluctuation caused by the cyclic nature of ground-generation AWES, it is likely better to deploy multiple smaller scale devices rather than a single large-scale system. Determining the ideal, site-specific AWES size needs to be determined by realistic mass scaling and the local wind resource.  . AEP ratio for mass scaling exponent κ = 3 (dashed lines) and κ = 3.3 (dotted lines) relative to AEP of κ = 2.7 over aircraft wing area Awing. Figure summarizes data for both onshore (blue) and offshore (orange) location as well as both sets aerodynamic coefficients HL (circle) and AP2 (square). Results are based on the cycle-average power P derived from p5, p50, p95 wind velocity profiles within each of the k=10 WRF-simulated clusters. Missing data points indicate that no feasible solution for any wind velocity profile was found.

Weight and drag impact
The most effective AWES concept benefit from increased apparent wind speed during crosswind flight (Loyd, 1980), such as the ground-generation concept investigated in this study. Such crosswind trajectories, whether circular or figure-of-eight, always include an ascent during each loop where the aircraft needs to overcome gravity to gain altitude. This leads to a deceleration and therefore reduction of aerodynamic lift. AWESs with excess mass fail to overcome weight and drag and can no longer 365 climb.
With an increased wing area, the entire aircraft, particularly the load carrying structures such as the wing box, need to increase in size and weight in order to withstand increased aerodynamic loads produced. Aircraft mass scales with volume (m aircraft ∼ b 3 ; wing span b), assuming pure geometric scaling without design improvements, while lift force and therefore power only scales with the wing area (F lift ∼ b 2 ). Similarly, conventional WT power and AEP scales with the rotor diameter 370 square, while theoretic WT mass scales with the cube of the rotor diameter (Gasch and Twele, 2012). However, comparing both wind energy converters under these assumptions, AWES perform worse as their flight path degrades with increasing system size and mass. This can be attributed to the fact that AWES need to produce enough lift to carry their own weight to operate, while WT are supported by a tower.
These facts limit AWES size. The prevailing wind resource does not improve enough within the lower parts of the atmosphere 375 to produce sufficient aerodynamic lift to overcome the increased system drag and weight, associated with larger systems. Wind speed only increases marginally with height, especially offshore or at times of unstable of neutral stratification (compare figure   2). Furthermore, higher operating altitudes also lead to increased "cosine losses", unless offset by a longer tether which in turn results in more drag and weight. Better aerodynamics or lighter, more durable aircraft and tether materials can only push this boundary, but not overcome it.

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A comparison of tether weight W tether during the production phase (reel-out) to total system weight (W total = W aircraft + W tether ) in figure 11 (top) shows that the tether makes up 10 to 30 % of the entire system weight during these times. Note that the tether cross sectional area is sized with a safety factor of 3. Tether cross sectional area mostly scales with aerodynamic force and therefore wing area, while the aircraft weight scales with a mass scaling exponent κ = 2.7, 3.0, 3.3 which results in decreasing trend lines. This value is higher for high lift airfoils (circle) as the tether diameter is larger to withstand the higher 385 aerodynamic forces. For lighter aircraft, scaled with κ = 2.7 (dash-dotted), the portion of tether weight is higher, because the tether diameter remains constant while the aircraft mass is lighter.
The bottom sub-figure reveals that tether drag makes up about 15 to 40 % of the entire system drag during the production phase. Tether diameter d tether and therefore face area (A face tether = d tether l tether ) scales beneficially with wing area, leading to the downward trend. For this evaluation half the simulated tether drag is attributed to the aircraft and the other half to the 390 ground station. More detailed models could explore the impact of tether dynamics and tether drag in more detail.
It is critical for crosswind AWES to ascend during each loop of the production or reel-out phase. The aircraft needs to produce enough aerodynamic lift, which decreases as the aircraft slows down during ascent (compare 4), to overcome gravity and maintain tether tension. The top sub-figure in figure 12 contrasts the AWES equivalent of the aeronautic load factor, here defined as the ratio of average lift force L wing to total AWES weight W total , including aircraft and tether mass (cross 395 sectional safety factor of 3), during the reel-out phase for all aircraft sizes A wing = 10 − 150 m 2 , mass scaling exponents κ = 2.7, 3.0, 3.3 and aerodynamic coefficients HL, AP2. The average load factor decreases from about 10 -20 to 10 -5, depending on aerodynamic performance and mass scaling, which is approximately the maneuvering load factor of an acrobatic airplane n acrobatic = 6.0 (Federal Aviation Agency, 2017). For utility airplanes this value is about n utility = 4.4. The beneficial effect of better aerodynamics and mass scaling are clearly visible in a higher lift to weight ratio. High system mass with 400 insufficient lift on the other hand leads to infeasible solutions and missing data.
The bottom sub-figure of figure 12 shows a slight increase of average lift L wing to total average drag D total (including tether drag) ratio with increasing wing area. Overall however, this ratio remains almost constant around 14 -15. The decrease for A wing = 100, 150 m 2 , κ = 3 and AP2 aerodynamics is likely caused by local optimization minima and few feasible wind speed profiles. For this investigation half the tether drag is assigned to aircraft and the other half to ground station.

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No feasible solution of too heavy aircraft lead to missing data points. For example, no feasible solution could be found for a large-scale aircraft with an area of A wing = 150 m 2 , scaled with the lightest mass scaling exponent of κ = 2.7, and AP2  Figure 11. Percentage of cycle-average tether weight W tether to total weight W total (top) and tether drag D tether to total drag D total (bottom) during production phase (reel-out) for all aircraft sizes Awing = 10 − 150 m 2 , sets of aerodynamic coefficients AP2, HL and mass scaling exponents κ = 2.7, 3, 3.3 for wind data at the offshore location.
reference aerodynamic coefficients at low wind speeds U ref < 5 ms −1 . This can be seen in figure 13 which shows the average lift L wing to total weight W total , including tether and aircraft, ratio for all aircraft sizes with AP2 reference aerodynamic scaled with κ = 2.7 over reference wind speed . Lift to weight ratio increases up to U ref ≈ 5 ms −1 , above which it remains almost 410 constant. This can likely be attributed to the applied apparent flight speed constraint of U max app = 80 ms −1 which seems to already be achieved at this reference wind speed. These data suggest that the minimum viable load factor is about 5 (equivalent to a maximum viable weight to lift ratio of 20 %) for the given flight speed constraint.
The bottom subfigure of figure 13 shows the lift L wing to total drag D total , including tether drag, ratio over reference wind speed for all aircraft sizes scaled with κ = 2.7 and AP2 reference aerodynamic coefficients. Data for all aircraft sizes show a 415 similar trend with the lift to drag ratio halving from about 20 to 10. This decrease is primarily caused by longer tether lengths at higher wind speeds (compare figure 5), which results in more drag and weight. Heavier system weight also leads to an angle of attack α increase as the aircraft needs to produce more lift.

Power losses
Increased aircraft wing area not only leads to increased power potential, but is also accompanied by increased tether losses 420 due to weight and drag. Tether mass scales with aircraft wing area, because higher aerodynamic force requires a larger tether diameter, assuming constant tensile tether strength. Tether length increases with AWES size and wind speed (see subsection 4.2) which further increases tether drag and weight. Figure 14 compares the average power loss associated with tether drag P drag tether , relative to average cycle power P for all aircraft wing sizes A wing = 10 − 150 m 2 , mass scaling exponents κ = 2.7, 3.0, 3.3 and both sets of aerodynamic coefficients 425 (HL, AP2). The relative tether drag loss decreases with wing area, because tether diameter scales beneficially with the square root of the tether force which scales linearly with wing area (F tether simA tether ∼ d tether ).This scaling trend is encouraging, but counteracted and dominated by increasing tether and aircraft mass with wing area, highlighted in earlier sections. As expected, the high lift airfoil HL (dotted lines) experiences less relative drag loss than the AP2 reference airfoil (dashed lines), due to higher average cycle power.    AP2; κ = 2.7 HL; κ = 2.7 AP2; κ = 3 HL; κ = 3 AP2; κ = 3.3 HL; κ = 3.3 Figure 14. Ratio of cycle-average power losses due to tether drag P drag tether to avearge produced power P over aircraft size Awing for both sets of aerodynamic coefficients AP2, HL, all mass scaling exponent of κ = 2.7, 3.0, 3.3 and wind data at the offshore location.
This study presents AWES scaling trends and explores the AWES design space subject to representative onshore (Pritzwalk in northern Germany) and offshore (FINO3 research platform in the North Sea) wind conditions. We evaluate the impact of wing area and mass scaling as well as nonlinear aerodynamic properties on optimal trajectories, reaction forces and moments, power generation and AEP, based on the awebox power and trajectory optimization model. Our analyses estimate a maximum 435 average weight to average lift ratio (equivalent to a load factor of about 5) to allow viable AWES operation of about 20 %.
Our results imply the existence of an upper limit of AWES weight relative to AWES size or lift, which is plausible since mass scales with aircraft volume and lift scales with aircraft area. In comparison, conventional WT power scales with the square and mass with the cube of the rotor diameter. Under the same assumptions AWES performance scales worse because the aircraft needs to carry its own increasing weight, instead of being supported by a tower. Therefore, the optimal AWES size is always 440 defined by the maximum weight which the aircraft can support, subject to local wind conditions. In this work we described and analyzed ground-generation AWES scaling effects subject to realistic wind velocity profiles for a set of representative AWES. We compare the impact of several design parameters based on the Ampyx AP2 reference model. We analyze AWES performance for two sets of nonlinear aerodynamic coefficients, the AP2 reference and a wing with high lift airfoil. To assess AWES scaling potential, several wing areas between A wing = 10 − 150 m, with mass properties 445 scaled according to a geometric scaling law with three different mass scaling exponents κ = 2.7, 3.0, 3.3, were implemented into the awebox power and trajectory optimization toolbox. A representative set of k-means clustered onshore and offshore wind velocity profiles, derived from the mesoscale WRF model, were used to define wind inflow conditions. We discussed the impact of mass and system size on typical trajectories and time series data which confirms that instantaneous power can drop to zero during the reel-out phase. This is caused by insufficient lift as the aircraft tries to overcome 450 gravity and maintain tether tension. The minimum wind speed to sustain positive power production during the reel-out phase as well as tether length and average operating altitude increase with system size and weight. However, operating heights beyond 500 m are rare and mostly occur as the system de-powers above rated wind speed to stay within tether force and flight speed constraints. As these constraints become active, the resulting trajectory deforms and diverge from the expected paths seen for lower wind speeds. This is especially true for high lift airfoils as they reach these limits faster. Since detailed design and stress 455 analysis is beyond the scope of this paper, we limit ourselves to the estimation of maximum mechanical wing loads, assuming a elliptical lift distribution. Shear force scales linearly with wing area, while bending moment increases nonlinearly with wing area and wing span.
Analyzing the AWES power curve we determine that rated power scales linearly with wing area, assuming that tether speed constraint are kept constant and the tether diameter is adjusted appropriately. We chose to size the tether diameter so that 460 rated power is achieved at about U ref = 10ms −1 , independent of size, mass and location. A larger tether diameter would increase rated power and shift rated speed towards higher wind speeds, which might be beneficial for faster offshore wind conditions, but would impact tether drag and weight. Improving aerodynamic efficiency increases power production. For the sets of aerodynamic coefficients used in this study, average power increased by approximately 30% to 80 %, depending on wing area. We proposed the nonlinear AWES power coefficient c AWES p c −1 wing from the aircraft path length and wing area to 465 collapse power curves.
We estimate AEP and cf based on the power curve analysis and wind speed probability distribution at reference height between 100 ≤ z ref ≤ 400 m. Offshore AEP is generally higher than onshore, while the power curves are almost identical even though clustered profiles differ, due to higher wind speeds. Increased aircraft mass leads to significant reduction in AEP, as lower wind speeds become infeasible to fly in until finally no feasible solutions, even at higher wind speeds, can be found. This 470 is particularly true for the onshore location and AP2 reference aerodynamics, as these conditions do can not produce sufficient lift force to overcome system weight. Wind farm setups might therefore benefit from the deployment of multiple smaller AWES rather than few large-scale AWES. This could also reduce the overall power loss when synchronizing the flight trajectories of AWESs within a farm. Determining the ideal, site-specific AWES size needs to be determined subject to realistic mass scaling, the available area and the local wind resource.

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Furthermore, we describe the tether contribution to total weight and drag relative to aircraft wing size as well as tetherassociated power losses. Our results show that even though relative tether power losses decrease with wing size, they still use up a significant portion (20 -60 %) of the average mechanical AWES power.
Lastly, we try to determine the maximum AWES weight to lift ratio. Our data shows that total AWES weight, including tether and aircraft, should not exceed 20 % of the produced aerodynamic lift to operate. The limitation of crosswind AWES 480 operations seems to be the upward climb within each loop. During this ascent the aircraft decelerates by approximately 20%-25%, which reduces aerodynamic lift by about 35% -45%, which could be offset by the deployment of additional high-lift devices. As a result the system can not produce enough lift to overcome gravity and maintain tether tension, leading to a reduction in tether speed and produced power up until a complete drop to zero for lower wind speeds.
6 Future work 485 Defining the AWES design space subject to realistic wind conditions and operating constraints is crucial for scaling this technology for large-scale deployment of grid-integration. We therefore propose to build upon this study and further investigate the design space using design optimization. A possible approach is to utilize the already existing AWES power and trajectory optimization toolbox awebox and implement it into a design optimization framework that varies parameters such as aspect ratio, wing area and wing box dimensions. Adding a cost model would allow to optimize for levelized cost of electricity.

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Analyzing the dynamic aircraft wing loads caused by the cyclic nature of crosswind AWES and turbulence could improve AWES durability and further explore AWES design by considering fatigue loads to explore wing concepts to minimize κ.
Ultimately, AWES must compete with conventional wind. Scaling and moving offshore are logical goals for both technologies.
The relative merits of large-scale AWES must be further explored to set design and development targets, particularly since this study highlighted that offshore AWES are not particularly beneficial relative to conventional wind, given the generally lower