Estimating the Lidar Ratios of Modeled Aerosol Species to Help Inform Selection for Marine Aerosol Lidar Ratios in a Future CALIPSO Data Products Release
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A computer simulation is presented which shows how the gear contact ratio affects the dynamic load on a spur gear transmission. The contact ratio can be affected by the tooth addendum, the pressure angle, the tooth size (diametral pitch), and the center distance. The analysis presented was performed using the NASA gear dynamics code, DANST. In the analysis, the contact ratio was varied over the range 1.20 to 2.40 by changing the length of the tooth addendum. In order to simplify the analysis, other parameters related to contact ratio were held constant. The contact ratio was found to have a significant influence on gear dynamics. Over a wide range of operating speeds, a contact ratio close to 2.0 minimized dynamic load. For low contact ratio gears (contact ratio less than 2.0), increasing the contact ratio reduced the gear dynamic load. For high contact ratio gears (contact ratio = or greater than 2.0), the selection of contact ratio should take into consideration the intended operating speeds. In general, high contact ratio gears minimized dynamic load better than low contact ratio gears.
New orbit-averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity-space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS (Velasco et al. , J. Comput. Phys. , vol. 418, 2020, 109512; Velasco et al. , Nucl. Fusion , vol. 61, 2021, 116013). The equations are used to study the $1/\nu$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/\nu$ regime transitions directly into the $\nu$ regime, without passing through a $\sqrt {\nu }$ regime. An explicit formula for the neoclassical fluxes in the $\nu$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrt {\nu }$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by Calvo et al. ( Plasma Phys. Control. Fusion , vol. 59, 2017, 055014). In these stellarators, the $\sqrt {\nu }$ regime exists in the collisionality interval $(a/R) \ln (R/a) \ll \nu _{ii} R a/\rho _i v_{ti} \ll R/a$ . In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrt {\nu }$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $\delta$ : $\delta ^{2} |\ln \delta | \ll \nu _{ii} R a/\rho _i v_{ti} \ll 1$ . Here, $\nu _{ii}$ is the ion–ion collision frequency, $\rho _i$ and $v_{ti}$ are the ion gyroradius and thermal speed, and $a$ and $R$ are the minor and major radii.
The author has identified the following significant results. The production of ratio images from multispectral scanner data is described and several examples of ratio images from aircraft and ERTS-1 data are given for visible, reflective infrared, and thermal infrared wavelengths. The application of photogrammetric techniques to ratio images, defined for this paper as ratio scannergrammetry, is considerably aided by the lesser dependence of ratio images on atmospheric and solar illumination variations, compared with single channel scanner imagery or aerial photos. Ratio scannergrammetry is further aided by the proportionality between ratios of a target deduced from ratio images and ratios of reflectances calculated from laboratory spectra of samples from the target area. Consequently, ratios calculated from laboratory data can be used to predict which ratios are best for discriminating a given rock or mineral, to predict what other rocks or minerals will be confused with it, and finally, to place ratio scannergrammetry on an absolute basis, within an estimated standard error on the order of 5% to 10%. Examples of relative agreement between laboratory data and ratio images are given from two iron oxides, hematite and magnetite.
The structural integrity of high pressure liquid propellant rocket engine thrust chambers is typically maintained through regenerative cooling. The coolant flows through passages formed either by constructing the chamber liner from tubes or by milling channels in a solid liner. Recently, Carlile and Quentmeyer showed life extending advantages (by lowering hot gas wall temperatures) of milling channels with larger height to width aspect ratios (AR is greater than 4) than the traditional, approximately square cross section, passages. Further, the total coolant pressure drop in the thrust chamber could also be reduced, resulting in lower turbomachinery power requirements. High aspect ratio cooling channels could offer many benefits to designers developing new high performance engines, such as the European Vulcain engine (which uses an aspect ratio up to 9). With platelet manufacturing technology, channel aspect ratios up to 15 could be formed offering potentially greater benefits. Some issues still exist with the high aspect ratio coolant channels. In a coolant passage of circular or square cross section, strong secondary vortices develop as the fluid passes through the curved throat region. These vortices mix the fluid and bring lower temperature coolant to the hot wall. Typically, the circulation enhances the heat transfer at the hot gas wall by about 40 percent over a straight channel. The effect that increasing channel aspect ratio has on the curvature heat transfer enhancement has not been sufficiently studied. If the increase in aspect ratio degrades the secondary flow, the fluid mixing will be reduced. Analysis has shown that reduced coolant mixing will result in significantly higher wall temperatures, due to thermal stratification in the coolant, thus decreasing the benefits of the high aspect ratio geometry. A better understanding of the fundamental flow phenomena in high aspect ratio channels with curvature is needed to fully evaluate the benefits of this geometry. The fluid dynamic and conjugate heat transfer problem of high aspect ratio rocket engine coolant channels are being investigated numerically, but these efforts have been hampered by a lack of validating data. Wall temperature data is available for the conjugate problem for channels without curvature and aspect ratio = 5.0, and unheated fluid dynamic data are available for square and circular cross section channels with curvature at Reynold's numbers up to 40,000. But the effects of aspect ratio on secondary flow development have not been experimentally studied. To provide some insight into the effects of channel aspect ratio on secondary flow and to qualitatively provide anchoring for the numerical codes, a flow visualization experiment was initiated at the NASA Lewis Research Center.
Cornu's method is an elegant calculation besieged by an impractical approach to obtain accurate estimates for Poisson's ratio. Conventionally, Cornu's method requires several components, and each component can adversely affect the accuracy of the measurement. Furthermore, Cornu's conventional method requires a long beam because beams with short length-to-width ratios cause the estimate of Poisson's ratio to diverge from the true value of Poisson's ratio. We believe that, with the right modifications, Cornu's method can become an attractive approach to obtaining precise estimates for Poisson's ratio from mode shapes. Here we use finite element simulations to show how to use Cornu's method to estimate Poisson's ratio from a mode shape. Our modified Cornu's method removes knife-edges and loading components for a hinged-hinged plate under steady-state excitation. Given the true value of Poisson's ratio, as a performance specification, we show that simple parametric expressions can fit estimates for Poisson's ratio for different length-to-width ratios of thin hinged-hinged plates. Additionally, we show that estimates for Poisson's ratio from higher modes align with the results from the first mode and explain our expectation for this outcome. Furthermore, our results challenge the idea that anticlastic, monoclastic, and synclastic deformation uniquely correspond to positive, zero, and negative estimates of Poisson's ratio, respectively. With the emergence of materials-by-design, we expect that this parametric technique will be able to assist in experimental qualification of thin beam and plate structures with respect to the desired value of Poisson's ratio.
Overall sound-pressure levels and frequency spectra have been obtained under static conditions on a transonic propeller with an advance ratio of 4.0. This advance ratio represents a practical minimum tip speed for transonic flight speeds. The three-blade, 6.85-foot-diameter, 1,710-rpm propeller is powered by a turbine engine and is designed to operate at a forward Mach number of 0.82 at an altitude of 35,000 feet. The results consist of overall sound-pressure levels and frequency spectra obtained from analyses made of recordings taken during ground runups of the propeller with an advance ratio of 4.0. These results are compared with similar results obtained from a supersonic propeller having an advance ratio of 2.2 reported in NACA Technical Note 4059 and from a modified supersonic propeller having an advance ratio of 3.2 reported in NACA Technical Note 4172. The advance-ratio-4.0 propeller of the present investigation produced a maximum sound-pressure level of 117.5 decibels when corrected to 1,400 horsepower. This overall noise output represents a lowering of the maximum overall sound-pressure level by approximately 5 decibels from that of the advance-ratio-3.2 propeller and by 14 decibels from that of the advance-ratio-2.2 propeller at comparable engine horsepowers. The frequency spectrum for the present propeller was the same as that for the advance-ratio-3.2 propeller, that is, high sound-pressure levels for the low-blade-passage harmonics with a rapid decrease in level with increasing order of harmonic. The 5-decibels reduction, under static conditions, is not considered sufficient to warrant the increased weight and operational penalties that would accompany this selection over the more efficient advance-ratio-3.2 propeller. At high forward speeds, however, the noise level of the present advance-ratio-4.0 propeller, especially in the fre- quency range where passenger comfort is important, should probably be substantially lower than that of the advance-ratio-3.2 propeller.
Particle analysis has benefitted from the advent of single particle inductively coupled plasma-mass spectrometry (spICP-MS) due to its robustness, sensitivity, and high-throughput nature. Previous methods of spICP-MS have typically utilized quadrupole or time-of-flight mass analyzers and therefore employ electron multiplier-based detectors (such as secondary electron multipliers or microchannel plates). However, to obtain precise measurements on elemental or isotopic ratios within individual particles, multi-collector ICP-MS (MC-ICP-MS) can be used. Here, we investigate Ce isotope ratios, specifically 142 Ce/ 140 Ce, by spMC-ICP-MS using an all-Faraday cup collector array. Using 1 μm (diameter) cerium dioxide particles, integration times of the Faraday cup detectors were varied from 50–500 ms. The signal from the cerium isotopes in the particles was used to determine isotope ratios, which closely matched the expected natural isotopic abundances. Due to the signal decay response from the Faraday cups, the signal from particles lasts much longer than the expected 1–2 ms (up to 100 s of ms). To explore this effect on isotope ratio analysis, multiple ratio analysis methods were used to determine how to obtain optimal precision and accuracy. Relative differences were around 2% for methods that calculated isotope ratios from summing the total signal of an individual particle before calculating the ratio (rather than using every data point individually). It was found that summing all data points per particle, or integrating under the signal peak, yielded both accurate and precise isotope ratios within the particle population. Particles were also sampled off a solid substrate via microextraction, and isotope ratios were determined with relative differences of 0.13% to 9%. This demonstrates the ability to use spMC-ICP-MS to obtain isotope ratios on particles, with little to no relative difference in comparison to the expected ratio, even when operating Faraday detectors at fast 50 ms integration times.
Vehicle/engine analysis studies have identified the High/Dual Mixture Ratio O2/H2 Engine cycle as a leading candidate for an advanced Single Stage to Orbit (SSTO) propulsion system. This cycle is designed to allow operation at a higher than normal O/F ratio of 12 during liftoff and then transition to a more optimum O/F ratio of 6 at altitude. While operation at high mixture ratios lowers specific impulse, the resultant high propellant bulk density and high power density combine to minimize the influence of atmospheric drag and low altitude gravitational forces. Transition to a lower mixture ratio at altitude then provides improved specific impulse relative to a single mixture ratio engine that must select a mixture ratio that is balanced for both low and high altitude operation. This combination of increased altitude specific impulse and high propellant bulk density more than offsets the compromised low altitude performance and results in an overall mission benefit. Two areas of technical concern relative to the execution of this dual mixture ratio cycle concept are addressed. First, actions required to transition from high to low mixture ratio are examined, including an assessment of the main chamber environment as the main chamber mixture ratio passes through stoichiometric. Secondly, two approaches to meet a requirement for high turbine power at high mixture ratio condition are examined. One approach uses high turbine temperature to produce the power and requires cooled turbines. The other approach incorporates an oxidizer-rich preburner to increase turbine work capability via increased turbine mass flow.
This report is based upon engine tests made at the Bureau of Standards during 1920, 1921, 1922, and 1923. The majority of these tests were of aviation engines and were made in the Altitude Laboratory. For a small portion of the work a single cylinder experimental engine was used. This, however, was operated only at sea-level pressures. The report shows that an increase in break horsepower and a decrease in the pounds of fuel used per brake horsepower hour usually results from an increase in compression ratio. This holds true at least up to the highest ratio investigated, 14 to 1, provided there is no serious preignition or detonation at any ratio. To avoid preignition and detonation when employing high-compression ratios, it is often necessary to use some fuel other than gasoline. It has been found that the consumption of some of these fuels in pounds per brake horsepower hour is so much greater than the consumption of gasoline that it offsets the decrease derived from the use of the high-compression ratio. The changes in indicated thermal efficiency with changes in compression ratio are in close agreement with what would be anticipated from a consideration of the air cycle efficiencies at the various ratios. In so far as these tests are concerned there is no evidence that a change in compression ratio produces an appreciable, consistent change in friction horsepower, volumetric efficiency, or in the range of fuel-air ratios over which the engine can operate. The ratio between the heat loss to the jacket water and the heat converted into brake horsepower or indicated horsepower decreases with increase in compression ratio. (author)
We discuss the ratio of ortho- to para-H2 in photodissociation regions (PDRs). We draw attention to an apparent confusion in the literature between the ortho-to-para ratio of molecules in FUV-pumped vibrationally excited states and the total H2 ortho-to-para abundance ratio. These ratios are not the same because the process of FUV pumping of fluorescent H2 emission in PDRs occurs via optically thick absorption lines. Thus gas with an equilibrium ratio of ortho- to para-H2 equal to 3 will yield FUV-pumped vibrationally excited ortho-to-para ratios smaller than 3, because the ortho-H2 pumping rates are preferentially reduced by optical depth effects. Indeed, if the ortho and para pumping lines are on the "square root" part of the curve of growth, then the expected ratio of ortho and para vibrational line strengths is 3(sup 1/2) approximately 1.7, close to the typically observed value. Thus, contrary to what has sometimes been stated in the literature, most previous measurements of the ratio of ortho- to para-H2 in vibrationally excited states are entirely consistent with a total ortho-to-para ratio of 3, the equilibrium value for temperatures greater than 200 K. We present an analysis and several detailed models that illustrate the relationship between the total ratios of ortho- to para-H2 and the vibrationally excited ortho-to-para ratios in PDRs. Recent Infrared Space Observatory measurements of pure rotational and vibrational H2 emissions from the PDR in the star-forming region S140 provide strong observational support for our conclusions.
A wind-tunnel investigation has been made on modified-square and circular cylinders to determine the effects of fineness ratio and Reynolds numbers on the crosswind drag characteristics. Fineness ratios from 2 to 14 were investigated over a Reynolds number range from approximately 300,000 to 1,650,000 which corresponded to Mach numbers from 0.057 to 0.377.The result of the investigation show that at supercraft Reynolds numbers the drag coefficient of the circular cylinder increases with increasing Reynolds number for all fineness ratios but at low fineness ratios this effect is considerably less than at higher fineness ratios. For circular cylinders in the high fineness-ratio range there is a reduction in drag as the fineness ratio is decreased except for Reynolds numbers of 900,000 and 1,000,000, whereas at low fineness ratios the opposite trend generally occurs. The addition of hemispherical ends to the circular cylinder gave a substantial decrease in drag at a fineness ratio of 3.27 but the effect was negligible at fineness ratios of 5.27 and 10. The finite-length modified-square cylinder gave the reduction in drag over the two-dimensional modified-square cylinder for the complete range of test Reynolds numbers with the lowest fineness ratio giving the lowest drag at Reynolds numbers above 3O0,OOO.
An investigation was conducted on a 12-cylinder V-type liquid-cooled aircraft engine of 1710-cubic-inch displacement to determine the minimum specific fuel consumption at constant cruising engine speed and compression ratios of 6.65, 7.93, and 9.68. At each compression ratio, the effect.of the following variables was investigated at manifold pressures of 28, 34, 40, and 50 inches of mercury absolute: temperature of the inlet-air to the auxiliary-stage supercharger, fuel-air ratio, and spark advance. Standard sea-level atmospheric pressure was maintained at the auxiliary-stage supercharger inlet and the exhaust pressure was atmospheric. Advancing the spark timing from 34 deg and 28 deg B.T.C. (exhaust and intake, respectively) to 42 deg and 36 deg B.T.C. at a compression ratio of 6.65 resulted in a decrease of approximately 3 percent in brake specific fuel consumption. Further decreases in brake specific fuel consumption of 10.5 to 14.1 percent (depending on power level) were observed as the compression ratio was increased from 6.65 to 9.68, maintaining at each compression ratio the spark advance required for maximum torque at a fuel-air ratio of 0.06. This increase in compression ratio with a power output of 0.585 horsepower per cubic inch required a change from . a fuel- lend of 6-percent triptane with 94-percent 68--R fuel at a compression ratio of 6.65 to a fuel blend of 58-percent, triptane with 42-percent 28-R fuel at a compression ratio of 9.68 to provide for knock-free engine operation. As an aid in the evaluation of engine mechanical endurance, peak cylinder pressures were measured on a single-cylinder engine at several operating conditions. Peak cylinder pressures of 1900 pounds per square inch can be expected at a compression ratio of 9.68 and an indicated mean effective pressure of 320 pounds per square inch. The engine durability was considerably reduced at these conditions.
Anaerobic ammonium oxidizing (anammox) bacteria are utilized for high efficiency nitrogen removal from nitrogen-laden sidestreams in wastewater treatment plants. The anammox bacteria form a variety of competitive and mutualistic interactions with heterotrophic bacteria that often employ denitrification or dissimilatory nitrate reduction to ammonium (DNRA) for energy generation. These interactions can be heavily influenced by the influent ratio of ammonium to nitrite, NH 4 + :NO 2 - , where deviations from the widely acknowledged stoichiometric ratio (1:1.32) have been demonstrated to have deleterious effects on anammox efficiency. Thus, it is important to understand how variable NH 4 + :NO 2 - ratios impact the microbial ecology of anammox reactors. We observed the response of the microbial community in a lab scale anammox membrane bioreactor (MBR) to changes in the influent NH 4 + :NO 2 - ratio using both 16S rRNA gene and shotgun metagenomic sequencing. Ammonium removal efficiency decreased from 99.77 ± 0.04% when the ratio was 1:1.32 (prior to day 89) to 90.85 ± 0.29% when the ratio was decreased to 1:1.1 (day 89–202) and 90.14 ± 0.09% when the ratio was changed to 1:1.13 (day 169–200). Over this same timespan, the overall nitrogen removal efficiency (NRE) remained relatively unchanged (85.26 ± 0.01% from day 0–89, compared to 85.49 ± 0.01% from day 89–169, and 83.04 ± 0.01% from day 169–200). When the ratio was slightly increased to 1:1.17–1:1.2 (day 202–253), the ammonium removal efficiency increased to 97.28 ± 0.45% and the NRE increased to 88.21 ± 0.01%. Analysis of 16S rRNA gene sequences demonstrated increased relative abundance of taxa belonging to Bacteroidetes, Chloroflexi, and Ignavibacteriae over the course of the experiment. The relative abundance of Planctomycetes, the phylum to which anammox bacteria belong, decreased from 77.19% at the beginning of the experiment to 12.24% by the end of the experiment. Analysis of metagenome assembled genomes (MAGs) indicated increased abundance of bacteria with nrfAH genes used for DNRA after the introduction of lower influent NH 4 + :NO 2 - ratios. The high relative abundance of DNRA bacteria coinciding with sustained bioreactor performance indicates a mutualistic relationship between the anammox and DNRA bacteria. Understanding these interactions could support more robust bioreactor operation at variable nitrogen loading ratios.
The paper presents a study of low aspect blading for the inlet stages of a high pressure ratio, high-speed core compressor. The basic overall design variables were stage pressure ratio and blade aspect ratio; these four stages represent two levels of total pressure ratio, two levels of rotor blade aspect ratio, and two levels of stator vane aspect ratios. Comparisons of the overall performance, radial distributions of performance parameters, diffusion factors at the near-stall conditions, blade element data, and the axial distribution of rotor tip static pressures yielded the following results: (1) higher peak pressure ratio, high stage and rotor efficiencies, and greater stall margin were obtained with the lower aspect ratio blading, (2) the lower aspect ratio blading showed improved performance over the entire blade span, and (3) the lower aspect ratio rotors operated at higher diffusion factors and higher incidence angles over the entire blade span.
Sodium (Na) and Potassium (K) atoms can be seen in the exosphere of Mercury and the Moon because they are extremely efficient at scattering sunlight. These species must be derived from surface materials, so that we might expect the ratio of sodium to potassium to reflect the ratio of these elements in the surface crust. This expectation is approximately born out for the Moon, where the ratio of sodium to potassium in the lunar exosphere averages to be about 6, not too far from the ratio in lunar rocks of 2 to 7. However, the ratio in the Mercury exosphere was found to be in the range 80 to 190, and at least once, as high as 400. The sodium and potassium atoms seen in the Mercury exosphere represent a balance between production from the surface and loss to space. Only if the production efficiencies and loss rates for Na and K were equal, would the ratio of Na to K in the exosphere reflect the ratio in the surface rocks. Since a value of 100 or more for the ratio of sodium to potassium in the surface rocks seems very unlikely, the high values of the observed ratios suggests that either production efficiencies or loss processes for the two elements are not equivalent. It does not seem likely that source processes should be different on the Moon and Mercury by an order of magnitude. This suggests that loss processes rather than source processes are the cause of the difference between the two. The major loss processes for sodium and potassium on Mercury are radiation pressure and trapping of photoions by the solar wind. Radiation pressure can reach 50-70% of surface gravity, and can sweep sodium and potassium atoms off the planet, provided they are sufficiently hot. Photoionization followed by trapping of the ions in the solar wind is the other major loss process. Photoions are accelerated to keV energies in the magnetosphere, and may either intercept the magnetopause, and be lost from the planet, or impact the planetary surface. Ions that impact the surface are neutralized, and are then available for resupply to the exosphere. The loss efficiency depends on characteristics of the magnetosphere that determine the fraction of the ions that are recycled by neutralization on the surface. Over the preceding decade, we have collected sodium and potassium data for Mercury at irregular intervals. We analyzed these data to extract values for the Na/K ratio at a variety of conditions on Mercury. Additional information is contained in the original extended abstract.
An investigation was conducted to evaluate the possibilities of utilizing the high-performance characteristics of triptane and xylidines blended with 28-R fuel in order to increase fuel economy by the use of high compression ratios and maximum-economy spark setting. Full-scale single-cylinder knock tests were run with 20 deg B.T.C. and maximum-economy spark settings at compression ratios of 6.9, 8.0, and 10.0, and with two inlet-air temperatures. The fuels tested consisted of triptane, four triptane and one xylidines blend with 28-R, and 28-R fuel alone. Indicated specific fuel consumption at lean mixtures was decreased approximately 17 percent at a compression ratio of 10.0 and maximum-economy spark setting, as compared to that obtained with a compression ratio of 6.9 and normal spark setting. When compression ratio was increased from 6.9 to 10.0 at an inlet-air temperature of 150 F, normal spark setting, and a fuel-air ratio of 0.065, 55-percent triptane was required with 28-R fuel to maintain the knock-limited brake power level obtained with 28-R fuel at a compression ratio of 6.9. Brake specific fuel consumption was decreased 17.5 percent at a compression ratio of 10.0 relative to that obtained at a compression ratio of 6.9. Approximately similar results were noted at an inlet-air temperature of 250 F. For concentrations up through at least 20 percent, triptane can be more efficiently used at normal than at maximum-economy spark setting to maintain a constant knock-limited power output over the range of compression ratios tested.
A knock-limited performance investigation was conducted on blends of triptane and 28-P fuel with a 12-cylinder, V-type, liquid-cooled aircraft engine of 1710-cubic-inch displacement at three compression ratios: 6.65, 7.93, and 9.68. At each compression ratio, the effect of changes in temperature of the inlet air to the auxiliary-stage supercharger and in fuel-air ratio were investigated at engine speeds of 2280 and. 3000 rpm. The results show that knock-limited engine performance, as improved by the use of triptane, allowed operation at both take-off and cruising power at a compression ratio of 9.68. At an inlet-air temperature of 60 deg F, an engine speed of 3000 rpm ; and a fuel-air ratio of 0,095 (approximately take-off conditions), a knock-limited engine output of 1500 brake horsepower was possible with 100-percent 28-R fuel at a compression ratio of 6.65; 20-percent triptane was required for the same power output at a compression ratio of 7.93, and 75 percent at a compression ratio of 9.68 allowed an output of 1480 brake horsepower. Knock-limited power output was more sensitive to changes in fuel-air ratio as the engine speed was increased from 2280 to 3000 rpm, as the compression ratio is raised from 6.65 to 9.68, or as the inlet-air temperature is raised from 0 deg to 120 deg F.