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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

An Analysis of the Pressures, Forces and Moments Induced by the Ground Vortex Generated by a Single Impinging Jet

When a jet STOVL aircraft is in STOL operation the jets impinge on the ground and generate wall jets flowing radially outward from the points at which the jets impinge. When the forward flowing part of a wall jet meets the free stream flow it is rolled back on itself forming a parabolic shaped ground vortex. Positive pressures are induced on the lower surface of the configuration ahead of the ground vortex and suction pressures are induced over the ground vortex itself. In addition, the suction pressures induced aft of the jet out of ground effect are reduced and lifting pressures are induced on the upper surface. This study analyzes available pressure and force data and develops a method for estimating the forces and moments induced in ground effect. The method includes the effects of configuration variables, height and operating conditions, as well as the effects of the location, deflection and shape of the jet. However, it is limited to single jets at subcritical nozzle pressure ratios. An analysis of the effects of moving over the ground vs. tests over a fixed ground plane is included.

Kuhn, Richard E.↗
NASA NTRS2002

Effects of heavy particle irradiation and diet on amphetamine- and lithium chloride-induced taste avoidance learning in rats

Rats were maintained on diets containing either 2% blueberry or strawberry extract or a control diet for 8 weeks prior to being exposed to 1.5 Gy of 56Fe particles in the Alternating Gradient Synchrotron at Brookhaven National Laboratory. Three days following irradiation, the rats were tested for the effects of irradiation on the acquisition of an amphetamine- or lithium chloride-induced (LiCl) conditioned taste avoidance (CTA). The rats maintained on the control diet failed to show the acquisition of a CTA following injection of amphetamine. In contrast, the rats maintained on antioxidant diets (strawberry or blueberry extract) continued to show the development of an amphetamine-induced CTA following exposure to 56Fe particles. Neither irradiation nor diet had an effect on the acquisition of a LiCl-induced CTA. The results are interpreted as indicating that oxidative stress following exposure to 56Fe particles may be responsible for the disruption of the dopamine-mediated amphetamine-induced CTA in rats fed control diets; and that a reduction in oxidative stress produced by the antioxidant diets functions to reinstate the dopamine-mediated CTA. The failure of either irradiation or diet to influence LiCl-induced responding suggests that oxidative stress may not be involved in CTA learning following injection of LiCl.

Non-NASA Center↗
NASA NTRS1994

Characteristics and implications of prolonged fusicoccin-induced growth of Avena coleoptile sections

A study has been made of the prolonged growth of Avena coleoptile sections in response to fusicoccin (FC), a phytotoxin that promotes apoplastic acidification. The final amount of FC-induced growth is a function of the FC concentration. Removal of the epidermis speeds up the initial rate of elongation and shortens the duration of the response, without affecting the total amount of extension. A suboptimal FC concentration (7 x 10(-8) M) which induces the same rate of proton excretion as does optimal indoleacetic acid (IAA) (1 x 10(-5) M), causes elongation which is 60-75% of that induced by IAA in 4 h or 50-65% in 7 h. This suggests that acid-induced extension could make a major contribution to auxin-induced growth for at least 7 h.

Non-NASA Center↗
NASA NTRS1992

Comparative kinetics and reciprocal inhibition of nitrate and nitrite uptake in roots of uninduced and induced barley (Hordeum vulgare L.) seedlings

Nitrate and NO2- transport by roots of 8-day-old uninduced and induced intact barley (Hordeum vulgare L. var CM 72) seedlings were compared to kinetic patterns, reciprocal inhibition of the transport systems, and the effect of the inhibitor, p-hydroxymercuribenzoate. Net uptake of NO3- and NO2- was measured by following the depletion of the ions from the uptake solutions. The roots of uninduced seedlings possessed a low concentration, saturable, low Km, possibly a constitutive uptake system, and a linear system for both NO3- and NO2-. The low Km system followed Michaelis-Menten kinetics and approached saturation between 40 and 100 micromolar, whereas the linear system was detected between 100 and 500 micromolar. In roots of induced seedlings, rates for both NO3- and NO2- uptake followed Michaelis-Menten kinetics and approached saturation at about 200 micromolar. In induced roots, two kinetically identifiable transport systems were resolved for each anion. At the lower substrate concentrations, less than 10 micromolar, the apparent low Kms of NO3- and NO2- uptake were 7 and 9 micromolar, respectively, and were similar to those of the low Km system in uninduced roots. At substrate concentrations between 10 and 200 micromolar, the apparent high Km values of NO3- uptake ranged from 34 to 36 micromolar and of NO2- uptake ranged from 41 to 49 micromolar. A linear system was also found in induced seedlings at concentrations above 500 micromolar. Double reciprocal plots indicated that NO3- and NO2- inhibited the uptake of each other competitively in both uninduced and induced seedlings; however, Ki values showed that NO3- was a more effective inhibitor than NO2-. Nitrate and NO2- transport by both the low and high Km systems were greatly inhibited by p-hydroxymercuribenzoate, whereas the linear system was only slightly inhibited.

NASA Program CELSS↗
NASA NTRS2000

Particle irradiation induces FGF2 expression in normal human lens cells

Particle Irradiation Induces FGF2 Expression in Normal Human Lens Cells. Particle radiations, including both proton and helium-ion beams, have been used to successfully treat choroidal melanoma, but with the complication of radiation-induced cataract. We have investigated a role for radiation-induced changes in the expression of basic fibroblast growth factor (FGF2) gene expression as part of the mechanism(s) underlying lens cell injury associated with cataract. Normal human lens epithelial (HLE) cells were cultured in vitro on extracellular matrix (ECM) originated from bovine corneal endothelial cells. This study reports evidence for rapid but transient induction of FGF2 transcripts, an increase of between 5- and 8-fold, within 0.5 h after exposure to particle radiation, followed by another wave of increased transcription at 2-3 h postirradiation. Immunofluorescence results confirm the enhanced levels of FGF2 protein rapidly after exposure to protons or helium ions, followed by another wave of increased activity unique to helium at 6 h postirradiation. This second wave of increased immunoreactivity was not observed in the proton-irradiated samples. Total FGF2 protein analysis after helium-ion exposures shows induced expression of three FGF2 isoforms, with an increase of up to 2-fold in the 18-kDa low-molecular-weight species. Studies of the effects of protons on individual FGF2 protein isoforms are in progress. Several mechanisms involving a role for FGF2 in radiation-induced cataract are discussed.

NASA Discipline Radiation Health↗
NASA NTRS1995

Role of calcium in growth inhibition induced by a novel cell surface sialoglycopeptide

Our laboratory has purified an 18 kDa cell surface sialoglycopeptide growth inhibitor (CeReS-18) from intact bovine cerebral cortex cells. Evidence presented here demonstrates that sensitivity to CeReS-18-induced growth inhibition in BALB-c 3T3 cells is influenced by calcium, such that a decrease in the calcium concentration in the growth medium results in an increase in sensitivity to CeReS-18. Calcium did not alter CeReS-18 binding to its cell surface receptor and CeReS-18 does not bind calcium directly. Addition of calcium, but not magnesium, to CeReS-18-inhibited 3T3 cells results in reentry into the cell cycle. A greater than 3-hour exposure to increased calcium is required for escape from CeReS-18-induced growth inhibition. The calcium ionophore ionomycin could partially mimic the effect of increasing extracellular calcium, but thapsigargin was ineffective in inducing escape from growth inhibition. Increasing extracellular calcium 10-fold resulted in an approximately 7-fold increase in total cell-associated 45Ca+2, while free intracellular calcium only increased approximately 30%. However, addition of CeReS-18 did not affect total cell-associated calcium or the increase in total cell-associated calcium observed with an increase in extracellular calcium. Serum addition induced mobilization of intracellular calcium and influx across the plasma membrane in 3T3 cells, and pretreatment of 3T3 cells with CeReS-18 appeared to inhibit these calcium mobilization events. These results suggest that a calcium-sensitive step exists in the recovery from CeReS-18-induced growth inhibition. CeReS-18 may inhibit cell proliferation through a novel mechanism involving altering the intracellular calcium mobilization/regulation necessary for cell cycle progression.

Non-NASA Center↗
NASA NTRS1994

Calcium influences sensitivity to growth inhibition induced by a cell surface sialoglycopeptide

While studies concerning mitogenic factors have been an important area of research for many years, much less is understood about the mechanisms of action of cell surface growth inhibitors. We have purified an 18 kDa cell surface sialoglycopeptide growth inhibitor (CeReS-18) which can reversibly inhibit the proliferation of diverse cell types. The studies discussed in this article show that three mouse keratinocyte cell lines exhibit sixty-fold greater sensitivity than other fibroblasts and epithelial-like cells to CeReS-18-induced growth inhibition. Growth inhibition induced by CeReS-18 treatment is a reversible process, and the three mouse keratinocyte cell lines exhibited either single or multiple cell cycle arrest points, although a predominantly G0/G1 cell cycle arrest point was exhibited in Swiss 3T3 fibroblasts. The sensitivity of the mouse keratinocyte cell lines to CeReS-18-induced growth inhibition was not affected by the degree of tumorigenic progression in the cell lines and was not due to differences in CeReS-18 binding affinity or number of cell surface receptors per cell. However, the sensitivity of both murine fibroblasts and keratinocytes could be altered by changing the extracellular calcium concentration, such that increased extracellular calcium concentrations resulted in decreased sensitivity to CeReS-18-induced proliferation inhibition. Thus the increased sensitivity of the murine keratinocyte cell lines to CeReS-18 could be ascribed to the low calcium concentration used in their propagation. Studies are currently under way investigating the role of calcium in CeReS-18-induced growth arrest. The CeReS-18 may serve as a very useful tool to study negative growth control and the signal transduction events associated with cell cycling.

NASA Discipline Cell Biology↗
NASA NTRS1992

Nystagmus induced by electrical stimulation of the vestibular and prepositus hypoglossi nuclei in the monkey: evidence for site of induction of velocity storage

Electrical stimulation of the vestibular nuclei (VN) and prepositus hypoglossi nuclei (PPH) of alert cynomolgus monkeys evoked nystagmus and eye deviation while they were in darkness. At some sites in VN, nystagmus and after-nystagmus were induced with characteristics suggesting that velocity storage had been excited. We analyzed these responses and compared them to the slow component of optokinetic nystagmus (OKN) and to optokinetic after-nystagmus (OKAN). We then recorded unit activity in VN and determined which types of nystagmus would be evoked from the sites of recording. Nystagmus and eye deviations were also elicited by electrical stimulation of PPH, and we characterized the responses where unit activity was recorded in PPH. Horizontal slow phase velocity of the VN "storage" responses was contralateral to the side of stimulation. The rising time constants and peak steady-state velocities were similar to those of OKN, and the falling time constants of the after-nystagmus and of OKAN were approximately equal. Both the induced after-nystagmus and OKAN were habituated by stimulation of the VN. When horizontal after-nystagmus was evoked with animals on their sides, it developed yaw and pitch components that tended to shift the vector of the slow phase velocity toward the spatial vertical. Similar "cross-coupling" occurs for horizontal OKAN or for vestibular post-rotatory nystagmus elicited in tilted positions. Thus, the storage component of nystagmus induced by VN stimulation had the same characteristics as the slow component of OKN and the VOR. Positive stimulus sites for inducing nystagmus with typical storage components were located in rostral portions of VN. They lay in caudal ventral superior vestibular nucleus (SVN), dorsal portions of central medial vestibular nucleus (MVN) caudal to the abducens nuclei and in adjacent lateral vestibular nucleus (LVN). More complex stimulus responses, but with contralateral after-nystagmus, were induced from surrounding regions of ventral MVN and LVN, rostral descending vestibular nucleus and the marginal zone between MVN and PPH. Vestibular-only (VO), vestibular plus saccade (VPS) and tonic vestibular pause (TVP) units were identified by extracellular recording. Stimulation near type I lateral and vertical canal-related VO units elicited typical "storage" responses with after-nystagmus in 23 of 29 tracks (79%). Stimulus responses were more complex from the region of neurons with oculomotor-related signals, i.e., TVP or VPS cells, although after-nystagmus was also elicited from these sites. Effects of vestibular nerve and nucleus stimulation were compared.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Neuroscience↗
NASA NTRS2005

Modeling of the EUV and X-Ray Emission Spectra Induced by the Solar Winds Ions in the Heliosphere

We have carried out investigation of the EUV and X-ray emission spectra induced in interaction between the Solar Wind (SW) and interstellar neutral gas. The spectra of most important SW ions have been computed for the charge-exchange mechanism of X-ray emission using new accurate spectroscopic data from recent laboratory measurements and theoretical calculations. Total spectra have been constructed as a sum of spectra induced in the charge-exchange collisions by individual O(exp q+), C(exp q+), N(exp q+), Ne(exp q+), Mg (exp q+) and Fe(exp q+) ions. Calculations have been performed for X-ray emission from the heliospheric hydrogen and helium gas. X-ray maps of the heliosphere have been computed. The power density of X-ray sources in the heliospheric ecliptic plane is shown for the H gas and for the He gas. Distances from the Sun (0,0) are given in AU. The helium cone is clear seen in the X-ray map of the charge-exchange emission induced by the solar wind. X-ray emission spectra detected by the Chandra X-ray telescope from the "dark" side of Moon has been identified as a X-ray background emission induced by the solar wind from the geocorona. Spectra and intensities of this charge-exchange X-rays have been compared with the heliospheric component of the X-ray background. Observations and modeling of the SW spectra induced from the geocorona indicate a strong presence of emission lines of highly charged oxygen ions. Anisotropy in distribution of heliospheric X-rays has been predicted and calculated for the regions of the fast and slow solar winds.

Kharchenko, Vasili↗
NASA NTRS2006

Space Shuttle Main Engine Low Pressure Oxidizer Turbo-Pump Inducer Dynamic Environment Characterization through Water Model and Hot-Fire Testing

The Low Pressure Oxidizer Turbopump (LPOTP) inducer on the Block II configuration Space Shuttle Main Engine (SSME) experienced blade leading edge ripples during hot firing. This undesirable condition led to a minor redesign of the inducer blades. This resulted in the need to evaluate the performance and the dynamic environment of the redesign, relative to the current configuration, as part of the design acceptance process. Sub-scale water model tests of the two inducer configurations were performed, with emphasis on the dynamic environment due to cavitation induced vibrations. Water model tests were performed over a wide range of inlet flow coefficient and pressure conditions, representative of the scaled operating envelope of the Block II SSME, both in flight and in ground hot-fire tests, including all power levels. The water test hardware, facility set-up, type and placement of instrumentation, the scope of the test program, specific test objectives, data evaluation process and water test results that characterize and compare the two SSME LPOTP inducers are discussed. In addition, dynamic characteristics of the two water models were compared to hot fire data from specially instrumented ground tests. In general, good agreement between the water model and hot fire data was found, which confirms the value of water model testing for dynamic characterization of rocket engine turbomachinery.

Patrick Arellano↗
NASA NTRS2006

Diapir-Induced Reorientation of Enceladus

A viewgraph presentation on the diapir-induced reorientation of Enceladus is shown. The contents include: 1) Activity on Enceladus; 2) Miranda's Coronae: Origin above Diapirs; 3) Reorientation of Miranda; 4) Planetary Reorientation; 5) Modeling Diapir-Induced Reorientation; 6) Diapir-Induced Reorientation: Results; 7) Tectonic Implications of Reorientation; 8) Additional Tests of Reorientation; 9) Diapir-Induced Reorientation of Enceladus: Conclusions; and 10) Diapir-Induced Reorientation: Future Work

Enceladu↗
NASA NTRS2008

Induced Contamination Predictions for JAXA's MPAC&SEED Devices

Externally mounted ISS payloads are exposed to the induced ISS environment, including material outgassing and thruster plume contamination. The Boeing Space Environments Team developed analytical and semiempirical models to predict material outgassing and thruster plume induced contamination. JAXA s SM/MPAC&SEED experiment provides an unique opportunity to compare induced contamination predications with measurements. Analysis results are qualitatively consistent with XPS measurements. Calculated depth of contamination within a factor of 2-3 of measured contamination. Represents extremely good agreement, especially considering long duration of experiment and number of outgassing sources. Despite XPS limitations in quantifying plume contamination, the measured and predicted results are of similar scale for the wake-facing surfaces. JAXA s JEM/MPAC&SEED experiment will also be exposed to induced contamination due to JEM and ISS hardware. Predicted material outgassing induced contamination to JEM/MPAC&SEED ranges from 44 to 262 (depending on surface temperature) for a 3 year exposure duration.

Steagall, Courtney↗
NASA NTRS2009

M-BAND Study of Radiation-Induced Chromosome Aberrations in Human Epithelial Cells: Radiation Quality and Dose Rate Effects

The advantage of the multicolor banding in situ hybridization (mBAND) technique is its ability to identify both inter- (translocation to unpainted chromosomes) and intra- (inversions and deletions within a single painted chromosome) chromosome aberrations simultaneously. To study the detailed rearrangement of low- and high-LET radiation induced chromosome aberrations in human epithelial cells (CH184B5F5/M10) in vitro, we performed a series of experiments with Cs-137 gamma rays of both low and high dose rates, neutrons of low dose rate and 600 MeV/u Fe ions of high dose rate, with chromosome 3 painted with multi-binding colors. We also compared the chromosome aberrations in both 2- and 3-dimensional cell cultures. Results of these experiments revealed the highest chromosome aberration frequencies after low dose rate neutron exposures. However, detailed analysis of the radiation induced inversions revealed that all three radiation types induced a low incidence of simple inversions. Most of the inversions in gamma-ray irradiated samples were accompanied by other types of intra-chromosomal aberrations but few inversions were accompanied by inter-chromosomal aberrations. In contrast, neutrons and Fe ions induced a significant fraction of inversions that involved complex rearrangements of both inter- and intrachromosomal exchanges. The location of the breaks involved in chromosome exchanges was analyzed along the painted chromosome. The breakpoint distribution was found to be randomly localized on chromosome 3 after neutron or Fe ion exposure, whereas non-random distribution with clustering breakpoints was observed after -ray exposure. Our comparison of chromosome aberration yields between 2- and 3-dimensional cell cultures indicated a significant difference for gamma exposures, but not for Fe ion exposures. These experimental results indicated that the track structure of the radiation and the cellular/chromosome structure can both affect radiation-induced chromosome aberrations.

Hada, Megumi↗
NASA NTRS2008

J-2X Fuel Turbopump Point of Departure: The Performance of the J-2s Fuel Turbopump Inducer

To aid the J-2X program design effort with detailed performance and environment information, the J-2S fuel turbopump (FTP) inducer has undergone a thorough test series in both water and hydrogen. The test series utilizes both inducer only and a complete pump configuration to assess the inducer interaction to the overall turbopump system. The test goals include verification of suction performance against heritage J-2S data, head production, effects of thermodynamic suppression head (TSH), and evaluation of the inducer dynamic pressure caused by cavitation instabilities. Test facilities at both Pratt & Whitney Rocketdyne (PWR) and NASA s Stennis Space Center (SSC) are employed for the testing. The inducer only water test effort conducted at PWR established performance curves for suction performance, head production, and efficiency over a wide operating range. Because the heritage J-2S suction performance data set is in hydrogen, it is desired to obtain current suction performance data in hydrogen as well, thus avoiding the reliance on a theoretical TSH correlation for direct comparison. This data then provides an empirically based TSH correlation allowing for the comparison of water test suction data to system suction requirements. The FTP testing performed at SSC provides these suction performance relationships as well as inlet duct dynamic pressures during liquid hydrogen operation. The test effort successfully confirms the heritage J-2S suction performance and establishes the amount of TSH between water and hydrogen operation at the design flow coefficient. Correlating data is also obtained for cavitating instability frequency content, illustrating the validity of using the wide flow range water test data to predict hydrogen performance.

Sargent, S. R.↗
NASA NTRS2004

Induced Anisotropy in FeCo-Based Nanocrystalline Ferromagnetic Alloys (HITPERM) by Very High Field Annealing

Very high magnetic field annealing is shown to affect the magnetic anisotropy in FeCo-base nanocrystalline soft ferromagnetic alloys. Alloys of composition Fe(44.5)Co(44.5)Zr(7)B(4) were prepared by melt spinning into amorphous ribbons, then wound to form toroidal bobbin cores. One set of cores was crystallized in a zero field at 600 deg. C for 1 h, then, field annealed at 17 tesla (T) at 480 deg. C for 1 h. Another set was crystallized in a 17-T field at 480 deg. C for 1 h. Field orientation was transverse to the magnetic path of the toroidal cores. An induced anisotropy is indicated by a sheared hysteresis loop. Sensitive torque magnetometry measurements with a Si cantilever sensor indicated a strong, uniaxial, longitudinal easy axis in the zero-field-crystallized sample. The source is most likely magnetoelastic anisotropy, caused by the residual stress from nanocrystallization and the nonzero magnetostriction coefficient for this material. The magnetostrictive coefficient lambda(5) is measured to be 36 ppm by a strain gage technique. Field annealing reduces the magnitude of the induced anisotropy. Core loss measurements were made in the zero-field-crystallized, zero-field-crystallized- than-field-annealed, and field-crystallized states. Core loss is reduced 30%-50% (depending on frequency) by field annealing. X-ray diffraction reveals no evidence of crystalline texture or orientation that would cause the induced anisotropy. Diffusional pair ordering is thought to be the cause of the induced anisotropy. However, reannealing the samples in the absence of a magnetic field at 480 deg. C does not completely remove the induced anisotropy.

FERROMAGNETIC ALLOYS↗
NASA NTRS2010

SSME Investment in Turbomachinery Inducer Impeller Design Tools and Methodology

Within the rocket engine industry, SSME turbomachines are the de facto standards of success with regard to meeting aggressive performance requirements under challenging operational environments. Over the Shuttle era, SSME has invested heavily in our national inducer impeller design infrastructure. While both low and high pressure turbopump failures/anomaly resolution efforts spurred some of these investments, the SSME program was a major benefactor of key areas of turbomachinery inducer-impeller research outside of flight manifest pressures. Over the past several decades, key turbopump internal environments have been interrogated via highly instrumented hot-fire and cold-flow testing. Likewise, SSME has sponsored the advancement of time accurate and cavitating inducer impeller computation fluid dynamics (CFD) tools. These investments together have led to a better understanding of the complex internal flow fields within aggressive high performing inducers and impellers. New design tools and methodologies have evolved which intend to provide confident blade designs which strike an appropriate balance between performance and self induced load management.

Zoladz, Thomas↗
NASA NTRS2010

High LET Radiation Can Enhance TGF(Beta) Induced EMT and Cross-Talk with ATM Pathways

The TGF(Beta) pathway has been shown to regulate or directly interact with the ATM pathway in the response to radiation in mammary epithelial cells. We investigated possible interactions between the TGF(Beta) and ATM pathways following simulated space radiation using hTERT immortalized human esophageal epithelial cells (EPC-hTERT), mink lung epithelial cells (Mv1lu), and several human fibroblast cell lines. TGF(Beta) is a key modulator of the Epithelial-Mesenchymal Transition (EMT), important in cancer progression and metastasis. The implication of EMT by radiation also has several lines of developing evidence, however is poorly understood. The identification of TGF(Beta) induced EMT can be shown in changes to morphology, related gene over expression or down regulation, which can be detected by RT-PCR, and immunostaining and western blotting. In this study, we have observed morphologic and molecular alternations consistent with EMT after Mv1lu cells were treated with TGF(Beta) High LET radiation enhanced TGF(Beta) mediated EMT with a dose as low as 0.1Gy. In order to consider the TGF(Beta) interaction with ATM we used a potent ATM inhibitor Ku55933 and investigated gene expression changes and Smad signaling kinetics. Ku559933 was observed to reverse TGF(Beta) induced EMT, while this was not observed in dual treated cells (radiation+TGF(Beta)). In EPC-hTERT cells, TGF(Beta) alone was not able to induce EMT after 3 days of application. A combined treatment with high LET, however, significantly caused the alteration of EMT markers. To study the function of p53 in the process of EMT, we knocked down P53 through RNA interference. Morphology changes associated with EMT were observed in epithelial cells with silenced p53. Our study indicates: high LET radiation can enhance TGF(Beta) induced EMT; while ATM is triggering the process of TGF(Beta)-induced EMT, p53 might be an essential repressor for EMT phenotypes.

Wang, Minli↗
NASA NTRS2010

On the Minimum Induced Drag of Wings

Of all the types of drag, induced drag is associated with the creation and generation of lift over wings. Induced drag is directly driven by the span load that the aircraft is flying at. The tools by which to calculate and predict induced drag we use were created by Ludwig Prandtl in 1903. Within a decade after Prandtl created a tool for calculating induced drag, Prandtl and his students had optimized the problem to solve the minimum induced drag for a wing of a given span, formalized and written about in 1920. This solution is quoted in textbooks extensively today. Prandtl did not stop with this first solution, and came to a dramatically different solution in 1932. Subsequent development of this 1932 solution solves several aeronautics design difficulties simultaneously, including maximum performance, minimum structure, minimum drag loss due to control input, and solution to adverse yaw without a vertical tail. This presentation lists that solution by Prandtl, and the refinements by Horten, Jones, Kline, Viswanathan, and Whitcomb

Bowers, Albion H.↗