36th European Forum, Paris, France, September 7-9, 2010 Paper Identification Number 089

A Qualitative Introduction to the Vortex-Ring-State, , and Optimal Autorotation

Skander Taamallah ∗† ∗ Avionics Systems Department, National Aerospace Laboratory (NLR) 1059 CM Amsterdam, The Netherlands ([email protected]). † Delft Center for Systems and Control (DCSC) Faculty of Mechanical, Maritime and Materials Engineering Delft University of Technology, 2628 CD Delft, The Netherlands.

Keywords: Vortex-Ring-State (VRS); autorotation; Height-Velocity diagram; optimal control; optimal autorotation

Abstract: The main objective of this pa- 1 Introduction per is to provide the reader with some qualita- tive insight into the areas of Vortex-Ring-State This paper summarizes the results of a brief (VRS), autorotation, and optimal autorota- literature survey, of relevant work in the open tion. First this paper summarizes the results literature, covering the areas of the VRS, of a brief VRS literature survey, where the em- autorotation, and optimal autorotation. Due phasis has been placed on a qualitative descrip- to time and space constraints, only published tion of the following items: conditions leading accounts relative to standard to VRS flight, the VRS region, avoiding the configurations will be covered, omitting thus VRS, the early symptoms, recovery from VRS, other types such as tilt-rotor, side-by-side, experimental investigations, and VRS model- tandem, and co-axial. Presenting a complete ing. The focus of the paper is subsequently survey of a field as diverse as helicopter VRS, moved towards the autorotation phenomenon, autorotation, and optimal trajectories in where a review of the following items is given: autorotation is a daunting task. Hence the the maneuver, the height-velocity zones, and review is from a common qualitative approach, factors affecting autorotation. Finally the pa- with emphasis on concepts rather than on per concludes by providing a literature survey details. relative to single-engine helicopter optimal au- torotation, and its associated problem formu- The paper is organized as follows: in lation as a nonlinear, constrained, optimal con- Section 2, a review of the four rotor operating trol problem. conditions in vertical flight is given. In Section 3, the VRS is presented, including a review of aspects affecting the VRS, the VRS region, and VRS modeling. In Section 4, a review of published accounts in the field of

1 autorotation, aspects affecting the maneuver, • The normal working state region 0 ≤ and the associated height-velocity diagram Vc/vh. It includes climb and hover. Here are provided. In Section 5, a literature survey the velocity throughout the main rotor relative to the optimal autorotation problem, flow field is always downwards, hence a and its solution through constrained optimal wake model with a definite slipstream3 is control, is presented. Finally, conclusions and valid for this rotor state, resulting in good future directions are presented in Section 6. estimates of rotor performance, in climb and hover, by theory [90]. As a final introductory note, many inter- • The VRS region Vtr/vh ≤ Vc/vh < 0, esting and important contributions or founda- 4 where Vtr refers to the transition veloc- tional works related to the VRS and autoro- ity between the VRS and the turbulent tation have not been surveyed in this paper. wake state regions. Over the years, several In this, and many other respects, we sincerely transition velocities or transition velocity ask for the kind understanding of readers and ranges have been reported, for example authors alike. in [90, 116]. There is indeed no clear-cut value for Vtr as can be seen from measure- 2 Vertical flight ments scatter reported in Fig. 3, where the figure shows the universal empirical Before addressing the areas of VRS and au- induced velocity curve. This curve can be torotation, we start by giving a quick review of constructed on the basis of estimates of the four rotor operating conditions in vertical the profile power coefficient. Hence the in- flight, see Fig. 1 for a schematic representation. duced velocity always shows some scatter, due to errors in the profile power calcu- 1 Fig. 2 shows the momentum theory solu- lation, and other aspects such as tip loss tions for a main rotor in vertical climb or de- and blade twist [90]. Further in the VRS scent. The lines Vc = 0, Vc + vi = 0, and region, a definite slipstream does not exist 2 Vc + 2vi = 0 divide the (Vc, vi) plane into four anymore, since the flow in the far wake in- regions. The area of the plane right of line side and outside the slipstream are in op- Vc = 0 defines the normal working state rotor. posite direction. At first for low descent The area of the plane between lines Vc = 0 rates −0.5 ≤ Vc/vh < 0, momentum the- and Vc + vi = 0 defines the VRS region. The ory is still valid [90]. As the descent rate area of the plane between lines Vc + vi = 0 and increases Vtr/vh ≤ Vc/vh < −0.5, the flow Vc + 2vi = 0 defines the turbulent wake state. becomes turbulent and has large recircula- Finally the area left of line Vc + 2vi = 0 de- tion, resulting in rotor vibrations and de- fines the windmill brake state [100]. We pro- graded control [90]. In this region momen- vide next a succinct review of those four re- tum theory is not valid anymore. gions, a much more detailed discussion can be found in [90]. • The turbulent wake state −2 ≤ Vc/vh < Vtr/vh. Here the flow pattern above the 1 Momentum theory refers to the conservation of rotor disk is very similar to the turbulent mass, momentum, and energy in the case of an inviscid, incompressible, steady, irrotational, and 1-D flow [90] 3The stream of air forced downwards by rotating 2 With Vc being the climb velocity, vi the main rotor blades 4 induced velocity, and vh the main rotor induced velocity In this paper we will assume that Vtr/vh ∈ in hover [−1.9, −1.6]

2 wake of a bluff body [90]. In this region, loss of control effectiveness [102, 101]. when compared to the VRS, flow recircu- lation through the rotor has diminished 3.1 VRS: a hazardous flight condi- and rotor vibrations have also decreased. tion But the rotor still experiences some rough- ness due to the (high) turbulence [90]. It For a helicopter main rotor, VRS may occur is also in this region that equilibrium au- for example in a descending flight, while for a torotation occurs. Note also that here too helicopter , VRS may occur during momentum theory is invalid. a sidewards flight, or while in hover with a crosswind. For the case of a main rotor VRS • The windmill brake state Vc/vh < −2. In condition, the symptoms are generally exces- this region the flow is again smooth with a sive vibrations, large unsteady blade loads, definite upwards slipstream, and momen- thrust/torque fluctuations, excessive loss of tum theory is applicable, providing good altitude, and loss of control effectiveness [126]. rotor performance estimates [90]. Hence flight in the VRS is a dangerous flight condition, especially if entered at low altitude. 3 The Vortex-Ring-State For the case of a tail rotor VRS, it is the vehicle yaw control (i.e. heading) that may A horizontal rotor creates a downward flow become difficult or impaired. induced by the thrust generation. If the ro- tor moves along the direction of its induced For the 1982 - 1997 time frame, data from 5 flow, i.e. down, the downward induced flow the U.S. NTSB , U.S. Navy & Army, and the will compete with the upward flow due to the U.K. Air Accidents Investigation Branch show descent motion. As a result, the smooth slip- that 32 helicopter accidents were caused by stream around the rotor disk is gradually de- flight into the VRS, most of them at altitudes stroyed. In particular, when the descent rate less than 200 feet and at low airspeeds [141]. approaches the rotor induced velocity, the ro- In April 2000, a Marine Corps V-22 Osprey tor enters its own wake, resulting in blade tilt-rotor crashed in Arizona, resulting in the tip vortices recirculation. These vortices will tragic loss of all 19 Marines on board. It was then tend to pile up at the disk plane to cre- later determined that a contributing cause of ate a so-called doughnut-shaped vortex ring that accident was flight into the VRS [49, 43]. [102, 101, 43]. Moreover, the onset and devel- opment of this so-called can It is nowadays well known that a signifi- be viewed as a spatial and temporal wake insta- cant number of VRS accidents were the result bility. By instability one means vortex rings as of accepting slight tailwinds or downwind ap- a result of wake recirculation in the plane of the proaches, hence reducing the actual horizontal 6 rotor [102, 101]. Periodically however the char- air velocity . acter of this recirculation changes, as a partial 5National Transportation Safety Board vortex collapse causes flow asymmetry at the 6This is often a point of concern for helicopter pilots, rotor disk. This phenomenon results in large since the airspeed indication on most civil is fluctuations in rotor and torque [33]. More somewhat ineffective below 35 to 40 knots [141]. This specifically these include high amplitude, low problem however can be solved by algorithmic methods, which use an internal model, available control inputs, frequency blade flapping, low frequency verti- and sensors measurements to infer airspeed and sideslip cal bounce of the helicopter, and substantial angle see [55, 60, 108, 71]

3 Figure 1: Helicopter axial flight (from [127])

Figure 2: Axial flight: induced velocity variation as a function of vertical velocity (from [100])

4 Figure 3: Axial flight: induced velocity scatter in descending flight through the VRS (from [101])

3.2 conditions leading to the For a helicopter tail rotor, VRS may occur VRS in the following conditions

For a helicopter main rotor, VRS may occur in • In sidewards flight the following conditions • While hovering in a crosswind • In an axial descent with the rate of descent being about equal to the hover induced • During a hover, turn over a spot [127] velocity 3.3 The VRS region • At low speeds and steep descent angles Knowledge of the location of the VRS onset • When descending downwind into a land- boundary, see Fig. 5, is important for safety ing area [116] procedures and operational reasons. One such example is when at low airspeeds it • In the final stages of a quick stop maneu- may be necessary for a helicopter to briefly ver (such maneuvers are typically carried transition through the VRS, in order to reach out close to the ground [116]) equilibrium autorotation [36]. • When starting a power recovery after en- gine power off [61] It is also well known that the VRS onset boundary is significantly influenced by the • When settling into the downwash of an- specific criterion used to define it [47]. Indeed other a boundary based on torque fluctuations

5 may be slightly different from the classic Fig. 4 shows the influence of vehicle mass in- boundaries predicted using thrust fluctuations crease (in other words increase) or blade flapping. A good review of various on the Dauphin helicopter VRS boundary re- researched criteria, such as thrust or torque gion, where the blue line corresponds to an in- fluctuations can be found in [43, 91]. crease in vehicle mass. Note also that in this figure the velocities are not normalized by the An experimental determination of the VRS induced velocity in hover. As the vehicle mass boundary may be done by sequentially map- is increased we see that the size of the regime, ping out combinations of flight path angle, de- where VRS is encountered, shifts downwards scent velocity, and forward velocity, where the and grows dimensionally with the hover in- 8 rotor experiences high fluctuations in thrust, duced velocity vi . Conversely this also means torque, and blade flapping [36]. that even though lightly loaded vehicles, such as helicopter UAVs9, will encounter the VRS 3.3.1 Factors affecting the VRS region for low vertical descent rates, a low forward speed should be sufficient for these UAVs to It is known that the effect of a maneuver avoid the VRS. distorts the rotor wake, and hence may affect wake stability, and may potentially affect the VRS boundary. Acceleration or angular rate are indeed known to affect the onset and de- 3.4 Avoiding the VRS velopment of the VRS [109, 14]. For example for pull-ups or for other types of maneuvers As can be seen from Fig. 5, VRS is unlikely that increase the rotor disk angle of attack, to occur if the speed along the flightpath is VRS onset conditions could be attained at reasonably high. For example it was reported a lower rate of descent and/or at higher in [78] that a speed of 2 - 2.5 times the hover forward speed, than predicted by the VRS induced velocity safely avoids the VRS for boundary [102, 101]. Additional aspects that any glide slope. The ONERA tests found that may also influence the VRS are rotor/fuselage VRS effects were not observed beyond 1 time aerodynamic interference [37], rotor disk angle the hover induced velocity [88]. of attack [101], blade [109], blade root cut out location, blade planform taper [109], and Further VRS is unlikely to occur if the glide 7 blade spanwise loading distribution . On the slope is shallow. Limiting glide slopes to 20 - other hand however, it appeared that the VRS 30◦ avoids it at almost any forward speed [78]. region was insensitive to tail rotor interference This is confirmed by the 30◦ limit set by the [37]. U.S. Army [91]. Hence one should avoid ver- tical or steep descents whenever possible. If Before concluding this section on the VRS vertical descent is required, it should be at- region, we want to add one last comment on tempted from the minimum allowable height the issue of disk loading DL. This aspect was above the ground, and at the minimum possi- addressed through a series of flight tests, per- ble descent rate. formed by ONERA almost a decade ago [87].

7 8 Which is particularly affected by blade twist for low Since vi = pDL/2ρ disk loading [36], with the disk loading DL being equal 9Which typically tend to have a lower disk loading to thrust divided by rotor disk area than manned helicopters

6 Figure 4: Helicopter mass influence on the Dauphin VRS domain (from [87])

Figure 5: Helicopter VRS Boundaries (from [91])

7 3.5 VRS: the symptoms For torque fluctuations, which may lead to directional (yaw) control problems, the follow- For a helicopter main rotor, VRS may occur in ing results were reported a descending flight, and historically the VRS has also been associated with the so-called • The increase in torque indicates the be- power settling, where more power is required ginning of the VRS, Vc/vh ≃ −0.4 [148] to descend than to hover [127]. Indeed the power extracted from the airstream is less • The period of the torque fluctuation is than the induced power10 loss. In other words about 3.7 sec, for a model rotor tested in a substantial increase in the required power for [148] equilibrium flight becomes necessary, basically • to overcome the additional aerodynamic losses The torque fluctuation of a rotor with as the rotor descends into its own wake [103]. lower disk loading is larger than that of a rotor with higher disk loading [148]

Aside from the power settling phenomenon, • Compared with changes in rotor thrust, early signs of VRS flight may be given by rotor torque variations are less significant thrust and/or torque fluctuations. [43]

For thrust oscillations the following results 3.6 Recovery from the VRS were reported First it should be noted that any recovery • They are more severe than torque varia- from the VRS is likely to result in a significant tions [19] loss of altitude. • They are more pronounced at oblique de- We provide now a few guidelines for a VRS scent, with he angle of attack α such that recovery (α = 60◦ − 70◦) rather than at vertical descent (α = 90◦) [19] • Exiting the VRS is best handled by a • The loss in thrust indicates the most tur- quick increase in forward or sidewards air- bulent region of the VRS −0.8 ≤ Vc/vh < speed through cyclic control, which effect −0.6 [148] is to sweep the recirculating wake away from the rotor disk [88, 102], and then ap- • The period of the thrust fluctuations lies ply collective pitch to cancel the rate of in the range 0.3 - 0.6 sec, for a model rotor descent [91] tested in [148] • The U.S. Navy NATOPS11 states that the • Thrust oscillations appear to be indepen- only solution for fully developed VRS is to dent of the disk loading [148] enter autorotation to break the vortex ring and, when cyclic authority is regained, in- • The range of variations of thrust oscilla- crease forward airspeed [91] tions lies in the order of 12 - 15 to 20 % of mean thrust, with the lower values • Maneuvers suppress the effects of VRS. A reported in [87, 36], and the upper limit rotor can maneuver but the vortex rings given in [101] 11Naval Air Training and Operating Procedures 10Induced power is the power required to generate lift Standardization

8 cannot, hence these will not stay in the survey of flight and wind tunnel test data in rotor disk [31] the VRS, and [135] for recent flow visualiza- tions. 3.7 Aspects of rotor/blade design Back in 1949, one of the first VRS wind We provide here a few guidelines related to ro- tunnel test and flow visualization was per- tor and blade design considerations formed in The Netherlands (Amsterdam), at • There are no substantial differences in what is now the NLR, by Dutch helicopter VRS inflow curves due to variations in ro- pioneer Jan Meyer Drees [54, 53]. tor RPM and rotor radius [43] In the 1950s and 1960s, several other • The effect of blade taper on VRS is weaker researchers investigated the VRS. For instance than the effect of blade twist [43] the authors in [19] succeeded in measuring the thrust and torque oscillations of a rotor • For moderate blade twist, blade stall has in the VRS. Fast forwarding to the 1990s, the no effect on the descent rate for VRS on- authors in [148] performed a series of wind set. It is still possible however that stall tunnel tests on a model helicopter, and stated could influence the subsequent develop- that the turbulence associated with the VRS ment of the VRS [13] seemed to be the highest when the descent • For moderate blade twist, the influence of angle was between 60 - 75◦, hence higher than twist on the behavior of the rotor is rela- for vertical descent. A few years later, the tively minor [13] authors in [33] found that within the VRS, recirculation occurred across most of the disk • For high blade twist, the influence of twist plane, while a conical region of reverse flow on the behavior of the rotor is more pro- existed at the disk center. They reported nounced. Such rotors with high blade that when the VRS was fully developed, a twist seem to be more susceptible to VRS symmetric, low frequency, stable limit cycle onset [102, 101]. But the appearance of behavior was evident in the inflow dynamics, blade stall on the inboard parts of a ro- blade dynamics and rigid body dynamics. tor, with highly twisted blades, was also shown to reduce the violence of the VRS In the past decade, the authors in [109] [36] noted that there had been a disturbing • Thrust settling is associated with a con- tendency for rotor behavior to vary from siderable fall in blade loading but only at one VRS test to another. Indeed vehicles the outboard sections of the blade. The with similar configurations had behaved inboard sections of the blade play only differently during VRS flight tests. One of a small role in the thrust settling phe- the results was that helicopter acceleration nomenon [13] and angular rate may have a significant in- fluence on the location of the VRS boundary, 3.8 VRS: experimental investiga- and that blade twist, blade root cut out, blade taper, and blade stall could all play a tions role in the development of the flow in the VRS. We provide here a very brief review of pub- lished accounts, see [91] for a comprehensive As a final note, ONERA performed a se-

9 ries of flight tests [88, 138] on an instrumented authors modified the mass flow parame- Dauphin 6075. One of the striking results was ters for both dynamic inflow and dynamic that contrary to the common assumption, col- wake models to allow for a more realistic lective increase did not amplify VRS effects. uniform inflow component in the VRS re- The helicopter in VRS was generally insen- gion sitive to collective inputs. The authors also found that two VRS flights starting from close • Russian results were translated into En- conditions could imply very different helicopter glish in the early 1970s by Shaydakov, and reactions. It was stipulated that the nature expressions for rotor induced velocity in of the VRS turbulent flow could explain this the VRS can be found in [132] chaotic behavior. • The Young model [149]

3.9 VRS: induced velocity models • The Wang/Perry model [143, 119]. Here a relation between the induced velocity of In the last thirty years, several VRS induced the rotor and the descent velocity of the velocity models for flight dynamics simulations helicopter was obtained by classical vortex have been formulated. We provide here a brief theory, where basically the mean wake is shortlist modeled as a truncated vortex tube. The model however was limited to uniform in- • The Georgia Tech model by Chen and flow in vertical descent Prasad [46, 126, 44, 45, 43]. The authors developed an inflow model, based on [146], Aside from induced velocity models, we refer to account for the additional induced in- also to the application of momentum theory to flow at the rotor due to rotor-wake inter- the prediction of VRS boundaries in [146, 120], action in the VRS and for minimum power requirements of an ideal rotor in descent in [78]. For an applica- • The Johnson models [89, 91] tion of bifurcation theory to the problem of ro- tor aerodynamic instability in descending flight • The ONERA model [87, 88]. Here an an- see [21]. alytical criterion, based on [146], giving VRS limits and intensity was formulated. Further induced velocity and its fluctua- 3.10 VRS: wake models tions were also modeled through an addi- Finally we conclude this VRS section by tional pseudo-harmonic function, in which providing a brief review of published accounts the computed spectrum was matched with relative to wake models. For a recent survey the experimental one see [81]. • The Peters/He model [77, 121]. At first 12 The first results are related to the Vorticity in [77] the Peters/He finite state wake 13 Model of [34, 35] which was used model [122, 123] was extended by deriving to analyze a VRS rotor flow in [109, 13]. Some an empirical formula for the uniform in- duced flow in the VRS. Later in [121], the 13Basically a direct computational solution of the in- compressible Navier-Stokes equations, expressed in vor- 12This approach is currently implemented in ticity velocity form, which is used to simulate the evo- FLIGHTLAB lution of the wake of a [34]

10 of the results have already been reported in dead engine during an autorotative flight [127]. this paper, in Sections 3.3.1 and 3.7. As This flight condition is somewhat comparable a last comment, it was also reported that to gliding for a fixed- aircraft, without an a better description for the wake dynamics operating power plant. encountered in VRS might be obtained by analogy with the low-Reynolds number vortex 4.1 Engine failure shedding from bluff bodies [109]. For the 1990 - 1996 time frame, the U.S. NTSB For free vortex wake models14 capable of assembled data over 1165 U.S. civilian heli- capturing the distortion of the wake geome- copter accidents, which have been analyzed in try during maneuvers and VRS descent flight, [84]. For the purpose of this accidents analysis, see for example the research in [102, 101, 128], helicopters had been split into four cost cate- where some of the main conclusions have al- gories: low cost 0 - 600K$, medium cost 600K$ ready been reported in the previous sections of - 1.5M$, high cost 1.5M$ - 4M$, and very high this paper. Perhaps as a last additional com- cost >4M$. The data show that the loss of ment we can refer to the hysteresis effect men- engine power was the most frequent (> 25%) 15 tioned in [101], which states that reversing the first event in helicopter accidents, for all but combination of VRS airspeed and rate of de- the most expensive helicopter category. For scent back to the initial flight condition may the most expensive helicopters, airframe and not lead to the same time-history of the air- system failure/malfunction was the most com- loads. mon first event. Indeed in the very high cost category there is a much higher proportion of twin-engine vehicles, hence the lower rate of 4 Autorotation accidents due to engine failure. For the other three helicopter categories, and assuming that Autorotation, in the case of a helicopter, is a the data would still be representative for to- flight condition in which no powerplant torque day’s systems, one needs thus to consider en- is applied to the main and tail rotors. During gine failure as a probable and potentially haz- an autorotation, the main rotor is not driven ardous event. by a running engine, but by air flowing through the rotor disk bottom-up, while the helicopter is descending [7]. For comparison, in autoro- 4.2 Autorotation: a risky maneuver tation about as much buoyancy is provided as Now in case of an engine failure, i.e. an emer- a round parachute of the same rotor diameter gency situation, autorotation as mentioned [6]. An autorotative flight is thus entered when earlier is the approved response for such an the engine fails on a single-engine helicopter, or emergency. when a tail rotor failure requires the pilot to shut down the engine. The power required to Unfortunately autorotation is a risky ma- keep the rotor spinning is obtained from the neuver. Autorotation on a manned helicopter vehicle’s potential and . All heli- requires a good deal of training, if disaster is copters are thus equipped with an overrunning to be avoided. Quick reaction and critically clutch between the transmission and the en- timed control inputs are indeed required for gine, so that the rotor does not have to drive a 15The first event is the first anomalous occurrence 14For an introduction see [100] that the NTSB codes as part of the accident sequence

11 a safe autorotative landing [16]. A delayed or stance displaying control guidance cues on a improperly performed autorotation can turn cockpit display [17]. an incident into an accident or fatality [76]. Autorotation is thus sometimes regarded as a 4.3 Detecting engine failure take what comes and pray maneuver [20, 18]. For the case of an autorotative flight following For instance a 1980 statistics, see [124], main rotor engine failure, first the engine out showed that at least 27% of all emergency event needs to be recognized. autorotations involving the AH-1, UH-1, OH-58, and OH-6 helicopters resulted in some A sudden reduction in engine torque if degree of vehicle damage or personnel injury. accompanied by either reduced collective Also mapping out the height-velocity diagram, pitch or accelerating rotor speed, would not see Fig. 6 and Section 4.5, through a series indicate an engine failure. However a sudden of flight tests had historically been an area of reduction in torque, if accompanied by fixed high risk [27]. An additional 1980 paper stated collective stick and decelerating rotor speed, that there had been very few helicopters which would be indicative of an engine failure [106]. had completed qualification testing, without Further a jerk is generally also felt on the yaw an accident of some kind during height- channel, since the tail rotor overcompensates velocity or autorotational landing maneuvers the reduced main rotor torque. This said, the [27]. A further 1998 study [76] showed that case where engine power is not lost suddenly helicopter autorotation accounted for 7% of but gradually may be more subtle or elusive 1852 helicopter accidents. Such a finding was to detect. found to be particularly disconcerting, since the autorotation maneuver is the approved Once an engine failure has been detected, response to an emergency, rather than an the pilot’s (or computer) task during autorota- emergency itself [130]. tive flight becomes mainly one of energy man- agement [98]. In fact and due to safety concerns, both the U.S. Army and U.S. Air Force stopped 4.4 Autorotation: the maneuver performing autorotation training after studies showed that there were more injuries and From a performance standpoint, autorotation aircraft damage from practicing autorotation, may be considered as a four phase maneuver than from autorotations required by actual [7, 6, 4, 5, 2]. We describe hereunder general engine failures [130]. Idem on the civilian side, maneuver guidelines for the case of a single where in-flight autorotation training is a rare main rotor, manned helicopter. event [18]. Moreover, autorotation training in a simulator occurs infrequently, as even The entry. An autorotation maneuver the best simulators poorly reproduce the cues depends on the flight condition before engine required for an actual autorotation [18]. failure [98].

Hence the need for either having a fully au- First the main rotor torque loss will require tomated autorotation system, or for having a a tail rotor control change to reduce tail rotor semi-automatic system capable of assisting a thrust. pilot in performing the maneuver, by for in-

12 Then at low altitude and airspeed, below input should be that which provides the best the so-called knee of the height-velocity curve compromise between achieving minimum rotor (Vcr, hcr) see Fig. 6, the recommendation is speed decay, acceptable rotor flapping excur- to use increased collective to reduce the sink sions, and acceptable flight characteristics rate as the helicopter approaches 10 to 15 [106]. feet above the ground [98]. At about 10 feet above the ground the fuselage is leveled and Now for the case of even higher altitude collective is increased as the helicopter settles. entries, a 25◦ nose-down pitch attitude could be a guideline, producing a rapid airspeed Now for the case of higher airspeeds, still increase until minimum rate of descent is below the airspeed at the knee, the collec- reached [65]. According to [65], shallower tive may be reduced somewhat to regain or pitch attitudes delayed reaching the target maintain rotor RPM, while the helicopter is airspeed and increased the altitude lost in decelerated using a cyclic flare [98]. In both the entry maneuver, while steeper nose down these previous conditions, the rotor does not attitudes to quickly gain airspeed reduced the enter into a true condition of autorotation. initial altitude loss but produced also higher rate of descents16 which eventually resulted in We consider now the case of higher altitude excessive altitude loss. entries, i.e. above the altitude at the knee of the curve hcr. Here the collective is generally Steady autorotation. This refers to reduced, as to prevent blade stall and rapid the stabilized autorotation phase in which decay in rotor RPM, and the cyclic is moved the helicopter descends at a constant rate, forward to pitch the nose down in order to which may be chosen for minimum rate of gain some forward airspeed. Attaining higher descent17 or maximum glide distance. In airspeed avoids entering the VRS, allows for general the rotor RPM and rate of descent are buildup of rotor RPM and allows for minimum controlled by collective setting, while airspeed sink rate until the pilot initiates the flare is controlled by cyclic settings. maneuver [98]. It should also be noted that some flight conditions are considered more Regarding the main rotor, some stations on critical than others, especially when collective the rotor will absorb power from the air, while pitch and engine torque are high at the instant others will consume power, such that the net of power loss. For example this may be the power at the rotor shaft is zero, or sufficiently case when loss of engine power occurs while negative to make up for losses in the tail rotor, the helicopter is in either one of these flying transmissions, and accessories [127, 100]. In conditions: heavy weight, high altitude, hover, autorotation the helicopter needs a little less or vertical climb. In these situations collective power than in powered flight, since the tail should be lowered quickly to avoid a too high rotor does not require as much power. RPM speed decay [98].

This said, a too rapid lowering of collective 16Note that high rate of descents and high airspeed pitch is also not advisable. Indeed this complicate the flare maneuver since more energy needs to be dissipated could potentially lead to extreme rotor blade 17 Minimum rate of descent in power-off autorotation flapping excursions and/or extreme rotor in forward flight occurs at the minimum power speed force increments [106]. Therefore the control [90], the so-called bucket speed

13 Concerning the rate of descent, an increase It should be noted that there is an optimal in solidity18 would result in a decrease of the altitude above ground at which the flare rate of descent [51, 63], while an increase in should be initiated, and this altitude becomes bank angle or sideslip angle would result in an increasingly critical as vehicle weight is in- increase of the rate of descent [61]. creased20. This optimal altitude depends on many factors, including descent rate, airspeed, Additionally, main rotor collective plays a headwind component, and the bandwidth of crucial role in steady autorotation. On the the control system. one hand, as the air starts flowing up through the rotor system, the main rotor RPM will As a final note on flare, one should be aware start to increase, and hence may get too high. that the helicopter flare capability is even In this case, an increase in collective pitch is more important for power-off landings than required to lower main rotor RPM. On the the steady-state descent rate [90]. The flare other hand, main rotor collective pitch angle capability depends among others on a high should be kept low enough to prevent rotor rotor kinetic energy [134], which requires a stall. Indeed the angle of attack over the high rotor speed and/or a large blade moment inboard stations of the rotor blades is gen- of inertia. Additionally the flare capability is erally high, hence corresponding to a stalled also improved as disk loading decreases [134], region. Therefore collective pitch should be and further depends also on blade stall limits. kept low enough to prevent stall propagating In general blade stall margin should be high21, out from the blade root region, which will both for good flare characteristics, and for a tend to quickly decrease RPM, because of minimal loss of rotor speed before lowering the high profile associated with stall [100]. collective just after power failure [90, 142].

Flare for landing. The approach to the Touchdown. Here for obvious reasons, landing area should preferably be done into maximum rate of decent and airspeeds should the wind19. The purpose of the flare is to not be exceeded. Helicopter horizontal decel- reduce the sink rate, reduce forward airspeed, eration is further achieved through the maintain or increase rotor RPM, and level force between the ground and the skids/wheels. the attitude for a proper landing, i.e. tail rotor clearance. This is generally done in the 4.5 The Height-Velocity (H-V) dia- following way [63]: by first moving cyclic to gram the rear as to reduce the sink rate and reduce forward airspeed. The next step is to apply The capability of a helicopter to perform a safe cyclic forward in order to level the attitude, autorotative landing after a power failure is while increasing collective. The increase in limited by the structural and aerodynamic de- collective is generally done to prevent rotor sign of the helicopter, for certain combinations overspeed, and reduce the sink rate even of altitude above ground and airspeed [117]. further. In fact power failure within the dangerous or

20Note that an increase in weight may also result in 18Relative blade area rotor overspeed 19Note that wind shear and direction changes near 21Even though a transient flare maneuver will result the ground may suddenly reduce an apparent safe con- in a delayed blade stall and lift overshoot, or so-called dition to an unsafe one [61] dynamic stall

14 Figure 6: Typical Height-Velocity diagram (from [117]) unsafe regions defined by these combinations helicopter was ram-jet powered, and these of geometric height and airspeed may result were positioned at the blade tips. This in high risk of severe damage to the aircraft resulted in very high main rotor rotational and/or injury to its occupants. These limiting inertia. Later in the U.S.A. the concept of the combinations of airspeed and height are often so-called High Energy Rotor (HER) [147, 52] expressed as the height-velocity diagram22, was investigated, using blades with high see Fig. 6. rotational inertia. The goal of the HER was to eliminate the unsafe regions, but also to allow Knowledge of these dangerous regions is im- for less demanding autorotation maneuvers, portant for safety procedures and operational and finally to use the rotor kinetic energy reasons. Ideally one would like to eliminate as a source of transient power for better these unsafe regions altogether, or at least maneuverability. reduce their size. For example, eliminating height-velocity restrictions had already been Now operations in these unsafe regions demonstrated with the Kolibrie helicopter, are not uncommon, and may occur during built by the Nederlandse Helikopter Industrie specific missions, such as cargo sling, hoist23 (NHI) in the late 1950s. It was designed operations, or aerial photography [23]. Con- by Dutch helicopter engineers and pioneers sequently, pilots operating in these unsafe Jan M. Drees and Gerard F. Verhage. The 23The mechanism by which external loads may be 22Also called the deadmans zone raised or lowered vertically

15 regions are exposed to a higher level of risk, blades with large moment of inertia. because the potential to recover from an emergency, such as power and drive train For autorotative flight tests and perfor- failure, is significantly reduced. mance investigations in terms of rate of descent, and lift to drag ratio see [68, 139], Height-velocity investigations can be traced for the effect of collective pitch see [118], for back to the late 1950s and early 1960s, see the effect of weight see [117, 144, 65, 3], for [93, 85, 73]. In [117] flight-test data was used to the effect of Reynolds number see [110], for derive semi-empirical functions of a generalized the effect of air density see [117, 127], for the non dimensional height-velocity diagram, in- effect of flight path angle see [67], and for a dependent of density altitude and gross weight review of autorotation indices see [124]. variations. In the late 1970s it was pointed out in [23] that high rotor inertia, low disk loading, We elaborate here a little further on the and a high maximum thrust coefficient could effect of weight. It is known that an increase reduce the size of these unsafe zones. Finally in vehicle weight does not appreciably affect more recent height-velocity flight tests can be touchdown rate of descent and ground run found in [137] for the Bell 430, and in [58] for distance [144, 3]. However at heavy weight, three Bell 407 main rotor configurations. frequent collective control adjustments are required to prevent overspeeding of the main 4.6 Factors affecting autorotation rotor during the flare, hence the timing of the collective application becomes more critical at We provide here a brief review of published heavy weight. accounts related to autorotative experimental investigations and analytical modeling. For Regarding aeromechanical stability during additional topics such as rotor autorotation, it is known that dynamic inflow dynamics at high advance ratio see [129], significantly improves body damping corre- and for a detailed review of passive and lation with experimental results, in roll and active autorotational assist concepts, such as pitch mode [66]. Further there is an intimate auxiliary energy devices, tip jets, flywheel, relationship between main rotor RPM and multiple engines, compressed gas, hydraulic the low frequency rigid-body modes, such as turbine, batteries, electric motor, magnetic pitching-moment [79]. Also the roll attitude rotor head, extra tip weights, rotor overspeed, is reversed in autorotation, the absence of parachute, rockets, improved , the tail rotor force means that the main and air bag, see [145, 133, 32]. rotor in-plane sideforce24 can now dominate, resulting in an opposite roll attitude [80]. Autorotation investigations can be traced There is also a reduced speed stability in back to the 1920s in [70, 104]. Later in autorotation [80]. Finally a high autorotative the 1940s it was found in [112, 111] that rate of descent in a fairly level attitude gives for steady autorotative vertical descent, the a large positive tail plane angle of attack, approximation of a constant induced velocity producing a considerable nose down moment, lost its significance once the blades stalled, at hence requiring a more aft cyclic position [80]. higher pitch angle. It was already stated in these studies that blade stall could be avoided 24This sideforce is due to the nonuniform inflow along by reducing blade pitch rapidly, and by using the rotor disk

16 against catastrophic engine failure. By elimi- Before finishing our discussion on autoro- nating the need for multi-engine helicopters, tation, we address one last aspect related to the availability of such a system could obvi- blade design. It was already found sixty rears ously translate into substantial cost savings, ago that twist had a significant effect on inflow especially since helicopter purchase price is during descent [42]. Recently in [48] the down- even more sensitive to installed power than to wash and upwash regions along blade span empty weight [75]. were analyzed and it was shown that, for the case of vertical autorotation, a large positive We move now our discussion towards the blade linear twist leads to the highest autoro- field of optimal control. tation efficiency, i.e. rotor thrust being maxi- mum for a given vertical flight velocity. 5.2 Optimal control First a helicopter can be seen as a dynamical 5 Optimal autorotation system, which is at any given time defined Finally the purpose of our paper is to provide by its state. The system accepts inputs, a literature review relative to the optimal, and over which it has no direct command but to possibly automatic, autorotation problem, and transform them into outputs. When one or its solution through optimal control. The re- more of the systems output variables need to viewed research covers the case where an au- follow some desired value over time, i.e. a torotative landing of a single-engine helicopter reference signal, a controller may manipulate is formulated as a nonlinear, constrained opti- the systems inputs to obtain the desired effect mal control problem. on the output [64]. A further extension of this concept is provided by optimal control, in which the controller determines the input 5.1 Automatic autorotation signals in order to minimize some performance It is first relevant to point out that currently criterion, while satisfying the system physical in service manned helicopters do not autoro- constraints [125, 94, 38]. tate automatically. This said, the concept of having an avionics system performing an As with most nonlinear control problems, automatic autorotation is not new. In 1970 the resulting formulation does not have a such a system was already described for high closed-form solution, hence not solvable an- powered, high speed helicopters in [106]. alytically but through numerical algorithms Its role was to detect engine failure and to [74, 57, 82, 24, 83]. Numerical algorithms for automatically lower collective stick in a timely nonlinear optimal control can be separated manner, before rotor stall was encountered. into two main categories: indirect and direct The concept however did not go as far as to methods [131]. describe automatic landing of a helicopter after power failure. In the early years of optimal control (1950s- 1980s) the favored approach for solving general It is also interesting to note that an auto- optimal control problems was that of indirect matic autorotation system could potentially methods. In an indirect method, the calculus represent an alternative to multiple engine of variations [125] is employed to obtain helicopter configurations [106], as a safeguard the first-order optimality conditions. These

17 conditions result in an infinite dimensional 5.3 Optimal autorotation through non-linear two-point or multi-point boundary indirect methods value problem. To solve this problem, a One of the first accounts of optimal autoro- suitable numerical method is used to render tative flight dates back to the early 1970s it of finite dimension. Examples of numerical [95]. The helicopter model was a 2-D25 methods include shooting methods, finite quasi-steady point mass approximation, which element discretization, and gradient methods was subsequently linearized about a trimmed such as the Sequential Gradient Restoration flight condition. Further unsteady aerody- Algorithm (SGRA). Indirect methods are namics effects, such as blade dynamics, were known to show a fast numerical convergence in neglected. Also an instantaneous response in the neighborhood of the optimal solution, and vehicle pitch was assumed, and rotor RPM to deliver highly accurate solutions [72]. How- was allowed to vary. Additionally, and to ever they require the derivation of the optimal allow for simplicity, thrust inclination and control equations, a potentially complicated its magnitude were taken as control inputs, task for complex systems. An additional instead of the pilot controls. The constraints disadvantage resides in the necessity and included bounds on thrust tilt angle, angle of difficulty to provide suitable starting guesses, attack, rotor RPM, and rate of descent. for all variables including the adjoint variables. The first application of nonlinear optimal On the other hand, direct methods have control to the problem of optimal autorotative risen to prominence in numerical optimal flight path was presented in [89]. The heli- control since the late 1980s [1]. In a direct copter model was a 2-D nonlinear model, see method, discretization is followed by opti- [69]. Here the 1-D inflow model was based on mization. The discretization can be done in a momentum theory, with a time lag, including number of ways, such as collocation, control a correction for ground effect, and an empirical discretization, shooting, direct transcription, model for the induced flow in the VRS26. The and pseudospectral. The cost function, cost function of the optimal control problem constraints and boundary conditions, are all was a weighted sum of the squared horizontal expressed in terms of the discrete values of and vertical velocities at touchdown. To allow the states and controls. This in turn defines for simplicity, the force coefficients CX and a finite-dimensional Non-Linear-Programming CT were taken as control inputs, instead of the (NLP) problem [22]. The obtained NLP pilot controls. A steepest descent algorithm problem is efficiently solved by Interior Point was implemented to solve for a two-point (IP) methods [92], or by Sequential-Quadratic- boundary problem. The method showed that Programming (SQP) [113]. An additional the optimal control solution for descent from feature of direct methods is that they enjoy hover, after power loss, was a purely vertical large convergence radius, allowing for a con- flight27. verged optimal solution from a large range of different initial guesses [72]. 25 Hence in the vertical plane 26It was pointed out in [142] that the basis for this We provide next a literature survey relative inflow model was experimental data from helicopter ro- tors with blades having low twist to optimal autorotation through nonlinear op- 27However in practice some forward speed is highly timal control. advisable as to avoid the VRS

18 A similar model and cost objective were problem was extended here with the inclusion used in [98, 97], with this time the additional of bounds on control input rates, and the cost inclusion of inequality constraints on the functional included also an integral part, ba- control inputs to represent the limitation sically a running cost over time, to penalize of the rotor thrust coefficient, and a path deviations from nominal values on main rotor inequality constraint on vehicle sink-rate RPM, and helicopter forward and vertical ve- during descent. The optimal problem was locities. solved with the SGRA algorithm. In [96] the model was modified to include bounds 5.4 Optimal autorotation through on collective pitch, and rotor angular speed, direct methods which are more closely related to physical limits. It was also shown that a substantial re- The first application of a direct method to duction in the height-velocity restriction zone solve a nonlinear autorotative optimal control could be made using nonlinear optimal control. problem was presented in [39], for a 2-D non- linear model of a aircraft. The direct Further attempts to find and minimize collocation method was used to discretize the height-velocity zone were presented in the problem, which resulted in a large- [115, 114]. Here a more detailed 2-D nonlinear scale NLP problem. The numerical optimizer model was used. In particular it included NPSOL [8] was then used to solve the problem. quasisteady Tip-Path-Plane (TPP) flapping motion, and an empirical inflow model valid The first application in the case of a heli- in the VRS, although different from the one copter was presented in [40]. The model was presented in [89, 98]. The optimal problem again a 2-D nonlinear model, similar to the included bounds on control inputs and states, one of [89], with wind and RPM degrees of and was solved with the SGRA algorithm. freedom, but excluding rotor dynamics, and In particular these studies found that pilot having the thrust coefficient and TPP angle reaction time to engine failure, location of the as control inputs. Constraints included also landing area, and wind speed had a significant bounds on control input rates. Here too the impact on the success of the emergency ma- collocation method was selected, coupled this neuver. Additionally the knee point (Vcr, hcr) time to the SNOPT numerical optimizer [9]. A in Fig. 6 had a higher velocity and a lower similar optimization problem was also investi- height when the helicopter was climbing rather gated in [20], and see also [86, 20, 41] for the than descending. In climb mode the power derivation of height-velocity diagrams. requirement was obviously higher, therefore Later the results of [40, 20] were extended at the instant of power failure the decay of in [16, 17] by including a flare law, that rotor speed would be more rapid than if the would take over from the optimal guidance helicopter was in a descent mode. at a pre-determined altitude near the ground, and flare the helicopter based on a more A recent contribution was presented in [62], conventional compensatory control law. The where partial power recovery to a flyaway con- system was also used to provide guidance dition, partial power landing, and autorotation cues on a cockpit pilot display, and was flight were analyzed, based on a 2-D nonlinear model tested on a flight simulator [17]. [69, 89]. The optimal problem was also solved with the SGRA algorithm. The optimization The first application to solve a 3-D non-

19 linear autorotative optimal control problem on the knowledge of the provided outcome was presented in [25, 26]. The model included [56]. The three main classes of concern are the usual rigid body motion kinematics, supervised learning, unsupervised learning with additional degrees of freedom in main and reinforcement learning29 [56]. rotor RPM, and available shaft power. Also Glauert’s formula was used for the induced In 2004 a group at Chiba University (Japan) inflow model, and quasisteady blade flapping [59] investigated the autorotation flight of a was included. However the model was not R/C30 helicopter, based on a coupled Propor- published in English. The functional cost tional Integral neural network controller. It is included weights which were made altitude de- however unclear whether the group success- 28 pendent. It is assumed that a Nelder-Mead fully flight tested an automatic autorotation [105] numerical algorithm was used to solve system, since results have only been published the optimal control problem. in Japanese.

In [50] the use of an on-line, nonlinear, The first reported automatic autorotation model-predictive controller augmented by was performed at Stanford University in 2008, a recurrent neural network was presented. on a R/C helicopter [12, 11, 10], using an The helicopter model was similar to the apprenticeship learning based approach. The one presented in [89, 98], and the optimal procedure included the collection of flight data problem was solved by a series of recurrent from an expert pilot. The data was then used neural networks. However an investigation of to build a dynamics model of the helicopter in the convergence characteristics of the neural autorotation. An autorotation trajectory was network, i.e. whether convergence can be further split into three flight phases: glide, guarantied and under what conditions, is still flare, and landing. The model included the necessary. usual rigid body motion kinematics, with an additional degree of freedom in main We conclude here by mentioning extensive rotor RPM. Finally Differential Dynamic results for general helicopter trajectory opti- Programming (DDP), an extension of the mization in 2-D in [28], and in 3-D in [29, 30]. Linear Quadratic Regulator (LQR) formalism for non-linear systems, was used to derive a 5.5 Optimal autorotation through feedback controllern. robot learning Further work in automatic autorotation Machine and robot learning represent a through reinforcement learning can be found branch of statistics and computer science, in [99], where the algorithm was evaluated by which explores algorithms and associated simulations based on a point-mass model of architectures that learn from observed facts a modified OH-58A helicopter, similar to the [107, 136, 15]. Additionally, and ideally, the 2-D model presented in [89]. robots need to be able to adapt to future real-world changes. The algorithms of machine We conclude here by mentioning results for learning are organized by a taxonomy based a pilot support system utilizing fuzzy system 28Based on evaluating a function at the vertices of a simplex, then iteratively shrinking the simplex as better 29Also known as neuro-dynamic programming points are found until some desired bound is obtained 30Remotely Controlled

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