Performance and Controllability Assessment of an Overlapping Quad-Rotor Concept Michael Avera
Hao Kang Rajneesh Singh Aerospace Engineer U.S. Army Research Laboratory Aberdeen Proving Ground, MD, USA ABSTRACT
A numerical study was conducted to characterize the influence on vehicle performance and controlability due to partially overlapped rotors. Partially overlapping rotors on a quad-rotor configuration is as an approach to mitgate the influence of geometric constraints on the vehicle design. A comprehensive analysis model of a pair of 3 bladed overlapped rotors with 0.66D shaft separation was assessed using a free vortex wake and the results were compared to published experimental data. A full quad-rotor vehicle analysis model was constructed to trim the vehicle and characterize the flight performance and controlability in steady forward flight, coordinated turns, pedal turns, sideward flight, and to determine sensitivity to variation in center of gravity during coordinated turns. The finite state interference model used for vehicle trim was configured based upon the results from the comprehensive analysis assessment. In the steady flight maneuvers assessed, the rotors behaved similarly in pairs of with the upper rotors carrying up to 12% more load in forward flight than the lower pair of rotors. Small magnitude reductions in power consumption were realized for turns and center of gravity shifts dependent upon turn direction. Increasing the vehicle gross weight exacerbates the separation in rotor speeds between the upper and lower pairs during manuevers. Aerodynamic rotor-on-rotor interference introduces a coupling of opposite spinning rotors, but the reduction lateral rotor separation had a greater impact on controlability.
INTRODUCTION
arrangement results in a larger total disk area than would be possible if all four rotors were coplanar and not overlapped for the same overall footprint. A side effect of this rotor arrangement is that the rotors now interfere with each other. The wake of the upper rotor is partially impinging on the lower rotor. Also, the lateral separation between rotor spin axes is reduced when the rotors are overlapped.
Rotorcraft design theory suggests that a larger open rotor rather than a smaller heavily loaded rotor will provide a more efficient means of vertical takeoff and landing (VTOL) flight (Ref. 1). However, in cases where the aircraft’s overall footprint is constrained, large open rotors may not be feasible and other design techniques are necessary to regain efficiency lost as a consequence of the geometric constraints. While folding blades and pylon kits address this issue on helicopters such as the Sikorsky UH-60M, these mechanical subsystems could account for a significant increase in empty weight for a light helicopter or personal air vehicle and introduce complexity and points of failure. The U.S. Army Research Laboratory (ARL) has investigated a quad-rotor concept with overlapping rotor pairs as a potential solution to utilize larger rotors while maintaining vehicle geometric constraints.
The concept chosen for this research was a personal air vehicle (PAV) that has similar outer dimensions to a passenger automobile and carries one passenger in a manned version. In an urban theater of war, such a vehicle would be advantageous to maneuver within the streets and alleyways, between buildings, and also be able to avoid pressure-sensitive improvised explosive devices (IED) and quickly pass over any road obstructions or even small buildings. It was recently suggested that for future megacity combat operations, reconnaissance, surveillance, and target acquisition (SRTA) squadrons would need a platform capable of VTOL, hovering, horizontal movement, and loitering to be effective in such an environment (Ref. 2). Megacities are defined as urban population centers with populations of approximately 10 million or greater. Manned quad-copters were also suggested for a similar role in rapid equipment and team displacement, combat evacuation, and search and rescue operations in megacities (Ref. 3).
The overlapping quad-rotor concept is similar to a traditional quad-rotor configuration with the significant difference being the left and right pairs of rotors overlap one another. Within the fore and aft pairs, one rotor is positioned slightly above the other as shown in Figures 1 and 2. This Presented at the AHS 72nd Annual Forum, West Palm Beach, Florida, May 15–17, 2015. This is a work of the U.S. Government and is not subject to copyright protection in the United States.
Since urban environments are arranged based upon the 1
roads and alleys for motor vehicle traffic, a PAV constrained to an overall footprint of 6 ft wide and 12 ft long would be able to navigate the confines constrained to the size of standard roads and alleyways (Ref. 4). Such a vehicle with approximately 500 lb payload capacity would have the capability to carry one loaded soldier along with various other weapons and electronic payloads. A state-of-the-art payload fraction of near 50% would bring the total gross weight to approximately 1000 lb. The design space of hover- capable vehicles with 50–1000 lb gross weight—larger than typical hobbyist multi-rotors and smaller than a Robinson R22—has a very small number of vehicles in development and warrants further investigation. The research presented in this paper consists of an assessment using a comprehensive analysis model of a pair of partially overlapped rotors and a study of steady-state flight conditions and center-of-gravity sensitivity using a full vehicle flight dynamics model. The interference effects present in tandem and coaxial configurations have previously been studied (Ref. 5). However, partially overlapped rotors have not been so rigorously researched.
Fig. 3. Experimental setup of a pair of 3-bladed rotors used in Ref. 6 to characterize the performance of overlapping rotors. turns was also conducted to capture any potential effects due the asymmetry of the rotor layout for this vehicle configuration. The results of these investigations provides insight for designing a VTOL PAV that is size-constrained by characterizing the performance and controllability effects of the aerodynamic rotor-on-rotor interaction and vehicle control sensitivity.
A pair of 3-bladed, linearly twisted rotors from experiments by Ramasamy (Ref. 6) is reproduced in Figure 3. An analytical model of these rotors was constructed to correlate the rotor-on-rotor interference effects captured by comprehensive analysis to the experimental work from Ref. 6 and to configure a lower fidelity interference model used for flight analyses. A second analytical model of the entire overlapping quad-rotor vehicle was constructed in Flightlab, a rotorcraft flight analysis software. With a basic control system applied to the vehicle, the PAV’s performance was assessed for forward flight, sideward flight, and coordinated turns. A center-of-gravity (CG) sensitivity analysis in coordinated
Comprehensive Analysis Rotor Model The analytical rotor model was developed using RCAS, a comprehensive analysis code which uses finite-element based, flexible, multibody dynamics. RCAS allows for the construction of arbitrarily complex models of rotor systems from a library of primitive elements, including nonlinear beams, rigid body masses, rigid bars, springs, dampers, and mechanically applied loads as well as hinges and slides. It also provides numerous options in modeling the vortex wake system of a rotor, the aerodynamic interference between rotors, the airloads acting at a blade section, the dynamics of a multibody system, and the trim conditions of rotors. Equilibrium trim and periodic solution processes are based on the solution of the nonlinear system of equations at a series of time steps. The Newmark-Beta time integration approach, extended by the Hilber-Hughes-Taylor α-method, was used for integration. Within each time step, the iterative Newton-Raphson method was used to achieve a converged solution of the system equations. A detailed description of the program can be found in (Ref. 7).
Fig. 1. An example of an overlapping quad-rotor layout
RCAS’s rigid beams are used to model the blades in this study. A pitch hinge was placed at blade root locations to allow for control of blade pitch. RCAS’s free vortex wake model was used to calculate the induced velocity and rotor to rotor aerodynamic interference. The nonlinear quasi-steady lifting lines model was used to calculate the blade section airloads. These models are described in brief here.
Fig. 2. A section view of a single pair of overlapped rotors. 2
Aerodynamic Model
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The rotor blades are modeled as lifting lines, i.e. as bound vortices located along the blade quarter chord lines. Each lifting line is discretized into a series of spanwise aerodynamic segments, or ”aerosegments.” The wake behind the blade is comprised of vortices trailing from the edge of each of the aerosegments. Shed vortices can also be optionally included to model the effects of azimuthally varying blade circulation distribution. A small azimuthal region behind the blade called the ”near-wake” includes all of these individual vortices over the entire blade span. For numerical efficiency, this near-wake extends only a small number of azimuthal steps (wake age) behind the blade, after which a simpler far-wake model is used. The far-wake is comprised of a discrete tip vortex, a root vortex, and a large-core vortex representing the inboard wake sheet trailing from the entire blade span. The tip vortex strength and the relative strengths, between the root vortex and the sheet vortices, are all determined from the actual loading distribution on the blade.
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Fig. 4. Comparison of analytical overlapping rotor model with test data. rotors to assess correlation. FM is a measure of efficiency of rotors which is the ratio of total power required to the theoretical minimum or ideal induced power. A higher FM represents a more efficient rotor. The following equation was used to determine FM for each rotor in the pair.
The extent of the near wake and far wake are set to a wake age of 15 and 20 revolutions, respectively. This same discretized wake model was consistently used for RCAS hover calculations of isolated rotors presented earlier by Ho. (Ref. 8). RCAS’s free vortex wake model is used to calculate the interference inflow velocity at the other rotor. It also calculates the interference effects whereby the wake of one rotor alters the wake geometry of the other rotor. Sectional lift, drag, and pitching moment along the blade are determined from C81 lookup tables with a Reynolds number correction on drag. The Reynolds number correction is to modify the value of the drag coefficient from the C81 tables so that RCAS performance predictions would be in good agreement with measured data for the isolated single, rotor configuration.
CT 3/2 FM = √ 2CQ
CT is the rotor thrust coefficient and CW is the rotor torque coefficient. Figure 4 shows the comprehensive analysis predicted FM of the upper and lower rotors compared to the experimental results from Ref. 6. The predictions of Figure of Merit for both upper (red line) and lower (blue line) rotors demonstrated a good correlation with the test data. At d/D=0, representing a coaxial rotor configuration, the upper rotor operates at a higher Figure of Merit (i.e. more efficiently) than the lower rotor. As d/D increases, the difference in hover efficiency between the two rotors shrinks until both rotors operate at the same Figure of Merit. After this point, the lower rotor operates at a higher efficiency and both rotors trend toward the FM of a single isolated rotor once they become far enough apart such that no interference takes place.
Trim Analysis The blade collective pitch of each rotor is determined from a trim analysis. These two collective pitch angles are adjusted to simultaneously satisfy total thrust and zero torque of the entire tandem rotor system as was done by Ramasamy (Ref. 6). The axial separation, z/D, between the two rotors is constant with a value of 0.07. The horizontal distance between two rotor axes, d/D, was varied from 0.00 to 1.00.
The intersection of the red and blue lines in Figure 4 is of interest as it is the point at which the upper rotor becomes less efficient than the lower rotor. In the experimental data, this occurs at d/D=0.5 and in the comprehensive analysis results, this occurs at about d/D=0.75. This crossover point is significant in that when the two rotors operate at different efficiencies, they produce unequal amounts of torque when producing the same thrust. The point where the efficiency changes means that the net torque reaction of the two rotors will change direction requiring further control input to balance the vehicle. Ramasamy notes in Ref. 6 that the efficiency crossover for untwisted test blades occurs at d/D=0.9, suggesting that the d/D at which this phenomenon occurs is highly dependent on the blade geometry. Further investigation is warranted to determine
Test data of a tandem rotor configuration with different overlap was used to validate the analytical models. A description of these tests can be found in (Ref. 6). The tandem rotors consist of two threebladed, modelscale rotors. The rotor used highly twisted XV15like blades featuring NACA 64-series, fivedigit airfoils. The airfoil thickness varies nonlinearly from the 64-X32 section at the blade root to the 64-X08 section at the blade tip. The airfoil at the tip is rotated relative to the root by 37 degrees due to blade twist, which also varies nonlinearly across the span. The rotor speed tested was 1200 RPM. The Figure of Merit (FM) of the comprehensive analysis rotor model was compared to the FM of the experimental 3
the relationship between various blade design parameters and their impact on the efficiency variance between overlapped rotors.
time invariant or periodic in time. A detailed description of the program can be found in Ref. 9. A top view of the vehicle configuration examined in this paper is shown in Figure 7. At the front of the vehicle, the left rotor (black) partially covers the right rotor (red). The opposite overlap occurs at the rear of the vehicle where left rear rotor (green) is partially overlapped by the right rear rotor (blue). The distance between the left and right rotor axes is 66% of one rotor diameter, or d/D=0.66. A summary of the major vehicle geometric parameters is listed in Table 1. The color of each rotor shown in Figure 7 correlates to the colors used in Figures 11–17 to indicate individual rotor data in the results section of this paper.
A visual indication of the interaction captured by RCAS and the free wake model is shown in Figures 5 and 6, which show the induced velocity distribution of a pair of overlapped rotors in hover and the normal force distribution on the same pair of rotors in hover. Of note are the two localized areas of lower induced velocity due to rotor-on-rotor interference at approximately 230 deg and 150 deg azimuth on the upper rotor and at 330 deg and 50 deg azimuth on the lower rotor. A similar phenomenon appears in the normal force distributions of both rotors at similar blade azimuths.
Table 1. Overlapping Quad-Rotor Model Characteristics. Length 11.3 ft Width 5.8ft Rotor Diameter 3.6 ft Rotor Axes Separation (d/D) 0.66 Rotor Plane Separation (z/D) 0.10 Blades per Rotor 2 Gross Weight 450 lb / 950 lb
VEHICLE MODEL Next, a vehicle model was constructed in Flightlab to characterize effects caused by the overlapping rotors in steady flight conditions. The vehicle model uses a lower fidelity interference model based upon the comprehensive analysis model to reduce computation time. Flightlab is a rotorcraft vehicle analysis package capable of modeling a range of complex rotorcraft configurations operating in hover, forward flight, and maneuvering flight and analyzing rotorcraft problems including performance, stability and control, aeroelastic stability, and loads and vibration. The Flightlab modeling library includes modules formulated for structural dynamics, aerodynamics, propulsion, control, and numerical solution of nonlinear systems. The trim analysis includes solutions of the nonlinear equations that are either
(a) Upper rotor
An ideal engine model was used to supply power to each rotor. The model generates shaft torque required by each rotor with no limitations unlike an actual vehicle which has a maximum power available that can be dependent on atmospheric conditions. Vehicle weight was estimated from a buildup of major component weights in a hybrid electric propulsion system using subsystem-specific weights from Ref. 10. A gross weight of approximately 450 lb represents an unmanned concept with no payload while the 950 lb gross weight concept represents a manned PAV configuration with additional payload including the soldier’s gear and mission specific load outs. An area of 2 ft2 was estimated for an equivalent flat plate drag area and used in parasitic drag calculations. Two vehicles of approximately 450 lb with no payload and 950 lb with full payload were examined here.
(b) Lower rotor
Rotor Model
Fig. 5. Induced velocity distribution on a pair of overlapping 3-bladed rotors.
(a) Upper rotor
The airloads for each rotor were calculated using a linear unsteady airloads model based upon thin airfoil theory with a 5.73 lift curve slope, 0◦ zero-lift angle of attack, 16◦ stall angle of attack, a 0.0087 zero-lift drag coefficient, and 0.92 tip loss factor. The 13 aerodynamic nodes were spaced approximately .04–.1R apart with the finer resolution occurring near the blade tip. The blade geometry resembles a off-the-shelf two-bladed paraglider propeller with the chord and twist distributions as shown in Figures 8(a) and 8(b). Induced velocity was calculated using a Peters-He three-state inflow model. The interference model for each rotor was calculated using a three-state dynamic wake model in which the front two rotors experience mutual interference and the rear rotors experience mutual interference. There is no interference between the front and rear pairs of rotors. The velocity decay parameters were adjusted such that the
(b) Lower rotor
Fig. 6. Airloads distribution on a pair of overlapping 3-bladed rotors. 4
changes all four rotors’ speed. Pitching motion is achieved by differential rotor speed (and therefore, thrust) between the front and rear rotors. Rolling motion is achieved by a differential rotor speed between the left side and right side rotors. Yaw is the result of differential torque between the upper rotors (front left and rear right) which spin in a counterclockwise direction and the lower rotors (front right and rear left) which spin in a clockwise direction. The control system for the vehicle was a simple controls mixing architecture which consists of the pilot control inputs to achieve desired changes in rotor speed. This is sufficient for the present study as all flight states assessed herein are steady-state. A feedback control system will be implemented in future work to perform maneuvers and assess handling qualities. Visual depictions of the flight conditions investigated in this paper are shown in Figure 9. The steady-state flight conditions assessed were 0–100 kts forward flight, 10–80 kts sideward flight, 0–40 deg/sec turn rate in a coordinated turn at 20–50 kts forward flight speed, 0–40 deg/sec2 yaw acceleration in a pedal turn while in 0–100 kts forward flight, and finally CG shifts for during the same coordinated turn states.
Fig. 7. The PAV is about as wide as a standard road lane and as long as a typical compact automobile. resultant interference effects achieved with the Flightlab model were similar to those from the previously discussed higher fidelity RCAS model. The use of a lower fidelity interference model significantly reduces computation time for the vehicle analyses.
(a) Chord distribution
Fig. 9. Steady state flight conditions characterized with overlapping quad-rotor vehicle flight model. The vehicle was trimmed to zero translational and rotational acceleration along the three body axes. The trim variables were the collective rotor speed, lateral differential rotor speed, longitudinal differential rotor speed, pedals, roll angle (positive left), and pitch angle (positive nose down). Flightlab uses a Newton trim method wherein a Jacobian is calculated from initial conditions based upon prescribed perturbations. The Jacobian is used to determine the flight states as pilot inputs are modulated. After a specified number of iterations, a new Jacobian is calculated and the process repeats until the zero acceleration trim conditions are within a specified tolerance.
(b) Twist distribution
Fig. 8. PAV rotor blade geometry.
CG sensitivity Coaxial configuration rotorcraft typically achieve lateral control of the main rotor with cyclic blade pitch changes. Since the PAV quad-rotor uses fixed pitch rotor blades, lateral control is achieved by modulating the rotor speed of
Control The overlapping quad-rotor has similar controls to a traditional quad-rotor. A collective input simultaneously 5
the rotors on either side of the vehicle to create a rolling moment. The magnitude of the applied rolling moment is directly proportional to the lateral distance of the rotor axes to the vehicle CG. Therefore, as d/D decreases at larger rotor overlaps, the force required (and therefore power) by the rotors to achieve the same roll moment is greater in comparison to a non-overlapped coplanar quad-rotor. This behavior was characterized by varying the location of the vehicle’s CG at about 40 locations and assessing the change in power required to complete a coordinated turn for various turn radii at 20–50 kts forward airspeed. As the vehicle does not have the symmetry as a quad-rotor, it is expected that contour plots of power required for various CG shifts will also not be symmetric.
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Sideward flight rotor performance was similar to forward flight rotor performance in that the lower pair of rotors carried more of the load than the upper pair of rotors as shown in Figure 12. However, there is a marked difference in the rotor speed among the two lower rotors for forward speeds above 40 kts as can be seen in Figure 13. For sideward flight above 40 kts, the front right rotor (red line) rotates faster than the rear left rotor (green line). However, the front right rotor produces less vertical thrust that the left rear rotor. This suggests that the difference in efficiency between the two lower rotors does not remain constant in forward flight.
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In regards to balance of thrust laterally, the sum of the thrust produced by the left two rotors is balanced by the right two rotors such that there is no resultant lateral motion. The gap between the thrust produced by among the two left rotors increases for the higher gross weight configuration as does the gap between the thrust produced by the right side rotors.
Figure 10 shows the rotor speed each of the four rotors over a range 0–100 kts forward airspeed for the 450 lb configurations. In hover, the upper rotors (Front-Left and Rear-Right) are spinning slightly faster than the lower rotors and produce slightly more thrust. This aligns with the notion that the lower rotors are more efficient in hover (Ref. 6). However, once the vehicle begins moving forward, the lower rotors (Front-Right and Rear-Left) produce the majority of the thrust and operate at higher speeds. At 40 kts, the upper rotors produce 12% more thrust than the lower rotors. This behavior occurs for both weight configurations.
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each pair of rotors. Among the lower rotors (green and red lines), the front rotor produces less thrust than the rear rotor as depicted by the gap between the green and red lines in Figure 11. This behavior also occurs for the upper pair of rotors (blue and black). This suggests that in forward flight, the rear rotors are operating more efficiently than the front rotors.
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Fig. 11. Individual rotor thrust in steady forward flight for 450 lb configurations.
The selected results from the analysis of steady-state flight conditions are presented here. For most flight conditions, the upper rotors behave in a similar manner to each other and the lower rotors behave also similarly as a pair. This behavior is dissimilar to a traditional non-overlapped quad-rotor where all four rotors operate at similar conditions for steady flight. This pairing of rotor performance is a result of the coupling due to the rotor-on-rotor interference and the similar rotation directions of each pair of upper and lower rotors.
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Fig. 12. Individual rotor thrust during right hand sideward flight for 450 lb gross weight configuration.
Also of note is that all four rotors produce different amounts of thrust which is a result of the coupled nature of 6
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Fig. 13. Individual rotor speeds during right hand sideward flight for 450 lb gross weight configuration.
Fig. 15. Individual rotor thrust during forward flight for 450 lb gross weight configuration.
Coordinated Turn
At zero yaw acceleration, the result is the same as the forward flight analysis with the lower rotors spinning faster. The gap between the rotor speeds of the upper and lower rotors increases for counterclockwise turns. That is, the upper rotors become more heavily loaded to produce more torque in the opposite direction of their spin. The opposite effect occurs for clockwise turns. The lower rotors now become more heavily loaded to produce clockwise torque. At about 10 deg/sec2 of clockwise acceleration, all 4 rotors are spinning at approximately 2500 RPM and the vehicle is torque-balanced for the 80 kts forward flight case. The crossover in rotor speed occurs at a higher turn rate for the 950 lb vehicle as shown in Figure 17. The torque equilibrium also occurs at higher clockwise accelerations for successively higher forward flight speeds. This can be attributed to the lower rotors producing more thrust in forward flight and thus requiring an even more counter torque to be applied by the opposite spinning upper rotors.
A coordinated turn is a steady level turn where the vehicle has a non-zero roll angle in the direction of the turn. This maneuver requires a combination of roll, pitch, and yaw inputs to maintain constant altitude during the turn. Figure 14 shows the individual rotor speeds during a coordinated turn at 30 kts forward airspeed for the 450 lb vehicle. The same trend appear as previous flight conditions in that the lower rotors operate at higher speeds and produce more thrust than the upper rotors. Figure 15 shows that the load sharing between the upper and lower rotors does change slightly with increased turn rate as it did for increased forward or sideward airspeed. A left hand coordinated turn increases this gap while a right hand turn decreases it. 3600
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Fig. 14. Individual rotor speeds during forward flight for 450 lb gross weight configuration.
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Fig. 16. Individual rotor speed during a steady pedal turn at 80 kts forward airspeed for the 450 lb configuration. Pedal Turns CG Envelope in a Coordinated Turn
The pedal turn is a rotation about the vehicle’s yaw axis with zero degrees of pitch and roll attitude. This maneuver is dependent mainly on the vehicle’s yaw authority and is assessed in terms of the applied yaw acceleration during steady forward flight. Figure 16 shows the individual rotor speeds during a steady pedal turn at 80 kts forward airspeed with yaw accelerations from -40–40 deg/sec2 where a negative acceleration is a counterclockwise rotation and a positive acceleration is a clockwise rotation.
Figures 18 and 19 show the relative vehicle power required in a coordinated turn with the CG shifted from its neutral position in the vehicle center. Plots are shown for increasing turn radii at 20 and 50 kts forward air speed. Each point represents a trimmed flight condition representing a specific longitudinal and lateral position of the vehicle CG. The contour lines of constant ∆power are linearly interpolated 7
• The reduction in lateral rotor axes separation has a larger impact on the vehicle’s sensitivity to a CG shift than aerodynamic effects from rotor-on-rotor interference.
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• While overlapping the rotors introduces an asymmetric coupling between rotors, the vehicle is controllable in steady flight maneuvers.
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Further investigation into the mechanics of the interacting airflows is warranted to better understand the changeover point of efficiency between overlapped rotors. A parametric study would support asymmetric rotor design wherein the upper and lower rotors have different designs, accounting for the behavior of the rotor efficiencies in regards to number of blades, rotor phasing, twist and taper profiles, and airfoil sections. ARL has already begun computational fluid dynamics (CFD) analysis to investigate the flow field mechanics of partially overlapped rotors. The authors also plan to implement a feedback control system into the vehicle model to perform transient maneuvers, assess the vehicle’s handling qualities, and investigate the potential need for increased yaw authority and more efficient torque balance using techniques investigated in Refl. 11.
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Fig. 17. Individual rotor speed during a steady pedal turn at 80 kts forward airspeed for the 950 lb and configuration. from these points. In all cases, a forward CG shift reduced total power required and an rearward CG shift increased the power required to complete a coordinated turn. This is most apparent in 19(c) when the neutral CG point is not within the smallest contour line. A lateral CG shift increased power from the neutral CG case but, a lateral shift of the CG in the direction of the coordinated turn required less power than a CG shift in the opposite direction of the turn. While the coupled nature of the overlapped rotors produced only slight lateral asymmetry in the presence of CG shifts, the reduction in the lateral distance of the rotor axes from the center of gravity had the largest impact on CG sensitivity. This behavior is a key idea from the use of reducing a vehicles overall footprint by overlapping rotors.
Author Contact Michael Avera,
[email protected] Hao Kang,
[email protected] Rajneesh Singh,
[email protected]
CONCLUSIONS
REFERENCES
A series of analytical experiments were conducted to investigate the impact of partially overlapping rotors on a quad-rotor configuration VTOL aircraft. A comprehensive analysis model of a single pair of partially overlapped rotors was constructed using a Free Vortex Wake model to capture the rotor-on-rotor interference and was compared against prior experimental results. The comprehensive analysis model was then used to configure the aerodynamic interference model as part of a complete vehicle model used to assess the concept’s performance in a number of flight conditions. A summary of the conclusions drawn from these analyses is:
1 Leishman,
J. G.,Principles of Helicopter Aerodynamics, Cambridge University Press, New York, 2006. 2 Hartrich,
J. P., ”Adapting the Army to Win Decisively in Megacities,” Army Press Online Journal. Vol. 15, (7), Jan. 2016 3 Prautz, F., ”U.S. Army Mega City Operations: Enduring Principles and Innovative Technologies,” Small Wars Journal. Feb. 2016. http://smallwarsjournal.com/jrnl/art/us-army-meg a-city-operations-enduring-principles-and-innovative-technol ogies .
• Aerodynamic rotor-on-rotor interference causes one of the two rotors to operate more efficiently than the other causing an imbalance in torque and thrust production.
4 ”A
Policy on Geometric Design of Highways and Streets,” American Association of State Highway and Transportation Officials. 2001
• In forward flight, the clockwise spinning lower rotors are more heavily loaded than the counterclockwise spinning upper rotors. The difference in upper to lower rotor is a result of balancing torque produced by rotors that are coupled and rotating in opposite directions.
5 Stepniewski,
W. Z., and Keys, C. N., Rotary-Wing Aerodynamics, Dover, New York, NY, 1984. 6 Ramasamy,
M., ”Measurements Comparing Hover Performance of Single, Coaxial, Tandem, and Tilt-Rotor Configurations,” Proceedings of the American Helicopter Society 69th Annual Forum, Phoenix, AZ, May 21–23, 2013.
• Increased gross weight and higher forward airspeed exacerbates rotor-on-rotor interference and the differential thrust and power between the upper rotor pair and lower rotor pairs.
7 Advanced
Rotorcraft Technology, Inc, RCAS Theory Manual, January, 2011. 8
8 Yeo,
∆ Power Required (HP) .0 1 2
5.0
9.0
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1.0
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V.T., Chopra, I., ”Explorations of Novel Powerplant Architectures for Hybrid Electric Helicopters,” Proceedings of the American Helicopter Society 71st Annual Forum, Virginia Beach, VA, May 5–7, 2015.
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10 Nagaraj,
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Rotorcraft Technology, Inc, Flightlab Theory Manual, January, 2011.
18
9 Advanced
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1.0
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H., Bhagwat, M., Ho, J., ”Validation of Rotorcraft Comprehensive Analysis Performance Predictions for Coaxial Rotors in Hover,” Proceedings of the American Helicopter Society 71st Annual Forum, Virginia Beach, VA, May 5–7, 2015.
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11 Bogdanowicz,
C., Hrishikeshavan, V., Chopra, I., ”Development of a Quad-Rotor Biplane MAV with Enhanced Roll Control Authority in Fixed Wing Mode,” Proceedings of the American Helicopter Society 71st Annual Forum, Virginia Beach, VA, May 5–7, 2015.
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0.5
1.0
(c) 300 ft turn radius. Fig. 18. Power required with CG shift in coordinated turn at 20 kts forward airspeed.
9
∆ Power Required (HP) .0
.0
3
5
30 18.0
21.0
9.0
3.0
12.0
27.0
1.0
0.5
5.0
0.0
15.0
−1.0 −1.0
8
7
.0
.0
−0.5
1
2
.0
2
1
.0
0.0
Lateral CG shift (ft)
3
0
.0
.0
1 .0
5
7
3
.0
7
2
5
.0
−0.5
3
24.0
9.0
15.0
24.0
30.0
Longitudinal CG shift (ft)
1.0
4
0
.0
0.5
1.0
(a) 200 ft turn radius.
∆ Power Required (HP) 4
.0
5
.0
40
−1.0 −1.0
18.0
8
.0
1
−0.5
2
.0 2
1
.0 .0 5 0 3 4
.0
4 5 5. 0 0 .0
1
30.0
7.0
5.0
12.0
21.0 24.0
35.0
−0.5
3 4 0 4 0. .0 5 0 .0
24.0 27.0
15.0
1.0
3.0
9.0
0.0
15.0
27.0
0.5
40.0
Longitudinal CG shift (ft)
1.0
0.0
Lateral CG shift (ft)
0.5
1.0
(b) 300 ft turn radius.
∆ Power Required (HP) 4
.0 5
0
.0 35.0
27.0
21.0
15.0
5.0
3.0
1.0
7.0
15.0
27.0
0.5
0.0
5 −1.0 −1.0
3 0
.0
5
2
.0
−0.5
1
1 .0
2
.0
1
2
.0 2
4
.0
0.0
Lateral CG shift (ft)
4
0
.0
0.5
5
0
45
30.0
18.0
18.0
−0.5
.0
9.0
24.0
30.0
45.0
Longitudinal CG shift (ft)
45
0
.0
1.0
.0 0 . 0 6 1.0
(c) 400 ft turn radius. Fig. 19. Power required with CG shift in coordinated turn at 50 kts forward airspeed.
10
