We now turn to the dynamics of the launcher as it rises to orbit. The launch of a spacecraft is conducted in a particular way, in order to ensure that the launch vehicle can carry a good payload mass into orbit. Three of the most commonly used strategies to attempt to maximize the launcher's payload mass are discussed in the following subsections.
A typical expendable launch vehicle adopts the method of staging to reach orbit, which involves shedding mass on the ascent. The vehicle is made up of stages, usually three, as illustrated in Figure 5.6. The launcher is lifted from its pad using the first-stage engines. The vehicle then climbs and accelerates until the first-stage fuel is exhausted. At this point, the first stage separates and falls back to Earth; there is no need to lift the first stage to orbit since it would serve no purpose there. It is jettisoned to save the expenditure of precious propellant in accelerating useless mass to orbit. After separation, small rocket thrusters are often fired in the first stage to slow the rocket down and move it away from the second-stage engines. At this point, prior to the ignition of the second-stage engines, the upper stages and satellite payload are in a state of free-fall—like the hypothetical elevator discussed in Chapter 2. As a consequence, the second-stage propellant and oxidizer are effectively in a state of weightlessness in the tanks. To settle the liquids again at the base of the tanks, in order to feed them into the combustion chamber, small rocket thrusters attached to the second stage are fired to speed it up. This acceleration produces a bit of artificial gravity to aid this necessary management of the propellant. The second-stage main engines are then fired to continue the powered ascent to orbit. When the second-stage fuel is used up, the process is repeated; the second stage too is jettisoned, before the third-stage engine is lit to take the satellite payload to orbital speed and altitude. It is often the case that the third stage and satellite payload are both injected into the final orbit.
Staging is a vital strategy in the operation of a conventional expendable launch vehicle. Fuel mass is not wasted accelerating rocket components to orbit where they would be useless, but instead is used to maximize the mass of the spacecraft being launched. Also the change in speed required to reach orbit is acquired using conservative engine technology in each stage. Rocket
engines having lower specific impulses can be used (lower certainly than the high performance space shuttle main engines), which implies lower combustion temperatures and pressures. This in turn means that the level of mechanical and thermal stress imposed on the engine components is generally less, which is good news for engine reliability and costs.
Another aspect ensuring that the launch vehicle can carry a good payload mass into orbit is the optimization of the ascent trajectory. This is a mathematics- and computer-intensive activity, usually carried out by the launch agency, to minimize the amount of rocket propellant needed to reach the desired orbit. If we achieve this minimization of fuel mass, then it follows that we can invest the resulting mass savings in making the spacecraft payload that the launcher it is carrying bigger and more capable. Clearly, the ascent trajectory optimization is an important task, and if not done correctly it can seriously compromise the vehicle's launch capability.
Despite the mathematical complexities of the process, we can gain some understanding of the ascent optimization by thinking about the tasks achieved by the launcher's propellant on the ascent. First, and most obviously, propellant mass is used to gain speed; the launcher starts out with effectively zero speed on the launch pad, and has to be accelerated to around 8 km/sec (5 miles/sec) to achieve a low Earth orbit (LEO). Second, and perhaps less obviously, propellant mass is used to overcome the forces of gravity and aerodynamic drag, which act on the launcher during its ascent.
Expending propellant to overcome gravity is referred to as gravity loss. This idea is nicely illustrated by a vertical takeoff aircraft, like a Harrier jump jet, when it hovers just above the ground. In this state, it is using its fuel entirely for the purpose of overcoming the force of gravity. Similarly, if a launcher's ascent trajectory has an uphill slope—and yes, of course, it would have to in order to reach orbit—then some part of its fuel is being used the overcome the force of gravity. When the launch vehicle is initially climbing vertically from its launch pad, the gravity loss incurred is large, but if it can roll over into a more gently sloping flight path soon afterward, the gravity loss is reduced.
Propellant is also used to overcome aerodynamic forces (see also the discussion of aerodynamic forces acting on spacecraft in Chapter 3), principally drag, acting on the launch vehicle during the ascent. This is referred to as drag loss. We can feel the effect of aerodynamic drag by holding a hand out of an open car window on a summer's day; the flow of air produces a force on your hand that resists its motion through the air. By this simple means we can also get an idea of how the drag force varies with speed. For example, the drag force on your hand feels much more significant at 60 mph than at 30 mph. If you were able to measure it, you would find the force at 60 mph to be four times bigger than the force at 30 mph, suggesting that the drag force varies as the square of the speed. As the launcher's speed doubles, the drag force increases by a factor of 4 (22), and as its speed trebles the drag increases by a factor of 9 (32), and so on. Given the speed that the launcher ultimately attains to reach orbit, this sounds like bad news, but the saving grace is that the drag loss occurs only in the lower, denser part of the atmosphere from which the launcher can escape fairly quickly.
The magnitudes of the gravity and drag losses are dependent on the launch vehicle being used, but typically if we are having to accelerate to a speed of 8 km/sec to reach orbit, we would have to burn propellant equivalent to an additional 1.0 to 1.5 km/sec to overcome gravity, and something like an extra 0.3 km/sec to combat the effects of drag.
Returning to our discussion of optimization of the ascent trajectory, we can now see that we want to design the flight path to ensure that most fuel is used to acquire speed, and that the amount used to overcome gravity and drag losses is minimized. One way of acquiring orbit is to ascend vertically to orbital height, and then rotate the launcher's flight path into the horizontal direction to inject into orbit. Although this strategy will minimize drag loss—the vehicle climbs vertically through the denser part of the atmosphere quickly—it does, however, entail accumulating a huge gravity loss. Alternatively, the launcher can climb into orbit on a gently sloping trajectory, like that of an airplane, with a small climb angle. In this case the gravity losses would be minimized, but the vehicle would spend a long time climbing out of the denser part of the atmosphere, thus yielding a large drag loss. An optimized trajectory, therefore, tries to take a path between these two extremes. Consequently, the launcher will climb vertically for a relatively short period to escape the denser part of the atmosphere (to minimize drag loss), and then roll over into a shallow climb (to minimize gravity loss) to acquire orbit. Figure 5.7 shows a space shuttle adopting this strategy.
As well as staging and trajectory optimization, a third way of improving the mass that a launch vehicle can take to orbit is to use Earth rotation. To get a feeling for this, we note that when the launcher is just sitting on its pad doing nothing, it is already moving eastward at significant speed due to the fact that Earth is rotating. The only places where this is not true are the North and South Poles, and I am not aware of any launch facilities in these polar regions, apart from perhaps submarines in the Arctic Ocean! The magnitude of this speed depends on the location of the launch site, or more precisely on its latitude. If the site is located on the equator, at zero latitude, then by virtue of Earth rotation it is traveling at about 465 m/sec (1525 feet/sec) in an eastward direction. This speed decreases as we move away from the equator; for example, at a latitude of 28 degrees north, corresponding to the Cape Canaveral launch site in Florida, the launch pads are moving at a rate of around 410 m/sec (1350 feet/sec). Further north at a latitude of 60 degrees, the eastward movement of Earth's surface has reduced to half of that at the equator, and at the North Pole it has reduced to zero. As I write this in southern England at a latitude of 52 degrees, it is amazing to think that I am rushing eastward due to Earth rotation at about 285 m/sec (940 feet/sec), but I cannot feel a thing!
Getting back to our launch vehicle, we can see that if we take off vertically but then roll over and head down range in an easterly direction, we can take advantage of the effect of Earth's rotation. For example, a rocket launched from my garden is already moving east at 285 m/sec before I light the blue touch paper, so if it is guided down range toward the east, it will burn less fuel to reach orbital speed. This means that the saving in propellant mass can be used to increase the size of the satellite payload being lifted to orbit. Another consequence of this eastward-directed launch strategy is that the orbital inclination (see Chapter 2) of the resulting orbit is about the same as the latitude of the launch site. The geometry of this is illustrated in Figure 5.8. Consequently, a space shuttle launched in this way from Cape Canaveral at a latitude of 28 degrees will end up in a LEO inclined at 28 degrees to the equator.
A result of all this is that large spacecraft, for example, the Hubble Space Telescope, the Space Shuttle, and the International Space Station, orbit in low-inclination LEOs. The savings in fuel usage as a result of using Earth rotation allow generally larger payloads to be launched into this type of orbit. Also launch sites for satellites destined for geostationary Earth orbit (GEO) (see Chapter 2) are usually sited near the equator with good range safety to the east. The safety requirement usually means no human habitation beneath the flight path, which is often satisfied by having an expanse of ocean to the east of the launch site. A good example of this is the launch facility at Kourou in French Guyana, at a latitude of 5 degrees north,
Figure 5.8: A launch in an easterly direction results in an orbit with an inclination approximately equal to the latitude of the launch site.
from where the Ariane family of expendable launch vehicles are launched predominately, eastward over the Atlantic Ocean.
But rockets are not always launched toward the east. For example, if the inclination of the mission orbit is required to be near 90 degrees, then the launch vehicle would have to fly either north or south from the launch site to achieve this. Therefore, Earth rotation is of no benefit, and reaching orbit is more costly in terms of fuel mass. Consequently, this increase in fuel mass must be compensated for by having a lower satellite payload mass, all other things being equal. Generally speaking, launcher performance is reduced in terms of payload mass when, for example, a near-polar mission orbit is required.
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