Category Principles of Helicopter Aerodynamics Second Edition

Consider now the power required for flight with an autogiro versus that for a helicopter of equivalent weight. Such a comparison helps show the relative disadvantage of the autogiro. This issue had not gone unnoticed by Cierva [see Bennett (1933, 1961)] and had been analyzed by von Karman (1931). The results in Fig. 12.11 show such a comparison for a PCA-2 autogiro versus a modem helicopter in the 3,000-lb weight class. It is clear the power requirements for flight are generally larger for the autogiro. The rapid increase in power required by the autogiro at higher airspeeds is significant. This is partly because of the typically high parasitic drag of an autogiro, as well as because the rotor operates at

higher advance ratios (compared to a helicopter) with significant reverse flow and increased drag on the retreating side of the disk. However, with appropriate streamlining and general drag reduction it is also apparent that the power requirements for flight can be significantly reduced to values that are more consistent with a modem helicopter. The pay load of a modem helicopter is also nearly twice that which could be achieved with an early autogiro. Yet, the obvious mechanical simplicity of the autogiro suggests that with modem construction methods and materials, the empty weight fraction could be reduced and payload increased such that a modem autogiro might become an economically competitive means of achieving rotating-wing borne flight.

The performance of the autogiro in forward flight can be approached using the same basic principles of analysis (momentum and blade element theories) that were applied to the helicopter rotor in Chapters 2 and 3. Historically, the methods of helicopter analysis were mostly derived from the actuator disk analysis conducted on the autogiro by Glauert, Lock, Bennett, and Wheatley. There are two basic methods of approach: 1. An analysis based on energy principles (i. e., a net power analysis); and 2. A force and torque balance analysis on the rotor. In each case the principles of the momentum theory introduced in Chapter 2 for the analysis of the helicopter can be used as a basis.

Consider the autogiro in forward flight, as shown in Fig. 12.9. Vertical force equilibrium gives

L = W — T cos a,

▼ Weight, W

Figure 12.9 Forces acting on an autogiro in level flight.

and horizontal equilibrium gives

D = Я cos a + Dp = Tp. (12.13)

Using energy principles the net drag on the autogiro can be written simply as D = P / V^. We know from Chapter 3 that the power can be written as the sum of the profile and induced power required for the rotor, Pq + Р,-, and the power required to overcome airframe drag, Pp. While the rotor of an autogiro is unpowered at the shaft, energy is still required to turn the rotor and overcome induced and profile losses. This source of energy is the relative flow upward through the rotor, which is produced by propelling the aircraft forward with the engine and propeller. Therefore, the power required can be written as

P = P0 + Pi + Pp, (12.14)

as for the helicopter case. These power components are conveniently written in their nondi – mensional form as

Cp — CpQ + Cpj + Cpp, where each component can be determined as

Cp. = l (t) Д3- (12-18)

z л/

The induced inflow through the rotor is given by the usual result from Chapter 2 that

кСр

2 yj Д2 + kf

with the usual limits of validity in mind (Section 2.14.5). The induced power factor for the autorotating rotor is typically slightly larger than for the powered rotor in the normal working state (as shown by the results in Fig. 5.30), but it is sufficient to assume that к = 1.2 on average for autogiro performance calculations. Notice that the profile contribution to the power (or drag) must model the performance of the rotor at higher values of д because of the typically lower rpm of the autorotating rotor. Finally, the propulsive force on the autogiro, Tp is produced by a propeller with aerodynamic efficiency rjp. Therefore, the net shaft power required for the autogiro, Pshp is

There are several provisions on the use of the result in Eq. 12.20. First, it will not be applicable at very low airspeeds because it is apparent that P/V^ (or Cp/fi) will become singular. However, the autogiro cannot sustain level flight here anyway because there is a maximum resultant force coefficient that can be sustained on an autorotating rotor (i. e., Cp ~ 1.25). Under the conditions where level flight cannot be sustained, the autogiro will begin to descend and potential energy (altitude) is given up. Second, because of its lower tip speed the rotor operates at high д, so that the applicability of the approximation used for the rotor drag with reverse flow (Eq. 12.16) must be examined. Third, the theory cannot apply
when the disk AoA is large, although from Fig. 12.3 it is clear that this also only occurs at lower speeds and steep angles of descent. Therefore, Eq. 12.20 will apply over most practical level-flight airspeeds. However, it will be apparent that this first form of analysis gives no information about the rotor disk AoA required to actually produce autorotation.

An alternative form of analysis based on a force balance must consider the flow conditions required to produce autorotation (i. e., the AoA of the rotor to produce autorotation at a given airspeed must now be determined). The principles of this following approach was used by – Bennett (1933) and also by Glauert (1935) for his “lifting windmill” problem. To produce autorotation there must be a component of flow upward through the disk (i. e., a component Voo sin a). Because the rotor produces thrust it also creates an induced velocity vt. The net flow upward through the rotor will thus be Voo sin a — u,-, where a is not known a priori. Autorotational conditions will be obtained when the AoA and upward flow is sufficient to overcome both the induced and rotational torque losses of the rotor so that the net shaft torque required will be zero. These losses can be written as

Cq = Cq0 + Cq, = Cq0 + kXCt = 0 for autorotation, (12.21)

where Cq0 is the rotational component of profile torque on the rotor (see Section 5.4.2), which is given by

СЄо = ^(і+М2) (12.22)

and where the inflow ratio (see Section 2.14.1) is given by

Ct

X = ц, tan(—a) -1—- 7:-:_…. . …. (12.23)

2-У /z2 + X2

Notice that a negative sign preceding the a must be used here because the disk is now tilted back compared to the helicopter case. Thus we have

which can be solved numerically for the value of a required to produce autorotation; that is, the value of a required at any д to produce zero net torque (power) required at the rotor shaft. Notice that because vertical force equilibrium must be simultaneously satisfied using Eq. 12.12, the rotor thrust must also increase as a increases because the airspeed decreases (i. e., because CT ^ CV/ cos a). This will apply down to the lower limit of Cr ы 1.25. Having solved for a to produce autorotation, the drag on the autogiro will be

D — T sin a + H cos a – f Dp = Tp, (12.25)

where the rotor drag force coefficient is aC^ Л 1 -Л

CH = -^2n+-^J (12.26)

when including reverse flow but not radial drag – see Section 5.4.2. The shaft power required for flight is then found using

Fshp = TpVoo/r/p, (12.27)

as before. The results from both the energy and force methods are equivalent, although the latter approach has the advantage of being able to solve for the rotor disk AoA required to produce autorotation.

A representative curve of power required versus airspeed for the PCA-2 autogiro is shown in Fig. 12.10. While direct power measurements are not available, it is possible to derive the equivalent shaft pow’er at the engine by using the L/D results in Fig. 12.14 along with an assumed propeller efficiency. It is apparent that this type of performance analysis is in agreement with the measurements. Notice in this case, however, that, compared to a typical helicopter curve, the power requirements for an autogiro increase rapidly as airspeed bleeds off. The performance of the autogiro at these conditions is limited by either the power available or the maximum rotor lift coefficient (see Fig. 12.7). Furthermore, notice that the power requirements increase rapidly at higher airspeeds, which is a result of the high parasitic drag (large equivalent flat plate areas) of the early autogiros.

This theory can also be used to predict the gliding (power-off) rate of descent of the autogiro. The results have been shown previously in Fig. 12.2. Based on an energy balance and solving for the rate of descent, it is apparent that the theory is in excellent agreement with the measured performance of the PCA-2 and C-30 Autogiros, but only at higher forward flight speeds. This is because of the failure of the momentum theory to predict the induced velocity through the rotor at high disk angles of attack (low airspeeds, higher rates of descent). As also shown in Fig. 12.2, Harris’s approximate theory for these conditions seems to fill in nicely where the momentum theory fails.

A conventional momentum theory analysis of the autorotating rotor breaks down when the rotor is at large angles of attack to the relative wind. For larger disk angles of attack it is possible to equate the resultant force on the rotor to the weight of the autogiro (i. e., R ~ W). Furthermore, the resultant velocity, Уж, can be written as Vqo = y/Vf + Vd so that

W

CR = 1———————– . (12.7)

-p(.Vj + Vj)A

Harris (2003) shows that for large operational angles of attack it is possible to write

In pure vertical descent Vf = 0, so the vertical rate of descent in autorotation will be

at sea level, which compares favorably with the result given previously in Eq. 12.4 and also with results by Glauert (1926). The autorotative rate of descent, however, decreases quickly with increasing forward speed but only to a point, as has been shown previously in Fig. 12.2. For a series of horizontal velocities, V/, at the steeper angles of attack where Cr = Cd = 1-25, the rate of descent in autorotation, Vd, can be solved using

(12.10)

or in nondimensiohal terms

(12.11)

for which the predictions made using this latter equation are shown in Fig. 12.2. Note that for Vf = 0 this predicts Xd/kh = 1.79, which is consistent with the results shown in Section 2.13.7. While not exact, this equation does give a reasonably good result for Vd as a function of forward speed, V/, when the rotor disk is at steep angles of attack to the relative wind.

In 1925, Juan de la Cierva was invited to Britain by H. E. Wimperis [see also Wimperis (1926)] of the British Air Ministry and was provided with financial backing by the industrialist James G. Weir of the Weir Company. Cierva was shortly thereafter to found the Cierva Autogiro Company, Ltd. and Britain was then to become the home for Cierva’s work. His company was not set up for manufacturing, however, but for technical studies, management of patents and awarding of licenses to build his Autogiros. His Autogiros instead were built by established aircraft manufacturers, including the Avro (A. V. Roe) Company. Pitcairn and Kellett in the United States were later to become major licensees and were to produce various derivatives of the Cierva machines. This saw the beginning of the Pitcaim-Cierva Autogiro Company of America. In 1933, this enterprise was to become simply the Autogiro Company of America. See Harris (1992) for a history.

Cierva’s C-6 Autogiro was demonstrated at the RAE in 1925 and in the same year Cierva gave the first of three historical technical lectures to the membership of the RAeS [Cierva (1926)]. At the end of this (and all of the other lectures) there was considerable debate on the merits of his Autogiro. Cierva gave another lecture in 1930 [Cierva (1930a)] at a time when more than 100 autogiros were flying in Britain and the United States and he was to document the rapid technical developments of the autogiro that had taken place during the preceding five years. His final lecture and paper [Cierva (1935)] was to the RAeS in 1934 and he then described in detail the “jump” takeoff technique and the direct rotor control device (see Section 12.14).

Cierva’s first demonstration flights and lectures in Britain stimulated early experimental and theoretical work on rotating-wing aerodynamics by H. Glauert and C. Lock. Their theoretical work was pioneering and was supported by relatively advanced wind tunnel measurements on model rotors [see Lock & Townend (1928)]. In 1926, Glauert (1926) published a classic paper that was to be the first theoretical treatise on induced inflow and rotor performance – see also Glauert (1927). Glauert’s analysis quantified rotor performance in horizontal, climbing, and descending flight and set down the basic equations that could be used to relate rotor performance to certain design parameters. However, in descent or in autorotation (in particular) the theory was not exact, and even since then, there has been no exact theory derived from first principles to fully describe the aerodynamics of a rotor

Hub plane angle of attack – deg.

in the autorotative state. However, Cierva vehemently disagreed with Glauert’s analysis, based on his own theories and also his practical flight testing experience with the C-6. In a formal letter lodged with the RAeS, Cierva (1927) disagreed with Glauert’s estimation of the vertical autorotative rate of descent, claiming values for “practically vertical descents” that were half of Glauert’s estimate. He goes on further to draw concerns “with almost every point contained in Mr. Glauert’s developments.” Glauert seems to have been unruffled by such harsh criticism, standing confidently behind his theoretical studies – see Glauert (1927).

With hindsight, Glauert was probably closer to the truth of the matter than Cierva might have given him credit for. The analysis conducted previously has shown that the vertical rate of descent can be related to the rotor disk loading. The same result can be approached using measurements of the resultant force acting on the autorotating rotor, which are shown in Fig. 12.7. Cr is the resultant force coefficient, where R is the resultant force on the rotor as given by R = VL2 + D2, with L as the rotor lift force and D as the rotor drag force – see Fig. 12.8. It is significant that the resultant Cr on the rotor at large angles of attack (greater than 30°) is about 1.25 and nearly equivalent to the drag coefficient, Co, of a circular disk with a flow normal to its surface (i. e., at high angles of attack the rotor acts like a bluff body with its attendant turbulent downstream wake). Recall from page 92 that Co = 1-33 for an open hemisphere, which means that aerodynamically the rotor produces a resultant force equivalent to a parachute when in the vertical autorotative state. Yet, this was a-point vigorously disputed by Cierva (1930b). Herein lies the difficulty in analyzing the aerodynamics of the rotor, because the rotor in its autorotative flow state at low airspeeds creates a complex turbulent wake and, in fact, is often said to operate in the “turbulent wake” state – see Fig. 2.20. With forward speed, however, the flow state in autorotation is much smoother.

Later, Harold Pitcairn urged Cierva to consolidate his vast engineering knowledge of the autogiro and in 1929 commissioned him to write a reference book for American en­gineers. The first Cierva book was titled Engineering Theory of the Autogiro – see Cierva

(1930c). Sufficient data had been measured and analysis conducted that “a theory could be developed covering many probabilities of performance and possibilities of design beyond the actual achievement in construction to that time.,r [Cierva & Rose (1931)]. Later, Cierva wrote a comprehensive design manual titled Theory of Stresses in Autogiro Rotor Blades. Neither document was formally published, but they were copyrighted and made available to engineers at Pitcairn, the Kellett Autogiro Company, the NACA, the US Air Force, and the Bureau of Aeronautics. These engineering documents helped greatly in the certification of autogiros manufactured (and later designed) in the United States. Today, few original copies of these books exist, but they are a valuable chronicle in the technical development of rotating wing aircraft.

Because an autogiro rotor is not powered, the rotor needs to be brought up to speed by some means before takeoff. In Cierva’s day this was initially done by taxiing the aircraft around for several minutes. Later, a “spinning top” method was used, where a rope was
wound around the rotor shaft on pegs mounted on the bottom of the blades, the rope being pulled quickly (either manually by ground crew or by taxiing away from an anchor) to start the rotor. Instead, the Cierva C-12 model of 1929 saw the use of an alternative aerodynamic method to prerotate the rotor. Here, a “Scorpion” type of biplane tail was used to deflect the propeller slipstream up toward the blade tips. This horizontal tail was deflected at a steep incidence angle and the machine was held on the brakes and the throttle opened until the deflected propeller slipstream caused the rotor to autorotate and come up to speed. The tail incidence was then reduced back to its normal pitch before takeoff. The Scorpion tail design, however, was a relatively heavy solution and suffered from higher parasitic drag compared

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airspeeds because the vertical stabilizer and rudders were outside the propeller slipstream. Yet, the Scorpion tail was used on several models of the Cierva’s Autogiros and seemed to offer a reasonably good compromise as an interim practical solution to starting the rotor. However, by 1930 engineers were to develop a more powerful, lightweight prerotator. This mechanical starter allowed the rotor to be brought quickly up to speed, solving finally the problem once and for all.

Based on his many experiments with small models, Cierva noticed that the flexi­bility of the rattan (palm wood) spars on his models provided different aerodynamic effects compared to the relatively rigid blade structure used on his full-scale machines. This was the key Cierva needed and his “secret of success.” His fourth machine (the C-4), there­fore, incorporated blades with mechanical hinges (using horizontal pin joints) at their roots, which allowed the individual blades to flap up and down freely in response to the changing lift forces seen by the blades as they progressed around the shaft axis. Also acting on the blades are drag and centrifugal and gravitational forces, and as a result of free flapping, there are also inertia and Coriolis forces to contend with (see page 197). The blades on the C-4 were restrained by cables attached to the shaft to limit both downward and upward flapping angles and also so the blades would not droop to the ground when the rotor was stopped. Cierva noticed that the incorporation of the flapping hinge eliminated any adverse gyroscopic effects and also allowed the lift forces on the two sides of the rotor to become more equal in forward flight. However, Cierva’s omission of a lead-lag hinge to alleviate the in-plane blade motion from drag and Coriolis forces (resulting from the flapping motion) was an oversight that he would ultimately come to terms with.

In Cierva’s C-4 Autogiro of 1923 (see Fig. 12.6) a single rotor with four independent, freely flapping blades was mounted on a long shaft above an Avro 504 airplane fuselage. The blades were of high aspect ratio, similar to those of modern helicopter blades, and used a relatively efficient Gottingen 429 airfoil shape. A propeller, powered by a Le Rhone engine, provided propulsion. The first version of the C-4 used lateral tilting of the entire rotor disk to provide roll control. However, taxiing tests showed that the control forces involved in tilting the rotor were too high for the pilot and the control response also proved very sluggish. However, the natural tilting of the rotor TPP during flight also tilts the rotor lift

vector and produces side forces and moments on the autogiro. These must be compensated for by some means to maintain trimmed flight and proper control. On a helicopter, this is done by using cyclic pitch inputs to the blades. But on Cierva’s first machines, the rotor disk was uncontrolled and conventional “fixed-wing” aerodynamic control surfaces (ailerons, elevator, and rudder) were used to provide the necessary forces and moments on the aircraft to compensate for the natural tilting of the rotor disk. While not ideal, Cierva was satisfied with the simplicity of his interim solution to the problem.[45] Cierva’s C-4 Autogiro first flew successfully on January 9, 1923, making a controlled flight in a straight line and covering about 200 m (656 ft) – see Moreno-Caracciolo (1923).

As explained in Chapter 4, the use of a flapping hinge allows each blade to flap up and down independently in a periodic manner with respect to the blade azimuth angle under the action of the varying aerodynamic loads. The blades precess to an equilibrium condition when the local changes in AoA and the aerodynamic loads produced as a result of blade flapping are sufficient to compensate for local changes in the airloads resulting from periodic variations in the dynamic pressure. The flapping response lags the blade pitch (aerodynamic) inputs by about 90° (see Chapter 4, p. 183). Therefore, the main effect of the asymmetry in lift over a rotor with flapping blades is to cause the rotor disk to tilt back, in this case giving it a natural AoA – see Fig. 12.4. In addition, the rotor disk also has a tendency to tilt laterally slightly to the right (for a rotor turning in a counterclockwise direction) because of the coning of the rotor under the action of the lift forces.

On the first lightly loaded Cierva rotor designs, the in-plane forces were balanced by sets of wires connected between the blades, such that as one blade lagged back or forward, the motion was easily resisted by the other blades. However, by Cierva’s own admission [Cierva & Rose (1931)] his early Autogiros were “rather rough in flight owing to a sort of whipping action of the rotor blades which jerked at the mast as they turned in their circle.” Cierva was noticing Coriolis effects, which produce forces in the plane of rotation of the rotor and introduce an important dynamic coupling between flapping (or out-of-plane) motion and the lead-lag (or in-plane) motion of the rotor blades (see page 197).

With later bigger and heavier machines, the combination of higher drag and Coriolis forces produced relatively high cyclic in-plane stresses at the blade root, and flight tests with a C-6 were to show evidence of in-plane structural bending overloads and the onset of fatigue damage. Yet, Cierva initially resisted the use of a second hinge to relieve these Coriolis loads because of weight concerns. Eventually, on a version of the C-6, a blade failed and flew off resulting in the official grounding of all Cierva Autogiros. This episode finally convinced Cierva that another hinge, a lead-lag or “drag hinge,” must be required on the blades – see Fig. 4.1. Cierva tried out the idea of two hinges per blade on his model C-7, and after convincing the authorities of the renewed airworthiness, Cierva went on to develop the C-8 Autogiro. The incorporation of both a flapping hinge and a lead-lag hinge was an important step in the development of the fully articulated rotor hub discussed in Chapter 4, which is used today for many helicopters.

When either a helicopter rotor or autogiro rotor operates in forward flight with the rotor plane passing edgewise through the air, the blades encounter an asymmetric velocity field [see Fig. 2.1]. The asymmetry of the onset flow and dynamic pressure over the disk produces aerodynamic forces on the blades that are a function of blade azimuth. For blades that are rigidly attached to the shaft, the net effect of these asymmetric aerodynamic forces is an upsetting moment on the rotor and on the aircraft. This was Cierva’s first dilemma when developing the autogiro. As described in Chapter 4, the distribution of lift and induced inflow through the rotor will affect the inflow angle ф and the angle of attack at the blade sections and, therefore, the detailed distribution of aerodynamic lift and drag forces over the rotor. This subsequently affects the blade flapping response and so the aerodynamic loads on the blades. This coupled behavior is a complication with a rotating wing that makes its thorough analysis relatively difficult, a fact well appreciated by Cierva and a point alluded to throughout this book.

Cierva’s first Autogiro, the C-l, was built in 1920 and had a coaxial rotor design. He was to build two more machines, both with single rotors, before he achieved final success with the C-4 (Fig. 12.6) in January 1923. The problem of asymmetric lift between the advancing and retreating blades was initially approached using the idea of a contrarotating coaxial design such that the lower rotor would counteract the asymmetry of lift produced on the upper rotor, thereby balancing out any moments on the aircraft. However, when flight tests began it was found that the aerodynamic interference between the rotors resulted in different autorotational rotor speeds and this spoiled the required aerodynamic moment balance. Cierva considered the possibility of mechanically coupling the rotors to circumvent the problem, but this was quickly rejected because of the obvious mechanical complexity and significant weight penalty. Despite its failure to fly the C-l proved that the rotors would freely autorotate when the machine was taxied with sufficient forward speed.

The next Cierva design was the “compensating” rotor, which was tested in a three-bladed form on the C-3 in 1921 and in a five-bladed form on the C-2 in 1922. This idea used blade twisting in an attempt to compensate for the undesirable characteristic of asymmetric lift (i. e., by using nose-down twist on the advancing blade and nose-up twist on the retreating blade). Photographs of these two machines [see C. A. Cierva (1998)] show a series of cables attached to the trailing-edges of the blades, with the idea that the blade twist could be changed in a cyclic sense as the blades rotated about the shaft. However, while the basic principle was correct, the concept proved impractical and both the C-2 and C-3 were only to achieve short hops off the ground. Perhaps the use of cyclic blade feathering (as opposed to blade twisting) might have been more successful, but it was not to be until 1931 that Wilford in the United States demonstrated this concept on an autogiro – see Wheatley (1935), Larsen (1956), and Gustafson (1971).

Autorotation has been defined in Chapter 2 as a self-sustained rotation of the rotor without the application of any shaft torque (i. e., Q = 0 at the rotor shaft). In autorotation the energy to drive the rotor comes from the relative airstream, which is directed upward through the rotor. To see why, the problem can first be approached from momentum theory applied to a powered rotor in vertical descent, a method introduced in Chapter 2. In vertical climb or descent at a given rotor rpm, the torque ratio (the torque, <2, that is required to produce a given rotor thrust relative to the torque required for a shaft driven rotor to hover,

Qh) is

Q QQ F VC’

Qh QQh Fh Vh Vh

where Vc is the climb velocity, u, is the induced velocity through the rotor and Vh is the induced velocity in shaft-powered hovering flight (generally this is always used as a reference). The two terms on the right-hand side of this equation represent the torque associated with any change the potential energy of the rotor and the aerodynamic (induced) losses, respectively. The solution for Vi/vh can be calculated using momentum theory as a basis (see Section 2.13.4), although vertical autorotation actually occurs in a condition where momentum theory offers no exact solution for the induced velocity – see Fig. 2.20.

In practice, there are also profile losses to overcome. Therefore, in an actual autorotational condition then

Q — — (Ус + vi) + Qo — 0.

where T is the rotor thrust and Qo represents the torque to overcome blade profile losses.

Clearly Vc must be negative to produce autorotation (i. e., the aircraft must give up potential energy). When in a stable “gliding” autorotation with a constant airspeed and constant rotor rpm, there is an energy balance where the decrease in potential energy of the rotor, —TVC, just balances the sum of the induced and the profile losses of the rotor at that rpm. The ideas of an energy balance in autorotation were first explored by Cierva [see Cierva (1926)]. Using Eq. 12.2, this condition is achieved when

Ye. —

vh vh T vh

The second term on the right-hand side of Eq. 12.3 depends on the profile drag of the rotor blades (i. e., on the rotor solidity and the average drag coefficients of the airfoil sections used on the blades). However, compared to the induced part, which is defined by the curve that has been shown in Fig. 2.20, the extra rate of descent required to overcome profile losses is small. In practice, in a vertical autorotation the nondimensional rate of descent, Vc/vh, is found to be between —1.8 and —1.9. For the larger value, this is equivalent to a vertical rate of descent

1.9 [f [T

—j=J — = 27.55J — in units of ft/s V2pV A V A at sea level atmospheric conditions. Equation 12.4 shows that the autorotational descent rate is proportional to the square-root of the rotor disk loading, T/ A(= WJ A). Cierva’s early Autogiros all had disk loadings of about 2 lb/ft2 (96 N/m2), which is also typical of modem autogiro designs. This would give a vertical autorotative rate of descent at sea level of about 39 ft/s (12 m/s) or 2,340 ft/min (713 m/min).

Unlike the helicopter, the autogiro’s rotor must always operate in the autorotative working state, where the power to turn the rotor comes from a relative flow that is directed upward through the rotor disk. The low disk loading (T j A) of an autogiro’s rotor (and, therefore, the low induced velocity through the rotor disk) means that only a small upward flow normal to the rotor TPP is necessary for the rotor to enter into autorotation compared to a helicopter. While the autogiro is not a direct-lift machine (nor was it designed to be) and cannot hover, it requires only minimal forward airspeed to maintain flight. Therefore, in straight-and-level forward flight, the rotor disk needs to operate only with a slight positive AoA (backward tilt). As long as the machine keeps moving forward though the air, the rotor will continue to autorotate and produce lift. Reducing engine power will cause the machine to descend slowly and increasing power will cause it to climb. The stoppage of the engine is never really a problem on an autogiro because the rotor is always in the autorotative state and so the machine will descend safely to the ground. The rotor can, however, exit the autorotative state as a result of poor piloting technique.

Measurements documenting the performance of autogiros are rare and go back to the 1930s. Detailed in-flight measurements were conducted by the RAE using a Cierva C-30 [see Hufton et al. (1939)] and by NACA using a Pitcairn PCA-2 [see Wheatley (1933a)]. See also Harris (1992) for these data. The autorotational rate of descent, Vd, for both machines is plotted in Fig. 12.2 as a function of forward speed, V/, both parameters being

CsJ

nondimensionalized by V/-T’/2pA, which essentially removes the effects of disk loading from the results. It is apparent that the measured vertical rate of descent occurs at about Vd/VT/2pA = 1.9, which is in good agreement with the result given in Eq. 12.4 – see also Section 2.13.7. As previously mentioned, there is no exact theory describing the rotor aerodynamics in autorotation, even if the rotor has forward (translational) speed, but as airspeed builds momentum theory gives a better and better approximation to the predicted rate of descent in autorotation – see Section 12.9. The measurements in Fig. 12.2 clearly show a rapid decrease in the autorotational rate of descent as forward speed builds. A minimum rate of descent is reached at about Vf/^/T/2pA = 2 (in practice this corresponds to about 35-40 kts or 65 km/h to 74 km/h), which is the point where aerodynamic losses at the rotor are a minimum, and the rate of descent slowly increases again thereafter.

Also of interest is the autorotational rate of descent versus the rotor disk angle of attack. While the forgoing measurements were performed in descending “gliding” flight, autoro­tation is also possible in level flight with propulsion from a propeller to drive the autogiro forward. All that is required is that the rotor disk be held at a sufficient AoA such that the component of the relative wind upwards through the disk causes the rotor to autorotate. In the words of Juan de la Cierva himself [see Cierva & Rose (1931)] “It makes no difference at what angle the Autogiro is climbing or flying. The blades are always gliding toward a point a little below the focus of forward flight. It is impossible, therefore, for autorotation to stop while the machine is going anywhere.” This bold statement, however, excludes the possibility of bad piloting technique.

The results in Fig. 12.3 show the measured hub plane AoA as a function of the resultant nondimensional velocity of the aircraft. In a pure vertical descent it is apparent that the TPP and hub plane angles of attack are both essentially 90° (the resultant wind in this case is perpendicular to the disk). As forward speed builds, the hub plane needs to make a progressively smaller angle to the relative wind to enable autorotation, until at higher speeds the rotor must be held only at a shallow angle to produce enough lift in the autorotational
state. The rotor TPP angle is also inclined back but is not equal to the hub plane AoA because of blade flapping (see Fig. 12.4 and also discussion in Section 4.9). The natural tendency

to produce longitudinal napping (i. e., a pc component) component of velocity upward through the disk, which means the hub plane angle is always relatively small in forward flight. The TPP has a positive AoA much like a wing under these conditions – see page 94 and Glauert (1926, 1928).

Cierva juggled with the parameters affecting the magnitude and direction of the aerody­namic forces acting on the rotating blades and concluded that there could be many different combinations of rotor operating conditions where the net torque on the rotor shaft could be zero. Consider the flow environment encountered at a blade element on the rotor during autorotation, as shown in Fig. 12.5 where the relative velocity is directed upward toward the rotor. For autorotational equilibrium at that section the inflow angle, ф, must be inclined

Thrust force

NOTE: Angles exagerated for clarity

Net I Resultant velocity

upflow

In autorotation, flow is upward through the rotor Figure 12.5 Detail of the flow at a blade element in autorotational flight.

forward such that there is no net in-plane sectional force and, therefore, no contribution to rotor torque; that is, for force equilibrium at that section

dQ = (D – (f>L)y dy = 0, or that in coefficient form, we have Cd – фС1 = 0.

However, this is an equilibrium condition that cannot exist over all parts of the blade and only one radial station on the blade can actually be in proper autorotational equilibrium. In general, it has been shown previously by means of Fig. 5.24 that some portions on the rotor will absorb power from the relative airstream and some portions will consume power, such that the net torque at the rotor shaft is zero (i. e., fdQ = 0). For autorotational equilibrium the induced angles of attack over the inboard stations of the blade are relatively high and near the tip the values of ф are relatively low. We find that at the inboard part of the blade the net AoA results in a forward inclination of the sectional lift vector, providing a propulsive component greater than the profile drag and creating an accelerating torque – see Fig. 12.5. This blade element can be said to absorb energy from the relative airstream. Toward the tip of the blade where ф is lower and these sections of the blades consume energy because the propulsive component as a result of the forward inclination of the lift vector is insufficient to overcome the profile drag there (i. e., a net decelerating torque is produced).

As Cierva understood, in the fully established autorotational state at a given blade collec­tive pitch angle the rotor rpm will adjust itself until a zero torque equilibrium is obtained. Assuming unstalled blades, then this is a stable equilibrium because it can be deduced from Fig. 5.24 that if Q, increases, ф will decrease and the region of accelerating torque will decrease inboard and this tends to decrease rotor rpm. Conversely, if the rotor rpm decreases, then ф will increase and the region of accelerating torque will grow outward. Therefore, when fully established in the autorotative state, the rotor naturally seeks to find its own equilibrium rpm in response to any changing flight conditions. This is an inherent characteristic of the rotor that gives the autogiro very safe flight characteristics.

However, in the autorotational state the blade pitch must always be at a low value and the disk AoA must be positive to ensure that the inboard blade sections never reach high enough angles of attack to stall. Stall may occur if the rotor rpm decays below an acceptable threshold, such as when the disk AoA becomes negative, or a reduced or negative load factor is produced. These are flight conditions to be avoided. If stall does inadvertently occur, then the outward propagation of stall from the blade root region will cause rotor rpm to decrease quickly because of the associated high profile drag.

The outstanding inspiration of the Autogiro’s story was the recognition that there might be more than one type of flying machine, soundly mechanical but basically independent of conventional theory and practice.

Juan de la Cierva (1931)

12.1 Introduction

An autogiro or gyroplane has a rotor that can turn freely on a vertical shaft. However, unlike a helicopter, its rotor is not powered directly. Instead, the rotor disk inclines backward at a positive angle of attack, and, as the machine moves forward in level flight powered by a propeller, the resultant aerodynamic forces on the rotor blades causes the necessary torque to spin the rotor and produce lift. The natural self-rotation of the rotor is called autorotation, a phenomenon introduced in Chapter 2. The autorotating rotor provides the lift for the machine (perhaps also control), with forward propulsion being provided by a conventional tractor or pusher propeller arrangement — see Fig. 12.1. Compare this to the helicopter where the rotor provides both lift and propulsion, as well as control. If the machine also has a fixed wing, or has the capability to hover (using tip jets), but is still flown as an autogiro in forward flight, then the aircraft may be referred to as a gyroplane or perhaps even as a convertiplane or gyrodyne. The names autogiro, autogyro, giroplane, and gyroplane are, however, often used synonymously.

In 1923, the autogiro was the very first type of rotating-wing aircraft to fly successfully and thus to demonstrate a useful and practical role in aviation, pre-dating the first successful flights of helicopters by about fifteen years. The autogiro was also the first powered, heavier – than-air aircraft to fly successfully other than a conventional airplane. Conceived by Juan de la Cierva about 1920 [see Cierva & Rose (1931), Gablehouse (1967), C. A. Cierva (1998), and Chamov (2003)] over thirty different autogiro designs were produced in just fifteen years of development (1923-1938). Cierva proved that his Autogiros1 were very safe and because of their low flight speed capability they could be landed in confined areas. Takeoffs required a short runway to buildup airspeed, but this was rectified later with the advent of a prerotator for the rotor and the development of the “jump” and “towering” takeoff techniques. This gave the autogiro a capability that was comparable to that of the future helicopter in terms of overall performance. However, the autogiro often seems to be a half- forgotten machine that occupies a lower place in the list of aviation firsts. It has perhaps been viewed by many only as an interim step toward the helicopter, and a temporary makeshift

Figure 12.1 The autogiro rotor (a) provides lift to sustain flight, with forward propulsion being provided by a conventional propeller, compared to the helicopter (b), where the rotor provides both lift and propulsion.

at that. As discussed in Chapter 1, however, the autogiro played a fundamental role in the technological development of all types of modem rotating-wing aircraft. There are also several interesting technical aspects of autorotative flight that make this aircraft unique when compared to a helicopter. It is for this reason that a separate chapter on autogiros is an appropriate part of this book.

Autorotation can been seen naturally in the flight of a variety of seeds, such as maple or sycamore – see Azuma & Yasuda (1989) for an aerodynamic discussion. However, the somewhat curious aerodynamic phenomenon of “autorotating bodies” had been observed in variety of scientific experiments by the beginning of the twentieth-century, which probably were inspired by earlier theoretical work by the Scottish physicist James Maxwell – see Tokaty (1971). The Italian Gaetano Crocco and the Russian Boris Yuriev had examined the principle of autorotation on spinning rotors around 1910. Munk (1925) conducted experiments with “helicopter propellers,” where the phenomenon of autorotation was again demonstrated.

However, the Russian scientist Yuriev and his students probably made the most significant studies, showing that under some conditions of steeply descending and horizontal flight with the rotor at a positive angle of attack, a lifting rotor would actually turn of its own accord. Yuriev called this phenomenon “rotor gliding,” and he apparently realized, even then, that the ability of the rotor to self-rotate might be used to bring a helicopter safely to the ground in the event of an engine failure. The ability to autorotate in an emergency condition (such as after a power or tail rotor failure) is a fundamental safety of flight capability that must be designed into all helicopters (see Chapters 2 and 5).

Chapter 1 described the numerous types of primitive human-carrying helicopters pro­posed and built from 1900 to 1920. Yet nobody had previously considered the idea that a successful rotating-wing aircraft could be built such that the rotor was unpowered and always operated in the autorotative state during its normal flight. In the spring of 1920 Juan de la Cierva of Spain built small, unpowered free-flying models of a rotating wing

aircraft, with the rotor free to spin on its vertical shaft. The model had a rotor with five blades, with horizontal and vertical tails to give it stability. Cierva launched the model and the rotor spun freely of its own accord as the model glided softly to the ground. Cierva had rediscovered the principle of autorotation, which at first he was to call “autogiration.” These first experiments with models were to pave the way for the design of a completely new type of rotating-wing aircraft that Cierva was to ultimately call an Autogiro.

Juan de la Cierva had become interested in aviation as early as 1908 when the Wright Brothers demonstrated their Flyer machine in Europe. Cierva was subsequently to build the first Spanish airplane in 1912. His third airplane of 1919 was a large three-engined bomber. While the aircraft flew well, the test pilot became over ambitious and the machine stalled and crashed. This tragedy motivated Cierva to think of a way of improving the flight safety of an aircraft when it operated at low airspeeds and, in particular, when it was flying close to the ground. Cierva set out to design a safe flying machine that ensured “stability, uplift, and control should remain independent from forward speed” and suggested further that it should be one that could be flown by a pilot with average skill [see Cierva & Rose (1931)]. Cierva went on to point out that “the wings of such an aircraft should be moving in relation to the fuselage. The only mechanism able to satisfy this requirement is a circular motion and, moreover, in order to give adequate security to the aforementioned requirement it must be independent of the engine. It was thus necessary that these rotary wings were free-spinning and unpowered.”

Thus was borne the vision of an autogiro. Juan de la Cierva was not the first to suggest or observe the phenomenon of autorotation, but he was certainly the first to understand better the aerodynamic principles and to put the phenomenon toward serving a useful purpose. He was to make some of the first theoretical studies on rotors and conducted a series of wind tunnel tests [see Cierva & Rose (1931)] as he writes: “with valuable results, among them the determination of the fact that the rotor would continue to turn at every possible angle of flight – a point that was somewhat disputed by critics of my earlier experiments.”

The content of this chapter has described some of the important aerodynamic interactions that can take place between a helicopter rotor and its airframe. Because there are often (but not always) deleterious effects associated with these interactions that can have

a significant impact on the performance of the helicopter as a whole, the understanding and accurate prediction of aerodynamic interactions have become an important issue in helicopter design. Problems of interest include the need for a better understanding of the physics of rotor wake distortion caused by the fuselage and empennage, the effects of the fuselage on the rotor airloads, and the consequences of main rotor and tail rotor wake interactions on unsteady airloads and acoustics. The need to mitigate these effects at the design stage rather than after first flight has never been more imperative to the success of the modern helicopter.

There have been many wind tunnel experiments with subscale helicopter models to heir» quantify the various aerodynamic interactions between a rotor and an airframe. Some of these tests have been performed with simplified airframe topologies, which are ideal for understanding the physical phenomena, whereas other tests with scaled airframes are better for the validation of comprehensive flow models. Airloads on the fuselage and on the rotor have been measured in an attempt to assess the magnitude of the effects and to better understand the significance of aerodynamic interactions. At low flight speeds the helicopter fuselage is often immersed in the wake from the main rotor and so the downwash from the rotor will influence significantly the fuselage aerodynamics. The presence of the rotor wake creates a significant download on the fuselage that increases with increasing rotor thrust and decreases with advance ratio, but only to a point. An upload can be produced on the airframe by the rotor wake when the helicopter is in high-speed flight. The corresponding effect of the fuselage on the rotor can increase its mean thrust at low advance ratio. The rotor wake has been shown to produce substantial effects on the time-averaged fuselage pressures, especially at the boundaries of the rotor wake where the induced velocities are highest. These mean pressures are sensitive to variations of rotor thrust and/or advance ratio. The induced pressures on the fuselage are generally asymmetric and will result in a net side force on the fuselage. Overall, the results from several wind tunnel experiments and flight tests have shown the relative complexity of the interactional aerodynamic effects that exist between a thrusting rotor and its airframe.

Unsteady effects play an important, and perhaps underestimated, role in the understand­ing of interactional aerodynamic phenomena on helicopters and other types of rotorcraft. The unsteady pressure fluctuations induced on the fuselage by the rotor and its wake are very large; in fact, in many cases, the magnitude of these unsteady fluctuations exceeds the mean pressure values. However, the unsteady pressure fluctuations are not necessarily the greatest in the regions of highest mean pressure. Blade passage effects on the fuselage increase in proportion to the blade thrust (disk and blade loading) and may be an important factor in the design of new helicopters with high disk loadings and smaller rotor-fuselage spacings designed for low parasitic drag and high-speed flight. The dominant frequency of the unsteady pressure fluctuations corresponds to the blade passing frequency. Wake vortex impingement on the fuselage results in more complex transient pressure loadings. These loadings, however, are not the severest form of induced pressures obtained on the fuselage because close wake vortex-surface interactions appear to produce much stronger effects. While the complexity of the problems involved in rotor-airframe interactions pro­vides ample scope for both the theoretician and experimentalist, and indeed offer many new research opportunities, it provides a particularly good challenge for the more advanced CFD methods. These methods, and their limitations, are discussed further in Chapter 14.