GYROPLANE
Short Description
GYROPLANE...
Description
49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition 4 - 7 January 2011, Orlando, Florida
AIAA 2011-1191 2011-1191
Gyroplane Rotor Aerodynamics Aerodynamics Revisited Blade Flapping and RPM Variation in Zero-g Flight Eugene E. Niemi, Jr.,1 and B.V.Raghu Gowda 2 University of Massachusetts Lowell, Lowell, MA, 01854
This paper reviews some phenomena related to gyroplane rotors: the concept of “hump speed,” and the behavior of an autorotating autorotating rotor encountering zero-g flight. flight. Government accident reports on small sport gyroplanes are discussed, and the phenomena of thrust line offset, horizontal stabilizer use and rotor shaft pitch changes are discussed qualitatively. Equations for the rotor system alone, uncoupled from any airframe, are summarized and used to predict the behavior of rotor blades experiencing the equivalent of zero-g flight. Small scale rotor model tests on a 3 ft diameter autorotating rotor are presented, both qualitatively regarding zero-g flight and then quantitatively at high advance ratios regarding rotor hump speed.
Nomenclature a B b c cdo cl dCM e g I h I p l n q R V W x xc αs β γ θ 0 µ ξ ρ σ φ
= = = = = = = = = = = = = = = = = = = = = = = = = = = =
airfoil section lift curve slope tip-loss factor number of rotor blades blade section chord airfoil section profile drag coefficient airfoil section lift coefficient distance from flapping hinge to blade mass center distance from center of flapping hinge to rotor shaft center line acceleration due to gravity moment of inertia of rotor blade about flapping hinge polar moment of inertia of rotor system about shaft distance from pivot point on rotor shaft to rotor hub center index used in summation over number of rotor blades rotor shaft pitching rate radius of rotor blade velocity of rotorcraft weight of rotor blade ratio of blade element radius to rotor blade radius, r/R non-dimensional cutout radius, rc /R rotor shaft angle of attack blade flapping angle with respect to hub plane rotor blade Lock number, ρacR4 /Ih collective pitch angle at blade root advance ratio, Vcosα Vcosαs / ΩR non-dimensional non-dimensional hinge offset distance, e/R air density rotor solidity, bc/ πR inflow angle at blade element
1
Professor, Mechanical Engineering Dept., One University Ave., Senior Member. Graduate Student, Mechanical Engineering Dept., One University Ave., Student Member.
2
1 American Institute of Aeronautics and Astronautics
Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
ψ Ω
= blade azimuth angle measured from downwind position in direction of rotation = rotor angular velocity
I. Introduction
G
YROPLANE is the generic term for aircraft that rely on an autorotating rotor for their primary lift. Sometimes the term “autogyro” or “gyrocopter” is also used, but technically these are both proprietary names. No typecertified production gyroplanes are currently manufactured in the United States, although some are still in the certification process. However, sport gyroplanes have maintained their popularity, and see extensive use in many areas of this country and overseas. Also, a considerable number of recent journal articles (referenced later) show the continued strong interest in this type of aircraft. Leishman1 gives a summary of the history of gyroplane (autogyro) development, and a few points from his paper will be discussed later in the present article. Probably the most recent seminal report on gyroplanes is that presented by the British Civil Aviation Authority in Ref. 2, illustrating the current serious interest in gyroplane aerodynamics, especially overseas. While production gyroplanes generally have a good safety record, there still continues to be a significant accident rate with sport gyroplanes. The accident rate is high enough to warrant a technical discussion for some of the reasons. One of these important reasons is the situation of zero-g flight. Government accident reports on this type of aircraft can be found in Refs. 3 and 4. Although some of the information presented in the current paper has been discussed in qualitative form in the popular literature,5,6 this paper presents the information on a more quantitative technical level. A number of different designs of FAA type-certified gyroplanes have been manufactured in the past, and Fig. 1 illustrates a typical configuration. They usually have a 3-bladed articulated rotor, a horizontal stabilizer, and a pusher propeller as common features. These rotors have cyclic pitch control, but collective pitch is fixed at a relatively low angle, except for those designs that have a two position collective to provide for jump takeoffs. Sport gyroplanes, on the other hand, usually have a 2-bladed teetering rotor, pusher propeller, and a small horizontal stabilizer that is often no more than a flat plate having a short moment arm, as seen in Fig. 2. Early versions of sport gyroplanes sometimes had no horizontal stabilizer at all. Because of the simple configuration of the teetering rotor, rotor shaft tilt is used to achieve the same effect as cyclic pitch control. A jet propelled, folding gyroplane configuration was even once proposed for functioning as a pi lot ejection seat.
Fig. 1 Typical production gyroplane of the 1970’s (note 3-bladed fully articulated rotor)
2 American Institute of Aeronautics and Astronautics
Fig. 2 Typical sport gyroplane (note 2-bladed teetering rotor)
General performance data on sport gyroplanes can be found in the works of Schad 7,8 and Niemi,9,10 and more technical information on stabilit y and control of sport gyroplanes can be found i n the extensive works of Houston and others.11-15
II. Gyroplane Rotor Characteristics A gyroplane rotor is always operating i n autorotation except for short periods when the rotor may be pre-spun up to a certain rpm prior to the take-off run, or where it may be oversped temporarily for a jump takeoff. Otherwise the rotor operates in autorotation with forward propulsion being provided by a propeller or small jet engine. As such, the rotor disk (tip path plane) is tilted rearward relative to the velocity vector, producing lift and drag much like an airplane wing; rather than tilted forward and producing a forward component of thrust as well as lift, as with a helicopter. Figure 3, from Ref. 1, shows the coning and flapping angles typical of a rotor in autorotation. The blade flapping motion as a function of azimuth is often written in the form
Fig. 3 Illustration of blade flapping angles (Courtesy of J. G. Leishman and AIAA)
To understand how the rpm of an autorotating rotor varies under load, we must look at the concept of “accelerating” and “decelerating torques.”
3 American Institute of Aeronautics and Astronautics
(1)
A. Accelerating and Decelerating Torque Coefficients For a rotor in autorotation, there are certain regions within the rotor disk where the aerodynamic torques tend to accelerate the rotor rpm, and other regions of the disk where the aerodynamic torques te nd to decelerate the rotor. Steady-state autorotation occurs when the net effect o f the accelerating torques balances the effect of the decelerating torques. Figure 4 shows a schematic view of a cross section of an inboard rotor blade airfoil section where the net aerodynamic force is a driving force as well as a thrust force. As can be seen from this figure, the local section blade angle of attack at the inboard regions of the rotor is such that it provides a net forward component of force, thus tending to accelerate the rotor rpm. A view of the relative velocity components and forces at the outboard sections of the rotor would show a net rearward component of force tending t o decelerate the rotor.
Fig. 4 Section of rotor blade airfoil from inboard accelerating torque region (Courtesy of Leishman and AIAA)
Figure 5 shows a plan view of a rotor blade showing both the inboard accelerating torque region as well as the outboard decelerating torque region. The far inboard section of the rotor is the stalled region.
Fig. 5 Plan view of rotor blade showing accelerating and decelerating torque regions (Courtes of Leishman and AIAA)
An overall plan view of the entire rotor disk with accelerating and decelerating torque regions is shown in Fig. 6. 4 American Institute of Aeronautics and Astronautics
Fig. 6 Plan view of rotor disk showing the three regions of operation, acceleration, deceleration, and stall area (From Ref. 16, FAA)
An increase in rearward cyclic or shaft angle o f attack at a constant forward speed increases the proportion of the disk where accelerating torques act and the rotor rpm increases to a new steady-state value. This would be accompanied by more lift and a resulting climb. Conversely, a decrease in rearward cyclic or shaft angle of attack increases the region of decelerating torques in the rotor disk, and the rotor slows down to a new equilibrium rpm, accompanied by a decrease in lift and a descent. This is always occurring automatically in response to the pilot’s cyclic stick inputs to maintain the desired flight condition for whatever gross weight and velocity the aircraft is operating at. Two characteristics of gyroplane rotors will first be discussed here, the concept of “hump speed” when starting the rotor, and the rotor behavior in flight when encountering zero-g operation. B. Rotor Hump Speed The early sport gyroplane pilots followed a self-training procedure whereby the pilot learned to fly the gyroplane as an unpowered “glider” in towed flight behind an automobile, or sometimes on floats behind a motorboat. This type of operation is illustrated in Fig. 7 (now pilot training is just as often done in two seat powered gyroplanes).
Fig. 7 Sport gyroplane (gyroglider) in towed flight behind automobile
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These sport gyroplanes had rotors that had to be hand started from rest before commencing the take-off run. The procedure would typically be as follows, assuming no wind: With the gyroplane sitting at the end of the runway behind the tow car, the pilot would reach up and gradually start turning the rotor by hand. He would continue this procedure until he reached the maximum rpm he could physically achieve, typically on the order of 100 rpm. At that point, he would tilt the rotor shaft back to around 9o and the automobile would quickly accelerate to 15 to 18 mph and hold this speed. If this were done properly, the air passing through the rotor would gradually accelerate it to approx 200-250 rpm, then the rotor shaft could be tilted back to its full 18o and the car could gradually accelerate to something on the order of 30-40 mph. The procedure was a little different if wind existed. Takeoff would typically occur at approximately 30 mph and 300 rotor rpm (variations on all these numbers could exist, of course). If the car accelerated too quickly (too high an advance ratio) or the shaft was tilted too far back early in the procedure, the rotor rpm would decrease, accompanied by blade flapping to the stops, the so called “mast bumping” phenomenon, which could damage the rotor or the rotor head assembly. Many early pilots had trouble doing the correct procedure properly. Typically the first take-off ground run in this case was on the order of 1000 ft, but subsequent takeoffs could be done with a short ground roll on the order of a hundred feet if automobile speed and rotor shaft angle were handled properly. Accomplishing this procedure in a float mounted “hydroglider” could be extremely difficult if there was much wave action. In that case, it was very difficult to avoid some mast bumping. The term “hump speed” then came to be applied to the minimum rpm that had to be achieved by hand to make a successful takeoff. In more recent years, sport gyroplanes have been designed wit h a small (typically o ne hp) motor mounted at the top of the rotor mast to spin the rotor up to approximately 200 rpm prior to starting the takeoff roll (see Fig. 2 again). With this addition, the take-off roll could be reduced to 100 feet. Alternatively, flexible shaft drives have been used for a power takeoff from the main engine to pre-rotate the rotor for takeoff. C. Zero-g Flight Zero-g flight is a maneuver that should never be attempted in a gyroplane, but which has often occurred unintentionally with low time gyroplane pilots. Typically, this maneuver is performed in the same manner as it is deliberately done by the famous “Vomit Comet” airplane, by making a sharp pull up into a climb, followed by a gradual pushover into a dive. At the end of the dive, a pullout again follows before the airspeed builds up too much. If done properly (which really means improperly in the case of a gyroplane), zero-g occurs. During this maneuver, the rotor is producing no lift and its rotational speed decreases rapidly, and this will result in excessive blade flapping when lift is applied again. This excessive flapping can force the rotor blades down into the pusher propeller or vertical tail surfaces. Furthermore, if power is applied during the zero-g portion of the maneuver and the propeller thrust line does not pass through the rotorcraft c.g., this could lead to rapid pitch up, or more commonly pitch down (the so-called “buntover”), causing the rotorcraft to tumble inverted a few times, with similar disastrous consequences. As examples of the allowable rpm ranges for typical production gyroplane rotors, Table 1 below gives some values. Table 1. Production gyroplane rotor rpm limits Gyroplane designation
Gyroplane A Gyroplane B
Gross weight (lb)
Rotor diameter (ft)
Never exceed speed, Vne (mph)
Maximum rotor rpm
Minimum rotor rpm
1550 1800
26 35
106 97
480 320
300 200
The upper limit on the allowable rpm range is usually due to centrifugal force limits, while the lower rpm limits quoted (which could occur during partial unloading of the rotor or flight at very light weights) would be to prevent excessive blade flapping during subsequent loading of the blades again. Leishman1 alludes to this situation, but does not stress it seriously. Warnings against this maneuver have been presented often in the popular literature, but these types of accidents continue to happen in the sport gyroplane community. The small, low moment arm horizontal stabilizer or inadvertent thrust line offset does not help to prevent the situation either. This characteristic of rapid rotor slowdown with decrease in shaft angle as the rotor is unloaded is noticed immediately by gyroplane pilots when they land and begin taxiing, or stop taxiing even in a wind and reduce the cyclic pitch or shaft angle to zero. 6 American Institute of Aeronautics and Astronautics
III. Equations of Motion for a Pitching, Autorotating Rotor To study the behavior of an autorotating rotor undergoing the zero-g phenomenon, the equatio ns of motion were derived for a rotor pitching about some arbitrary point on the rotor shaft. The problem was approached as a basic applied mechanics problem with dynamic shaft motion inputs, rather than as a complete coupled aircraft, rotor system configuration. This was to separate the study from any particular airframe geometry or rotorcraft maneuver, focusing instead on the rotor system alone, and making the analysis consistent with small scale rotor model tests that were to be conducted. The focus was on how an autorotating rotor system would respond when the shaft was pitched forward through t he zero or negative angle of attack range, and then back to positive angles, and the items of interest were the blade flapping and the rpm variation during this type of maneuver. The equations of motion for a pitching, autorotating rotor with flapping hinges are derived in Refs. 19 and 20. Assumptions used to develop the theory were the classical ones of quasi-static, two-dimensional, non-linear aerodynamics, with a blade tip loss factor of 0.97. Blade sweep effects and radial flow were neglected, and the induced velocity was assumed to be uniform across the rotor disk. The blades were treated as rigid, with offset flapping hinges and no lag hinges. The blades were also assumed to have a uniform mass distribution. Airfoil data were obtained for each airfoil, or in some cases estimated, for the different Reynolds numbers encountered by the various size rotor models considered, and for the prototype gyroplane rotor that was studied. The equations derived were then programmed in FORTRAN for numerical solution. The final rotor blade equations of motion are listed below. The rotor blade flapping angle β is determined from the solution of Eq. 2, which accounts for the accelerations imposed on the blades by a pitching rotor shaft. This equation is coupled to the rotational equation through the variable angular velocity Ω term.
(2)
This equation can be simplified considerably if the shaft pitching angular velocity q is much less than the rotor angular velocity Ω, and if the rotor shaft angle of attack and blade flapping angles are small. Furthermore, if it is assumed that the rotor pitches about the rotor hub center, l = 0, and Eq. 2 simplifies to
(3)
This equation reduces to the flapping equation of Ref. 21 for the special case of no rotor shaft pitching, i.e., for q = = 0 and for Ω = constant. The rotational equation, as derived in Ref. 19, simplifies to Eq. 4 below:
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(4)
Solutions to Eqs. 3 and 4 for a typical gyroplane rotor are presented later in this paper. Equations 3 and 4 are also used for comparison with model rotor tests, as well as for predicting the behavior of a full scale rotor.
IV. Autorotating Rotor Model Tests A. Model Rotor Design To verify the previously discussed rotor characteristics, both qualitatively and quantitatively, a small model rotor was built for wind tunnel testing. The design selected was a three bladed rotor (to simulate the larger production gyroplanes), with flapping hinges but no lag hinges. The rotor was three feet in diameter and had blades of approximately two inch chord. The blades had a solid aluminum spar leading edge and a balsa wood trailing edge. They were designed such that the blade elastic axis, center of pressure, and center of mass were all within one percent chord of each other. This was to minimize the possibility of flutter problems that could conceivably arise in some types of testing, although the blades were very stiff. The blades were provided with flapping hinges but no lag hinges. The stops provided for the flapping hinge permitted flapping angles of ±30o. A photograph of the model rotor is shown in Fig. 8. The airfoil section used was the NASA 0012 airfoil. This airfoil has good autorotative tendencies even in small rotor models, as pointed out by Razak 22.
Fig. 8 Three ft diameter rotor model for autorotation tests
The collective pitch setting could be manually adjusted between tests by loosening two screws on each blade grip block and rotating the blades to the desired pitch setting. No provision was necessary for cyclic pitch control, this being simulated by rotor shaft tilt. Complete geometric and inertial data for the model rotor are presented in Table 2. Table 2. Model rotor geometric and inertia characteristics Geometric Parameters Values Diameter 36.24 in Number of blades 3 Chord 1.96 in Solidity, σ 0.104 Airfoil section NASA 0012 Blade twist None Cutout radius 3.31 in Flapping hinge offset 1.00 in (5.5% radius) Blade weight moment 0.222 ft-lb Blade flapping inertia 0.00588 slug-ft Lock number, γ 2.1 A simple test stand was built to allow rotor shaft angle changes that simulated a cyclic pitch change, with the rotor system designed to pivot about the center of the rotor hub; which remained located at the center of the wind tunnel while the rotor disk was changing angle of attack. A detailed description and illustration of the test stand can 8 American Institute of Aeronautics and Astronautics
be found in Ref. 19. The wind tunnel used was a 4 ft x 4 ft open jet wind tunnel at the University of Massachusetts Amherst. This tunnel has a maximum speed of 60 ft/s.
B. Experimental Procedure The model was used for both quantitative and qualitative evaluation of hump speed behavior and rotor blade flapping under various operating conditions. The qualitative results will be reported first.
1. Qualitative Evaluation of Rotor Hump Speed Qualitative experiments to explore the concept of hump speed were first conducted as follows: The blade collective pitch and shaft angle of attack were first set at the desired values. The rotor was then powered to approximately 800 rpm using a small electric motor temporarily attached to the lower end of the rotor shaft. The wind tunnel was then started and the driving torque was removed from the rotor. The tunnel jet speed was then increased to its maximum value and steady state autorotation of the model was established. This procedure was repeated for several different shaft angles of attack and three collective pitch setti ngs: 0o, +1o, and +2o. All tests were conducted at the maximum tunnel velocity of approximately 60 fps. The upper limit on shaft angle of attack was selected to keep the model rotor rpm below a maximum value of 2500 rpm, this limit being based on the maximum allowable centrifugal force in the flapping hinge pin. Autorotation was successfully achieved in all these cases, indicating that the initial rotor rpm of 800 was above the “hump” speed required for the tunnel speed of 60 fps and shaft angle of attack initially set. As the collective pitch setting was set at higher values, the shaft angle of attack required to maintain autorotation increased, while the advance ratio during autorotation decreased. Tests were not conducted at negative angles of collective pitch. Table 3 summarizes these experimental results. Table 3. Summary of conditions required for rotor model autorotation Collective pitch angle, θo (deg)
Tunnel velocity, V (ft/s)
Minimum shaft angle, αs, for autorotation (deg)
Advance ratio, µ
0 1 2 3
60 60 60 58
6.8 9 10.8 >24
0.37 0.31 0.22 not achieved
As seen from the table, at θo = 0o, the minimum shaft angle that would allow steady state autorotation was 6.8o, corresponding to an advance ratio of 0.37. At θo = 1o, the lowest shaft angle allowing autorotation was 9o, achieved at an advance ratio of 0.31. At θo = 2o, the minimum shaft angle allowing autorotation was 10.8o, at an advance ratio of 0.22. Operation at a collective pitch angle of +3o was found to be impossible for a tunnel speed of 58 fps and a shaft angle of at tack of 24 o or less. During an attempt to obtain autorotation under these conditions, the rotor would immediately slow down with the tunnel on when the driving torque was removed, even at the high positive shaft angle of attack. This showed that the hump speed had to be greater than 800 rpm in this case, or that the decelerating torques were greater than the accelerating torques for this collective pitc h regardless of shaft angle. Full scale rotors will autorotate at collective pitch settings as high as 6o, but Reynolds numb er effects prevent small rotor models from autorotating at such high pitch settings.
2. Qualitative Zero-g Rotor Behavior The rotor behavior was then investigated qualitatively in conditions simulating gyroplane zero-g flight. The shaft was pitched down to zero and then negative angles for short periods of time. This technique was approached cautiously by gradually approaching smaller shaft angles, and then increasing the shaft angle back up to positive values. During pitchdown to zero angle, the rotor rpm would rapidly decay, with a decrease in blade flapping, and then increase again with an increase in blade flapping as the shaft was pitched back up to the initial positive starting shaft angle. This behavior confirmed rotor behavior in zero-g flight. As mentioned earlier, if this situation were carried to an extreme in a prototype gyroplane, the increased blade flapping at low rotor rpm, especially when coupled with blade flexibility, could drive the rotor blades into the pusher propeller or tail surfaces. Furthermore, as pointed out in Ref. 4, improper pilot application of thrust could cause pitching moments (the so-called “buntover” 9 American Institute of Aeronautics and Astronautics
where the gyroplane tumbles, creating an unrecoverable flight situation). In the case of the wind tunnel model, if the model rotor shaft was maintained at a negative angle of attack, the rpm would rapidly decay to zero, and then the rotor would accelerate in the reverse direction, accompanied by blade flapping motion to the 30o stops. Obviously, these tests had to be done carefully to prevent damage to the blades and were not conducted on a prolonged basis. This behavior confirms the “hump-speed” concept discussed earlier. Rotor blades that need to be hand-started by sport gyroplane pilots have to be set on the hub at low pitch angles of -1o to perhaps 0o. If power assist prerotation is available, they can be set on the order of +1o and then give better overall performance. Steady state test data were also taken in a quantitative manner, as reported next.
V. Confirmation of Theory with Test Data A. Steady State Rotor Angular Velocity and Blade Flapping Angle Prediction The figures below give some of the steady state performance data for the model rotor. Figure 9 shows experimental data for rotor angular velocity versus shaft a ngle of attack for a model collective pitch of 2 o. The agreement between theory and experiment is seen to be generally good down to the lower rotor angular velocities.
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Fig. 9 Rotor angular velocity vs shaft angle of attack, 3 ft diameter model
Figure 10 presents a comparison between theory and experiment for the rotor blade flapping angles at 0 o and 180 azimuth angle. Again, the agreement between theory and experiment is seen to be reasonable. Similar data for blade collective pitch settings of 0o and 1o are reported in Ref. 23. Theory-experiment agreement is also good at these pitch settings. o
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Test data, ψ = 0° Test data, ψ = 180° ______ Theory
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Fig. 10 Blade flapping angles vs shaft angle of attack, θ0 = 2o, 3 ft diameter model
10 American Institute of Aeronautics and Astronautics
B. Accuracy of Model Tests Results A detailed discussion of the accuracy of all experimental measurements is presented in Ref. 19. To summarize this discussion, it is estimated that all rpm values were measured to 1% accuracy. Atmospheric conditions and the use of the perfect gas law for air density were estimated to be accurate within about 2%. Collective pitch values were probably a little less accurate primarily because of some play in the flapping hinges and partly due to the individual tolerance allowed in the setting of each blade’s collective pitch. This combination was such that the collective pitch angles were probably accurate to within ± 0.2o. Blade flapping angles were measured to an accuracy on the order of 1/ 2o. Because the primary purpose of the experiments was t he determination of rotor angular velocit y behavior, the lesser accuracy obtained in the measurement of blade flapping angles does not impose a significant limitation on the use of the results. The low rotor blade Lock number is partly responsible for the small flapping angle magnitudes. C. Unsteady-State Rotor Behavior Prediction Very few data appear to be available for autorotating rotors undergoing significant changes in a ngular velocity. The 3 ft diameter model rotor was not tested quantitatively under decelerating or accelerating rpm conditions, but some early test data were located for a 6 ft diameter gyroplane rotor undergoing varying rpm. These data are reported in Ref. 24. The characteristics of the model are summarized in Table 4. Table 4. Specifications for 6 ft diameter rotor model Geometric Parameters Values Rotor diameter 6.0 ft Number of blades 4 Chord 5.36 in Solidity, σ 0.189 Airfoil section Gottingen 429 (mod.) Collective pitch 3o Blade twist none Cutout radius 6 in Flapping hinge offset 2 in Blade weight moment 2.18 ft-lb Blade flapping inertia 0.118 sl-ft2 Lock number, γ 4.2 Rotor polar inertia 0.63 slug-ft2 The theory was compared with available experimental data for the model rotor decelerating from an initial angular velocity of 76 rads/s at a constant tunnel speed of 32ft/s. Figure 11 shows the comparison of experiment a nd theory carried out to 9 seconds time. It can be seen that the agreement is generally good, especially considering some estimates that had to be made for the rotor characteristics. �� Ω
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Time, t (seconds) Fig. 11 Comparision of theory and experiment for a 6 ft diameter, 4 bladed, decelerating rotor, θ0 = 3 o, αs= 17.5 o, V= 32ft/s
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A similar comparison of theory and experiment was made for the 6 ft rotor accelerating from an angular velocity just above the hump speed. Near the hump speed, rotor behavior is critically dependent on airfoil section drag coefficient data, and care must be taken to use reasonable data for the Reynolds numbers expected in operation. The comparison in Fig. 12 for these conditions indicates that there is good agreement out to about 11 seconds of calculation. �� Ω
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Time, t (seconds) Fig. 12 Comparision of theory and experiment for a 6 ft diameter, 4 bladed, accelerating rotor, θ0 = 3 o, αs= 17.5o, V= 32ft/s
In light of the level of agreement shown in all the preceding figures, the theory presented can be seen to provide a good tool for predicting prototype rotor behavior. This will be considered next.
V. Prediction of Rotor Behavior in Zero-g Flight To completely simulate gyroplane behavior in zero-g flight, one would need to select a particular rotorcraft geometry and use coupled rotor-airframe equations, and input control and propeller thrust variations to si mulate various maneuvers and determine the resulting rotor behavior. In a deliberately flown zero-g trajectory, the flight path angle would first increase with high propeller thrust applied for a pull-up, followed by rotor cyclic pitch or shaft angle being reduced to a low or zero angle. During the climb, airspeed would decrease to a minimum at the top of the trajectory and then increase again during the descent. Propeller thrust would normally be reduced to idle during the pushover portion of the maneuver. This would be followed by a pull-up with application of propeller thrust and rearward cyclic to resume level flight again. During the zero-g portion of the flight, rotor rpm would steadily decrease, and assuming the recovery were executed soon enough and the rotor slowdown were not t oo drastic; rotor rpm would increase again. However, the rate of rotor slowdown can be so rapid that any deliberate maneuver of this type is dangerous. Another more drastic way to enter zero-g flight would be a pushover from level flight into a zero-g descending arc. In this case velocity would increase due to gravity effects, as opposed to an initial velocity decrease if the maneuver is initiated with a climb. During the simulations presented here, the forward flight velocity was kept constant. A “rotor alone” analytical solution keeping the forward velocity constant is a compromise between these two types of zero-g flight. Obviously it is not practical to conduct flight tests to explore zero-g behavior, except possibly to approach it very cautiously closer and closer, so an analytical sol ution was conducted using the equations of motion for the rotor alone with a pitching rotor shaft. A. Prototype Configuration Selected A representative configuration typical of a production gyroplane was selected for analysis. Table 5 gives the characteristics of the rotor system selected. If compared to Table, 1 it will be seen that the values are for an average of a few different actual gyroplanes, so t hey are not representative of any one design, but similar to a variety of designs.
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Table 5. Representative full-scale gyroplane rotor system Rotor Parameters Rotor diameter Number of blades Chord Solidity, σ Airfoil section Collective pitch Blade twist Cutout radius Flapping hinge offset Blade weight moment Blade flapping inertia Lock number, γ Rotor polar inertia
Values 30 ft 3 9 in 0.0478 NASA 0015 6o none 1 ft 0.3 ft 294 ft-lb 90 slug-ft2 5.75 300 slug-ft2
B. Simulated Maneuvers Conducted The figures below give the behavior of t his 30 ft diameter, 3 bladed rotor based on Eqs. 3 and 4 for two selected flight maneuvers. The first case considered is a rotor shaft pitched from a positive 4 degree shaft angle down to zero degrees and return. Fig. 13 summarizes the rotor behavior for a relatively short 2 second time period pitch down and recovery. Initial conditions were a rotor rpm of 380, advance ratio µ = 0.20, and thrust coefficient CT = 0.005.
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Time, t (secs.) Fig. 13a Rotor dynamics for rapid pitchdown maneuver, shaft angle of attack vs. time, µ o = 0.2, C To = 0.005
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Fig. 13b Rotor dynamics for rapid pitchdown maneuver, rotor rpm vs. time
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Fig. 13c Rotor dynamics for rapid pitchdown maneuver, blade flapping angle vs. time for ψ = 180°
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Fig. 13d Rotor dynamics for rapid pitchdown maneuver, blade flapping angle vs. time for ψ = 0°
The blade flapping angle excursion is not severe, and the rotor rpm decays from an initial value of 380 to a minimum of approximately 365 and then starts to recover again. This rpm variation is not serious, but in an actual maneuver with the velocity initially decreasing in the climb portion of the zero-g, the rpm decrease would be even greater. Next, a more severe maneuver was considered where the rotor shaft is pitched do wn over a longer time period through zero to a negative angle of attack and then returned back to the original state. The rotor system behavior is shown in Fig. 14.
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� Time, t ( secs.)
�
�
Fig. 14a Rotor dynamics for pitchdown through negative shaft angles of attack, shaft angle of attack vs. time, µ o = 0.2, C To = 0.005
14 American Institute of Aeronautics and Astronautics
��� ���
M P R r ��� o t o R ��� ��� �
�
� Time, t ( secs.)
�
�
Fig. 14b Rotor dynamics for pitchdown through negative shaft angles of attack, rotor rpm vs. time
, e l g n A g ) . n g i e p d p ( a l F β e d a l B
�� � ψ � ���˚ � �� �
�
� Time, t ( secs.)
�
�
Fig. 14c Rotor dynamics for pitchdown through negative shaft angles of attack, blade flapping angle vs. ti me for ψ = 180°
��
β
, e l g n A g ) . n g i e p d p ( a l F e d a l B
�
ψ � �˚
�
�� �
�
�
�
�
Time, t ( secs.) Fig. 14d Rotor dynamics for pitchdown through negative shaft angles of attack, blade flapping angle vs. ti me for ψ = 0°
In this case, the rotor rpm has decreased from 380 down to approximately 335, and shows little sign of recovery when the rotor shaft is pitched back to a positive angle. The rpm decay has brought the rotor rpm down near the hump speed in which case rpm recovery would be too slow. This rotor rpm decay is much more serious, and does not show signs of a recovery to the original rpm. VI. Conclusions Equations for the behavior of a pitching rotor in autorotation have been derived and verified both qualitatively and quantitatively using data from two small rotor models. The equations have been used to predict the 15 American Institute of Aeronautics and Astronautics
behavior of a prototype gyroplane rotor undergoing pitching maneuvers. It is shown that extended operation with an unloaded rotor can lead to serious problems where the rotor rpm may not increase again during an attempted recovery, and negative blade flapping may occur. Possible collisions between the rotor blades and a pusher propeller or vertical tail surface can occur, especially if propeller thrust line location or horizontal stabilizer design is improper. This is a characteristic of autorotating rotors, which should always be flown in flight conditions maintaining a positive g load on the rotor.
References 1
Leishman, J.G., “Development of the Autogyro: A Technical Perspective,” Journal of Aircraft, 41 (4), July-Aug. 2004.
2
Anon., “The Aerodynamics of Gyroplanes,” CAA Paper 2009/02, UK Civil Aviation Authority, West Sussex, England, August 2010. 3
Anon., “Airworthiness Review of Air Command Gyroplanes,” Air Accidents Investigation branch, Aldershot, England, U.K., Sept. 1991. 4
Gremminger, G., “Safety Report: Gyroplane Accident Causes per NTSB Report,” Popular Rotorcraft Association, Mentone, Indiana, Sept. 2002. 5
Anon., “Pilot Talk, Zero “g” Flight,” Popular Rotorcraft Flying, 3(4), 1965.
6
Cudney, A., “Watch That Zero “G”, ” Popular Rotorcraft Flying, 8(5), 1970.
7
Schad, J. L., “Readers Forum – Small Autogyro Performance,” Journal of the American Helicopter Society, 10 (3), July 1965, pp 39-43. 8
Schad, J. L., “Gyrocopter Modifications and Their Performance,” Popular Rotorcraft Flying, 4(2), 1966.
9
Niemi, E., “The Effect of Various Cabin Designs on the Performance of a Small, Unstreamlined Autogyro,” M.S. Thesis, M.E. Dept., Worcester Polytechnic Institute, Worcester, MA, January 1964. 10
Niemi, E., “Know Your Gliding Speed and Range ,” Popular Rotorcraft Flying, 2(3), 1964.
11
Houston, S.S., “Identification of Autogyro Longitudinal Stability and Control Characteristics,” Journal of Guidance, Control and Dynamics, Vol. 21, No. 3, May-June 1998, pp. 391-399. 12
Houston, S.S., “Validation of a Rotorcraft Mathematical Model for Autogyro Simulation,” Journal of Aircraft, Vol. 37, No. 3, May-June 2000, pp. 403-409. 13
Houston, S.S., and Thomson, D.G., “Calculation of Rotorcraft Inflow Coefficients Using Blade Flapping Measurements,” Journal of Aircraft, Vol. 46, No. 5, Sept-Oct 2009, pp. 1569-1576. 14
Thomson, D.G., Houston, S.S., and Spathopoulos, V.M., “Experiments in Autogyro Airworthiness for Improved Handling Qualities ,” Journal of the American Helicopter Society, Vol. 50, No. 4, Oct. 2005, pp. 295-301. 15
Murakami, Y., and Houston, S.S., “Dynamic Inflow Modeling for Autorotating Rotors,” Aeronautical Journal, Vol. 112, No. 1127, Jan. 2008, pp. 47-53. 16
Anon., “Rotorcraft Flying Handbook,” FAA-H-8083-21, U.S. Dept. of Transportation, FAA, Washington, D.C., 2000.
17
McCulloch J-2 Gyroplane Approved Rotorcraft Flight Manual, McCulloch Aircraft Corporation, May 1970.
18
Air and Space 18A Gyroplane, FAA Approved Gyroplane Flight Manual, Air and Space Corporation, May 1965.
19
Niemi, E., “A Method for Determining the Effects of Rapid Inflow Changes on the Dynamics of an Autorotating Rotor,” Ph.D. Dissertation, University of Massachusetts Amherst, Amherst, MA, April 1974.
16 American Institute of Aeronautics and Astronautics
20
Niemi, E., “A Mathematical Model for Predicting the Dynamics of an Autorotating Helicopter Rotor ,” Proceedings of the SIAM 1986 National Meeting, Boston, MA, July 21-25, 1986. 21
Gessow, A. and Crim, A., “A Method for Studying the Transient Blade-Flapping Behavior of Lifting Rotors at Extreme Operating Conditions,” NACA TN 3366, Jan. 1955. 22
Razak, K., “Blade Section Variation on Small Scale Rotors,” Journal of the Aeronautical Sciences, 11, 1943.
23
Niemi, E., and Cromack, D.,”Comparison of Experimental and Analytical Data for a Wind Milling Model Rotor” , Journal of the American Helicopter Society, 21(1), pp. 27-31, Jan. 1976. 24
Lock, C.N.H., and Townend, H.C.H., “Wind Tunnel Experiments on a Model Autogyro at Small Angles of Incidence,” R & M No. 1154, British A.R.C., March 1928.
17 American Institute of Aeronautics and Astronautics
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