Pitch Mode Research Articles

Design of optimal decoupling controllers Application to VTOL

The method of linear-quadratic optimization, known as implicit optimal model-following, is applied to the decoupling of three modes, the horizontal, vertical and pitch modes of a hovering vertical take-off and landing (VTOL) aircraft. That is. instead of the pilot having to handle directly the four actual VTOL controls (the magnitudes and angle of two main jet engines and the differential magnitude of small pitching jets) which are all coupled to all the aircraft modes, ho is to be provided with three controls which control, via feedforward and feedback controllers, the three modes in an uncoupled fashion ; this greatly alleviates his control task in precision low-speed manoeuvres. The motion of the jet-controlled VTOL in the vertical plane of symmetry is described by differential equations having four state variables and four bounded control variables. Considerable decoupling was attainable within the bounds on the controls, by means of linear feedforward and feedback controllers, of 24 gains and 16 gain...

Dynamics of a Flexible Passive Space Array

A passive space communicator in synchronous orbit will consist of small aluminum beads chained together and aligned vertically by the Earth's gravity gradient. The analysis for small deviations from vertical uses a continuous-chain model, and pitch and roll frequencies and mode shapes are described with and without the attachment of substantial end masses. An end mass with appreciable moment of inertia can provide effective damping of the lowest-order, otherwise rigid and undamped, modes. The distortion of the chain by solar radiation pressure is estimated, assuming undesirable variations in the mass-to-area ratio of beads and end masses.

Dichotic perception of virtual pitch: Dependence on subjective lateral position of partials

Two general principles of pitch perception, analytic mode resulting in spectral pitch and synthetic mode resulting in virtual pitch have been investigated [E. J. Terhardt, Acoust. Soc. Am. 55, 1061–1069 (1974)]. It is assumed that virtual pitch is a product of Gestalt—perception, associated with some kind of learning process. If this concept is valid, it can be distinguished between spectral-pitch listeners (type I) and virtual-pitch listeners (type II). Complex tones consisting of components (a) 220, 330, 440, 550, and 660 Hz presented to the left ear and 550 and 660 Hz to the right ear were followed by (b) 200, 300, 400, 500, and 600 Hz left and 200, 400, and 600 right, which fused partially. The subjects were asked to decide whether pitch (a) or (b) was higher. Type I listeners responded (b) due to the spectral pitch of the corresponding lateral positions of the partials in the head, whereas type II listeners responded (a) referring to the missing fundamental of 110 Hz. In a second run the subjects were asked to pay specific attention to the different lateral positions too and again type I listeners differed from type II. The results are discussed in terms of Gestalt—rules and theory of pitch perception. [Work supported by AKG, Vienna.]

Perturbation-Energy Approach for the Development of the Nonlinear Equations of Ship Motion

A perturbation analysis of the nonlinear coupling between the pitch and roll modes is used to illustrate that an energy approach can be used to advantage in developing the nonlinear equations governing the motion of ships. It is shown that employing Taylor series expansions to determine the loads on the hull of a ship can lead to the physically unrealistic prediction of self-sustained oscillations, unless certain relationships among the nonlinear coefficients are satisfied. It is shown that the simplified equations of motion which result after imposing these relationships can be found directly from an energy formulation of the problem. The energy approach is used to develop the nonlinear equations governing the roll and pitch modes to third order and the equations governing motions having six degrees-of-freedom to second order.

Dynamic performance of the SRI Maglev vehicle

The stability and ride quality of a small scale MAGLEV test vehicle were determined by measuring its motions in five degrees of freedom during levitated flight. Various offsets were introduced into the guideway to stimulate strongly different modes of oscillation and to search for instabilities. These offsets, that were up to 25% of the equilibrium suspension height, induced motions that were analyzed to evaluate both passive and active damping systems used on the vehicle. In more than thirty tests of the vehicle, including stimulations of the heave, roll, pitch, yaw, and slip modes of oscillation, no instabilities were observed in any degree of freedom whether using passive or active damping. The active damping system, used in conjunction with the passive system, provided greater stability and ride quality than the passive system alone. The passive system, however, provided enough damping to achieve stability and is therefore a desirable back-up in the event of a failure in the active control system. The tests were simulated on a computer using a completely nonlinear dynamics model and provided good approximations to the data. Extrapolations to full-size vehicles have not been made.

Subharmonic and Superharmonic Resonances in the Pitch and Roll Modes of Ship Motions

We considered the motion of a ship with two degrees of freedom—pitch and roll—when secondorder, static couplings are included in the equations of motion, and we obtained a nonlinear analysis of the response of the ship to a harmonic excitation (i.e., a regular sea) using the method of multiple scales. In the first part of the paper, we considered the pitch frequency to be twice the roll frequency and found that a superharmonic response exists for any value of the amplitude of the excitation, but a subharmonic response is possible only if the amplitude of the excitation is above a critical value. In the second part of the paper, we considered ships without the two-to-one frequency ratio. We found that there are five resonant situations and, depending on the value of the parameters, three can involve large motions. Some of the present results were combined with some results from a previous paper to determine the variation of the amplitude of the response with the encounter frequency. Also, the accuracy of some of the present results was established by comparing them with a numerical solution.

Nonlinear Coupling of Pitch and Roll Modes in Ship Motions

An analysis is presented for the nonlinear coupling of the pitch (heave) and roll modes of ship motions in regular seas when their frequencies are in the ratio of two to one. When the frequency of encounter (excitation frequency) is near the pitch frequency, the pitch mode is excited if the encountered wave amplitude (excitation amplitude) is small. As the excitation amplitude increases, the amplitude of the pitch mode increases until it reaches a critical small value. As the excitation amplitude increases further, the pitch amplitude does not change from the critical value (i.e., the pitch mode is saturated), and all of the extra energy is transferred to the roll mode. Thus, for large excitation amplitudes, the amplitude of the roll mode is very much larger than that of the pitch mode. When the excitation frequency is near the roll frequency, there is no saturation phenomenon and at close to perfect resonance, there is no steady state response in some cases. The present results indicate that large roll amplitudes are likely in this case also.

Quadratic Performance Indices and Optimum Suspension Design

This paper presents some results obtained from the computer simulation of a two-dimensional linear vehicle model with coupled bounce and pitch modes. The effects of variations in the ratio of front to rear spring stiffnesses and the inertia coupling ratio on various performance indices for ride quality and road holding were investigated. Two forms of input to the system were considered, ( a) isolated smooth bumps of varying length and ( b) continuous random type excitations. Allowance was made for the time delay between the inputs at the front and rear wheels due to the forward speed of the vehicle.

Quadratic Performance Indices and Optimum Suspension Design

This paper presents some results obtained from the computer simulation of a two-dimensional linear vehicle model with coupled bounce and pitch modes. The effects of variations in the ratio of front to rear spring stiffnesses and the inertia coupling ratio on various performance indices for ride quality and road holding were investigated. Two forms of input to the system were considered, ( a) isolated smooth bumps of varying length and ( b) continuous random type excitations. Allowance was made for the time delay between the inputs at the front and rear wheels due to the forward speed of the vehicle.

Experimental Determination of Steady and Unsteady Loads on a Surface Piercing, Ventilated Hydrofoil

Measured steady and unsteady section lift and moment coefficients at two spanwise locations on a surface-piercing ventilated hydrofoil are presented. The foil, of wedge cross section, was supported vertically, and submerged one chord length from the tip. Excitation in rigid-body rolling and pitching modes to the cantilevered foil produced the unsteady loads. All tests were made at a nominal angle of attack of 12 deg.

Experimental Determination of Steady and Unsteady Loads on a Submerged Supercavitating Hydrofoil

Measured spanwise distributions of steady-state and oscillatory lift and moment on a fully submerged supercavitating hydrofoil are presented. The foil had a rectangular planform of aspect ratio 5, and was excited in rigid-body rolling and pitching modes for the oscillatory tests. Considerable difficulty was experienced in the data reduction because of high noise levels, but a significant amount of data was recovered. All tests were made at a single angle of attack of 1 2 deg.

Effect of masking on the pitch of periodic pulses.

The pulse-train pitch-matching experiments of Flanagan and Guttman have been extended to investigate the effect of selective masking on the pitch of these stimuli. For unmasked stimuli, at pulse repetition rates below approximately 150 pps, a pitch mode correlated with the pulse repetition rate is generally obtained; at fundamental frequencies higher than approximately 150 cps (and below 800 cps), a pitch mode correlated with the fundamental frequency is generally obtained even if the fundamental component has been rejected from the challenge stimulus by filtering. There is a transition region of repetition rates of the challenge stimulus in which the cues for both pitch modes are strongly competing. Present results indicate that if, to challenge stimuli in or near the transition region, high-pass noise (1000-cps cutoff) is added the “buzz” quality associated with the pulse-rate mode can be masked and a fundamental-frequency pitch judgment elicited. Conversely, low-pass noise (1000-cps cutoff) can mask the “tonal” quality associated with the fundamental-frequency mode and elicit pulse-rate pitch judgments. Narrow bands of noise or sinusoids are equally effective as maskers. Fundamental-frequency pitch judgments and pulse-rate pitch judgments are suppressed by narrow bands of noise or sinusoids centered at about 500 and 5000 cps, respectively. It is concluded that, for pulse-train stimuli with repetition rates in or near the transition region, fundamental-frequency and pulse-rate pitch modes are associated with distinct auditory channels below 1000 and above 1000 cps, respectively, with special prominence to the regions near 500 and 5000 cps, respectively. It is further suggested that these results tend to support periodicity mechanisms for mediating these modes of pitch perception.

Ride comfort for tractor operators: III. Investigation of tractor dynamics by analogue computer simulation

The derivation is discussed of an analogue computer model for investigating the vertical and pitch modes of ride vibration of a tractor. Measurements of pitch moment of inertia are reported together with the dynamic characteristics of a range of pneumatic tyres, measured by transient analysis. A comparison between the dynamic performance of the simulated computer model and the original tractor showed good agreement despite considerable approximation in assuming linear tyre characteristics.

SOME APPLICATIONS OF DETAILED WIND PROFILE DATA TO LAUNCH VEHICLE RESPONSE PROBLEMS

SOME APPLICATIONS OF DETAILED WIND PROFILE DATA TO LAUNCH VEHICLE RESPONSE PROBLEMS

Pitch of Periodic Pulses without Fundamental Component

The pitch of a periodic pulse train is matched to that of another train whose fundamental component of frequency is rejected. Three modes of pitch perception are found. The first obtains for pulse rates less than 100 pps. Here, in a manner similar to that found previously for unfiltered stimuli, the pitches are matched to equate pulse rate, regardless of the polarity patterns of the trains. The second mode occurs for fundamental frequencies in the approximate range 200–500 cps. Here there is a decided tendency to equate fundamental frequencies. The third mode is manifested for fundamental frequencies of the order of 1000 cps and higher. In this range subjects tend to equate the fundamental of the matching tone to the lowest spectral component present in the matched stimulus. Between the modes, transition regions exist in which the pitch assignment generally is difficult and uncertain. The stimuli are studied with an electrical analog of the basilar membrane. Waveforms of membrane displacement and first spatial derivative of displacement are obtained from the analog. The three (psychophysical) pitch modes are found to be manifested in these mechanical functions of the basilar membrane.

On the Pitch of Periodic Pulses

Subjects adjusted the frequency of one periodic pulse train to match the pitch of another train fixed in frequency. Two modes of pitch perception are found. In the first mode, for pulse rates less than 100 pps, the pulse trains are ascribed a pitch equal to the number of pulses per second, regardless of the polarity pattern of the pulses. In the second mode, for fundamental frequencies in excess of 200 cps, the sounds are assigned a pitch equal to the fundamental frequency. Between these frequency regions a mode transition occurs in which the pitch judgments generally fall between the pulse-rate and fundamental-frequency values. Amplitude and phase spectra are computed for the stimuli. The stimuli are studied on an electrical analog of the basilar membrane. Waveforms of membrane displacement and first spatial derivative of displacement are obtained from the analog. An effort is made to correlate the psychophysical results with the displacement and derivative patterns observed on the analog membrane. The two pitch modes are found to be manifested in the mechanical operation of the cochlea.

The Riding Qualities of Wheeled Vehicles

A wheeled vehicle traversing an irregular road surface is subjected to forced vibration. This vibration is analysed into heaving, pitching, and rolling modes, and means are described to compute or simulate the response of the vehicle both to continuous excitation at definite frequencies, and to isolated obstacles affecting one wheel at a time. It is shown that a simple model, comprising only rigid masses, linear springs, and velocity damping, suffices to represent the riding quality of the vehicle, and a procedure by which the model may be matched to the vehicle as closely as possible is described. The theory is illustrated by computation of the impact loads imposed on the wheels of a six-wheeled lorry when surmounting artificial obstacles, allowance being made for the effects both of the wheels leaving the road, and of interaction between the four wheels in the rear truck. Good agreement with experimental records of wheel load is shown, and it is suggested that similar computation or simulation applied to passenger-carrying vehicles would prove of value in the improvement of riding quality.

Improving the dynamic response of airplanes by means of electric equipment

This paper begins with an elementary discussion of the mechanics of airplane flight and control. Following this discussion electrical methods for improving the transient response of an airplane in the yawing and pitching modes are outlined and illustrated by two examples. The paper is concluded by a brief discussion of a method by which an airplane cable control system can be replaced by an electric servomechanism. Results of analyses using differential equations and Nyquist plots are discussed and compared with results obtained on an analogue computer.