# Modeling and Analysis of a Generic Internal Cargo Airdrop System for a Tandem Helicopter
## 4 Trim Analysis
### Case of Helicopter Flight Operation Loading an Internal Cargo  
Trim analysis of CH-47B tandem rotor helicopter flying with an internal cargo, with the mass of 3000 kg, 4500 kg, or 6000 kg, is numerically conducted. The flight dynamics model for CH-47B tandem rotor helicopter without internal cargo has been preliminary validated [44]. Here, more detailed work is conducted in Figures 3-6. Trim results of the thrust, cyclic and pedal controls, and the pitching and rolling attitude angles are compared with the flight test data [45] and the reference data [40]. Error deviations relative to the flight test data and the reference data and trim deviation relative to the case of helicopter flight operation without internal cargo are also presented. Figure 2: Flow chart of the dynamic simulation. Figure 4: Trim results and error/trim deviation of (**a**) the longitudinal cyclic control and (**b**) the lateral cyclic control. Figure 3: Trim results and error/trim deviations of the thrust control. As shown in Figures 3-6, the present trim results of helicopter flying without internal cargo are in good agreement with the flight test data and the reference data. Thus, it can be concluded that the present model and methodology are suitable for this study. In detail, the maximum trim errors of the thrust, longitudinal/lateral cyclic and pedal controls are less than 6.0%, 3.0%, 1.0%, and 4% of travels, respectively. The maximum trim errors of the pitching and rolling attitude angles are less than 1.5 deg and 0.4 deg, respectively. Furthermore, the present trim results match with the reference data much better than the flight test data. The probable reason might be that the present flight dynamics model uses the Rotor Momentum Theory (RMT) to simulate the twin-rotor aerodynamics. Because the RMT assumes that the flow through the rotor is one-dimensional, quasi-steady, incompressible, and inviscid, but the actual physical flow about the twin rotors comprise a complicated wake structure, thus the RMT can hardly catch the twin-rotor aerodynamic phenomena,  
Figure 5: Trim results and error/trim deviation of the pedal control. Figure 6: Trim results and error/trim deviation of **(a)** the pitching attitude angle and **(b)** the rolling attitude angle. including the aerodynamic interaction of twin rotors and the aerodynamic interaction of rotor/fuselage, etc. Using the Free-Vortex System or Computational Fluid Dynamics (CFD) method to simulate the twin-rotor aerodynamics may improve the present trim data. By comparing with the trim results of helicopter flight operation with/without internal cargo, it can be drawn as follows:  
1. Flight operation loading an internal cargo mainly evidently affects the trim positions of the thrust and longitudinal cyclic controls, especially flying at a large flight velocity, as shown in Figures 3 and 4a. In detail, it decreases the trim position of the longitudinal cyclic control, except for hovering and flying at a low flight velocity less than 10 knots. It also increases the trim position of the thrust control due to the mass of the cargo. In addition, the increase in the mass of the cargo would decrease the trim position of the longitudinal cyclic control and further increase the trim position of the thrust control. Taking the trim results of the helicopter that flies with a cargo of 6000 kg as an example, the maximum negative trim deviation of the longitudinal cyclic control reaches by \(-6\%\) of the travel and the maximum positive trim deviation of the thrust control by \(+16\%\) of the travel. 2. In most practical applications, the internal cargo is generally set in the longitudinal symmetry plane of the helicopter with no lateral movement; thus, there is a small effect on the trim positions of the lateral cyclic and pedal controls, as shown in Figures 4 and 5. In detail, compared with the trim results of helicopter flying without internal cargo, the maximum change in the trim positions of the lateral cyclic and pedal controls with internal cargo (maximum mass of 6000 kg) is less than 1.5%.