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A method is presented for determining the lateral-stability derivatives, transfer-function coefficients, and the modes for lateral motion from frequency-response data for a rigid aircraft. The method is based on the application of the vector technique to the equations of lateral motion, so that the three equations of lateral motion can be separated into six equations. The method of least squares is then applied to the data for each of these equations to yield the coefficients of the equations of lateral motion from which the lateral-stability derivatives and lateral transfer-function coefficients are computed. Two numerical examples are given to demonstrate the use of the method.
Half-tipped primary and lateral roots of Phaseolus vulgaris bend toward the side of the root on which the intact half tip remains. Therefore, tips of lateral and primary roots produce growth effectors capable of inducing gravicurvature. The asymmetrical placement of a tip of a lateral root onto a detipped primary root results in the root bending toward the side of the root onto which the tip was placed. That is, the lesser graviresponsiveness of lateral roots as compared with primary roots is not due to the inability of their caps to produce growth inhibitors. The more pronounced graviresponsiveness of primary roots is positively correlated with the presence of columella tissues that are 3.8 times longer, 1.7 times wider, and 10.5 times more voluminous than the columellas of lateral roots. We propose that the lack of graviresponsiveness exhibited by lateral roots is due to the fact that they (i) produce smaller amounts of the inhibitor than primary (i.e., strongly graviresponsive) roots and (ii) are unable to redistribute the inhibitor so as to be able to create a concentration gradient sufficient to induce a pronounced gravitropic response.
A theoretical investigation was conducted to determine the importance of the lateral acceleration (beta) derivatives in the extraction of lateral-directional stability derivatives for swept wing airplanes at high angles of attack. Representative values of lateral acceleration derivatives in yaw and roll (Cn beta and Cl beta) were used in a computer program to generate representative flight motions at several angles of attack and altitudes. The computer-generated motions were then subjected to a parameter identification process based on a modified Newton-Raphson method. Two identification techniques were evaluated, one which included the beta derivatives and one which neglected them. The results of the study indicate that omission of the beta derivatives from mathematical models used in the derivative-extraction techniques can produce erroneous values for the lateral-directional stability derivatives particularly at high angles of attack, where the beta derivatives are large. The largest errors occur in the dynamic derivatives, but large errors may also occur in the static derivatives for cases in which the beta derivatives have large effects on the flight motions of the airplane. In addition, the resulting identified mathematical models provide poor motion prediction as well as erroneous predictions of dynamic modal characteristics. These results strongly indicate that the effects of beta derivatives should be considered in any attempt to extract lateral-directional aerodynamic parameters at high angles of attack.
In Marsilea quadrifolia, lateral roots arise from modified single cells of the endodermis located opposite the protoxylem poles within the meristematic region of the parent root. The initial cell divides in four specific planes to establish a five-celled lateral root primordium, with a tetrahedral apical cell in the centre and the oldest merophytes and the root cap along the sides. The cells of the merophyte divide in a precise pattern to give rise to the cells of the cortex, endodermis, pericycle, and vascular tissues of the emerging lateral root. Although the construction of the parent root is more complicated than that of lateral roots, patterns of cell division and tissue formation are similar in both types of roots, with the various tissues being arranged in similar positions in relation to the central axis. Vascular connection between the lateral root primordium and the parent root is derived from the pericycle cells lying between the former and the protoxylem members of the latter. It is proposed that the central axis of the root is not only a geometric centre, but also a physiological centre which determines the fate of the different cell types.
A summary of methods for making dynamic lateral stability and response calculations and for estimating the aerodynamic stability derivatives required for use in these calculations is presented. The processes of performing calculations of the time histories of lateral motions, of the period and damping of these motions, and of the lateral stability boundaries are presented as a series of simple straightforward steps. Existing methods for estimating the stability derivatives are summarized and, in some cases, simple new empirical formulas are presented. Reference is also made to reports presenting experimental data that should be useful in making estimates of the derivatives. Detailed estimating methods are presented for low-subsonic-speed conditions but only a brief discussion and a list of references are given for transonic- and supersonic-speed conditions.
A method to evaluate the lateral ride quality of a B-1 aircraft subjected to a reduction in lateral static stability is developed. Ride quality is then found for three different relaxed static stability configurations which are augmented by yaw rate feedback to restore specified handling qualities. These cases are compared to the ride quality of the unrelaxed aircraft with the same handling qualities.
Tests have been conducted in the Langley high-speed 7- by 10-foot tunnel over a Mach number range from 0.40 to 0.91 to determine the stability and control characteristics of an 0.08-scale model of the Chance Vought XF7U-1 airplane. The basic lateral stability characteristics of the complete model with undeflected control surfaces are presented in the present report with a very limited analysis of the results.
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We have investigated the influences of lateral variations of viscosity on the moment of inertia tensor from viscous flows due to the density anomalies in the mantle inferred from seismic tomographic models. The scaling relations between the density and the seismic anomalies is taken as either a constant or a function increasing with depth in accord with the recent high-pressure experimental studies. The viscosity is taken as an exponential function of the 3D density anomaly. In models with an isoviscous background, the effects on the perturbed moment of inertia tensor from the lateral viscosity variations are smaller than those due to variations in the radial viscosity profiles. In mantle models with a background viscosity increasing with depth, the influences of the lateral viscosity variations are significant. The most striking feature in the latter case is that the two off-diagonal elements delta I(sub xz) and delta I(sub yz) in the inertia tensor exhibit greatest sensitivity to lateral variations of the viscosity. While the other elements of the inertia change by only about a few tens of percent in the range of lateral viscosity contrast considered (less than 300), delta I(sub xz) and delta I(sub yz) can vary up to 40 times even with a change in sign, depending on the radial viscosity stratification and the location of the strongest lateral variations. The increase in the velocity-density scaling relation with depth can reduce the influences of the lateral viscosity variations, but it does not change the overall sensitive nature of delta I(sub xz) and delta I(sub yz). This study demonstrates clearly that the lateral viscosity variations, especially in the upper mantle, must be considered in the determination of long-term polar wander, since the variations in the delta I(sub xz) and delta I(sub yz) terms are directly responsible for exciting rotational movements.
A flight experiment was conducted to investigate the lateral attenuation of high by pass ratio engined airplanes. A B-747 was flown at low altitudes over the ends of two microphone arrays. One array covering a lateral distance of 1600 m consisted of 14 microphones positioned over grass. The second array covered a lateral distance of 1200 m and consisted of 6 microphones positioned over a concrete runway. Sixteen runs were flown at altitudes ranging from 30 to 960 m. The acoustic information recorded in the field was reduced to one third octave band spectral time histories and synchronized with tracking and weather information. Lateral attenuation as a function of elevation angle was calculated in overall, A-weighted, tone-corrected perceived noise level, and effective perceived noise level units. The B-747 results are compared with similar results for a turbojet-powered T-38 airplane and the SAE recommended lateral attenuation prediction procedure. Less lateral attenuation was measured for the B-747 than for the T-38. The B-747 lateral attenuation values also fell below the SAE curve.
Research on gravity responses in plants has mostly focused on primary roots and shoots, which typically orient to a vertical orientation. However, the distribution of lateral organs and their characteristically non-vertical growth orientation are critical for the determination of plant form. For example, in Arabidopsis, when lateral roots emerge from the primary root, they grow at a nearly horizontal orientation. As they elongate, the roots slowly curve until they eventually reach a vertical orientation. The regulation of this lateral root orientation is an important component affecting overall root system architecture. We found that this change in orientation is not simply due to the onset of gravitropic competence, as non-vertical lateral roots are capable of both positive and negative gravitropism. Thus, the horizontal growth of new lateral roots appears to be determined by what is called the gravitropic set-point angle (GSA). This developmental control of the GSA of lateral roots in Arabidopsis provides a useful system for investigating the components involved in regulating gravitropic responses. Using this system, we have identified several Arabidopsis mutants that have altered lateral root orientations but maintain normal primary root orientation. c2003 COSPAR. Published by Elsevier Ltd. All rights reserved.