FLIGHT PERFORMANCE
4.6. EFFECT OF PROPULSION SYSTEM ON VEHICLE PERFORMANCE This section gives several methods for improving flight vehicle performance and most
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4.6. EFFECT OF PROPULSION SYSTEM ON VEHICLE PERFORMANCE 133 Precise attitude angular corrections can also be achieved by the use of inertial or high-speed rotating reaction wheels, which apply torques when their rotational speed is increased or decreased. While these wheels are quite simple and effective, the total amount of angular momentum change they can supply is limited. By using pairs of supplementary attitude control thrust rocket units, it is possible to unload or even respin each wheel so it can continue to supply small angular position corrections as needed.
The torque T of a pair of thrust chambers of thrust F and separation distance l provides the vehicle with an angular or rotational moment of inertia Ma an angular acceleration of magnitude𝛼:
T = Fl = Ma𝛼 (4–33)
For a cylinder of radius r and of equally distributed mass the rotational moment of inertia is Ma = 1
2mr2 and for a homogeneous sphere it is Ma= 25mr2. The largest possible practical value of moment arm l will minimize thrust and propellant require-ments. If the angular acceleration is constant over a time t, the vehicle will move at an angular speed𝜔 and through a displacement angle 𝜃, namely,
𝜔 = 𝛼t and 𝜃 = 12𝛼t2 (4–34)
Commonly, the control system senses a small angular disturbance and then com-mands an appropriate correction. For detection of angular position changes by an accurate sensor, it is usually necessary for the vehicle to undergo a slight angular displacement. Care must be taken to avoid overcorrection and hunting of the vehi-cle’s position by the control system. This is one of the reasons many spacecraft use extremely short multiple pulses (0.010 to 0.040 sec per pulse) and low thrust (0.01 to 100 N) (see Refs. 4–11, 4–13, and 4–14).
Reaction control systems may be characterized by the magnitude of the total impulse and by the number, thrust level, and direction of the thrusters and their duty cycles. The duty cycle refers to the number of thrust pulses, their operating times, times between thrust applications, and timing of short operations during the mission operating period. For any given thruster, a 30% duty cycle would mean an average active cumulative thrust period of 30% during the propulsion system’s flight duration. These propulsion parameters can be determined from the mission, the guidance and control approach, the desired accuracy, flight stability, the likely thrust misalignments of the main propulsion systems, the three-dimensional flight path variations, the perturbations to the trajectory, and several other factors. Some of these parameters can often be difficult to determine.
4.6. EFFECT OF PROPULSION SYSTEM ON VEHICLE PERFORMANCE
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performance improvements do not depend on the propulsion system. Most of those listed below apply to all missions, but some are peculiar to some missions only.
1. The effective exhaust velocity c or its equivalent the specific impulse Isusually have a direct effect on the vehicle’s overall performance. The vehicle’s final velocity increment Δu may be increased by a higher Is. This can be done by using more energetic chemical propellants (see Chapters 7 and 12), by higher chamber pressures and, for upper stages operating at high altitudes, also by larger nozzle area ratios provided that all these do not appreciably increase the vehicle’s inert mass. With electrical propulsion a higher available Is can enhance vehicle performance but, as explained in Chapter 17, their very low thrusts do limit their use to certain space missions.
2. The vehicle mass ratio’s (m0/mf) logarithmic effect can be increased in several ways. One way is by reducing the final mass mf (which consists of the inert hardware and payload plus the nonusable, residual propellant mass). Reducing the inert mass implies lighter structures, smaller payloads, lighter guidance/
control devices, and/or less unavailable residual propellant; this often means going to stronger structural materials at higher stresses, more efficient power supplies, or smaller electronic packages. During design, there is always great emphasis on reducing all hardware and residual propellant masses to their prac-tical minima. Another way is to increase the initial vehicle mass, and use higher thrust and more propellant, but with accompanying small increases in the struc-ture or inert propulsion system mass.
3. Reducing the burning time (i.e., increasing the thrust level) will reduce the gravitational loss in some applications. However, higher accelerations usually require more structural and propulsion system mass, which in turn cause the mass ratio to be less favorable.
4. Atmospheric drag, which can be considered as negative thrust, can be reduced in at least four ways. Drag has several components: (a) Form drag depends on the flight vehicle’s aerodynamic shape; slender pointed noses or sharp, thin leading edges on fins or wings have less drag than stubby, blunt shapes. (b) A vehicle with a small cross-sectional area has less drag; propulsion designs that can be packaged in long, thin shapes will be preferred. (c) Drag is propor-tional to the cross-secpropor-tional or frontal vehicle area; higher propellant densities will decrease propellant volume and therefore will allow smaller cross sections.
(d) Skin drag is caused by the friction of the gas flowing over all vehicle’s outer surfaces; smooth contours and polished surfaces are preferred; skin drag also depends on higher propellant densities because they require smaller volumes and thus lower surface areas. (e) Base drag is the fourth component; it is a function of the ambient pressure acting over the surface of the vehicle’s base or rear section; it is influenced by the nozzle exit gas pressure and turbulence, any discharges of turbine exhaust gases, and by the geometry of the vehicle base design. These are discussed further in Chapter 20.
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4.6. EFFECT OF PROPULSION SYSTEM ON VEHICLE PERFORMANCE 135 5. The length of the propulsion nozzle is often a significant contributor to the over-all vehicle or stage length. As described in Chapter 3, for each mission there is an optimum nozzle contour and length, which can be determined by trade-off analyses. A shorter nozzle length or multiple nozzles on the same propulsion system may allow a somewhat shorter vehicle; in many designs this implies a somewhat lighter vehicle structure and a slightly better vehicle mass ratio.
6. The final vehicle velocity at propulsion termination can be increased by increas-ing the initial velocity u0. By launching a satellite in an eastward direction the rotational speed of the Earth adds to the final satellite orbital velocity. This Earth tangential velocity is as high as 464 m/sec or 1523 ft/sec at the equator;
Sea Launch, a commercial enterprise, launched from a ship at the equator to take full advantage of this velocity increment. For an easterly launch at John F.
Kennedy Space Center (latitude of 28.5∘ north) this extra velocity is less, about 408 m/sec or 1340 ft/sec. Conversely, a westerly satellite launch has a negative initial velocity and thus requires higher-velocity increments. Another way to increase u is to launch a spacecraft or an air-to-surface missile from a satel-lite or an aircraft, which imparts its initial vehicle velocity vector and allows launching in the desired direction. An example is the Pegasus three-stage space vehicle, which is launched from an airplane.
7. For vehicles that fly within the atmosphere it is possible to increase their range when aerodynamic lift is used to counteract gravity and reduce gravity losses.
Using a set of wings and flying at an angle of attack increases the lift, but also adds to the drag. Vehicle lift may also be used to increase the maneuverability and trajectory flexibility.
8. When the vehicle’s flight velocity u is close to the rocket’s effective exhaust velocity c, the propulsive efficiency is highest (Eq. 2–22 or Fig. 2–3) and more of the rocket exhaust gas energy is transformed into the vehicle’s flight energy.
When u = c this propulsive efficiency reaches 100%. Trajectories where u is close in value to c for a major portion of the flight therefore would need less propellant.
9. When a mission is changed during flight, the liquid propellant of a particular rocket engine (in a multistage vehicle) may not be fully used and such unused propellant is then available to be transferred within the vehicle to augment the propellant of a different rocket engine system unit. An example was the transfer of storable liquid propellant in the Space Shuttle from the Orbital Maneuvering System (OMS) to the Reaction Control System (RCS – 14 small bipropellant thrusters). This transfer allowed for additional orbit maintenance operations and more time in orbit.
Several of these influencing parameters can be optimized. Therefore, for every mission or flight application there is an optimum propulsion system design and the propulsion parameters that define the optimum condition are dependent on vehicle or flight parameters.
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