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All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Assessing the Impact of Soil Layer Depth Specification on the Observability of Modeled Soil Moisture and Brightness Temperature

The utility of hydrologic land surface models (LSMs) can be enhanced by using information from observational platforms, but mismatches between the two are common.This study assesses the degree to which model agreement with observations (observability) is affected by two mechanisms in particular: 1) physical incongruities between the support volumes being characterized and 2) inadequateor inconsistent parameterizations of physical processes. The Noah and Noah-MP LSMs by default characterize surface soil moisture (SSM) in the top 10 cm of the soil column. This depth may be reasonable when comparing against soil moisture from in situ probes centered at 5 cm,but it is notably different from the 5 cm (or less) sensing depth of NASA’s Soil Moisture Active Passive (SMAP) satellite mission. These depth inconsistencies are examined by using thinner model layers in the Noah and Noah-MP LSMs and comparing resultant simulations to in situ and SMAP soil moisture. In addition, a forward radiative transfer model to simulate microwave brightness temperatures (Tbs) is used to facilitate direct comparisons of LSM-based and SMAP-based L-band Tb retrievals. Observability is quantified using Kolmogorov-Smirnov distance values, calculated from empirical cumulative distribution functions of SSM and Tb time series. Experiment results depend on the particular subspace being analyzed (SSM or Tb). This study concludes that therole of increasedsoil layer discretizationon LSM observability is secondary to the influence of component parameterizations, the effects of which dominate systematic differences with observations

SMAP↗
NASA NTRS2018

Evaluating the Assumptions in an Empirical Jet-Surface Interaction Noise Model

A set of empirical jet-surface interaction noise models, developed for single-stream round nozzles exhausting over a simple surface in a static ambient, are evaluated for use in more realistic applications that include multi-stream nozzle systems, multi-plane surface geometries, and a flight-stream. The simple-single-stream models have several advantages when used in system-level noise studies: they are robust, they are quickly computed, and they are generally applicable to a wide range of configurations. However, these models require simplifying assumptions when applied to more complex jet exhaust systems; for example, previous work on multi-stream jets used an empirical formula to compute a single-stream equivalent jet potential core length that could be used to predict the noise using simple-single-stream jet-surface interaction models. This paper considers the effect of flight and multi-plane surfaces using a similar approach: introducing assumptions to simplify the complex system, applying the simple-single-stream models, and evaluating the uncertainty.

Jet Noise↗
NASA NTRS2018

Evaluating the Assumptions in an Empirical Jet-Surface Interaction Noise Model

A set of empirical jet-surface interaction noise models, developed for single-stream round nozzles exhausting over a simple surface in a static ambient, are evaluated for use in more realistic applications that include multi-stream nozzle systems, multi-plane surface geometries, and a flight-steam. The simple-single-stream models have several advantages when used in system-level noise studies: they are robust, they are quickly computed, and they are generally applicable to a wide range of configurations. However, these models require simplifying assumptions when applied to more complex jet exhaust systems; for example, previous work on multi-stream jets used an empirical formula to compute a single-stream equivalent jet potential core length that could be used to predict the noise using simple-single-stream jet-surface interaction models. This paper considers the effect of flight and multi-plane surfaces using a similar approach: introducing assumptions to simplify the complex system, applying the simple-single-stream models, and evaluating the uncertainty.

Jet Noise↗
NASA NTRS2016

HST-STIS Spectra of Saturn's Rings and Implications for Their Reddening Agent

We obtained HST-STIS spectra of Saturn's main rings in May 2011, using the G230L (and G430L) gratings, with final averaged radial resolution of 160 (and 330) km/pixel. The dataset filled a previous 200-330nm "spectral gap" between Cassini and ground-based spectra. The data provide radial profiles as a function of wavelength, but our most basic product at this point is a set of very low-noise spectra, radially averaged over broad regions of the rings (A, B, C, and Cassini Division). The raw spectra required special processing to remove artifacts due to extended-source grating scatter. We have modeled the spectra using a new particle surface model, which corrects for on-surface shadowing due to the likely very rough ring particle surfaces, and avoids overestimation of intra-mixed "neutral absorber". We correct for non-classical layer effects and finite ring optical depth, and relate our observed reflectivities to the spherical albedos of individual smooth particles. We model these smooth particle albedos using standard Hapke theory for regolith grain mixtures that are either homogeneous and "intramixed" (nonicy absorbers dispersed in water ice regolith grains) or heterogeneous "intimate" mixtures. As candidates for the nonicy contaminants we have considered amorphous carbon, aromatic-rich and aliphatic-rich organic tholins, silicates, hematite and iron metal. For the A and B rings, we find that iron metal (including a new theoretical estimate of the refractive indices of nanometer-sized grains of iron) is not spectrally steep enough in the 200-300nm range, and that aliphatic-rich tholins are either too steep at short wavelengths or too flat at long wavelengths. However, less than 1% by mass of aromatic-rich tholins provides a very good fit across the entire spectral range with no gratuitous "neutral absorber" needed, and a minimum of additional free parameters. The best fits require forward-scattering regolith grains. For the C Ring and Cassini Division, additional absorbers are needed (updated results will be given).

Saturn's Rings↗
NASA NTRS2018

Improving the SMAP Level-4 Soil Moisture Product

The NASA Soil Moisture Active Passive (SMAP) mission generates, among other data sets, the Level 4 Soil Moisture (L4 SM) product. The L4 SM algorithm is based on the assimilation of SMAP radiometer brightness temperature observations into the NASA Catchment land surface model using a spatially distributed ensemble Kalman filter. The L4 SM data are published with a mean latency of approx. 2.5 days from the time of observation and provide global, three-hourly, 9 km resolution estimates of surface and root-zone soil moisture and related land surface states and fluxes. In 2018, the product was upgraded from Version 3 to Version 4. Underlying the new version is a revised modeling system that includes improved input parameter datasets for land cover, topography, and vegetation height that are based on recent, high quality space-borne remote sensing observations. Land cover inputs were updated to the GlobCover2009 product, which is based on satellite observations from the Medium Resolution Imaging Spectrometer. Topographic statistics now rely on observations from the Shuttle Radar Topography Mission. Finally, vegetation height inputs are derived from space-borne Lidar measurements. Additionally, SMAP Level-2 soil moisture retrievals and in situ soil moisture measurements were used to calibrate a particular Catchment model parameter that governs the recharge of soil moisture from the models root-zone excess reservoir into the surface excess reservoir. Specifically, the replenishment of soil moisture near the surface from below under non-equilibrium conditions was substantially reduced, which brings the models surface soil moisture more in line with the SMAP Level 2 and in situ soil moisture. Finally, the calibration of the assimilated SMAP brightness temperatures changed substantially from Version 3 to Version 4. Considerable effort went into the version upgrade, creating an expectation that the new version is improved over the old version. Indeed, some aspects of the new version are clearly better. However, other aspects are not, and on balance, the overall improvement is modest at best. In this presentation we summarize the skill of the new and old versions vs. independent in situ measurements and in terms of data assimilation diagnostics, including, for example, the statistics of the (soil moisture) analysis increments and the observation minus forecast (brightness temperatures) residuals. We share our experience with trying to improve to the L4 SM product and the lessons learned from the effort.

Reichle, Rolf↗
NASA NTRS2019

Analyzing Machine Learning Predictions of Passive Microwave Brightness Temperature Spectral Difference Over Snow-Covered Terrain in High Mountain Asia

Snow is an important component of the terrestrial freshwater budget in high mountainAsia (HMA) and contributes to the runoff in Himalayan rivers through snowmelt. Despitethe importance of snow in HMA, considerable spatiotemporal uncertainty exists across the different estimates of snow water equivalent for this region. In order to better estimate snow water equivalent, radiative transfer models are often used in conjunction with microwave brightness temperature measurements. In this study, the efficacy of support vector machines (SVMs), a machine learning technique, to predict passive microwave brightness temperature spectral difference (1Tb) as a function of geophysical variables (snow water equivalent, snow depth, snow temperature, and snow density) is explored through a sensitivity analysis. The use of machine learning (as opposed to radiative transfer models) is a relatively new and novel approach for improving snow water equivalent estimates. The Noah-MP land surface model within the NASALand Information System framework is used to simulate the hydrologic cycle over HMA and model geophysical variables that are then used for SVM training. The SVMsserve as a nonlinear map between the geophysical space (modeled in Noah-MP) andthe observation space (1Tb as measured by the radiometer). Advanced MicrowaveScanning Radiometer-Earth Observing System measured passive microwave brightness temperatures over snow-covered locations in the HMA region are used as training data during the SVM training phase. Sensitivity of well-trained SVMs to each Noah-MP modeled state variable is assessed by computing normalized sensitivity coefficients. Sensitivity analysis results generally conform with the known first-order physics. Input states that increase volume scattering of microwave radiation, such as snow density and snow water equivalent, exhibit a plurality of positive normalized sensitivity coefficients. In general, snow temperature was the most sensitive input to the SVM predictions. The sensitivity of each state is location and time dependent. The signs of normalized sensitivity coefficients that indicate physical irrationality are ascribed to significant cross-correlation between Noah-MP simulated states and decreased SVM prediction capability at specific locations due to insufficient training data. SVM prediction pitfalls do exist that serve to highlight the limitations of this particular machine learning algorithm.

high mountain Asia↗
NASA NTRS2022

The Simulation and Subseasonal Forecasting of Hydrological Variables: Insights from a Simple Water Balance Model

Past work has shown that a land surface model’s (LSM’s) implicit (not explicitly coded) relationships between soil moisture and both evapotranspiration (ET) and runoff largely determine the LSM’s hydrological behavior. Here we estimate the relationships that appear to be operating in the real world and compare them to those of the LSM component of a state-of-the-art Earth system model (ESM). The two sets of relationships are determined by calibrating them within a simple water balance model (WBM): once using stream gauge observations from small, unregulated rivers over the eastern half of the U.S., and once using the runoffs generated by the LSM as part of a state-of-the-art atmospheric reanalysis. Hydrological simulations and subseasonal hydrological forecasts performed with the two calibrated versions of the WBM provide two key results. First, the version calibrated to the LSM-generated runoffs does successfully reproduce, to first order, the hydrological behavior of the full LSM within its ESM environment. Second, of the two WBM versions, the one calibrated to the observations reproduces more accurately a broad collection of fully independent streamflow observations as well as a similarly broad collection of in-situ soil moisture measurements. Taken together, the two results suggest that the observations-calibrated ET and runoff efficiency functions do successfully represent, at least to some degree, soil moisture controls over hydrological variability in Nature and can serve as potentially useful targets for further LSM development.

Water Balance Model↗
NASA NTRS2014

A System of Conservative Regridding for Ice-Atmosphere Coupling in a General Circulation Model (GCM)

The method of elevation classes, in which the ice surface model is run at multiple elevations within each grid cell, has proven to be a useful way for a low-resolution atmosphere inside a general circulation model (GCM) to produce high-resolution downscaled surface mass balance fields for use in one-way studies coupling atmospheres and ice flow models. Past uses of elevation classes have failed to conserve mass and energy because the transformation used to regrid to the atmosphere was inconsistent with the transformation used to downscale to the ice model. This would cause problems for two-way coupling. A strategy that resolves this conservation issue has been designed and is presented here. The approach identifies three grids between which data must be regridded and five transformations between those grids required by a typical coupled atmosphere-ice flow model. This paper develops a theoretical framework for the problem and shows how each of these transformations may be achieved in a consistent, conservative manner. These transformations are implemented in Glint2, a library used to couple atmosphere models with ice models. Source code and documentation are available for download. Confounding real-world issues are discussed, including the use of projections for ice modeling, how to handle dynamically changing ice geometry, and modifications required for finite element ice models.

Ice-atmosphere↗
NASA NTRS1991

Development of a laser-induced heat flux technique for measurement of convective heat transfer coefficients in a supersonic flowfield

A technique is developed to measure the local convective heat transfer coefficient on a model surface in a supersonic flow field. The technique uses a laser to apply a discrete local heat flux at the model test surface, and an infrared camera system determines the local temperature distribution due to heating. From this temperature distribution and an analysis of the heating process, a local convective heat transfer coefficient is determined. The technique was used to measure the load surface convective heat transfer coefficient distribution on a flat plate at nominal Mach numbers of 2.5, 3.0, 3.5, and 4.0. The flat plate boundary layer initially was laminar and became transitional in the measurement region. The experimental results agreed reasonably well with theoretical predictions of convective heat transfer of flat plate laminar boundary layers. The results indicate that this non-intrusive optical measurement technique has the potential to obtain high quality surface convective heat transfer measurements in high speed flowfields.

Porro, A. Robert↗
NASA NTRS1991

A laser-induced heat flux technique for convective heat transfer measurements in high speed flows

A technique is developed to measure the local convective heat transfer coefficient on a model surface in a supersonic flow field. The technique uses a laser to apply a discrete local heat flux at the model test surface, and an infrared camera system determines the local temperature distribution due to the heating. From this temperature distribution and an analysis of the heating process, a local convective heat transfer coefficient is determined. The technique was used to measure the local surface convective heat transfer coefficient distribution on a flat plate at nominal Mach numbers of 2.5, 3.0, 3.5, and 4.0. The flat plate boundary layer initially was laminar and became transitional in the measurement region. The experimentally determined convective heat transfer coefficients were generally higher than the theoretical predictions for flat plate laminar boundary layers. However, the results indicate that this nonintrusive optical measurement technique has the potential to measure surface convective heat transfer coefficients in high speed flow fields.

Porro, A. R.↗
NASA NTRS1991

A laser-induced heat flux technique for convective heat transfer measurements in high speed flows

A technique is developed to measure the local convective heat transfer coefficient on a model surface in a supersonic flow field. The technique uses a laser to apply a discrete local heat flux at the model test surface, and an infrared camera system determines the local temperature distribution due to the heating. From this temperature distribution and an analysis of the heating process, a local convective heat transfer coefficient is determined. The technique was used to measure the local surface convective heat transfer coefficient distribution on a flat plate at nominal Mach numbers of 2.5, 3.0, 3.5, and 4.0. The flat plate boundary layer initially was laminar and became transitional in the measurement region. The experimentally determined convective heat transfer coefficients were generally higher than the theoretical predictions for flat plate laminar boundary layers. However, the results indicate that this nonintrusive optical measurement technique has the potential to measure surface convective heat transfer coefficients in high-speed flowfields.

Porro, A. R.↗
NASA NTRS2019

Quantifying Water Storage Change and Land Subsidence Induced by Reservoir Impoundment Using GRACE, Landsat, and GPS Data

The construction of hydropower dams is a common strategy to support a country's increasing need for electricityand river water management for industry and agriculture. Although the hydrological and geophysical impacts ofwater relocation are usually assessed prior to impoundment, their accuracy is generally limited due to the lack ofin situ observations, especially in a remote area. This study presents a workflow to quantify the terrestrial waterstorage change (TWS) and land subsidence induced by a reservoir's water impoundment using multiple satelliteobservations (GRACE, Landsat), land surface models (CABLE, GLDAS, NCEP, ECMWF), and GPS data. The studysite is the Bakun Dam, located in Sarawak, Malaysia, which is the largest hydropower dam in Southeast Asia.Commencing operation in late 2010, the dam induced a change of water mass and lake surface area that wasclearly observed by GRACE and Landsat observations, respectively. During the 17-month impounding period(from August 2010 to December 2011), GRACE observed a dramatic increase of approximately 200mmequivalent water height, while Landsat detected an increased lake extent of around 600 km2. In this paper, aforward model is developed to determine the increased water surface level corresponding to GRACE observations,estimated to be about 120 m. In contrast to GRACE, the TWS derived from land surface models cannotcapture the increased TWS, due to the lack of reservoir routing algorithms in the models. In addition, the landsubsidence was calculated using the disk load model constructed based on the GRACE-derived lake level andLandsat-derived lake extent; the result is validated with the GPS data from BIN1 station, located at the westerncoast of Borneo. The commencement stage of the Bakun Dam induces the large-scale land subsidence, whichcauses the GPS-BIN1 station to subside by ~9 mm, and move toward the Bakun Lake by ~4 mm. Computation ofthe surface displacements directly from GRACE spherical harmonic coefficient data fails to capture the subsidencefeature, mainly due to the truncation error. Overall, this study demonstrates that evaluating GRACE inconjunction with Landsat, LSMs, and GPS data allows the exploitation of the gravity signal at a much smallerspatial scale than its intrinsic resolution. Benefiting from global coverage, the newly developed satellite-basedalgorithm is a valuable tool for assessing the impacts of reservoir operation on hydrological and geophysicalchanges from local to regional scales.

Tangdamrongsub, Natthachet↗
NASA NTRS2014

Land Surface Microwave Emissivity Dynamics: Observations, Analysis and Modeling

Land surface microwave emissivity affects remote sensing of both the atmosphere and the land surface. The dynamical behavior of microwave emissivity over a very diverse sample of land surface types is studied. With seven years of satellite measurements from AMSR-E, we identified various dynamical regimes of the land surface emission. In addition, we used two radiative transfer models (RTMs), the Community Radiative Transfer Model (CRTM) and the Community Microwave Emission Modeling Platform (CMEM), to simulate land surface emissivity dynamics. With both CRTM and CMEM coupled to NASA's Land Information System, global-scale land surface microwave emissivities were simulated for five years, and evaluated against AMSR-E observations. It is found that both models have successes and failures over various types of land surfaces. Among them, the desert shows the most consistent underestimates (by approx. 70-80%), due to limitations of the physical models used, and requires a revision in both systems. Other snow-free surface types exhibit various degrees of success and it is expected that parameter tuning can improve their performances.

Modeling↗
NASA NTRS2000

Optimization of Car Body under Constraints of Noise, Vibration, and Harshness (NVH), and Crash

To be competitive on the today's market, cars have to be as light as possible while meeting the Noise, Vibration, and Harshness (NVH) requirements and conforming to Government-man dated crash survival regulations. The latter are difficult to meet because they involve very compute-intensive, nonlinear analysis, e.g., the code RADIOSS capable of simulation of the dynamics, and the geometrical and material nonlinearities of a thin-walled car structure in crash, would require over 12 days of elapsed time for a single design of a 390K elastic degrees of freedom model, if executed on a single processor of the state-of-the-art SGI Origin2000 computer. Of course, in optimization that crash analysis would have to be invoked many times. Needless to say, that has rendered such optimization intractable until now. The car finite element model is shown. The advent of computers that comprise large numbers of concurrently operating processors has created a new environment wherein the above optimization, and other engineering problems heretofore regarded as intractable may be solved. The procedure, shown, is a piecewise approximation based method and involves using a sensitivity based Taylor series approximation model for NVH and a polynomial response surface model for Crash. In that method the NVH constraints are evaluated using a finite element code (MSC/NASTRAN) that yields the constraint values and their derivatives with respect to design variables. The crash constraints are evaluated using the explicit code RADIOSS on the Origin 2000 operating on 256 processors simultaneously to generate data for a polynomial response surface in the design variable domain. The NVH constraints and their derivatives combined with the response surface for the crash constraints form an approximation to the system analysis (surrogate analysis) that enables a cycle of multidisciplinary optimization within move limits. In the inner loop, the NVH sensitivities are recomputed to update the NVH approximation model while keeping the Crash response surface constant. In every outer loop, the Crash response surface approximation is updated, including a gradual increase in the order of the response surface and the response surface extension in the direction of the search. In this optimization task, the NVH discipline has 30 design variables while the crash discipline has 20 design variables. A subset of these design variables (10) are common to both the NVH and crash disciplines. In order to construct a linear response surface for the Crash discipline constraints, a minimum of 21 design points would have to be analyzed using the RADIOSS code. On a single processor in Origin 2000 that amount of computing would require over 9 months! In this work, these runs were carried out concurrently on the Origin 2000 using multiple processors, ranging from 8 to 16, for each crash (RADIOSS) analysis. Another figure shows the wall time required for a single RADIOSS analysis using varying number of processors, as well as provides a comparison of 2 different common data placement procedures within the allotted memories for each analysis. The initial design is an infeasible design with NVH discipline Static Torsion constraint violations of over 10%. The final optimized design is a feasible design with a weight reduction of 15 kg compared to the initial design. This work demonstrates how advanced methodology for optimization combined with the technology of concurrent processing enables applications that until now were out of reach because of very long time-to-solution.

Kodiyalam, Srinivas↗
NASA NTRS2019

Quantifying Water Storage Change and Land Subsidence Induced by Reservoir Impoundment Using GRACE, Landsat, and GPS Data

The construction of hydropower dams is a common strategy to support a country's increasing need for electricity and river water management for industry and agriculture. Although the hydrological and geophysical impacts of water relocation are usually assessed prior to impoundment, their accuracy is generally limited due to the lack of in situ observations, especially in a remote area. This study presents a workflow to quantify the terrestrial water storage change (TWS) and land subsidence induced by a reservoir's water impoundment using multiple satellite observations (GRACE, Landsat), land surface models (CABLE, GLDAS, NCEP, ECMWF), and GPS data. The study site is the Bakun Dam, located in Sarawak, Malaysia, which is the largest hydropower dam in Southeast Asia. Commencing operation in late 2010, the dam induced a change of water mass and lake surface area that was clearly observed by GRACE and Landsat observations, respectively. During the 17-month impounding period (from August 2010 to December 2011), GRACE observed a dramatic increase of approximately 200 mm equivalent water height, while Landsat detected an increased lake extent of around 600 km2. In this paper, a forward model is developed to determine the increased water surface level corresponding to GRACE observations, estimated to be about 120 m. In contrast to GRACE, the TWS derived from land surface models cannot capture the increased TWS, due to the lack of reservoir routing algorithms in the models. In addition, the land subsidence was calculated using the disk load model constructed based on the GRACE-derived lake level and Landsat-derived lake extent; the result is validated with the GPS data from BIN1 station, located at the western coast of Borneo. The commencement stage of the Bakun Dam induces the large-scale land subsidence, which causes the GPS-BIN1 station to subside by ~9 mm, and move toward the Bakun Lake by ~4 mm. Computation of the surface displacements directly from GRACE spherical harmonic coefficient data fails to capture the subsidence feature, mainly due to the truncation error. Overall, this study demonstrates that evaluating GRACE in conjunction with Landsat, LSMs, and GPS data allows the exploitation of the gravity signal at a much smaller spatial scale than its intrinsic resolution. Benefiting from global coverage, the newly developed satellite-based algorithm is a valuable tool for assessing the impacts of reservoir operation on hydrological and geophysical changes from local to regional scales.

Natthachet Tangdamrongsub↗
NASA NTRS2024

Improving the Fire Weather Index System for Peatlands Using Peat-Specific Hydrological Input Data

The Canadian Fire Weather Index (FWI) system, even though originally developed and calibrated for an upland Jack pine forest, is used globally to estimate fire danger for any fire environment. However, for some environments, such as peatlands, the applicability of the FWI in its current form, is often questioned. In this study, we replaced the original moisture codes of the FWI with hydrological estimates resulting from the assimilation of satellite-based L-band passive microwave observations into a peatland-specific land surface model. In a conservative approach that maintains the integrity of the original FWI structure, the distributions of the hydrological estimates were first matched to those of the corresponding original moisture codes before replacement. The resulting adapted FWI, hereafter called FWIpeat, was evaluated using satellite-based information on fire presence over boreal peatlands from 2010 through 2018. Adapting the FWI with model- and satellite-based hydrological information was found to be beneficial in estimating fire danger, especially when replacing the deeper moisture codes of the FWI. For late-season fires, further adaptations of the fine fuel moisture code show even more improvement due to the fact that late-season fires are more hydrologically driven. The proposed FWIpeat should enable improved monitoring of fire risk in boreal peatlands.

Canadian Fire Weather Index↗
NASA NTRS1988

Surface flow visualization in the cryogenic wind tunnel

The prospects are reviewed of a range of possible surface flow visualization methods for application to model testing in the large cryogenic wind tunnel. Desirable features are outlined, including the flow details which should be revealed by the various methods. The risks of model and tunnel contamination are discussed, also the coverage of the model surface to be expected, the advance planning and complexity of model design and tunnel equipment required by the visualization method, and the prospects of generating multiple flow images during one tunnel run. The techniques range from the untried to several on which already there is some experience in the cryogenic environment. Directions for further development are suggested.

Goodyer, M. J.↗
NASA NTRS1974

Calculation of the longitudinal aerodynamic characteristics of STOL aircraft with externally-blown jet-augmented flaps

A theoretical investigation was made to develop methods for predicting the longitudinal aerodynamic characteristics of externally-blown, jet-augmented wing-flap combinations. A potential flow analysis was used to develop two models: a wing-flap lifting surface model and a high-bypass-ratio turbofan engine wake model. Use of these two models in sequence provides for calculation of the wing-flap load distribution including the influence of the engine wake. The method can accommodate multiple engines per wing panel and part-span flaps but is limited to the case where the flow and geometry of the configuration are symmetric about a vertical plane containing the wing root chord. Comparisons of predicted and measured lift and pitching moment on unswept and swept wings with one and two engines per panel and with various flap deflection angles indicate satisfactory prediction of lift and moment for flap deflections up to 30 to 40 degrees. At higher flap angles with and without power, the method begins to overpredict lift, due probably to the appearance of flow separation on the flaps.

Dillenius, M. F. E.↗