# Modeling and Analysis of a Generic Internal Cargo Airdrop System for a Tandem Helicopter
## 1 Introduction  
The transport function of transport helicopters mainly includes two methods: external slung-load transport and internal cargo transport. Both of these methods can transport heavy cargos, but the helicopter flight speed for the former method is required to be slow due to the coupling dynamics effects of the helicopter and its slung-load. There is no special requirement for the helicopter flight speed for the latter method, but in the period of internal cargo airdropping, the effects of the moving internal cargo on helicopter flight are complicated, even threatening the safety of flying. Exploring the trim and flight characteristics of helicopter transport operations in the two methods is the basis of designing effective flight control laws and for ensuring the flight safety. Since the 1960s, most research on helicopters with slung-load have been focused on the modeling and dynamics [1; 2; 3; 4; 5; 6; 7], control [8; 9; 10; 11], and flight test and simulation [12; 13], etc. Studies on airdrop have also been considered as an important research field due to the vital role of airdrop in the military and civil fields [14]. Recently, the U.S. Army Combat Capabilities Development Command indicated the importance of developing an airdrop technology and depicted the development of the Airdrop Technology Multi-Operational Simulation (ATMOS) [15]. Early in 1995, Air Force Flight Test Center of USA has conducteda cargo airdropping experiment in order to evaluation the interface between cargo airdrop and the aircraft and to devise a modification for optimizing performance [16]. In 2018, a preliminary computational simulation of the extraction of a standard container express (CONEX) cargo container from an aircraft was conducted [17]. However, most of the airdrop technologies were mainly developed based on a fixed wing transport aircraft, including Low Velocity Airdrop (LVAD) [18; 19], Low Altitude Airdrop (LAAD) [20; 21; 22], Container Delivery System (CDS) [23; 24], and Precision Airdrop (PAD) [25; 26; 27]. Early in 1967, the headquarters of U.S. Army Materiel Command presented airdrop requirements and provided detailed airdrop design criteria [28] in terms of helicopters, but with a lack of detailed theoretical studies on modeling, dynamics, and control. Until 2010, only a control design for small-scale helicopters carrying out airdrop missions was conducted [29]. So far, few studies in the literature have focused on the problems of full-scale helicopters with an airdrop system. The process of airdrop is a complex multi-body dynamic process. With the cargo moving backward in a helicopter, its center of gravity will shift backward, especially heavy cargo. In this circumstance, the center of gravity would probably exceed the bound, thereby sharply changing the flight characteristics, reducing the stability and the handing qualities and might cause a flight accident. Furthermore, when the cargo rotates around the point of tipoff and is going to leave the helicopter, the force and moment provided by the cargo acting on the helicopter may become more complex. In 2019, some dynamic characteristics of a single rotor helicopter under heavy cargo airdrop condition were conducted [30], with the conclusions that the forward flight airdrop has a better attitude maintaining ability, compared with the hovering airdrop. The main methods used for modeling a cargo airdrop system are the analytical mechanics method [31] and the vector mechanics method [32]. The former method is based on the study of work and energy. The latter method is based on the study of vector and is more visualized, thus it is widely used. The vector mechanics method is also classified as the overall method [33; 34] that makes the instantaneous mass center of the airplane-cargo system as the reference point, and the separation method [35; 36; 37] that considers the mass center of the airplane as the reference point.