Constant Thrust Research Articles

Radially accelerated periodic orbits in the Clohessy-Wiltshire frame

A semi-analytic method for determining the periodic trajectories of a spacecraft under the influence of a constant small thrust directed from a central station in a circular orbit is presented using the Clohessy-Wiltshire equations. The amplitude and frequency of the radially accelerated periodic trajectories are semi-analytically derived. A simple on-off orbital control scheme to change the amplitude of these radially accelerated trajectories is also proposed and numerically verified. These radially accelerated periodic orbits are applicable for a smallthrust laser-propelled space vehicle mission in the vicinity of an Earth orbiting laser station.

Ferrous Fibre Network Materials for Jet Noise Reduction in Aeroengines Part I: Acoustic Effects

This paper describes an investigation into the acoustic effects of introducing tubular modules, made of highly porous ferrous materials, into the exhaust region of a small turbojet aeroengine. The modules are composed of sintered stainless steel fibre networks, with void contents in the approximate range of 80-95%. Some of the modules incorporated radial gradients of void content, produced by bonding together thin layers of different density. Measurements of acoustic intensity, as a function of frequency, have been made with various module geometries and locations, and data have also been acquired relating to engine thrust, engine speed and fuel consumption. It is shown that significant reductions in noise level (up to ~10 dB) can be achieved, at approximately constant thrust and fuel consumption, by the introduction of modules of this type. Such effects can arise both via modification to the gas flow field (and hence to noise generation characteristics) and by attenuation of acoustic waves within the modules. Reductions in noise creation will tend to be specific to the gas flow field within the engine concerned, but acoustic attenuation is expected to be a more general effect. In the second of this pair of papers, an investigation is presented into the thermo-mechanical stability of these fibre network materials in this environment.

GNC system scheme for lunar soft landing spacecraft

A pinpoint autonomous GNC system scheme for lunar soft landing is proposed. First, the descriptions of the mission outline for lunar soft landing are provided. Second, the GNC system design of the spacecraft is proposed. The baseline is a 3-axis stabilized system during all the phases of the mission. Orbit maneuvers are achieved by an assembled constant thrust or a throttleable main engine. The attitude control actuators are thrusters. The attitude and orbit determination is performed by sun sensors, star sensors, Inertial Measurement Unit (IMU), altimeter, velocimeter and lunar imaging sensors. Third, some proposed autonomous navigation and guidance methods including hazard detection and avoidance for lunar soft landing are analyzed. Finally, we draw some conclusions.

Improved Edelbaum's Approach to Optimize Low Earth/Geostationary Orbits Low-Thrust Transfers

Edelbaum's approach to the optimization of low-thrust transfers is revisited and some simplifications are removed. The variation of the spacecraft mass due to the propellant consumption is considered in the case of constant thrust, and the corresponding numerical result is compared with Edelbaum's solution. The approach is then extended to consider variable specific impulse and thrust magnitude with constant power level. The payload increment is first computed maintaining Edelbaum's suboptimal control strategy (i.e., constant-thrust direction during each half-revolution). An analytical solution of the quasi-circular one-revolution transfer is then found using the optimal control of both the thrust direction and magnitude. The very-low-thrust multirevolution problem is easily solved by assembling many one-revolution basic trajectories; in particular, the transfer from a 28.5 deg inclined low Earth orbit to the equatorial geostationary orbit is considered. Exact numerical solutions for both constant and variable specific impulse have also been obtained using an indirect optimization method: the accuracy of the solution based on the quasi-circular approximation has been verified

Design and implementation of time efficient trajectories for autonomous underwater vehicles

This paper discusses control strategies adapted for practical implementation and efficient motion of autonomous underwater vehicles (AUVs). For AUVs we would like efficiency in both the measured time and the energy consumption, the mission dictating the weight to put on each of these cost. As a first approach to this problem, we focus in this paper on time minimization. Based on the structure of the time optimal trajectories and of the pure motions, we develop an algorithm to design time efficient trajectories corresponding to piecewise constant thrust arcs with few actuator switchings. We do that by solving a new optimization problem where the unknowns are the time period between two actuator switchings as well as the values of the constant thrust arcs. We apply a direct method to compute the solutions numerically. With our algorithm, we gain considerable computational time. Moreover, with as few as three actuator switchings, the duration of our trajectories is within 10% of the optimal trajectories. Since our control strategies have a simple structure they can be implemented on a test-bed vehicle. For the experiments displayed in this paper we use a spherical underwater vehicle which exhibits with almost no preference of direction or orientation for movement; this gives us a very controllable and versatile vehicle.

Performance of a Low-Power Cylindrical Hall Thruster

Recent mission studies have shown that a Hall thruster which operates at relatively constant thrust efficiency (45-55%) over a broad power range (300W - 3kW) is enabling for deep space science missions when compared with slate-of-the-art ion thrusters. While conventional (annular) Hall thrusters can operate at high thrust efficiency at kW power levels, it is difficult to construct one that operates over a broad power envelope down to 0 (100 W) while maintaining relatively high efficiency. In this note we report the measured performance (I(sub sp), thrust and efficiency) of a cylindrical Hall thruster operating at 0 (100 W) input power.

Do trout swim better than eels? Challenges for estimating performance based on the wake of self-propelled bodies

Engineers and biologists have long desired to compare propulsive performance for fishes and underwater vehicles of different sizes, shapes, and modes of propulsion. Ideally, such a comparison would be made on the basis of either propulsive efficiency, total power output or both. However, estimating the efficiency and power output of self-propelled bodies, and particularly fishes, is methodologically challenging because it requires an estimate of thrust. For such systems traveling at a constant velocity, thrust and drag are equal, and can rarely be separated on the basis of flow measured in the wake. This problem is demonstrated using flow fields from swimming American eels, Anguilla rostrata, measured using particle image velocimetry (PIV) and high-speed video. Eels balance thrust and drag quite evenly, resulting in virtually no wake momentum in the swimming (axial) direction. On average, their wakes resemble those of self-propelled jet propulsors, which have been studied extensively. Theoretical studies of such wakes may provide methods for the estimation of thrust separately from drag. These flow fields are compared with those measured in the wakes of rainbow trout, Oncorhynchus mykiss, and bluegill sunfish, Lepomis macrochirus. In contrast to eels, these fishes produce wakes with axial momentum. Although the net momentum flux must be zero on average, it is neither spatially nor temporally homogeneous; the heterogeneity may provide an alternative route for estimating thrust. This review shows examples of wakes and velocity profiles from the three fishes, indicating challenges in estimating efficiency and power output and suggesting several routes for further experiments. Because these estimates will be complicated, a much simpler method for comparing performance is outlined, using as a point of comparison the power lost producing the wake. This wake power, a component of the efficiency and total power, can be estimated in a straightforward way from the flow fields. Although it does not provide complete information about the performance, it can be used to place constraints on the relative efficiency and cost of transport for the fishes.

Control of Lagrange point orbits using solar sail propulsion

Several missions have utilised halo orbits around the L 1 and L 2 Lagrange points of the Earth–Sun system. Due to the instability of these orbits, station-keeping techniques are required to prevent escape after orbit insertion. This paper considers using solar sail propulsion to provide station-keeping at quasi-periodic orbits around L 1 and L 2 . Stable manifolds will be identified which provide near-Earth insertion to a quasi-periodic trajectory around the libration point. The possible control techniques investigated include solar sail area variation and solar sail pitch and yaw angle variation. Hill's equations are used to model the dynamics of the problem and optimal control laws are developed to minimise the control requirements. The constant thrust available using solar sails can be used to generate artificial libration points Sunwards of L 1 or Earthwards of L 2 . A possible mission to position a science payload Sunward of L 1 will be investigated. After insertion to a halo orbit at L 1 , gradual solar sail deployment can be performed to spiral Sunwards along the Sun–Earth axis. Insertion Δ V requirements and area variation control requirements will be examined. This mission could provide advance warning of Earthbound coronal mass ejections (CMEs) responsible for magnetic storms.

Geometric approach to capture analysis of PN guidance law

A novel approach to capture analysis of the proportional navigation (PN) guidance law is presented in this paper. The capturabilities of the pure PN guidance law and the true PN guidance law are qualitatively studied using the differential geometric formulations. A unified post-launch capture condition for PN guidance law is developed and expressed in terms of geometric angle and relative motion parameters instead of the initial conditions. Simulation results indicate that the proposed capture condition is more crucial at the end of the engagement. Also, the acceleration/deceleration of the missile has a distinct influence on the interception performance of the PN guidance law, and a constant thrust works viable and effectively in improving the performance of the PN guidance law.

Comparison of the rocket engines efficiency in the case of low thrust orbit-to-orbit transfers

The main task of this paper is to compare two types of low thrust rocket engines: constant thrust vs. variable-thrust engines. We will be concerned with efficiency, where efficiency is evaluated in the case of the orbit-to-orbit transfer with maximum payload mass in the central Newtonian gravity field. The launch mass of the space vehicle is supposed to be fixed. The traditional solution is the decomposition of the problem into parametric and dynamical parts. The corresponding variational problems differ for two rocket thruster types under consideration. We propose change of variables, which makes it possible to reduce averaged equations of optimal motion of a spacecraft with the mentioned engines to the unified form. Using this unified form comparison of the performance of constant- and variable-thrust engines is conducted.

An optimum braking strategy

Car-drivers often are required tobring their vehicle to a sudden stop when at a given speed to avoid colliding, for example, with a fixed obstacle (see Fig. 1). The first impulse is to exert and maintain maximum pressure on the brake until the car is halted, but this response is inadvisable since excessive decelerationmay cause skidding, and alsomay result in injury to the driver and passengers even when seat belts areworn. Just as importantly, a constant thrust on the brake pedal does not produce constant deceleration. Decades of experimental research on how shoe brakes effect the motion of wheels have conclusively demonstrated that the magnitude of the braking force decays rapidly with speed. It follows that, when the driver brakes at high initial speed, the braking force, small at the beginning, gradually increases to a given amount

Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces

In this article, we solve in closed form a system of nonlinear differential equations modelling the elastica in space of a thin, flexible, straight rod, loaded by a constant thrust at its free end. Common linearizations of strength of materials are of course not applicable any way, because we analyze great deformations, even if not so large to go off the linear elasticity range. By passing to cylindrical coordinates ρ, θ, z, we earn a more tractable differential system evaluating ρ as elliptic function of polar anomaly θ and also providing z through elliptic integrals of I and III kind. Deformed rod’s centerline is then completely described under both tensile or compressive load. Finally, the planar case comes out as a degeneracy, where the Bernoulli lemniscatic integral appears.

Trajectories for Human Missions to Mars, Part 2: Low-Thrust Transfers

We compute optimal low-thrust transfers (with constant thrust and constant specific impulse) between Earth and Mars over a range of flight times (from 120 to 270 days) and launch years (between 2009 and 2022). Unlike impulsive transfers, the mass-optimal trajectory depends strongly on the thrust and specific impulse of the propulsion system. A low-thrust version of the rocket equation is provided where the initial mass or thrust may be minimized by varying the initial acceleration and specific impulse for a given power-system specific mass and for a trajectory time of flight. With fixed time-of-flight transfers there is a minimum thrust and a maximum allowable specific mass; that is, if the available thrust is too low or the specific mass is too large then the desired transfer does not exist. We find the minimum allowable thrust for constrained time-of-flight missions is on the order of a few Newtons per metric ton of payload for power systems with tens of kg/kW. As expected, the thrust and AV requirements of the trajectories decrease with increasing flight times. By extending the flight time from 180 to 270 days the A V is reduced by 40% for powered captures and up to 35% for aeroassisted capture trajectories.

Relativistic rocket and space flight

We introduce the new concept of “proper speed”. It turns out that relativistic space flight can be sized and described more adequately by this concept. In particular, it is shown that the physics and equations of relativistic and classical space flight have a one-to-one relationship. The rocket equations are even identical. In addition, we generalize the expressions for the rocket exhaust speed to systems with mass and/or photon propulsion. With this new insight the basic relativistic spaceflight are easily derived and summarized and it is shown that they can be readily transformed into those of classical space flight. We also provide the space-time transformation equations for a cruising rocket, for a rocket with constant acceleration, and for a rocket with constant thrust (with and without inflight thrust reversal to slow down to zero speed at the target). For each of these cases a representative flight through the milky way with a ultimate matter–antimatter annihilation drive is calculated.

About international federation of societies of endoscopic surgeons

About international federation of societies of endoscopic surgeons

Study on the design of propeller blade sections using the optimization algorithm

A new method for designing propeller blade sections is presented. A vortex lattice method is used to evaluate the performance and the time-dependent pressure distribution on the blade surface in a non-uniform flow, while efficient optimization algorithms are used to modify the blade sections. Two different designs were carried out in this study. The first was a design to realize a target pressure distribution in a rotating three-dimensional flow. A two-dimensional wing theory was used to obtain the target pressure distribution. The predicted increase in efficiency and the reduction in the cavity volume were confirmed by model experiments. The second was a design to maximize the propeller efficiency. By this method, the propeller efficiency was improved by 1.2% under the constrains of constant thrust and a prescribed margin for face cavitation.

Energy-Efficient Trajectories of Unmanned Aerial Vehicles Flying through Thermals

This study presents optimal energy-efficient flight trajectories of a generic unmanned aerial vehicle (UAV) flying through a vertical moving thermal cell. A two-dimensional point-mass model of a jet-engined UAV in the vertical plane is used. UAV equations of motion and the thermal wind expression are normalized for numerical efficiency and four fundamental parameters are identified. UAV flights through a thermal cell are formulated as nonlinear optimal control problems that minimize the average thrust per unit time, subject to UAV performance constraints and periodic flight boundary conditions. These problems are converted into parameter optimizations and solved numerically. Fuel efficiencies of these optimal trajectories are compared with those of reference optimal flights in the lack of thermal winds. Both constant thrust and variable thrust solutions are obtained. Two patterns of optimal flights through thermals are identified, and their characteristics are analyzed. Both patterns of optimal flights are also explained from an energy maximization point of view. Effects of the fundamental parameters on optimal UAV flights are examined. Results suggest that significant improvements in UAV fuel consumption are possible by taking advantage of thermal energies.

Fan Unit Physics

A lightweight motor-driven propeller mounted on a low-friction cart provides a nearly constant thrust over a moderate range of velocities and can be a powerful pedagogical tool for investigating force and motion. A variety of homemade and commercial versions are now available. This article revisits and extends the topic of fan unit use described earlier.1 It looks at the rationale for use of fan units, gives examples of teaching ideas, and describes construction of two homemade versions of fan units.

Planar High-Thrust and Low-Thrust Orbital Transfers from Earth to Europa

We review analytical formulae for low-thrust orbital transfers from a circular initial orbit to a circular target orbit and to escape, using constant thrust applied in the same direction as the velocity vector, or in the opposite direction. The formulae give approximations for the maneuver time, final mass fraction, and evolution of the semimajor axis. For comparison, the associated results for high-thrust Hohmann and Oberth transfers are summarized. A simple computer program employing the aforementioned relationships is a useful tool for analysis of planar planetary and interplanetary space missions. This implementation yields fast and reasonably accurate approximations to trajectory performance boundaries. Consequently, the approach can provide trajectory analysis for each spacecraft configuration during the conceptual space mission design phase. As an example, a mission from Low-Earth Orbit (LEO) to Jupiter’s moon Europa is analyzed.

Minimum fuel powered dynamic soaring of unmanned aerial vehicles utilizing wind gradients

AbstractThis paper studies optimal powered dynamic soaring flights of unmanned aerial vehicles (UAVs) that utilize low‐altitude wind gradients for reducing fuel consumptions. Three‐dimensional point‐mass UAV equations of motion are used, and linear wind gradients are assumed. Fundamental UAV performance parameters are identified through the normalization of the equations of motion. In particular, a single wind condition parameter is defined that represents the combined effect of air density, UAV wing loading, and wind gradient slope on UAV flight. An optimal control problem is first used to determine bounds on wind conditions over which optimal powered dynamic soaring is meaningful. Then, powered UAV dynamic soaring flights through wind gradients are formulated as non‐linear optimal control problems. For a jet‐engined UAV, performance indices are selected to minimize the average thrust required per cycle of powered dynamic soaring that employs either variable or constant thrust. For a propeller‐driven UAV, in comparison, performance indices are selected to minimize the average power required per cycle of powered dynamic soaring with either variable or constant power. All problem formulations are subject to UAV equations of motion, UAV operational constraints, proper initial conditions, and terminal conditions that enforce a periodic flight. These optimal control problems are converted into parameter optimization with a collocation method and solved numerically using the parameter optimization software NPSOL. Analytical gradient expressions are derived for the numerical solution process. Extensive numerical solutions are obtained for a wide range of wind conditions and UAV performance parameters. Results reveal basic features of powered dynamic soaring flights through linear wind gradients. Copyright © 2004 John Wiley & Sons, Ltd.