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A Linear Programming Approach to Backtracking for Single-Axis Trackers on Rolling Terrain

In this article, we present a computationally efficient method for determining optimal backtracking rotations for single-axis solar trackers on nonuniform terrain. The method allows for ganged tracking, mechanical rotation constraints, uneven row spacing, and arbitrary maximum allowable shaded fractions (to enable “fractional backtracking”). As with previous 2-D approaches, the method is suitable for terrain that varies in the transverse direction with respect to the rotation axis of the trackers. The novelty of the method lies in formulating the problem of shade avoidance as a linear problem, which is achieved by using the row interception width as the optimization variable instead of rotation angles. Formulating backtracking as a linear problem enables the use of extremely efficient linear programming algorithms, making the method highly scalable, requiring less than 1 min to compute optimal rotation schedules for hundreds of trackers. It also produces more effective backtracking rotations, reducing the frequency of shading by 4× and improving system energy output by 1%–2%.

Optimization

Performance Improvements Through Advanced PV Backtracking on Uneven Terrain

The climatic sensitivity of new terrain-aware backtracking algorithms is evaluated across 800 locations in the continental USA on a representative synthetic rolling terrain. We find that a global optimization approach to backtracking results in climate-specific annual energy gains of 2.4%–3.2% relative to a traditional backtracking algorithm baseline. We identify a strong logarithmic correlation between local diffuse fraction and yield improvement, and highlight the effect of seasonal precipitation on performance gains. We also find that a backtracking approach, which approximates the terrain as constant, does not offer significant annual energy gains over the baseline on the synthetic terrain. Our findings suggest that specific yield from backtracking in the USA can be improved by as much as 88 kWh/kW by considering terrain when selecting a backtracking algorithm.

Backtracking

Spectral scales in the atmospheric boundary layer

Wind data taken from 10 levels between 18 and 305 m were examined to determine the properties of atmospheric turbulence within and above the atmospheric surface layer into the PBL. The samples were averaged over 40 min intervals, with all periods of rain, fog, and other disturbances being eliminated from the 16 days of monitoring. Turbulence spectra were calculated using a fast Fourier transformation. The tower was located in rolling terrain covered with pine forests, waist-high scrub, and cultivated fields. Results are presented for the wavelength and Eulerian length scales, considering the neutral, stable, and unstable PBL. Correlation coefficients were found between velocity fluctuations and wavelengths for the stability classes. Good agreements were found for measured and computed spectra in all but unstable conditions.

Weber, A. H.

Interpretation of laser/multi-sensor data for short range terrain modeling and hazard detection

A terrain modeling algorithm that would reconstruct the sensed ground images formed by the triangulation scheme, and classify as unsafe any terrain feature that would pose a hazard to a roving vehicle is described. This modeler greatly reduces quantization errors inherent in a laser/sensing system through the use of a thinning algorithm. Dual filters are employed to separate terrain steps from the general landscape, simplifying the analysis of terrain features. A crosspath analysis is utilized to detect and avoid obstacles that would adversely affect the roll of the vehicle. Computer simulations of the rover on various terrains examine the performance of the modeler.

Messing, B. S.

The influence of wind shear on aerodynamic coefficients

The purpose of this study is to investigate the influence of wind shear on the lift, drag, roll and yaw moments of a wing in a horizontal wind gradient at various elevations and roll angles. The models of wind shear considered are those proposed by Leurs (1973) for atmospheric flow over horizontally homogeneous and uniform terrain. A general series solution for the distribution of lift along the wing span following the method of Houghton and Brock (1970) is employed to compute the loads and moments on the airfoil. Results of the computations indicate that wind shear can have a significant effect on the rolling and yawing moments of the wing of an aircraft flying with one wing low in the atmospheric boundary layer. These moments are directly influenced by the magnitude of the wind gradient in the neutral atmosphere reflected by the magnitude of the friction velocity. The effect of wind shear on lift and drag is negligible. Stability of the atmosphere tends to increase the magnitude of the rolling moment while decreasing its variation with elevation.

Frost, W.

Preliminary geologic terrain map of Mercury

A geologic terrain map of Mercury has been constructed by use of the photogeologic methods employed for the moon and Mars. The oldest and most widespread unit, intercrater plains, forms nearly level to rolling surfaces on which are superposed numerous secondary impact craters. This unit may represent a very old surface that predates the last heavy bombardment of the inner planets. The effects of this bombardment are recorded in a second widespread unit, heavily cratered terrain, consisting of closely spaced craters and basins from 30 km to several hundred kilometers in diameter. Units formed by excavation of the 1300-km-diameter Caloris basin are widespread on one hemisphere of the planet. The development of the Caloris basin was followed relatively quickly by emplacement of widespread plains materials, most of which are probably volcanic.

Trask, N. J.

Sources of low-level wind shear around airports

Some potential sources of low-level wind shear in and around airports and their likely effects are probed and analyzed. Wind shear over flat terrain with near-homogeneous surface properties (roughness, specific heat), the turning layer, shear flows over inhomogeneous terrain (airport + urban areas), thunderstorms, turbulent flowfields over bluff bodies (individual buildings), and recirculating wake flow downstream of three-dimensional block bodies are among the topics covered. Overshoot or undershoot of runways, and induced moments (pitch, roll, yaw) in takeoff and landing, and other potential hazards traceable to wind shear patterns at low heights are discussed, with emphasis on mean flow or steady-state wind shear (time-averaged, say 2-min averaged, wind fields). Wind tunnel studies and V/STOL operations are included in the study.

Fichtl, G. H.

A piloted simulator study on augmentation systems to improve helicopter flying qualities in terrain flight

Four basic single-rotor helicopters, one teetering, on articulated, and two hingeless, which were found to have a variety of major deficiencies in a previous fixed-based simulator study, were selected as baseline configurations. The stability and control augmentation systems (SCAS) include simple control augmentation systems to decouple pitch and yaw responses due to collective input and to quicken the pitch and roll control responses; SCAS of rate-command type designed to optimize the sensitivity and damping and to decouple the pitch-roll due to aircraft angular tate; and attitude-command type SCAS. Pilot ratings and commentary are presented as well as performance data related to the task. SCAS control usages and their gain levels associated with specific rotor types are also discussed.

Chen, R. T. N.

Method for predicting impulsive noise generated by wind turbine rotors

Large wind turbines can generate both broad band and impulsive noises. These noises can be controlled by proper choice of rotor design parameters such as rotor location with respect to the supporting tower, tower geometry and tip speed. A method was developed to calculate the impulsive noise generated when the wind turbine blade experiences air forces that are periodic functions of the rotational frequency. This phenomenon can occur when the blades operate in the wake of the support tower and the nonuniform velocity field near the ground due to wind shear. Results from this method were compared with measured sound spectra taken at locations of one to two rotor diameters from the DOE/NASA Mod-1 wind turbine. The calculated spectra generally agreed with the measured data in both the amplitude of the predominant harmonics and the roll of rate with frequency. Measured sound pressure levels far from the Mod-1 (15 rotor diameters), however, were higher than predicted. Simultaneous measurements in the near and far field indicated that the propagation effects could enhance the sound levels by more than 10 dB above that expected by spherical dispersion. These propagation effects are believed to be due to terrain and atmospheric characteristics of the Mod-1 site.

Viterna, L. A.

Soil moisture detection by Skylab's microwave sensors

The author has identified the following significant results. Terrain microwave backscatter and emission response to soil moisture variations were investigated using Skylab's 13.9 GHz RADSCAT (radiometer/scatterometer) system. Data acquired on June 5, 1973, over a test site in west-central Texas indicated a fair degree of correlation with composite rainfall. The scan made was cross-track contiguous (CTC) with a pitch of 29.4 deg and no roll effect. Vertical polarization was employed with both radiometer and scatterometer. The composite rainfall was computed according to the flood prediction technique using rainfall data supplied by weather reporting stations.

Moore, R. K.

Soil moisture detection by Skylab's microwave sensors

Terrain microwave backscatter and emission response to soil moisture variations are investigated using Skylab's 13.9 GHz RADSCAT (Radiometer-Scatterometer) system. Data acquired on June 5, 1973 over a test site in west-central Texas indicates a fair degree of correlation with composite rainfall. The scan mode was cross-track contiguous (CTC) with a pitch of 29.4 deg and no roll offset. Vertical polarization was employed with both radiometer and scatterometer. The composite rainfall was computed according to the flood prediction technique using rainfall data supplied by weather reporting stations.

Ulaby, F. T.

Equations of motion of the lunar roving vehicle.

Equations of motion have been formulated for a four-wheel vehicle as it traverses a terrain characterized by slopes, craters, bumps, washboards, or a power spectrum. Independent suspension and electric motor propulsion are considered. These equations were programmed on the UNIVAC 1108 digital computer. Results are given for the steerability of the Lunar Roving Vehicle (LRV) which was found to be satisfactory for normal operating speeds and turning radii. The vehicle was also found to be satisfactory against overturning in both the pitch and roll mode, and results are presented for various speeds as the LRV engages a bump on meter in diameter and of varying heights. Speed, power consumption, and load characteristics are presented for the LRV traversing a simulated lunar soil at full throttle. Comparisons are given against data compiled from the Apollo 15 mission.

Kaufman, S.

Effects of rotor parameter variations on handling qualities of unaugmented helicopters in simulated terrain flight

A coordinated analysis and ground simulator experiment was performed to investigate the effects on single rotor helicopter handling qualities of systematic variations in the main rotor hinge restraint, hub hinge offset, pitch-flap coupling, and blade lock number. Teetering rotor, articulated rotor, and hingeless rotor helicopters were evaluated by research pilots in special low level flying tasks involving obstacle avoidance at 60 to 100 knots airspeed. The results of the experiment are in the form of pilot ratings, pilot commentary, and some objective performance measures. Criteria for damping and sensitivity are reexamined when combined with the additional factors of cross coupling due to pitch and roll rates, pitch coupling with collective pitch, and longitudinal static stability. Ratings obtained with and without motion are compared. Acceptable flying qualities were obtained within each rotor type by suitable adjustment of the hub parameters, however, pure teetering rotors were found to lack control power for the tasks. A limit for the coupling parameter L sub q/L sub p of 0.35 is suggested.

Talbot, P. D.

Skylab program. Earth resources experiment package. Sensor performance report. Volume 7 (S190B): SL2, SL3 and SL4 evaluations

The S190B Earth Terrain Camera (ETC) operated acceptably for all of its scheduled EREP passes throughout the SL2 mission. The crew reported no problems in unstowing the camera, changing filters, installing the ETC window in the SAL, or installing the camera onto the window. The ETC was operated for a total of seven times with no failures. The clock on the ETC was checked on DOY 170 (June 19, 1973) and was found to be 30 min. and 58 sec. slower than GMT. The change in time was expected since a similar circumstance was experienced during ETC qualification testing for launch vibration. A leak existed in the seal of the spare magazine to the camera vacuum interface. For EREP passes 08 and 10, black-and-white film EK 3414 (roll no. 82) was installed in this spare magazine. Since there was an audible hiss, the vacuum hose was not connected to the camera. This caused the vacuum platen to be inoperable, resulting in some degradation in resolution for this roll of film. The vegetation of the South American jungle areas proved to be much darker than vegetation found in the United States, and was consequently about 1/2 stop underexposed in all cases.

Kenney, G. P.