1. Introduction
Since the former Soviet Union cosmonaut Gagarin [
1] entered space for the first time, after more than 60 years of continuous exploration and development in the field of manned space flight, so far, there are two types of manned spacecraft in the world that can carry out missions between space and earth: the space shuttle of the United States [
2] and manned spacecraft represented by Soyuz of Russia and Shenzhou of China [
3,
4]. However, except for a small part of the space shuttle, other manned spacecraft are not reusable, and the maintenance cost of space shuttles is very expensive, so the cost of space travel has been exceedingly high, which greatly restricts the pace of human exploration of outer space.
Starship and Super Heavy are the next generation of reusable space transportation systems proposed by Musk, founder of SpaceX, based on the vision of Mars colonization. According to the company’s assumption, a wide range of missions can be accomplished through a variety of combinations of the two core spacecraft: interplanetary missions such as manned landing on Mars, near-earth missions such as space station transportation, satellite deployment, and globally ultra-fast passenger transportation. A recent lunar version of the starship program also won NASA’s bid for the Moon landing mission. As a result, this system can theoretically meet the requirements of large-span transportation activities between different spaces, ranging from near-earth activities to Mars colonization.
In recent years, with the development of civil aerospace enterprises, new opportunities and challenges have been brought to the aerospace field. Since SpaceX publicized the ITS program in 2016, the Starship program has undergone several major design changes and evolutions. In 2019, the first starship prototype was publicly displayed. Since then, SpaceX has accelerated the research and manufacturing of starships by adopting the strategy of rapid testing and iterative verification of prototypes: In 2019, the free suspension test and safe landing test of the star worm preliminary verifier were completed [
5]. Since 2020, through intensive flight tests of prototypes SN5–SN15 [
6,
7,
8,
9,
10], SpaceX gradually mastered the key technologies of suspension at a low altitude of 150 m, flight at a high altitude of 10 km, roll maneuver, engine restarting powered braking, vertically soft landing at a fixed point, and so on [
11,
12,
13,
14,
15]. According to the current progress, the orbital flight test of the Starship–Super Heavy system with high integration and comprehensive assessment is expected to be realized soon, and the system is planned to be used for carrying out manned missions such as landing on the Moon and Mars in the future [
16,
17,
18].
The Starship–Super Heavy transportation system uses a two-stage fully reusable vehicle scheme with a designed loading capacity of 100 t. After the superheavy booster completes the first-stage powered flight separation, the starship continues the second-stage powered flight and continues to accelerate to enter orbit. The design of the starship is a combination of a two-stage rocket, orbiter, and reentry vehicle. The crew and payload are placed in the load cabin at the front of the starship, which has a reentry and return capability similar to that of the space shuttle orbiter [
18,
19,
20]. The starship can carry a 50 t payload on return and uses a power-braking vertical fixed-point recovery scheme during the landing phase, which is similar to the Falcon 9 rocket [
21,
22]. With a simple shape and body of cone-column combination, the starship adopts a unique tailless canard aerodynamic configuration, and in order to meet the requirements of reentry flight, thermal tiles are laid on the windward side to deal with the thermal environment during reentry flight [
23]. The current aerodynamic layout scheme of the starship is different not only from the manned spacecraft and space shuttle schemes of the traditional space transportation system, but also from the radical air-space shuttle scheme, and it is even significantly different from the earlier scheme, thus attracting huge attention once proposed [
24,
25]. Different from both the conventional manned spacecraft that is recovered by parachutes after semi-ballistic reentry into the atmosphere, and the space shuttle that lands horizontally on the airport, the landing method that the starship adopts is more similar to the recovery landing method of the rocket “Falcon”, which realizes the vertical landing by the coordinated control of rudder surfaces and vector thrust. A new rudder surface control that is different from the traditional lift-body aircraft is adopted in the starship for this special takeoff and landing way [
26]. Traditional lift-body aircraft realize the control of attitude and path by adopting the ailerons and vertical and horizontal tails, while the starship controls its body through two pairs of wings scattered on the nose and tail, which can deflect along the axial direction [
27]. Zuo [
27] made a detailed analysis of aerodynamic characteristics of the shape of the early starships (2019) in the landing and low-speed stages. Combined with aerodynamic characteristics such as lift/drag obtained from the simulation of subsonic separation flow field under a large angle of attack and the changing rules of the vertex moment along the deflection angle of leading and rear wings, a conclusion that four wings of the starship layout are subject to the three-channel control was given. While during the hypersonic and supersonic flight of reentry process, how about the wide speed-domain characteristics of this configuration, whether reentry trimming at full speed domain can be realized, how about the characteristics of the center of mass, whether the three channels are stable, what outstanding characteristics and advantages this configuration have, why such a unique design is taken, and many other problems remain to be further analyzed and researched.
At present, domestic and foreign studies on manipulativeness stability characteristics analysis are only limited to aircraft or taxiway takeoff and landing vehicles, and the structure is relatively simple, such as studies on multivariable stability margin of reentry aircraft [
28], definitions of static stability margin of aircraft [
29], and state feedback control and stability analysis of hypersonic aircraft [
30]. There is also research on modal stability analysis of hypersonic aircraft with lift-body configuration [
31], aerodynamic characteristics analysis of X-33-like vehicles [
32], longitudinal and lateral flight quality research of saucer aircraft [
26,
27], flight quality research of short take-off and vertical landing aircraft, criterion analysis of Robert Weissman, etc. However, there is little research on the manipulativeness and stability characteristics and flight quality of RLVs that can take off and land vertically.
This paper focuses on the starships, in view of the large angle of attack flight characteristics during the recovery phase. The stability characteristics of aerodynamic derivatives are analyzed, classical theory of flight dynamics of linearized small perturbation method is applied to work out the motion characteristic root of longitudinal and lateral direction, and analysis is carried out. At the same time, the principle of criteria is used to analyze the lateral-directional stability and control the deviation of the starship. Finally, time-history open-loop simulation is used to verify the above analysis.
2. Aerodynamic Configuration of Starships
This paper models the starship according to the size parameters publicized on the official website of SpaceX, as shown in
Figure 1. The wings are arranged according to the canard layout, a pair of front wings are arranged at the cone section, and a pair of rear wings are arranged at the end of the column section, both of which adopt trapezoidal wings. The whole ship is 50 m in length, 9 m in diameter, about 18 m in rear wingspan, and 15 m in front wingspan. The projected area of the whole plane is about 545 square meters. The weight of the whole ship is
, and the fuselage is made of stainless steel. In light of the shape and the distribution of the inner fuel tank and engine, the center of gravity of the whole ship is estimated at 40 m from the nose, and the pitching axial inertia moment coming through the center of gravity is
.
Overall, as a lift reentry vehicle, its simple shape gives itself distinctive characteristics, but it also brings several questions.
The simple and coordinated shape of the cone-column -wing, which is facially symmetrical, intuitively facilitates the series combination with superheavy boosters with the same diameter to form a simple two-stage rocket configuration, and this is much more compact than the complicated parallel layout of the orbiter-fuel tank-booster of the space shuttle, and the corresponding aerodynamic characteristics, flight control, and design of booster separation during the active period are also much simpler. Is this simple configuration suitable for lift reentry and return flight in a superwide speed domain?
A canard layout with a front-rear wings combination is adopted. The canard layout is common in the design of tactical missiles and highly maneuverable fighters, but there is no precedent in the design of reentry vehicles. The canard layout with relaxed static stability technology can realize that all wings generate positive lift at the trimming state and improve the aerodynamic efficiency of the aircraft. However, is it necessary for the returning stage? In addition, the canard is located very near the front, which means that the starship may face a severe aerodynamic heating environment during supersonic flight, and will it cause a serious problem for thermal protection?
It is a significant change in comparison to the earlier starship schemes (both the September 2018 and December 2018 versions had vertical tails) that the new version adopts a tailless layout without vertical tails and ventral fin. Tailless design and canard configuration will lead to the directional pressure center moving forward significantly. Intuitively, it can be judged that the starship’s directional pressure center will be too forward in most ranges of flight velocity and angle of attack. Will this pose a serious risk to the lateral-directional static stability?
6. Simulation Results of Nonlinear Open Loop
6.1. Longitudinal Simulation Results
Now the accuracy of the above analysis results has been verified by the time response simulation of the starship scaling model under
. A unit step response is given to the rudder-like when the starship is in the trimming state. The response curves of angle of attack, pitch rate, and pitch angle over time are shown in
Figure 28,
Figure 29 and
Figure 30.
It can be seen from the figures that short period characteristics of the starship are obvious during the unit step deflection of elevator-like, whose reflection on the angle of attack and pitch angular rate is that the starship could turn to the stable state quickly. At the same time, from the response curve of the pitch angle over time, the pitch angle also quickly returned to a stable state without accompanying oscillation, indicating that the long period degenerated into the third mode, which is an exponentially monotonous and convergent motion. Therefore, in the perspective of simulation results, it is consistent with the above analysis of control stability characteristics, and it verifies the accuracy of the above analysis.
6.2. Lateral-Directional Simulation Results
Now a unit step response is given to the aileron-like under , and the original is ensured. The response curves along time of sideslip angle, roll angle, roll angular rate, and yaw angle are shown as follows.
Figure 31,
Figure 32,
Figure 33 and
Figure 34 show that after a step response is given to aileron-like, because the roll mode belongs to level 2 flying quality, this makes it slow for the roll angle to recover to the stable state. According to
Figure 31 and
Figure 32, when the aileron-like steps, it takes the rolling angle 30 s to recover to a stable state. Because the lateral force caused by aileron-like deflection is small, coupling yaw motions are also small, and the yaw angle returns faster to the stable state than the roll angle. The starship is short of vertical tails, so its
, which plays a role in the recovery of Dutch rolling motion, is small. Moreover, the
is also small, which leads the directional damping further reduced, resulting in the instability of the Dutch roll mode. Because the starship’s spiral mode is close to its imaginary axis, and its roll mode is also located at the left of the imaginary axis, it could be approximately assumed that its roll and spiral modes are stable. Therefore, the half-life of the roll response is about 0.3 s.
Meanwhile, it can be seen from the analysis in the last section that the dynamic instability of the yaw motion of the starship is divergent, and by controlling the aileron, the sideslip could be eliminated, and the divergence trend could be weakened. As can be seen from
Figure 30 and
Figure 33, the simulation results are consistent with the analysis mentioned in the last section.
Now a unit step response is given to the rudder-like under , and at the same time, , the response curves of sideslip angle, yaw angle, roll angle, and yaw angle rate along the time are shown below.
According to the analysis in the previous section, sideslip can be eliminated by the combined control of aileron-like and rudder-like, so the sideslip angle in
Figure 34 can recover to a stable state. However, when the rudder-like steps, the lateral-directional motion wholly diverges, which is caused by the instability of the Dutch roll mode of the starship itself. From the analysis of the roll and swing ratio characteristics in the last segment, it can be seen that the yaw motion accounts for a large proportion of the Dutch roll, so when the rudder-like steps, the yaw motion diverges. Meanwhile, according to the Weissman criterion, some of the state points of the starship fall in the strong yaw divergence zone during lateral–directional motions. It can be concluded that when the rudder-like steps, the simulation results are also consistent with the characteristics analysis. And the response curves, namely, sideslip angle, yaw, roll angle, yaw rate, versus time are showed as
Figure 35,
Figure 36,
Figure 37 and
Figure 38 below.
As can be seen from the lateral-directional simulation results, the characteristics of the lateral-directional motions are consistent with the lateral-directional characteristics analysis in the previous section.
7. Conclusions
After the aerodynamic characteristics analysis, modal analysis, and deviation criterion analysis of the starship, the following conclusions are drawn:
The starship is longitudinally stable when , and becomes longitudinally statically unstable when , at which time the center of gravity moves to the focus. It does not have rolling static stability when . When , it has rolling static stability; The starship is always yaw statically stable within the range of angle of attack.
Both long and short longitudinal period mode of the starship meet the level 1 flight quality, and the motion response of the third mode after degradation is exponentially monotonous convergent. The lateral-directional roll mode meets level 2 flight quality, and the spiral mode meets level 1 flight quality. A pair of conjugate complex roots corresponding to the Dutch roll mode is in the right plane, which is in an unstable state. The Dutch roll mode is mainly reflected in yaw motion, which is divergent.
Through the comprehensive analysis of dynamic deviation and lateral control stability criteria, it can be seen that when , if sideslip occurs, the anticontrol phenomenon is easy to occur, thus the design of directional control systems deserves attention.
The effect of combined control of rudder-like and aileron-like is better than that of single control of either rudder-like or aileron-like, and the best control effect is achieved when the compensation gain of rudder-like to aileron-like is 1. When the compensation gain is negative, the rudder-like cannot compensate the aileron-like.
The simulation result of open-loop ontology shows that when a unit step response is given to elevator-like and rudder-like and aileron-like, after the elevator-like and aileron-like step, the starship ontology can recover to a stable state, but after the rudder-like step, the lateral-directional motion of the whole starship diverges, which indicates that the direction of the starship ontology is unstable, and a directional stability augmentation controller is necessary to be designed.