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NASA NTRS2005

NASA Structural Analysis Report on the American Airlines Flight 587 Accident - Local Analysis of the Right Rear Lug

A detailed finite element analysis of the right rear lug of the American Airlines Flight 587 - Airbus A300-600R was performed as part of the National Transportation Safety Board s failure investigation of the accident that occurred on November 12, 2001. The loads experienced by the right rear lug are evaluated using global models of the vertical tail, local models near the right rear lug, and a global-local analysis procedure. The right rear lug was analyzed using two modeling approaches. In the first approach, solid-shell type modeling is used, and in the second approach, layered-shell type modeling is used. The solid-shell and the layered-shell modeling approaches were used in progressive failure analyses (PFA) to determine the load, mode, and location of failure in the right rear lug under loading representative of an Airbus certification test conducted in 1985 (the 1985-certification test). Both analyses were in excellent agreement with each other on the predicted failure loads, failure mode, and location of failure. The solid-shell type modeling was then used to analyze both a subcomponent test conducted by Airbus in 2003 (the 2003-subcomponent test) and the accident condition. Excellent agreement was observed between the analyses and the observed failures in both cases. From the analyses conducted and presented in this paper, the following conclusions were drawn. The moment, Mx (moment about the fuselage longitudinal axis), has significant effect on the failure load of the lugs. Higher absolute values of Mx give lower failure loads. The predicted load, mode, and location of the failure of the 1985-certification test, 2003-subcomponent test, and the accident condition are in very good agreement. This agreement suggests that the 1985-certification and 2003- subcomponent tests represent the accident condition accurately. The failure mode of the right rear lug for the 1985-certification test, 2003-subcomponent test, and the accident load case is identified as a cleavage-type failure. For the accident case, the predicted failure load for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs. I.

Raju, Ivatury S↗

NASA NTRS2006

Structural Analysis of the Right Rear Lug of American Airlines Flight 587

A detailed finite element analysis of the right rear lug of the American Airlines Flight 587 - Airbus A300-600R was performed as part of the National Transportation Safety Board s failure investigation of the accident that occurred on November 12, 2001. The loads experienced by the right rear lug are evaluated using global models of the vertical tail, local models near the right rear lug, and a global-local analysis procedure. The right rear lug was analyzed using two modeling approaches. In the first approach, solid-shell type modeling is used, and in the second approach, layered-shell type modeling is used. The solid-shell and the layered-shell modeling approaches were used in progressive failure analyses (PFA) to determine the load, mode, and location of failure in the right rear lug under loading representative of an Airbus certification test conducted in 1985 (the 1985-certification test). Both analyses were in excellent agreement with each other on the predicted failure loads, failure mode, and location of failure. The solid-shell type modeling was then used to analyze both a subcomponent test conducted by Airbus in 2003 (the 2003-subcomponent test) and the accident condition. Excellent agreement was observed between the analyses and the observed failures in both cases. The moment, Mx (moment about the fuselage longitudinal axis), has significant effect on the failure load of the lugs. Higher absolute values of Mx give lower failure loads. The predicted load, mode, and location of the failure of the 1985- certification test, 2003-subcomponent test, and the accident condition are in very good agreement. This agreement suggests that the 1985-certification and 2003-subcomponent tests represent the accident condition accurately. The failure mode of the right rear lug for the 1985-certification test, 2003-subcomponent test, and the accident load case is identified as a cleavage-type failure. For the accident case, the predicted failure load for the right rear lug from the PFA is greater than 1.98 times the limit load of the lugs.

Raju, Ivatury S.↗

NASA NTRS2002

Experimental Study of the Richtmyer-Meshkov Instability of Incompressible Fluids

The Richtmyer-Meshkov instability of a low Atwood number, miscible, two-liquid system is investigated experimentally. The initially stratified fluids are contained within a rectangular tank mounted to a sled that rides on a vertical set of rails. The instability is generated by dropping the sled onto a coil spring, producing a nearly impulsive upward acceleration. The subsequent freefall that occurs as the container travels upward and then downward on the rails allows the instability to evolve in the absence of gravity. The interface separating the two liquids initially has a well-defined, sinusoidal perturbation that quickly inverts and then grows in amplitude after undergoing the impulsive acceleration. Disturbance amplitudes are measured and compared to theoretical predictions. Linear stability theory gives excellent agreement with the measured initial growth rate, a(sub 0), for single-mode perturbations with the predicted amplitudes differing by less than 10% from experimental measurements up to a nondimensional time ka(sub 0)t = 0.7, where k is the wavenumber. Linear stability theory also provides excellent agreement for the individual mode amplitudes of multi-mode initial perturbations up until the interface becomes multi-valued. Comparison with previously published weakly nonlinear single-mode models shows good agreement up to ka(sub 0)t = 3, while published nonlinear single-mode models provide good agreement up to ka(sub 0)t = 30. The effects of Reynolds number on the vortex core evolution and overall growth rate of the interface are also investigated. Measurements of the overall amplitude are found to be unaffected by the Reynolds number for the range of values studied here. However, experiments carried out at lower values of Reynolds numbers were found to have decreased vortex core rotation rates. In addition, an instability in the vortex cores is observed.

Niederhaus, Charles↗

NASA NTRS1973

A mathematical model for jet engine combustor pollutant emissions

Mathematical modeling for the description of the origin and disposition of combustion-generated pollutants in gas turbines is presented. A unified model in modular form is proposed which includes kinetics, recirculation, turbulent mixing, multiphase flow effects, swirl and secondary air injection. Subelements of the overall model were applied to data relevant to laboratory reactors and practical combustor configurations. Comparisons between the theory and available data show excellent agreement for basic CO/H2/Air chemical systems. For hydrocarbons the trends are predicted well including higher-than-equilibrium NO levels within the fuel rich regime. Although the need for improved accuracy in fuel rich combustion is indicated, comparisons with actual jet engine data in terms of the effect of combustor-inlet temperature is excellent. In addition, excellent agreement with data is obtained regarding reduced NO emissions with water droplet and steam injection.

Boccio, J. L.↗

NASA NTRS2023

HLPW-4: Wall-Modeled LES and Lattice-Boltzmann Technology Focus Group Workshop Summary

TTT↗

NASA NTRS1995

The Anharmonic Force Field of Ethylene, C2H4, by Means of Accurate Ab Initio Calculations

The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the C-12 isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals could be reproduced to better than 10 per centimeter, except for three cases of severe Fermi type 1 resonance. The problem with these three bands is identified as a systematic overestimate of the Kiij Fermi resonance constants by a factor of two or more; if this is corrected for, the predicted fundamentals come into excellent agreement with experiment. No such systematic overestimate is seen for Fermi type 2 resonances. Our computed harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch-bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the v8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper.

Martin, Jan M. L.↗

NASA NTRS1987

Higher order diffractions from a circular disk

The backscattering from a circular disk is analyzed using the geometrical theory of diffraction. First-, second-, and third-order diffractions are included in the hard polarization analysis, while first-, second-, and third-order slope diffractions are included for soft polarization. Improvements in the prediction of the monostatic radar cross section over previous works are noted. For hard polarization, an excellent agreement is exhibited between experimental and theoretical results, while a very good agreement is noted for soft polarization. To further improve the soft polarization results for wide angles, a model for the creeping wave or circulating current on the edge of the disk is obtained and used to find an additional component of the backscattered field. The addition of this component significantly improves the results for wide angles, leading to excellent agreement for soft polarization also. An axial-caustic correction method using equivalent currents is also included in the analysis.

Marsland, Diane P.↗

NASA NTRS2020

Re-Computation of Numerical Results Contained in NACA Report No. 685

In an engineering note published in the Journal of Aircraft in the year 2000, Thomas A. Zeiler made generally known that some of the early works on aeroelastic flutter by Theodore Theodorsen and I.E. Garrick (NACA Report Nos. 496, 685, and 741) contained numerical errors in some of their numerical examples. Some of the plots containing numerical errors were later reproduced in two classic aeroelasticity texts (BAH and BA). Because these foundational papers and texts are often used in graduate courses on aeroelasticity, Zeiler recommended that an effort be undertaken to employ the computational resources available today (digital computers) to recompute the example problems in these early works and to publish the results to provide a complete and error-free set of numerical examples. This paper presents recomputed theoretical results contained in NACA Report No. 685 (NACA 685), “Mechanism of Flutter, A Theoretical and Experimental Investigation of the Flutter Problem,” by Theodore Theodorsen and I.E. Garrick. The recomputations were performed employing the solution method described in NACA 685, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in good-to-excellent agreement with the recomputed results, a surprising but gratifying result considering that the NACA 685 results were computed “by hand” using pencil, paper, slide rules, and mechanical calculators called comptometers. Checks on the recomputations (about 25% were checked) were performed using the so-called 𝑝𝑝-method of flutter solution. In all cases, including those where the original and recomputed results differed significantly, the checks were in excellent agreement with the recomputed results.

Boyd Perry, III↗

NASA NTRS1999

Vertical Profiles of Latent Heat Release and Their Retrieval for TOGA COARE Convective Systems Using a Cloud Resolving Model, SSM/I, and Ship-borne Radar Data

Latent heating profiles associated with three (TOGA COARE) Tropical Ocean and Global Atmosphere Coupled Ocean Atmosphere Response Experiment active convective episodes (December 10-17 1992; December 19-27 1992; and February 9-13 1993) are examined using the Goddard Cumulus Ensemble (GCE) Model and retrieved by using the Goddard Convective and Stratiform Heating (CSH) algorithm . The following sources of rainfall information are input into the CSH algorithm: Special Sensor Microwave Imager (SSM/1), Radar and the GCE model. Diagnostically determined latent heating profiles calculated using 6 hourly soundings are used for validation. The GCE model simulated rainfall and latent heating profiles are in excellent agreement with those estimated by soundings. In addition, the typical convective and stratiform heating structures (or shapes) are well captured by the GCE model. Radar measured rainfall is smaller than that both estimated by the GCE model and SSM/I in all three different COARE IFA periods. SSM/I derived rainfall is more than the GCE model simulated for the December 19-27 and February 9-13 periods, but is in excellent agreement with the GCE model for the December 10-17 period. The GCE model estimated stratiform amount is about 50% for December 19-27, 42% for December 11-17 and 56% for the February 9-13 case. These results are consistent with large-scale analyses. The accurate estimates of stratiform amount is needed for good latent heating retrieval. A higher (lower) percentage of stratiform rain can imply a maximum heating rate at a higher (lower) altitude. The GCE model always simulates more stratiform rain (10 to 20%) than the radar for all three convective episodes. SSM/I derived stratiform amount is about 37% for December 19-27, 48% for December 11-17 and 41% for the February 9-13 case. Temporal variability of CSH algorithm retrieved latent heating profiles using either GCE model simulated or radar estimated rainfall and stratiform amount is in good agreement with that diagnostically determined for all three periods. However, less rainfall and a smaller stratiform percentage estimated by radar resulted in a weaker (underestimated) latent heating profile and a lower maximum latent heating level compared to those determined diagnostically. Rainfall information from SSM/I can not retrieve individual convective events due to poor temporal sampling. Nevertheless, this study suggests that a good 4r, rainfall retrieval from SSM/I for a convective event always leads to a good latent heating retrieval. Sensitivity testing has been performed and the results indicate that the SSM/I derived time averaged stratiform amount may be underestimated for December 19-27. Time averaged heating profiles derived from SSM/I, however, are not in bad agreement with those derived by soundings for the December 10-17 convective period. The heating retrievals may be more accurate for longer time scales provided there is no bias in the sampling.

Tao, Wei-Kuo↗

NASA NTRS2006

Evaluation of AIRS, MODIS, and HIRS 11 Micron Brightness Temperature Difference Changes from 2002 through 2006

In an effort to validate the accuracy and stability of AIRS data at low scene temperatures (200-250 K range), we evaluated brightness temperatures at 11 microns with Aqua MODIS band 31 and HIRS/3 channel 8 for Antarctic granules between September 2002 and May 2006. We found excellent agreement with MODIS (at the 0.2 K level) over the full emperature range in data from early in the Aqua mission. However, in more recent data, starting in April 2005, we found a scene temperature dependence in MODIS-AIRS brightness temperature differences, with a discrepancy of 1- 1.5 K at 200 K. The comparison between AIRS and HIRS/3 (channel 8) on NOAA 16 for the same time period yields excellent agreement. The cause and time dependence of the disagreement with MODIS is under evaluation, but the change was coincident with a change in the MODIS production software from collection 4 to 5.

MODIS↗

NASA NTRS2023

Re-Computation of Numerical Results Contained in NACA Report No. 741

This paper presents recomputed theoretical results and compares those results with original results contained in NACA Report No. 741 (NACA 741), “Flutter Calculations in Three Degrees of Freedom,” by Theodore Theodorsen and I.E. Garrick. The recomputations were performed employing the solution method described in NACA 741 but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in good-to-excellent agreement with the recomputed results, a surprising but gratifying result considering that the NACA 741 results were computed “by hand” using pencil, paper, slide rules, and mechanical calculators called comptometers. Checks on the recomputations (about 25% to 30% were checked) were performed using the so-called k-method of flutter solution. In all cases, including those where the original and recomputed results differed significantly, the checks were in excellent agreement with the recomputed results.

Numerical results↗

NASA NTRS1981

Theoretical Treatment of the X(sup 1)Sigma(sup +), A(sup 1)Sigma(sup +), and B(sup 1)Pi states of LiH

Ab initio self-consistent-field plus configuration-interaction calculations are reported for the X(sup 1)Sigma(sup +), A(sup 1)Sigma(sup +), and B(sup 1)Pi states of LiH using a 22(sugma)12(pi)7(delta) function Slater basis set. The resulting dissociation energies, with the experimental values in parentheses, are D(sub e)(X(sup 1)Sigma(sup +)) = 19 972 (20288)/ cm, and D(sub e)(A(sup 1)Sigma(sup +)) = 9042 (8682)/ cm, and D(sup e)(B(sup 1)Pi) = 284 (288) /cm. This is the first ab initio treatment to quantitatively account for the binding in the B(sup 1)Pi state. Calculated dipole moments and electronic transition moments for the X(sup 1)Sigma(sup+)-A(sup 1)Sigma(sup +), X(sup 1)Sigma(sup +)-B((sup 1)Pi, and A(sup 1)Sigma(sup +)- B(sup 1)PI band systems are in excellent agreement with existing theoretical and experimental data. Radiative transition probabilities and lifetimes, including both the bound-bound and bound-free contributions, are computed for all vibrational levels of the A(sup 1)Sigma(sup+) and B(sup 1)Pi states. Comparison with previous results using experimentally based potentials provides insight into the sensitivity of the radiative lifetimes to the detailed nature of the uppermost region of the potentials. Our calculated lifetimes for the lower vibrational levels of the A(sup 1)Sigma(sup +) state are within the experimental uncertainty. Our calculated lifetimes for the three vibrational levels of the B(sup 1)Pi state are in excellent agreement with those of Zemke and Stwalley (values in parentheses), increasing with (upsilon)' from 11.3 (11.3) nsec at (upsilon)' = 0, to 17.0 (17.0) nsec at (upsilon)' = 1, and then to 23.5 (24.0) nsec at (upsilon)' = 2.

Partridge, Harry↗

NASA NTRSDate not supplied

Comparison between Hayabusa 2 Spectral Measurements and Simulations

This paper compares recent Hayabusa 2 spectral measurements with state-of-the-art shock-layer radiation simulations resulting from the LAURA/HARA code suite. These simulations include coupled ablation, which accounts for the injection of ablation products into the flowfield, and coupled radiation, which accounts for radiative energy loss in the flowfield. To enable the coupled ablation simulations, a best-estimate model is developed for Hayabusa’s carbon-phenolic ablator, based on the limited available published information. The comparison between the simulations and measurements focuses on two atomic nitrogen lines and two atomic oxygen lines, as well as the CN Violet band system. For the atomic lines, the measurements and simulations agree within 25% over most of the trajectory. This excellent agreement is unprecedented for observed radiation measurements of atomic lines, where previous Stardust and Hayabusa 1 comparisons were significantly worse. The improved agreement for these Hayabusa 2 comparisons is both the result of improved measurement quality and enhanced flowfield/radiation modeling. To provide a link between these observed radiation measurements and the radiative heating to a vehicle surface, the recently developed flowfield property binning approach is used to identify flowfield properties that provide the dominant emission contribution to the measured spectrum. These identified flowfield properties are then shown to match those for the surface radiative heating to the currently developed Mars Sample Return (MSR) Earth Entry System (EES) at a specific trajectory point and surface location. This matching of flowfield properties indicates that this EES radiative heating and Hayabusa 2 observed radiation simulations are equivalent radiation problems. Therefore, the excellent agreement between Hayabusa 2 measurements and simulations may be leveraged to inform the radiation heating margin for the MSR EES.

Christopher O Johnston↗

NASA NTRS2000

Laser-Induced Fluorescence Measurements and Modeling of Nitric Oxide in Counterflow Diffusion Flames

The feasibility of making quantitative nonintrusive NO concentration ([NO]) measurements in nonpremixed flames has been assessed by obtaining laser-induced fluorescence (LIF) measurements of [NO] in counterflow diffusion flames at atmospheric and higher pressures. Comparisons at atmospheric pressure between laser-saturated fluorescence (LSF) and linear LIF measurements in four diluted ethane-air counterflow diffusion flames with strain rates from 5 to 48/s yielded excellent agreement from fuel-lean to moderately fuel-rich conditions, thus indicating the utility of a model-based quenching correction technique, which was then extended to higher pressures. Quantitative LIF measurements of [NO] in three diluted methane-air counterflow diffusion flames with strain rates from 5 to 35/s were compared with OPPDIF model predictions using the GRI (version 2.11) chemical kinetic mechanism. The comparisons revealed that the GRI mechanism underpredicts prompt-NO by 30-50% at atmospheric pressure. Based on these measurements, a modified reaction rate coefficient for the prompt-NO initiation reaction was proposed which causes the predictions to match experimental data. Temperature measurements using thin filament pyrometry (TFP) in conjunction with a new calibration method utilizing a near-adiabatic H2-air Hencken burner gave very good comparisons with model predictions in these counterflow diffusion flames. Quantitative LIF measurements of [NO] were also obtained in four methane-air counterflow partially-premixed flames with fuel-side equivalence ratios (phi(sub B)) of 1.45, 1.6, 1.8 and 2.0. The measurements were in excellent agreement with model predictions when accounting for radiative heat loss. Spatial separation between regions dominated by the prompt and thermal NO mechanisms was observed in the phi(sub B) = 1.45 flame. The modified rate coefficient proposed earlier for the prompt-NO initiation reaction improved agreement between code predictions and measurements in the region where prompt-NO dominates. Finally, LIF measurements of NO were obtained in counterflow diffusion flames at 2 to 5 atm. Comparisons between [NO] measurements and predictions show that the GRI mechanism underpredicts prompt-NO by a factor of two to three at all pressures. In general, the results indicate a need for refinement of the CH chemistry, especially the pressure-dependent CH formation and destruction reactions.

Ravikrishna, Rayavarapu V.↗

NASA NTRSDate not supplied

HLPW-4/GMGW-3: Wall-Modeled LES and Lattice-Boltzmann Technology Focus Group Workshop Summary

A summary of the nine submissions to the Wall-Modeled LES and Lattice-Boltzmann(WMLESLB) Technical Focus Group (TFG) at the 4th High lift Prediction Workshop is provided. The focus of this TFG was to assess the current capabilities of WMLES and Lattice-Boltzmann methods on a complex high-lift configuration across a wide range of angles of attack. Preliminary analysis of the submitted data suggests that>250𝑀spatial degrees of freedom are needed to accurately predict pitching moments at high angles of attack due to large pressure gradients present on the outboard slat and main element for𝛼 >17◦(corrected for free-air).While some scatter is reported in pitching moments at the low-angles of attack (𝛼 <11◦) - likely caused by differences in flap separation possibly due to low Reynolds number effects - excellent agreement is observed between the submissions near the𝐶𝐿,max state. Objective superiority over steady state RANS can be seen in terms of lack of excess outboard separation; a majority of the good quality WMLES and LB submissions predict wedge-shaped separation patterns consistent with the experimental oil flow. Differences in the onset of stall mechanism in the free-air configuration for𝛼 >20◦is reported with two distinct topologies observed. Topology A is characterized by the onset of corner-flow separation which progressively grows to produce a pitch break in free-air with an angle of attack increase from𝛼=20.55◦to𝛼=21.47◦+𝜖where𝜖is a small perturbation (varying between submissions and likely to be within±0.3◦). Topology Bis characterized by boundary layer weakness emanating from the inboard side of the wing-pylon juncture substantially larger than any weakness in the wing-body juncture (due to corner-flow);submissions in this category do not show any tendency for occurrence of a pitch break for the free-air configuration within the vicinity of𝛼=21.47◦. The in-tunnel simulations submitted by3 participants using different discretizations, grids and closure models show excellent agreement with the experiment in terms of a) integrated loads, b) surface flow-topology, and c) mechanism for the onset of inboard stall. Further evidence is provided to demonstrate both qualitative and quantitative superiority of all 3 WMLES submissions over a single steady state RANS submission to the workshop.

TTT↗

NASA NTRS1996

Planetary Boundary Layer Simulation Using TASS

Boundary conditions to an existing large-eddy simulation model have been changed in order to simulate turbulence in the atmospheric boundary layer. Several options are now available, including the use of a surface energy balance. In addition, we compare convective boundary layer simulations with the Wangara and Minnesota field experiments as well as with other model results. We find excellent agreement of modelled mean profiles of wind and temperature with observations and good agreement for velocity variances. Neutral boundary simulation results are compared with theory and with previously used models. Agreement with theory is reasonable, while agreement with previous models is excellent.

Schowalter, David G.↗

NASA NTRS1972

In-orbit flexible spacecraft dynamics program

A continuous flexible body nonlinear dynamics computer program is used for simulating the spinning mode performance of a spacecraft under applied control torques. The program takes into account the continuous flexible nature of the antennas by representing deflections in terms of shape functions and integrated the spatial dependence in the formulation of the equations of motion. Comparison of RAE flight data on roll, pitch, and yaw with predictions of the computer program in the gravity gradient mode show fair to good agreement in roll and pitch and excellent agreement in the yaw angle.

Fedor, J. V.↗

NASA NTRS1994

Intercomparison of density and temperature profiles obtained by lidar, ionizatoin gauges, falling spheres, datasondes and radiosondes during the DYANA campaign

During the course of the DYnamics Adapted Network for the Atmosphere (DYANA) campaign in early 1990, various techniques to measure densities and temperatures from the ground up to the lower thermosphere were employed. Some of these measurements were performed near simultaneously (maximum allowed time difference: 1 h) and at the same location, and therefore offered the unique chance of intercomparison of different techniques. In this study, we will report on intercomparisons of data from ground-based instruments (Rayleigh- and sodium-lidar), balloon-borne methods (datasondes and radiosondes) and rocket-borne techniques (falling spheres and ionization gauges). The main result is that there is good agreement between the various measurements when considering the error bars. Only occasionally did we notice small but systematic differences (e.g. for the datasondes above 65 km). The most extensive intercomparison was possible between the Rayleigh lidar and the falling sphere technique, both employed in Biscarrosse (44 deg N, 1 deg W). Concerning densities, excellent agreement was found below 63 km: the mean of the deviations is less than 1% and the root mean square (RMS) is approximately 3%. Systematic differences of the order of 5% were noticed around 67 km and above 80 km. The former can be accounted for by an instrumental effect of the falling sphere (Ma = 1 transition; Ma = Mach number), whereas the latter is tentatively explained by the presence of Mie scatterers in the upper mesosphere. Concerning temperatures, the agreement is excellent between 35 and 65 km: the mean of the deviations is less than +/- 3 K and the variability is +/- 5 K. The two systematic density differences mentioned above also affect the temperatures: between 65 and 80 km, the Rayleigh lidar temperatures are systematically lower than the falling sphere values by approximately 5 K.

Lubken, F.-J.↗