Differential drag controllers have been examined in the context of a full system simulation of a target/chaser pair of spacecraft in low Earth orbit. An Extended Kalman Filter has been designed to process measurement sets from GPS receivers on the target and chaser spacecraft. The estimated state from the Kalman Filter is used in a differential drag control algorithm to determine the appropriate control action. Modifications are made to the standard differential drag control algorithms to reduce unnecessary actuations in the presence of errors in the dynamic modeling, control actuation, and incoming measurements. Detailed explanations of the algorithms, dynamic models, and derivations for both the Kalman Filter and the differential drag control laws are presented. Multiple test cases are used to validate the controller performance under a variety of initial conditions. In these simulations, the differential drag control algorithms successfully maneuver the chaser spacecraft from the initial conditions to a final state with instantaneous time-average position (relative to the target spacecraft) of not more than 10 meters in the radial and in-track directions. Modifications to the standard control algorithms ensure that extraneous control actuations are minimized. An optimization algorithm is used determine the time-optimal differential drag control history, and the results are compared to the standard control logic and modified control logic. Based on the optimization results, it is recommended that a system employing differential drag control (especially those with limited computational resources) should use the modified control logic, as it provides a standardized methodology that can be followed in any mission. / text

A mission architecture consisting of two NASA LONESTAR-2 satellites in Low Earth Orbit is considered. The craft are equipped with cross-communication radios and GPS units. Analyses are conducted for ejection, thruster and attitude maneuvers to achieve objectives of the mission, including sustained communications between the craft. Simulations are conducted to determine the duration of the communication window following the initial separation of the two craft. Recommendations are made to maximize this window while accounting for attitude constraints and the effects of atmospheric drag. Orbital mechanics and control theory are employed to form an algorithm for filtering GPS position fixes. The orbit-determination algorithm accounts for the effects of drag and Earth’s oblateness. Procedures are formed for verifying the initial separation velocities of two spacecraft and for measuring the velocity imparted by impulsive thruster maneuvers. An algorithm is also created to plan the timing and magnitude of corrective thruster maneuvers to align the orbital planes of the two craft. When the craft pass out of communication range, a ground station is used to relay data and commands to conduct state rendezvous procedures. A plan for coordinated attitude maneuvers is developed to strategically utilize the cumulative effects of drag and orbit decay to align the craft over long time periods. The methodologies developed here extend prior research into close proximity operations, forming the foundation for autonomous on-orbit rendezvous under a broader set of initial conditions. / text

The failed anchoring systems of mobile offshore drilling units from hurricanes occurring in 2004 and 2005 established a need to better understand the ultimate pullout capacity and trajectory of scaled model anchors under typical and out-of-plane loading conditions. The six degrees of freedom of small scale drag embedment anchors were studied in a laboratory testing environment with the intent that reasonable trends in anchor behavior will be found. Investigations within this experimental research program demonstrated the in-plane and out-of-plane loading behavior of conventional and prototype scaled model anchors embedded to predetermined depths in two different test beds of kaolinite clay with undrained shear strength profiles constant and increasing with depth. The anchors were loaded to failure in concentric, normal, concentric, shear, eccentric, normal, eccentric, shear, inclined, and drag embedment loading configurations. This series of pullout and drag embedment tests provided a suite of test results indicating behavioral trends of the varying holding capacities and anchor trajectories. Results were compared with similar research presented in the literature and an analytical model predicting out-of-plane loading behavior of similar anchors. It was concluded that increasing eccentricities from both concentric, normal and concentric, shear loading configurations resulted in decreasing bearing capacity factors, confirming the predicted trend from the analytical model for these loading configurations. Trajectories observed for the concentric, normal, concentric, shear, and eccentric, shear loading configurations showed that the anchors tracked straight out of the soil without deviation, but eccentric, normal loading found the anchor tending to track away from the initial loading location. For inclined loads, both anchors to track to whichever direction the anchor faced upon loading. Drag embedment trajectory was found to vary depending on the anchor, as the conventional anchor dove with an applied load and the prototype anchor rose towards the surface. / text

Mobile offshore drilling units are being used in the Gulf of Mexico to produce oil and gas. Anchoring systems such as drag embedment anchors and vertically loaded anchors are used to keep these units in place. Past mooring system failures due to hurricanes in 2004 and 2005 initiated a need to better understand the performance of these anchors to in-plane and out-of-plane loading conditions. In-plane and out-of-plane loading cause the anchor to translate or rotate in the directions of its six degrees of freedom. Behavior and holding capacity of the anchors when loaded in each of is six degrees of freedom are important in understanding and predicting their behavior. An experimental program was devised to investigate the behavior of anchors in pure translation and rotation loading. The scaled-model anchors were embedded at a measured depth in a soil bed of clay with an undrained shear strength between 10 and 20 psf and then loaded to failure. A rotation testing frame was designed to impose rotational loading in the yaw, roll and pitch directions. Test results from the experimental program are consistent and repeatable. The bearing factors for pure bearing fell well within the range of existing experimental and analytical studies on simple plates. Bearing factors for in-plane and out-of-plane shear and for all rotations are higher than those for simple plates due to presence of the shank. When the resistance is normalized by area of the fluke, the wider model provide greater normalized resistance to yawing, similar normalized resistance to pitching and rolling and less normalized resistance to bearing and shearing. It was concluded that the holding capacity of an anchor in its six degrees of freedom depends largely on its geometry, including the fluke and the shank. / text

This thesis reports on measurements of drag on an unbounded cylinder in a viscoelastic Stokes flow, and compares these values with a Newtonian equivalent. Cylinders of diameter 0.5 to 3.34 mm were submerged 10 to 36 mm into slowly rotating annular tanks with channel widths between 133 to 152 mm. Theoretical formulas and computer simulations were used to correct for the effects of ends and walls, yielding estimates of the unbounded drag. The methodology was verified by testing Newtonian fluids and comparing the results to Kaplun’s (1957) prediction for unbounded drag. The test fluids used were a silicone oil, a polybutene, and two Boger fluids. By comparing the Boger fluid results to equally viscous Newtonian results, the contributions of elasticity to the drag were determined. The Deborah number (De) was used to represent the magnitude of flow elasticity, and an onset of elastic effects was measured between 0.5 and 0.7.

This thesis reports on measurements of drag on an unbounded cylinder in a viscoelastic Stokes flow, and compares these values with a Newtonian equivalent. Cylinders of diameter 0.5 to 3.34 mm were submerged 10 to 36 mm into slowly rotating annular tanks with channel widths between 133 to 152 mm. Theoretical formulas and computer simulations were used to correct for the effects of ends and walls, yielding estimates of the unbounded drag. The methodology was verified by testing Newtonian fluids and comparing the results to Kaplun’s (1957) prediction for unbounded drag. The test fluids used were a silicone oil, a polybutene, and two Boger fluids. By comparing the Boger fluid results to equally viscous Newtonian results, the contributions of elasticity to the drag were determined. The Deborah number (De) was used to represent the magnitude of flow elasticity, and an onset of elastic effects was measured between 0.5 and 0.7.

Classical approaches to evaluate the stability of large woody debris (LWD) introduced in streams for habitat restoration or flood management purposes are usually based on inappropriate assumptions and hydraulic equations. Results suggest that the physics of small cylindrical elements located in large channels cannot be transferred to the case of a large roughness elements placed in small channels. The introduction of LWD in a small channel can generate a significant modification of the upstream hydraulic conditions. This modification has direct implications on the stability of the LWD. Experiments were performed in a controlled environment: a small stream section was represented by a low roughness rectangular flume and LWD were modeled with smooth PVC cylinders. Direct force measurements were performed with a load cell and results were used to identify an equation that evaluates the drag force acting on a large cylindrical element place in a rectangular channel. This equation does not depend on a drag coefficient. Water depths were also measured during the experiments and results were used to develop an approach that evaluates the upstream hydraulic impacts of a large cylinder introduced in a rectangular channel. The effect of the variation of the unit discharge (discharge per unit of width), cylinder size, cylinder elevation from the channel bed, and downstream hydraulic conditions, could be related to the upstream hydraulic conditions with relative success. Dimensionless parameters were developed to increase the versatility of the approach. The application of this approach to field cases is expected to require adjustments, mainly because of the roughness of natural environments differs from the smoothness of the controlled environment described in this work.

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<p>Granular impact, where a foreign object strikes a granular material like sand, is common in nature and industry. Due to experimental difficulties in obtaining sufficiently fast data at the scale of a single grain, a description of this process which connects to physics at the grain-scale is lacking. In this thesis, I will present data from a series of two-dimensional granular impact experiments. By cutting each grain out of a photoelastic material and using a very fast camera, we obtain data on the intruder trajectory, as well as the particle flow and force response of the granular material. Past experiments have shown that the decelerating force on an intruder moving through a granular medium is often well captured by a force law which is dominated by a velocity-squared drag force. Using the intruder trajectories, as well as the flow and force response of the granular material, I will demonstrate that, while these force laws describe the intruder trajectories on slow time scales, the instantaneous force on the intruder is highly fluctuating in space and time. I will particularly focus on the velocity-squared drag force, showing that it arises from random, locally normal collisions with chain-like clusters of particles which send energy and momentum away into the granular material. In this regime, the particles and intruder reach a kind of adiabatic steady state, where the particle motion scales linearly with the intruder speed. However, for impact velocities which are fast compared to the rate of momentum transfer within the granular material, the system response qualitatively changes, behaving like an elastic solid with a shock-like response at impact.</p> / Dissertation