Entry Dynamics of Space Shuttle in the Earth Atmosphere

Abstract

There are two entry methods that control the design of vehicles to return to the atmosphere from outer space: ballistic entry and lifting entry. In this chapter, we will study the process of entering the space shuttle into the Earth’s atmosphere. In the case of ballistic entry without lift at sufficiently large angle of inclination, both the gravity force and centrifugal force are neglected. The term ballistic entry is applied to the relatively steep atmosphere entry of non-lifting bodies, which involves linear paths through the atmosphere during the major deceleration, with assumptions: (1) A constant path angle. (2) A constant drag coefficient. (3) Gravitational force small compared to drag force. Program was designed by the author to calculate variation of velocity with altitude for various values of drag-weight parameter, variation of deceleration with altitude for various values of drag-weight parameter, variation of velocity with altitude for various values of initial angle of inclination, variation of deceleration with altitude for various values of initial angle of inclination, variation of velocity with altitude for various values of initial velocity and variation of deceleration with altitude for various values of initial velocity.

1. Introduction

Atmospheric entry is the movement of an object coming from space into the atmosphere of a particular planet. The process of entry is divided into two types, namely regular entry, as in spacecraft, and irregular entry, as in exploding meteorites, etc..

Objects that enter the atmosphere are subjected to a drag process due to the particles that make up the atmosphere, which causes a loss of mass for the entering body or may cause an explosion to some objects that cannot withstand high pressure. This depends on the entry speed and entry angle, as well as the density of the atmosphere [1].

There are two types of re-entry process from space to earth atmosphere:

1. Ballistic entry: This type of entry depends on the parameter ballistic coefficient β and can be calculated from equation below [2]:

   $$\beta =\frac{W}{C_{D}A}$$E1

   where W: the vehicle weight; $C_D$: the drag coefficient; A: the reference area used in the definition of the drag coefficient.

   If the value of β is low, this means that heating and deceleration are less than for a high β value. Early Inter-Continental Ballistic Missiles (ICBM) is one of the types of ballistic missiles that need to leave the atmosphere, then go to the desired target, and then re-enter the atmosphere for a second.

   How is the launch process? Upon takeoff, the ICBM enters the launch phase. During that stage, the auxiliary missiles that push the ICBM into the atmosphere are carried upwards, for a period of 2–5 min, until it reaches space. He adds that the ICBM can have up to three stages of auxiliary missiles. Each stage is disposed of after it burns; in other words, after the first stage stops burning, the auxiliary rocket No. 2 takes its turn, and so on. Moreover, these auxiliary missiles can have liquid or solid fuel. Liquid propellants continue to burn longer in the launch phase than solid propellant auxiliary rockets. In contrast, solid fuels “save their energy in a shorter time and burn faster”.

2. Lifting entry

   A lifting entry show in Figure 1 is one in which the primary force being generated is perpendicular to the flight path, that is, a “lift” force. Although drag is present throughout the entry, the resulting flight path can be adjusted continuously to change both vertical motion and flight direction, while the velocity is slowing. The gliding flight of a sailplane is an example of “lifting” entry without high velocities and heating. The primary design parameter for lifting entry is the lift to drag ratio, or L/DA lifting entry is one in which the primary force being generated is perpendicular to the flight path, that is, a “lift” force. Although drag is present throughout the entry, the resulting flight path can be adjusted continuously to change both vertical motion and flight direction while the velocity is slowing. The gliding flight of a sailplane is an example of “lifting” entry without high velocities and heating. The primary design parameter for lifting entry is the lift to drag ratio, or L/D

   $$\mathrm{L}/\mathrm{D}=\text{Lift}/\text{Drag}=C_L/C_D$$

Low L/D values result in low mobility, moderate heating levels, and moderate g loads. High L/D values result in very low g loads but extremely long-lasting entry with continual heating. As an illustration, consider the space shuttle’s re-entry, which took around 25 min overall and had an L/D value of about unity [3]. Although a lifting entrance’s peak temperatures are lower than a ballistic entry’s peak temperatures, the overall heat load that must be absorbed throughout the entry is larger. As the L/D increases, lateral mobility during entry (often referred to as “cross-range capability”) grows significantly.

Figure 1.

Lifting entry.

2. Dynamics and vehicle description

The 3-DOF point mass dynamics of the reentry vehicle over a spherical, rotating Earth, is described as follows:

$$\dot{r}=Vsin\gamma ,$$E2

$$\dot{\theta }=\frac{Vcos\gamma sin\psi }{rcos\phi }$$E3

$$\dot{\phi }=\frac{Vcos\gamma cos\psi }{r}$$E4

$$\dot{V}=-\frac{D}{m}-gsin\gamma +{\omega }^{2}rcos\phi \left(sin\gamma cos\phi -cos\gamma sin\phi cos\psi \right)$$E5

$$\dot{\gamma }=\begin{array}{l}\frac{1}{V}(\frac{Lcos\delta }{m}+\left(\frac{V^2}{r}-g\right)cos\gamma +2\mathit{\omega V}cos\phi sin\psi \\ +{\omega }^{2}rcos\phi \left(cos\gamma cos\phi +sin\gamma sin\phi cos\psi \right)),\end{array}$$E6

$$\dot{\psi }=\frac{1}{V}(\frac{Lsin\delta }{m}+\frac{V^2}{r}cos\gamma sin\psi tan\phi -2\mathit{\omega V}\left(cos\phi tan\gamma cos\psi -sin\phi \right)+\left(\frac{{\omega }^{2}r}{cos\gamma }sin\phi cos\phi sin\psi \right),$$E7

where r is the earth radius (the distance from center of earth to vehicle), h is latitude, the earth radius is 6378 m, and θ and φ are the longitude and latitude, respectively.

V is earth relative velocity, $\gamma$ is the flight path angle of the earth relative velocity, $\psi$ is the azimuth angle of the earth relative velocity, and m is the mass of vehicle [4].

3. System implications

The re-entry system designer can consider three main variables:

1. Ballistic coefficient β.

2. L/D for lift to drag.

3. Entry flight path angle.

Which regulate the re-entry system’s flight performance. We will now provide an illustration of how these criteria can be applied to the design of both ballistic and maneuverable warhead delivery systems. Slender sphere–cone geometries with several warheads on a single delivery bus are frequently used in modern ballistic trajectory nuclear weapon system delivery vehicles. The re-entry vehicle base diameter and vehicle length are chosen by the designer for a particular warhead and accompanying arming system, thus determining the cone half-angle [5]. Figure 2 shows the impacts of nose bluntness ratio on sphere–cone drag coefficient CD for a family of sphere-cone half-angles on classical Newtonian theory, and the nose bluntness ratio is then chosen based on drag and heat transfer concerns [6].

Figure 2.

Classical Newtonian drag coefficient for a sphere-cone.

The combined weight of the warhead, arming device, and re-entry vehicle serves as the vehicle’s fixed weight. A designer can now evaluate the ballistic trajectory performance of the design in relation to mission criteria, such as deceleration g loads, range, and flight time, since the ballistic coefficient β has been thoroughly determined. These mission requirements actually determine the entry flight path angle. Before all of the mission requirements are fully met, this process may need to be iterated on numerous times [7].

4. Results and discussion

4.1 Introduction

Trajectory analysis of re-entry vehicles has been modeled in two.

The dynamic equations of motion in 2DOF were solved numerically by adopting the fourth order Runge-Kutta method. Different values of lift-drag ratio were taken (positive, zero, and negative values). And different angles of inclination were taken (small, median, and large values), as well as different weight-area ratios and density–altitude. Further, the dynamic equations of motion in 2DOF were solved analytically. There are four cases for analytical solution.

4.2 Ballistic entry (L/D = 0) at large angles of inclination

In the case of ballistic entry without lift at sufficiently large angle of inclination, both the gravity force and centrifugal force are neglected.

The term ballistic entry is applied to the relatively steep atmosphere entry of non-lifting bodies, which involves linear paths through the atmosphere during the major deceleration, with assumptions:

1. A constant path angle.

2. A constant drag coefficient.

3. Gravitational force small compared to drag force.

The variation of velocity and deceleration with altitude is shown in Figures 3 and 4 for various values drag–weight parameter. In each case, it is seen that similar curves result with relative displacements for various values of this parameter.

Figure 3.

Variation of velocity with altitude for various values of drag-weight parameter.

Figure 4.

Variation of deceleration with altitude for various values of drag-weight parameter.

One interesting facet of these results is that the major deceleration of a body during atmospheric entry takes place in a stratum of the atmosphere of a constant thickness. The level of this stratum in the atmosphere is, however, dependent on the value of the parameter drag-weight ratio. Large values of this parameter because high deceleration in the atmosphere, while smaller values delay deceleration until the lower atmosphere is reached.

Because the decrease velocity during ballistic entry into the Earth’s atmosphere is greater than increase density, therefore, the maximum deceleration occurs. The maximum deceleration during entry is independent of drag–weight characteristics of the body.

It is dependent only on the initial angle of inclination, initial entry velocity, and on the density distribution in the Earth’s atmosphere; however, the altitude or altitude density at which the maximum deceleration occurs is dependent upon the weight-drag characteristics of the body. Figures 5 and 6 illustrate the effect of entry angle on the variation of velocity and deceleration during penetration of the Earth’s atmosphere from space by a body having the weight-drag characteristics.

Figure 5.

Variation of velocity with altitude for various values of initial angle of inclination.

Figure 6.

Variation of deceleration with altitude for various values of initial angle of inclination.

The initial angle of inclination has no effect on the shape of the curve velocity, but on the altitude at which the decrease velocity occurs.

The small values for initial angle of inclination cause decrease in the velocity in higher atmosphere, while the large values cause decrease in the velocity in lower atmosphere. This effect is shown in Figure 5.

Figure 6 illustrates variation of deceleration with altitude for various values of the initial angle of inclination. The smaller initial angle of inclination is seen to result in a deceleration higher in the atmosphere and a smaller peak deceleration.

Figure 7 illustrates the variation velocity with altitude for ballistic entry into the Earth’s atmosphere with various values of initial entry velocity. We note from this figure that the initial entry velocity has no effects on the shape of the velocity curves.

Figure 7.

Variation of velocity with altitude for various values of initial velocity.

The initial entry velocity effects the maximum deceleration for the large values for initial entry velocity generate high peak deceleration, while the small values generate low peak deceleration. These effects are shown in Figure 8.

Figure 8.

Variation of deceleration with altitude for various values of initial velocity.

It is interesting to note that these entry solutions are valid not only for relatively steep atmospheric entries from space at escape velocity or near orbital velocity but also for re-entry phase of long-range ballistic trajectories. In this case, the angle of inclination is also relatively constant over the critical parts of the re-entry portion of the trajectory.

5. Conclusion

When anybody enters the atmosphere, a friction process occurs with the particles that make up the atmosphere, and this depends on the cross-sectional area of the body, as the pressure is inversely proportional to the cross-sectional area. The larger the cross-sectional area, the greater the pressure, and vice versa. When the pressure increases, the process of friction with the particles of the atmosphere will increase, and thus, high heat will be generated, which can cause damage to the inner body. This also depends on the angle of entry, as well as the speed of entry and the density of the atmosphere, as the friction process decreases at entry, because the density is low, and when reaching low altitudes, friction increases due to the high density of particles that make up the atmosphere.