Yaw Oscillations Research Articles

Rotation Axes of the Head During Positioning, Head Shaking, and Locomotion

Static head orientations obey Donders' law and are postulated to be rotations constrained by a Fick gimbal. Head oscillations can be voluntary or generated during natural locomotion. Whether the rotation axes of the voluntary oscillations or during locomotion are constrained by the same gimbal is unknown and is the subject of this study. Head orientation was monitored with an Optotrak (Northern Digital). Human subjects viewed visual targets wearing pin-hole goggles to achieve static head positions with the eyes centered in the orbit. Incremental rotation axes were determined for pitch and yaw by computing the velocity vectors during head oscillation and during locomotion at 1.5 m/s on a treadmill. Static head orientation could be described by a generalization of the Fick gimbal by having the axis of the second rotation rotate by a fraction, k, of the angle of the first rotation without a third rotation. We have designated this as a k-gimbal system. Incremental rotation axes for both pitch and yaw oscillations were functions of the pitch but not the yaw head positions. The pivot point for head oscillations was close to the midpoint of the interaural line. During locomotion, however, the pivot point was considerably lower. These findings are well explained by an implementation of the k-gimbal model, which has a rotation axis superimposed on a Fick-gimbal system. This could be realized physiologically by the head interface with the dens and occipital condyles during head oscillation with a contribution of the lower spine to pitch during locomotion.

A Simple Differential Brake Control Algorithm for Attenuating Rearward Amplification in Doubles and Triples Combination Vehicles

SUMMARYA simple brake control algorithm useful for attenuating rearward amplification tendencies in doubles and triples combination trucks is described. The basic goal was to first design, and then to demonstrate through experimental testing, an automatic brake control system that could intervene—only when needed—to help suppress unwanted trailer yaw oscillations (commonly referred to as ‘rearward amplification’) in large combination vehicles (typically doubles and triples combinations in the U.S.). The system would only be enabled for highway speed operating conditions, and if possible, so simple that the system could be provided on a trailer-by-trailer basis. That is, the proposed system, when implemented on a particular trailer within a combination vehicle train, would not have to depend upon sensor information from units ahead of it or behind it in order to function properly and yet provide significant benefit. The primary focus therefore of this work was on the development and demonstration of a so-called “trailer-only” RAMS (Rearward A mplification Suppression) system [1].

Mechanical models for insect locomotion: stability and parameter studies

We extend the analysis of simple models for the dynamics of insect locomotion in the horizontal plane, developed in [Biol. Cybern. 83 (6) (2000) 501] and applied to cockroach running in [Biol. Cybern. 83 (6) (2000) 517]. The models consist of a rigid body with a pair of effective legs (each representing the insect’s support tripod) placed intermittently in ground contact. The forces generated may be prescribed as functions of time, or developed by compression of a passive leg spring. We find periodic gaits in both cases, and show that prescribed (sinusoidal) forces always produce unstable gaits, unless they are allowed to rotate with the body during stride, in which case a (small) range of physically unrealistic stable gaits does exist. Stability is much more robust in the passive spring case, in which angular momentum transfer at touchdown/liftoff can result in convergence to asymptotically straight motions with bounded yaw, fore-aft and lateral velocity oscillations. Using a non-dimensional formulation of the equations of motion, we also develop exact and approximate scaling relations that permit derivation of gait characteristics for a range of leg stiffnesses, lengths, touchdown angles, body masses and inertias, from a single gait family computed at ‘standard’ parameter values.

Lateral-Directional Coupling and Unsteady Aerodynamic Effects of Hypersonic Vehicles

Results from a joint research program of the Institutes of Fluid Dynamics and of Flight Mechanics and Flight Control of the Technical University of Munich on a two-stage space transportation system are presented. The unsteady aerodynamics resulting from an orbital stage at stage separation e ow conditions at Mach number 6.8 are e rst discussed. Unsteady e owe elds associated with yaw and roll oscillations of the orbital stage at a certain distanceabovethecarrierstageareinvestigated.Thecalculationsarebased ona e nitevolumemethodforreal-time solutions of the unsteady Euler equations. Theresultsfocus on pressuredistributions and aerodynamic coefe cients providing an essentialmeansforcarrying outstabilityand control investigations.Inthesecond part, e ightmechanics stability and control problems are addressed considering key issues of lateral ‐directional dynamics. Inherent vehicle characteristics can show specie c stability and e ying quality dee ciencies in hypersonic e ight, concerning a partially unstable dutch roll mode with high roll ‐yaw coupling and weak roll damping. There is also a coupling of the roll and spiral poles for certain cone gurations, yielding a slow, eventually unstable oscillation called lateral phugoid. Reasons and effects for the stability dee ciencies are discussed, including conditions of existence for the lateral phugoid.

The three-dimensional vestibulo-ocular reflex during prolonged microgravity.

Single-case, longitudinal studies of the three-dimensional vestibulo-ocular response (VOR) were conducted with two spaceflight subjects over a 180-day mission. For reference, a control study was performed in the laboratory with 13 healthy volunteers. Horizontal, vertical and torsional VOR was measured during active yaw, pitch and roll oscillations of the head, performed during visual fixation of real and imaginary targets. The control group was tested in the head-upright position, and in the gravity-neutral, onside and supine positions. Binocular eye movements were recorded throughout using videooculography, yielding eye position in Fick co-ordinates. Eye velocity was calculated using quaternion algebra. Head angular velocities were measured by a head-mounted rate sensor. Eye/head velocity gain and phase were evaluated for the horizontal, vertical and torsional VOR. The inclination of Listing's plane was also calculated for each test session. Control group gain for horizontal and vertical VOR was distributed closely around unity during real-target fixation, and reduced by 30-50% during imaginary-target trials. Phase was near zero throughout. During head pitch in the onside position, vertical VOR gain did not change significantly. Analysis of up/down asymmetry indicated that vertical VOR gain for downward head movement was significantly higher than for upward head movement. Average torsional VOR gain with real-target fixation was significantly higher than with imaginary-target fixation. No difference in phase was found. In contrast to vertical VOR gain, torsional VOR gain was significantly lower in the gravity-neutral supine position. Spaceflight subjects showed no notable modification of horizontal or vertical VOR gain or phase during real-target fixation over the course of the mission. However, the up/down asymmetry of vertical VOR gain was inverted in microgravity. Torsional VOR gain was clearly reduced in microgravity, with some recovery in the later phase. After landing, there was a dip in gain during the first 24 h, with subsequent recovery to near baseline over the 13-day period tested. Listing's plane appeared to remain stable throughout the mission. The findings reflect various functions of the otolith responses. The reduced torsional VOR gain in microgravity is attributed to the absence of the gravity-dependent, dynamic stimulation to the otoliths (primarily utricles). On the other hand, the reversal of vertical VOR up/down gain asymmetry in microgravity is attributed to the off-loading of the constant 1-g bias (primarily to the saccules) on Earth. The observed increase in torsional VOR gain from the 1st to the 6th month in microgravity demonstrates the existence of longer-term adaptive processes than have previously been considered. Likely factors are the adaptive reweighting of neck-proprioceptive afferents and/or enhancement of efference copy.

Numerical simulation of the lateral aerodynamics of an orbital stage at stage separation flow conditions

The unsteady flow of an idealized two-stage hypersonic vehicle during the separation process is investigated. In particular, the aerodynamic characteristics of the orbital stage performing yaw and roll oscillations with defined frequencies at a certain distance above the lower stage are addressed. The numerical simulations of the flowfield are based on an explicit finite-volume method for solutions of the three-dimensional unsteady Euler equations. The discretization of the computational domain around the entire configuration is performed using a flexible multiblock grid generator. The results focus on the flowfields and the pressure distributions as well as on the aerodynamic coefficients. The latter provide an essential mean for the stability and control evaluations for lateral motion in hypersonic flight. The analysis show that unsteadiness cannot be neglected.

Yaw and pitch visual-vestibular interaction in weightlessness

Both yaw and pitch visual-vestibular interactions at two separate frequencies of chair rotation (0.2 and 0.8 Hz) in combination with a single velocity of optokinetic stimulus (36 degrees/s) were used to investigate the effects of sustained weightlessness on neural strategies adopted by astronaut subjects to cope with the stimulus rearrangement of spaceflight. Pitch and yaw oscillation in darkness at 0.2 and 0.8 Hz without optokinetic stimulation, and constant velocity linear optokinetic stimulation at 18, 36, and 54 degrees/s presented relative to the head with the subject stationary, were used as controls for the visual-vestibular interactions. The results following 8 days of space flight showed no significant changes in: (1) either the horizontal and vertical vestibulo-ocular reflex (VOR) gain, phase, or bias; (2) the yaw visual-vestibular response (VVR); or (3) the horizontal or vertical optokinetic (OKN) slow phase velocity (SPV). However, significant changes were observed: (1) when during pitch VVR at 0.2 Hz late inflight, the contribution of the optokinetic input to the combined oculomotor response was smaller than during the stationary OKN SPV measurements, followed by an increased contribution during the immediate postflight testing; and (2) when during pitch VVR at 0.8 Hz, the component of the combined oculomotor response due to the underlying vertical VOR was more efficiently suppressed early inflight and less suppressed immediately postflight compared with preflight observations. The larger OKN response during pitch VVR at 0.2 Hz and the better suppression of VOR during pitch VVR at 0.8 Hz postflight are presumably due to the increased role of vision early inflight and immediately after spaceflight, as previously observed in various studies. These results suggest that the subjects adopted a neural strategy to structure their spatial orientation in weightlessness by reweighting visual, otolith, and perhaps tactile/somatic signals.

Interaction of Semicircular Canal Stimulation with Carotid Baroreceptor Reflex Control of Heart Rate

The carotid-cardiac baroreflex contributes to the prediction of orthostatic tolerance; experimental attenuation of the reflex response leads to orthostatic hypotension in humans and animals. Anecdotal observations indicate that rotational head movements about the vertical axis of the body can also induce orthostatic bradycardia and hypotension through increased parasympathetic activity. We therefore measured the chronotropic response to carotid baroreceptor stimulation in 12 men during varying conditions of vestibulo-oculomotor stimulation to test the hypothesis that stimulation of the semicircular canals associated with head movements in the yaw plane inhibits cardioacceleration through a vagally mediated baroreflex. Carotid-cardiac baroreflex response was assessed by plotting R-R intervals (ms) at each of 8 neck pressure steps with their respective carotid distending pressures (mmHg). Calculated baroreflex gain (maximal slope of the stimulus-response relationship) was measured under 4 experimental conditions: 1) sinusoidal whole-body yaw rotation of the subject in the dark without visual fixation (combined vestibular-oculomotor stimulation); 2) yaw oscillation of the subject while tracking a small head-fixed light moving with the subject (vestibular stimulation without eye movements); 3) subject stationary while fixating on a small light oscillating in yaw at the same frequency, peak acceleration, and velocity as the chair (eye movements without vestibular stimulation); and 4) subject stationary in the dark (no eye or head motion). Head motion alone and with eye movement reduced baseline baroreflex responsiveness to the same stimulus by 30%. Inhibition of cardioacceleration during rotational head movements may have significant impact on functional performance in aerospace environments, particularly in high-performance aircraft pilots during high angular acceleration in aerial combat maneuvers or in astronauts upon return from spaceflight who already have attenuated baroreflex functions.

MOTORCYCLE TYRE MEASUREMENTS AND MODELS

Motorcycle stability has been the research subject for a EU sponsored project in the Brite En Ram framework. The other partners were Pirelli, BMW and Marzocchi. A new steady state and a dynamic tyre model have been developed and incorporated in the simulation model at BMW. Steady state measurements were performed with the Delft tyre test trailer on public roads. The MF lyre model has been improved to fit the road measurements accurately at large camber angles and to ensure a consistent behaviour outside the measured domain. Dynamic experiments were carried out on two test rigs: The yaw oscillation and the pendulum lest rig, mounted on top of a rotating drum. Compared to these measurements it shows that the range of application of the simpler stretched string based model is limited due to gyroscopic effects of the tyre belt. A lyre model describing the tyre belt dynamics shows large improvements and is applicable to 25 Hz up to 250 km/h.

Effects of vestibular and oculomotor stimulation on responsiveness of the carotid-cardiac baroreflex.

Twelve healthy men underwent measurement of their carotid-cardiac baroreflex response during varying conditions of vestibulo-oculomotor stimulation to test the hypothesis that vestibular and/or oculomotor stimulation associated with head movements in the yaw plane inhibit baroreflex control of heart rate. We assessed the carotid-cardiac baroreflex response by plotting R-R intervals (in milliseconds) at each of eight neck pressure steps with their respective carotid distending pressures (in millimeters mercury). Baroreflex sensitivity was measured under four experimental conditions: 1) sinusoidal whole body yaw rotation of the subject in the dark without visual fixation (combined vestibular-oculomotor stimulation); 2) yaw oscillation of the subject while tracking a small head-fixed light moving with the subject (vestibular stimulation without eye movements); 3) subject stationary while fixating on a small light oscillating in yaw at the same frequency, peak acceleration, and velocity as the chair (eye movements without vestibular stimulation); and 4) subject stationary in the dark (no eye or head motion). Head motion alone reduced baseline baroreflex responsiveness by 30% from 3.8 +/- 0.5 to 2.6 +/- 0.5 ms/mmHg. Eye motion alone also reduced the baroreflex response by 13% (0.5 ms/mmHg) to 3.3 +/- 0.5 ms/mmHg. During head motion, the effect of eye motion was negligible (2.7 +/- 0.4 ms/mmHg). These results suggest that vestibular stimulation associated with head movements in yaw inhibits vagally mediated baroreflex control of heart rate, whereas oculomotor stimulation is less of a factor and only in the absence of vestibular stimulation.

Adaptation of primate vestibuloocular reflex to altered peripheral vestibular inputs. II Spatiotemporal properties of the adapted slow-phase eye velocity.

1. The ability of the vestibuloocular reflex (VOR) to undergo adaptive modification after selective changes in the peripheral vestibular system was investigated in rhesus monkeys by recording three-dimensional eye movements before and after inactivation of selective semicircular canals. In the preceding paper we showed that the horizontal VOR gain evoked by passive yaw oscillations after lateral semicircular canal inactivation recovers gradually over time in a frequency-specific manner. Here we present the spatial tuning of the adapted slow-phase eye velocity and describe its spatiotemporal properties as a function of time after canal inactivation. 2. The spatial organization of the VOR was investigated during oscillations at different head positions in the pitch, roll, and yaw planes, as well as in the right anterior/left posterior and left anterior/right posterior canal planes. Acutely after bilateral inactivation of the lateral semicircular canals, a small horizontal response could still be elicited that peaked during rotations in pitched head positions that would maximally stimulate vertical semicircular canals. In addition, the phase of horizontal slow-phase velocity abruptly reversed through 180 degrees at positions close to upright, similarly to torsional slow-phase velocity. These spatial response properties suggest that the small, residual horizontal response components that are present acutely after plugging of both lateral canals originate from vertical semicircular canal signals. 3. As the horizontal response amplitude increased over time, consistent changes were also observed in the spatiotemporal tuning of horizontal slow-phase velocity. 1) The spatiotemporal response properties of horizontal slow-phase velocity acquired noncosine tuning characteristics, primarily in the pitch plane, in the right anterior/left posterior and left anterior/right posterior canal planes. Accordingly, horizontal response amplitude was nonzero during rotation in any head position in these planes and response phase varied significantly as a function of head orientation. 2) The peak horizontal response amplitude shifted spatially over time, such that 5-10 mo after plugging it was maximal during rotations at head positions close to upright. 4. In parallel to these unique spatiotemporal response properties characterizing the adapted horizontal VOR, torsional slow-phase velocity also exhibited small spatiotemporal changes after lateral canal inactivation that tended to precede in time the changes associated with the horizontal response components. In contrast, vertical slow-phase velocity in the plugged animals was unaltered and continued to be characterized by cosine-tuned spatial properties in three dimensions. 5. Recovery of the horizontal response gain during yaw oscillations in upright position, as well as the unique, noncosine spatiotemporal characteristics of the adapted horizontal VOR, were also observed in an animal with all but one vertical semicircular canals inactivated. There was, however, no sign of VOR gain recovery up to 2 mo after all semicircular canals were inactivated. These results suggest that the observed recovery of horizontal VOR is at least partly due to signals originating from the remaining intact vertical canal(s). Even in the presence of a single intact vertical canal, the improvement in horizontal gaze stability is at least partly restored through spatiotemporal changes in the processing of vestibuloocular signals that improve the gain and spatial tuning of horizontal VOR at the expense of temporal response properties.

Adaptation of primate vestibuloocular reflex to altered peripheral vestibular inputs. I. Frequency-specific recovery of horizontal VOR after inactivation of the lateral semicircular canals.

1. The adaptive plasticity of the vestibuloocular reflex (VOR) following a selective lesion of the peripheral vestibular organs was investigated in rhesus monkeys whose lateral semicircular canals were inactivated by plugging of the canal lumen in both ears. Gain and phase of horizontal, vertical, and torsional slow-phase eye velocity were determined from three-dimensional eye movement recordings obtained acutely after the plugging operation, as well as in regular intervals up to 10 mo later. 2. Acutely after plugging, horizontal VOR was minimal during yaw rotation with gains of < 0.1 at all frequencies. Horizontal VOR gain gradually increased over time, reaching gains of 0.4-0.5 for yaw oscillations at 1.1 Hz approximately 5 mo after lateral canal inactivation. This response recovery was strongly frequency dependent: horizontal VOR gains were largest at the highest frequency tested and progressively decreased for lower frequencies. Below approximately 0.1 Hz, no consistent horizontal VOR could be elicited even 10 mo after plugging. 3. The frequency-dependent changes in gain paralleled changes in horizontal VOR phase. Below approximately 0.1-0.05 Hz large phase leads were present, similarly as in semicircular canal primary afferents. Smaller phase leads were also present at higher frequencies, particularly at 1.1 Hz (the highest frequency tested). 4. Consistent with the afferent-like dynamics of the adapted horizontal VOR, per- and postrotatory horizontal responses to constant-velocity yaw rotations were short lasting. Time constants of the slow-phase eye velocity envelope of the horizontal postrotatory nystagmus were approximately 2 s. Nonetheless, a consistent horizontal optokinetic afternystagmus was evoked in plugged animals. 5. A torsional component that was absent in intact animals was consistently present during yaw rotation acutely after lateral canal inactivation and remained approximately constant thereafter. The frequency response characteristics of this torsional component resembled those of the adapted horizontal slow-phase responses: gain decreased and large phase leads were introduced at frequencies below approximately 0.05-0.1 Hz. Torsional responses elicited by roll oscillations in supine position, on the other hand, were indistinguishable in their dynamics from intact animals. No consistent vertical nystagmus was elicited during yaw rotation. 6. Our results show that there is a slow, frequency-specific recovery of horizontal VOR after selective inactivation of the lateral semicircular canals. Both the spatial organization and the dynamic properties of the adapted VOR responses are distinctly different from responses in intact animals, suggesting complex changes in the underlying vestibuloocular circuitry.

Participation of the caudal fastigial nucleus in smooth-pursuit eye movements. I. Neuronal activity.

1. We recorded single-unit activity from neurons of an output of the cerebellum, the fastigial nucleus, in two rhesus macaques while the monkeys tracked small moving targets with their eyes. Many neurons in the caudal part of the fastigial nucleus exhibited a modulation in their discharge rates when smooth-pursuit eye movements were elicited by either sinusoidal or step-ramp motions of a small target. 2. The pursuit direction that elicited the most vigorous modulation in unit firing to sinusoidal target motion could be horizontal, vertical, or oblique. Most often, the preferred direction was in the contralateral and/or downward direction (50 of 69 neurons) or in the ipsilateral and/or upward direction (13 of 69). 3. For units whose preferred smooth-pursuit directions were either contralateral/downward or ipsilateral/upward during sinusoidal pursuit, peak firing as measured by the phase shift of periodic modulation at 0.5-0.8 Hz occurred near the time of peak velocity. The discharge of 80% of the neurons with contralateral/downward preferred directions preceded eye velocity by an average of -27 degrees; thus these neurons discharged maximally during eye acceleration. In contrast, neurons with ipsilateral/upward preferred directions lagged peak velocity by an average of +10.5 degrees and therefore discharged during eye deceleration. 4. The average eye velocity sensitivity for sinusoidal pursuit between 0.5 and 0.8 Hz was 0.83 +/- 0.57 (SD) spikes/s per degrees/s. We also tested 36 units during pursuit at a variety of frequencies in their preferred directions and found that firing rates increased monotonically with peak eye velocity. However, the firing rate saturated at velocities ranging from 20 to 60 degrees/s for different units. 5. When a monkey tracked a step-ramp target motion, three discharge patterns emerged in the 27 units tested. Just over half of the units discharged a burst of spikes that preceded (average lead of 27.4 +/- 17 ms) and lasted throughout the initial third of the eye acceleration; the burst was followed by a subsequent steady firing that continued after the eye had accelerated to its steady velocity. Fewer neurons discharged a burst that began late in the acceleration and was followed by steady firing. Occasional neurons showed only a gradual increase in firing rate during acceleration followed by a steady discharge. 6. Thirty of the 31 fastigial smooth-pursuit units tested also were modulated during sinusoidal yaw and/or pitch oscillations while the animals fixated a spot that rotated with them.(ABSTRACT TRUNCATED AT 400 WORDS)

Yaw modelling of small wind turbines

A simple modification to standard blade element modelling is described which addresses flow expansion through the rotor. This modification allows the calculation of rotor moments in yawed flow, which are important to the overall yaw behaviour of the machine. These results are used in a simple model of yaw behaviour and compared with yaw error, yaw oscillation and furling test data for a small wind turbine generator, the Marlec FM1800.

Yaw direction neurons in the cat inferior olive.

1. Single units that responded to yaw rotation were recorded extracellularly in the caudal inferior olive (IO) of barbiturate-anesthetized cats. Of 276 neurons, 55 responded reliably to yaw, and extensive quantitative data were recorded from 25. 2. No yaw-sensitive IO neuron responded to somatosensory or auditory stimuli but two responded, though unreliably, to flash. 3. Yaw-sensitive IO cells fired at low (1-4 spikes/s), irregular rates during one direction of rotation. Though cells responded reliably during yaw, firing rates varied considerably from cycle to cycle. Rotation speed and acceleration were not represented in any cell's firing rate. 4. Eighty five percent (47/55) of yaw-sensitive cells fired during contralateral rotation, 9% (5/55) during ipsilateral rotation, and 6% (3/55) fired from late in the ipsilateral phase of a sinusoidal oscillation to the middle of the contralateral phase. 5. Responses were tested to 0.1-Hz sinusoidal yaw oscillations with a range of peak angular velocities (1-200 degrees/s). Thresholds were not sharp because of the cycle to cycle variability in response rates but were estimated using averaged responses. The peak rate of the most sensitive cell was driven to criterion (2 SD above spontaneous rate) by an oscillation with a peak velocity of 1 degrees/s. Other cells reached criterion between 5 and 50 degrees/s. 6. Sinusoidal oscillation at all frequencies tested (0.01-0.5 Hz) elicited approximately the same firing rates. Even at 0.01 Hz cells responded well. Responses lagged acceleration by approximately 25 degrees at 0.01 Hz and shifted to later parts of the cycle as frequency increased so that firing lagged acceleration by approximately 200 degrees at 0.5 Hz. 7. Histological reconstruction showed that yaw-sensitive neurons were recorded in olivary subnucleus beta (N beta), the dorsal cap of Kooy (DC), the posterior medial region of the medial accessory division of the inferior olive (MAO), and in the medial-lateral center of the caudal MAO. 8. Yaw-sensitive neurons in the inferior olive provide a signal to the cerebellum that indicates the direction of passive rotation over a wide range of velocity and acceleration. The signal from individual neurons does not reliably encode either rotation velocity or acceleration. Yaw-sensitive IO neurons are therefore unlike other central vestibular neurons but are similar to somatosensory IO cells which signal the presence, but not the intensity of a stimulus.

Limit cycle stability of aerodynamically induced yaw oscillations

The aerodynamic yaw moment is written generally as a Taylors-Fourier series. Truncation of the series and assembly of the model leads to a second order non-linear differential equation which bears some similarity to the Van der Pol equation. The system is then examined both on the phase plane and by an approximate stability analysis. The stable and unstable limit cycles, nested around periodic foci are generated and discussed. Finally, loop diagrams are introduced; it is felt that these will have applications beyond the bounds of this paper.

Low-Speed Controllability of Ships in Wind

Aerodynamic and hydrodynamic data for the Manner-class vessel, gathered in earlier experiments, were used to formulate a mathematical model representing the dynamic behavior of ships in wind. A digital computer was used to solve the eigenvalues of the system. Perturbation equations were linearized, with respect to equilibrium conditions, from nonlinear equations of motion. In addition, ship trajectory in certain wind conditions was examined by means of numerical solutions of the nonlinear equations of motion. Results indicate that the ship in bow wind tends, even without an autopilot system, to maintain its original course-with perturbation in yaw inducing yaw oscillations, the convergence of which depends upon the magnitude of relative wind velocity. It is shown that beam wind creates greater difficulties, although the use of an adequate autopilot increases the region of stability in wind of certain velocities (except in some conditions of relatively strong beam wind). An increase in rudder size is shown to improve controllability in wind significantly. Computations with and without the assumption of constant longitudinal speed indicate that the effect of surge motion on yaw and sway responses in wind is important, especially in beam wind.

The initial disturbances affecting the direction of trajectory of a shot fired from a high-velocity gun

The object of the investigation was to determine, both theoretically and practically, the effect on the subsequent shot motion of the initial interactions between a high-velocity gun, its mounting, the gas discharge from the muzzle and the shot, in order to evaluate the unknown relative magnitudes of various causes of trajectory inconsistency, with a view to reducing such inconsistency in both existing and later designs of similar weapons. In the investigation theoretical considerations are compared with measurements made during an extensive experimental programme. This began with a study of the lateral muzzle movements of two gun types (6 and 17 pounders) by means of a novel optical-lever method which eliminates shock disturbances. The recorded movements were found to disagree with those calculated on an existing elastic theory based on a simplified model of the dynamical system, but during the course of the work a more elaborate model was shown to give some measure of agreement for one of the gun types. The measured muzzle displacement at shot ejection in general did not represent the major direct contribution to the 'jump’ recorded on the target. To determine the relative importance of other contributory causes the programme was extended to measurements of the yaw oscillations of the shot when travelling down the bore and through the post-ejection blast zone, these being achieved by means of a novel method in which a mirror was positioned on the nose of the shot, supplemented by X-ray flash photography in the blast zone and jump card observations just outside the blast zone. The work has enabled the major contributions to gun and projectile inaccuracies in the systems tested to be evaluated and explained, and indicates general principles for their improvement.