# Aerodynamic Modeling and Performance Analysis of Variable-Speed Coaxial Helicopter
## 1 Introduction  
In recent years, with the development of motor and speed control technology, the control of variable-speed aircraft such as multi-rotor aircraft has been evolving with more possibilities at low speed. The study has extensive applications in both the military and civil aircraft industry over conventional single rotor aircraft. This makes the variable-speed rotor aircraft a topic of concern for researchers across the globe. However, the traditional helicopter can fly at high speed, and there is a potential for its miniaturization and lightweight. This requires the integration of the earlier two to obtain a small variable-speed helicopter with lighter structure weight, better reliability and higher flight efficiency. The coaxial rotor produces a counterrotating torque which cancels out the need for an additional tail rotor, thereby reducing the weight and power consumed by the tail rotor. A study on a rigid coaxial blade based on the principle of the Advanced Blade concept (ABC) in support of the Sikorsky ABC helicopter program revealed an improved forward flight performance and reduced excessive tip deflections and extreme moments, thereby utilizing the maximum ability of the blade for generating lift [1]. There are limited studies on the aerodynamics of multirotor aircraft; however, the earliest research survey [2] carried out for multirotor aerodynamics revealed a positive insight into coaxial rotor in hover, since it has no tail rotor, along with the minimum power requirement when compared to conventional single axis rotor, and the forward flight performance revealed a lower power requirement for moderate advance ratios contradicting with high drag penalty for higher advance ratios. In 2012, [PERSON] and [PERSON] applied the blade element momentum theory (BEMT) method to calculate the load of variable-speed coaxial rotor, and they verifiedit through experiments [3]. A formal optimization model of coaxial rotor for helicopters operating in hover and the axial forward flight was studied by [4], which showed a better prediction of results when compared to the simple momentum theory. However, the BEMT method has a range of deficiencies, such as unclear physical meaning, which may lead to deviation of the results. Further, the coaxial rotor wake dynamics, wake structure and ground effects were optimized using the free-vortex filament method for maneuvering flight conditions [5; 6; 7]. The study by [8] studied the free Lagrangian Incompressible Navier-Stokes Equation. The full-scale wind tunnel experimental investigations were performed by [9], calculating the static thrust performance of both coaxial and single-axis rotor blades tapered in both planform and thickness ratio. This is followed by the study performed on a coaxial-configured-rotor and tandem-rotor arrangement, revealing an increase in hovering efficiency for tandem rotors spaced exactly one rotor diameter apart. The power requirement identifies with the previously available theories. The hover performance of single, coaxial, tandem and tiltrotor configurations was investigated by [10], briefing about the interference losses and rotor-on-rotor effect. A high-speed steady-level forward flight was simulated using CFD-CSD coupling correlated to the vortex wake model by [11], who stated the rotor interference was found to agree with the momentum theory and captured the cross transition of flow across the rotor blades, thereby quantifying the effects of pitching moment, which shows negligible torsional response on the rotor. While understanding the coaxial rotor system, trim becomes one of the important parameters, since the torque should be balanced between hover and forward flight, with the respective lift offset by providing proper controls.