# Study on the Mechanism of the Variable-Speed Rotor Affecting Rotor Aerodynamic Performance
## 1 Introduction  
The variable-speed rotor, also called the optimum speed rotor or slowed speed rotor, adjusts the helicopter or rotorcraft rotor speed along with variation in the flight condition to maintain a relatively high aerodynamic efficiency. For example, a helicopter may reduce its rotor speed under the condition of low payload or cruise flight speed, and a tilt-rotor may reduce its rotor speed when transferring to fixed-wing flight mode from helicopter mode. In recent years, the variable-speed rotor has proven to be a promising way to reduce rotor-required power, extend the flight speed, endurance and range, and the reduce rotor noise [1; 2; 3; 4]. Furthermore, research from the ACARE (Advisory Council for Aeronautics Research) has shown that there is a potential benefit of reducing exhaust pollutants by reducing the required power [5]. [PERSON] first proposed the Optimum Speed Rotor (OSR) concept in 1974, ran the OSR project, and finally, developed the hummingbird unmanned helicopter A160/A160T, which achieved a long-endurance flight test for about 20 h [4]. The Advancing Blade Concept (ABC) program implemented the variable-speed rotor in a coaxial helicopter (XH-59A), reducing the rotor speed by 30%, making high speed flights possible [6; 7]. The tilt-rotor Bell XV-3 changes the rotor speed from 532 rpm in helicopter hover mode to 324 rpm in fixed-wing cruise flight mode, which balances the hover figure of merit (FM) and cruise efficiency [8]. [PERSON], [PERSON] and [PERSON] [9] and [PERSON] [10] simulated the effect of the rotor speed on the required rotor power, shaft torque, maximum flight speed and ceiling and showed that the greatest improvement was achieved in cruise forward flight. The study of [PERSON] showed that the variable-speed rotorcan improve performance more significantly under conditions of low altitude and small take-off weight than with a high altitude and large take-off weight [11]. [PERSON], [PERSON] and [PERSON] et al. analyzed the variable-speed rotor with a turboshaft engine and optimized the rotor speed based on the minimal required power and minimal fuel consumption. The results showed that in hover and fast flight, these two optimizations lead to different optimal rotor speeds, and the one based on the required power could not reduce the entire vehicle fuel consumption due to the deterioration in engine efficiency [12]. Then, a continuously variable transmission concept was proposed to solve this problem [13; 14]. [PERSON], [PERSON] and [PERSON] compared the CFD (computational fluid dynamics) method and dynamic inflow modeling in a variable-speed rotor study, which revealed a high correlation between these two methods. Their results indicated that the shaft torque could increase along with an increase in power, leading to increased tail rotor thrust [15]. [PERSON] and [PERSON] studied the variable-speed in the tail rotor by setting three different tail rotor speed schedules, which achieved a 1.4% reduction in total helicopter power in cruise flight when the tail rotor speed and main rotor speed were independent and were both optimal. However, the results showed that this was ineffective for reducing the amount of power in high speed flight [16]. Many researchers have discussed the benefits of the variable-speed rotor on helicopter performance; however, previous investigations on the aeromechanics of the variable-speed rotor are scarce. [PERSON], [PERSON] and [PERSON] analyzed the aeromechanics of the variable-speed rotor and tested it on a 2.5 m scale rotor platform. The results showed that the airfoil AoA (angle of attack) and lift-to-drag ratio increased by optimizing the rotor speed; thus, the hover FM was improved by 32% and the cruise flight power was decreased by 22% [17]. [PERSON] and [PERSON] studied the mechanisms of the variable-speed rotor affecting the rotor's required power, mainly the levels of profile power in slow forward flight and fast forward flight [18; 19].