Zuu-Chang Hong

Approximate chattering arc for minimum time flight

Abstract The purpose of this paper is to investigate the G-constrained approximate chattering arc for the minimum-time aerobraking maneuver of the shuttle-type space vehicle at constant altitude. Theoretically, in a chattering arc of the first kind, the control chatters between its maximum and minimum values at an infinite rate. As an example, for flight at constant altitude, the bank angle switches between its positive and negative maximum values at an infinite rate to generate maximum drag. The resulting flight path is along the arc of a large circle and is one-dimensional. There is a complete analytical solution for this theoretical chattering arc. For practical application, switching of the bank control at an infinite rate is not possible. In the approximate chattering arc, the bank control switches at a finite rate. The resulting flight path is two-dimensional and there is the penalty of a shorter longitudinal range. If we allow the vehicle to coast for a short distance and then change to an approximate chattering arc, the longitudinal range is satisfied and longer flight time becomes the penalty. The penalty of longer flight time is minimized by increasing the number of control switchings and, at the same time, selecting the optimal instants for the switchings. It is found that when the number of control switchings is five, the resulting optimal trajectory is good enough. With more times of control switchings, too much numerical computation must be made while the improvement in the performance index is small. The G constraint has a significant effect on the trajectory.

Optimal vertical ascent to GEO with thrust acceleration and dynamic pressure constraints

Abstract The optimal trajectory for vertical ascent to the geosynchronous earth orbit (GEO) with both dynamic pressure and thrust acceleration constraints will be solved by using the parameter optimization method. The performance index is to maximize the final mass. In other words, the propellant consumption is to be minimized. The time derivative of the velocity magnitude of the vehicle is assumed to be a polynomial function of the flight time, with the coefficients and the flight time as free parameters to be selected. When the thrust control is interior, the required thrust magnitude and angle are derived as functions of the state variables and the polynomial. The acceleration due to the thrust is limited to 2.5 times the gravitational acceleration at the Earths surface. The dynamic pressure is limited to the maximum allowable level for a Space Shuttle ascending flight. For each constraint, the thrust control on the constraint boundary is derived, respectively. A first order polynomial function is adopted for numerical computation. The flight time and the two coefficients are selected such that the final condition for GEO insertion is satisfied and the final mass is maximized. The two constraints are considered separately at first, and then considered together. A laser propulsion system is used with different specific impulse values of 500, 1000, 1500, 2000 and 2500s, respectively. With both constraints, it is found that the final mass remaining is 0.1130, 3.371, 10.42, 18.34 and 25.74%, respectively. The ascending flight time is 1.992 h. The penalty on the performance index incurred by the constraints is less than 0.1%. For a vertical ascending trajectory, the relative speed of the vehicle with respect to the atmosphere is the vertical component of the inertial vehicle velocity.

Design and Application of Inter-Satellite Link in Weather Observation Constellation

This paper presents the design and application analysis of the inter-satellite link technique in weather observation satellite constellation. A Walker parameter 18/18/4 satellite constellation with circular orbit at 837 km altitude and 60 degree inclination has been considered. The purposes are to take the weather cloud images of the area from 60 to 180 degree in eastern longitude and 0 to 60 degree in northern latitude, and to transfer the images back to Taiwan ground station as soon as possible. The STK [1] simulation software has been used in analyzing the effects of Doppler phenomenon, azimuth angle, elevation angle and distance between each two satellites. It has been proved that through the use of inter-satellite link technique, the contact time duration between the constellation and ground station has been tremendously increased. Therefore, weather cloud images can be transferred back much more frequently. Analysis results presented in this paper could be the reference for onboard antenna auto-tracking design and power management of the satellite.

Vertical Ascent to Geosynchronous Orbit with Constrained Thrust Angle

A discussion is presented about the overall payload ratio of a solid-rocket-booster-assisted laser propulsion system forgeosynchronous-Earth-orbit payload launch with thrust-angleconstraint. A trajectory shaping method is used for constructing the vertical ascent trajectory in the equatorial plane. There is a thrust angle under which the payload ratio (ratio of e nal mass to initial mass ) is to be maximized. This maximum payload can be obtained only when the ground station can provide the required peak laser power. Now, if the peak laser power is limited to a lower level, the payload ratio that can be obtained will also be lower. When the peak laser power that can be provided is too low, the thrust-to-weight ratio will be less than one at the initial phase of the launch. To keep the performance of the launching system, we include in the model a strap-on solid rocket booster to compensate the system for thrust loss. It is found that the penalty can be reduced signie cantly.

Asymmetrical chattering arc in vertical plane flight

Abstract The asymmetrical chattering arc of a winged space vehicle in the vertical plane reentry flight has been studied. With the use of dimensionless variables, we need only two parameters to specify the aerodynamic characteristics of the vehicle, one is the ballistic coefficient and the other is the maximum lift-to-drag ratio. The control variable is the normalized lift coefficient (NLC), the ratio of the lift coefficient and the lift coefficient at the maximum lift-to-drag ratio. The chattering flight happens when the NLC switches rapidly between its maximum and minimum values. We use the chattering control on the NLC to obtain maximum drag, or say, maximum deceleration. The asymmetrical chattering arc will be existing when the maximum and minimum NLCs have different absolute values. We started the study of the asymmetrical chattering from an example of basic dynamical system. It is found that a singular arc can be replaced by either a symmetrical or an asymmetrical chattering arc. The net effects on the lift and drag will be the weighted sums of the first and second orders of the maximum and minimum NLCs, respectively. The weighting factor is the percentage of acting time. A typical asymmetrical chattering reentry flight has the characteristics of maximum deceleration and phugoid oscillation.

Optimal trajectory for vertical ascent to geosynchronous Earth orbit

Abstract In this paper, the optimal trajectory for vertical ascent to the geosynchronous Earth orbit is solved by using the parameter optimization technique. The performance index is to maximize the final mass. In other words, the propellant consumption is to be minimized. The time derivative of the velocity magnitude of the vehicle, called the acceleration profile, is assumed to be a polynomial function of the flight time, with the coefficients as free parameters to be selected. The required thrust vector is then derived as a function of the state variables and the acceleration profile. A first order polynomial function is adopted for the acceleration profile. The two coefficients along with the flight time are selected such that the final condition for geosynchronous Earth orbit insertion is satisfied and the final mass is maximized. When the initial mass is 430,000 kg and the initial flight path angle is 1°, and a laser propulsion system with 2500 s of specific impulse is used, the maximum final mass obtained is 110,965 kg. This best final mass is 25.81% of the initial mass. The ascending flight time is 1.923 h. For vertical ascending trajectory, the relative speed of the vehicle with respect to the atmosphere is the vertical component of the inertial vehicle velocity. Therefore, the dynamic pressure and the aerodynamic drag are reduced to lower levels.

Overall payload ratio of a combined laser and chemical propulsion system for geo launch

Abstract This paper gives a discussion about the overall payload ratio of solid-rocket-booster-assisted laser propulsion system for geosynchronous earth orbit payload launch. When the ground station can provide the required peak laser power, we can obtain the maximum payload ratio (ratio of final mass to initial mass). Now, if the peak laser power is limited to a lower level, the payload ratio which can be obtained will also be lower. When the peak laser power that can be provided is too low, the thrust-to-weight ratio will be

Optimal turning of winged space vehicles at constant altitude

Abstract The purpose of this paper is to give the optimal turning problem of winged space vehicles at constant altitude an extensive study. The trajectory optimization problem will be formulated into a very general form. The only control variable, i.e., the bank angle, can be solved from a general quadratic equation. Specific topics of interest are the maximum heading increment turn, the maximum range turn, and the turn to a point in minimum time. Particular effort will be devoted to investigate the shapes of the optimal turning trajectories at several different altitudes.

Flight envelopes for hypersonic aerorendezvous at constant altitude

Flight envelopes of a lifting space vehicle at constant-alti tude hypersonic coasting flight for the purpose of aerorendezvous with initial relative heading angles at 0,30, 60,..., and 180 deg are presented. Besides the final position, the final velocity vector (both magnitude and heading) also must be specified for aerorendezvous. Therefore, final conditions are very stringent and the coordinate-system rotation technique is used to ease the numerical computation and to save time. The two-point boundary-value problem resulting from the variational formulation is solved by using the direct shooting method. The flight envelopes are found to be functions of two angles: the initial position and the initial velocity heading of the space vehicle. Both are measured relative to the specified final velocity vector. The envelopes for 0 and 180 deg of initial relative heading angles are symmetric with respect to the longitudinal axis. There are two discontinuity points on each of the envelopes. The other flight envelopes are not symmetric, and each has one discontinuity point only.