A theoretical study of helicopter rotor noise

J. Sound Vib. (1969) 9 (2), 197-222

A THEORETICAL STUDY OF HELICOPTER ROTOR NOISE]" M. V. LOWSON;~ AND J. B. OLLERHEAD

Wyle Laboratories, 7800 Governors Drive West, Huntsville, Alabama, U.S.A. (Received 7 August 1968) A comprehensive theoretical study of the problem of helicopter rotor noise radiation is presented. The theory includes blade slap, rotation noise and vortex noise effects. Peak spectral levels over the "vortex noise" region are shown to be due to the higher harmonics of the rotational noise. An exact theoretical expression for the noise radiation has been used as the basis for the development of a comphrehensive computer program to calculate helicopter noise at any field point, including all effects of fluctuating airloads and all possible rigid and flexible blade motions. Under very reasonable approximations an analytic expression has been found for the sound field far from the helicopter. Computations based on this expression have also been made. The results show that it is the very high harmonics of the loading which contribute to the important harmonics of the sound field. For instance, calculation of the tenth harmonic of a four-bladed rotor requries a knowledge of loading harmonics up to the sixtieth. Details of such loadings are not available from theory or experiment. Rotor aerodynamic loadings have therefore been reviewed in detail and empirical harmonic decay laws derived. Loading phases appear to be best described as random, and this introduces simplification in the theory, together with the necessity for definition of a correlation length. Results of a parameter study show trends in agreement with experiment, both for overall levels and for spectrum shape. Sound at the higher harmonics is basically proportional to thrust times disc loading times tip velocity squared. For the lower harmonics the dependence on tip velocity is to the 2B power where B is the number of blades. The effect of forward speed is to increase the sound radiated forward and decrease that radiated aft, causing a difference of as much as 20 dB for the second and third harmonics at a forward Mach number of 0.25. The overall sound directionality pattern is found to have a minimum slightly above the plane of the disc and a broad maximum about 20 ° below. The effects of both the near field and blade motion effects are found to be small. The theory generally shows fair agreement with experiment for overall levels and good agreement for trends, and should therefore be of direct use for design trade-off studies to minimize noise in future helicopters. 1. INTRODUCTION The radiation of noise by a helicopter has caused many problems in both civilian and military operations. In the civil case, high radiated noise levels have prejudiced the very operation which the helicopter is uniquely fitted to perform--city center transportation. In the military field, the far-field noise gives unnecessarily early warning of the helicopter's approach. Internal noise problems are also significant, causing the helicopter to be unattractive to prospective civil passengers and, in the military case, internal noise levels often substantially exceed the accepted hazardous limits. Clearly, there is a considerable need for further understanding of helicopter noise and, hopefully, for new methods to control it. This paper concentrates on the problem of far-field noise radiation by a helicopter, in particular by the helicopter main rotor. The complete study, of which this is a part, is documented more fully in references 1 and 2. 1"An abbreviated version of this paper was presented at the AFOSR-UTIAS Symposium on Aerodynamic Noise, University of Toronto, Ontario, Canada, 20-21 May 1968. :~Now at Dept. Transport Technology, Loughborough University of Technology, Loughborough, Leics., England. 197

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M . V . LOWSON AND J. B. OLLERHEAD

Several studies of helicopter noise have now been performed both from the experimental [3 to 10] and theoretical [11 to 16] point of view. However, it is unfortunately still true that the basic noise problem is far from being solved, or even understood. Initial attempts to predict helicopter rotor noise utilized the analysis built up to describe the noise radiation from propellers [17, 18]. It was inevitably found that, although propeller noise theory was sometimes fairly accurate for the first harmonic of the helicopter rotational noise, it was grossly in error--by over 100 dB in many cases--for the higher harmonics. In fact, propeller noise theory was found to be unacceptable for predicting the higher harmonic sound radiation even for propellers. An obvious possible reason for the discrepancy between propeller theory and helicopter experiments was the existence of large fluctuating forces on the blades in the helicopter case. Unlike the conventional propeller, the helicopter rotor operates in a sideslip mode. The resulting aerodynamic asymmetries give rise to fluctuating airloads reaching frequencies up to many harmonics of the rotational speed. As a result of two detailed computational studies, by Schlegel et al. [15] and Loewy and Sutton [13, 14], the potential significance of these fluctuating airloads is now clear. It is the opinion of the present writers that all the significant higher harmonic sound effects (except possibly at transonic or supersonic speeds) can be attributed to these unsteady loadings. Thus, the object of this paper is to predict the noise radiated by the helicopter main rotor by applying the basic acoustical equations which give the sound radiation from a known fluctuating force distribution. These basic equations were recently derived in a convenient form by Lowson [11, 12]. The problem of predicting the noise radiation then reduces to the problem of predicting the rotor dynamic loads. Two approaches have been used for the noise calculations. One was to perform direct computations of the noise by integrating the airload distribution in the appropriate retarded time co-ordinates. A general computer program, described in detail in reference 2 has been written which enables the sound radiated to be calculated for any combination of fluctuating airload, blade flapping and lagging motion, and helicopter velocity in any direction. The program calculates the sound at any field point and includes all near-field effects. The second approach has been to specialize the problem to far-field radiation which enables analytic results to be obtained, as will be shown below. It is found that virtually all the significant features of the helicopter noise radiation are retained in this analysis. The two independent approaches used have given identical results for equivalent cases, and thus provide a powerful mutual check on the accuracy of both analysis and computer programming. 2. MECHANISMS The noise of a helicopter can aerodynamically and that arising distances from the helicopter, the subjective loudness of the sound, (i) (ii) (iii) (iv)

be roughly divided into two main groups: that arising mechanically. Cox and Lynn [5] found that at moderate various sources, listed in their order of importance to the are:

blade slap (when it occurs); piston engine exhaust noise; tail rotor rotational noise; main rotor "vortex" noise;

(v) (vi) (vii) (viii)

main rotor rotational noise; gearbox noise; turbine engine noise; other sources.

Some of these sources are identified in the UH-1 helicopter noise spectrum shown in Figure 1 which is derived from the results of Cox and Lynn [5]. Since the piston engine is obsolescent as a helicopter power supply, the four major noise sources are aerodynamic in origin and it is with such sources that this paper is concerned. Three "types" of main rotor noise are generally

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HELICOPTER ROTOR NOISE

recognized: blade slap, rotational noise and vortex noise. All three result from the fluctuations and motions of the distributed pressures acting on the blades and, as will be seen later, it is difficult in principle to draw a distinction between them. The differences are in fact more subjective than objective. However, for convenience, they will be treated separately in this introductory description although the similarities will become apparent. In order to understand the cause of these aerodynamic sound sources, it is necessary, first of all, to understand the nature of the rotor aerodynamics. The most important feature of the helicopter aerodynamics from the standpoint of noise and vibration is the rotor wake. Each blade acts in the same way as a wing in flight, and the lift on it generates a vortex wake behind it. This vortex wake has a strong tendency to roll up into concentrated vortices. Each blade must therefore pass over the concentrated vortex wake left by its predecessor. Depending on the exact value of aerodynamic parameters such as advance ratio, net lift force, and so on, this vortex may pass either extremely close to, or far away from, the following blade. If the vortex passes close to the blade then a substantial local increase in lift will occur temporarily. The magnitude of the increase is dependent on such features as vortex strength, inclination, -,& o

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Figure 1. UH-1A external noise spectrum. Derived from reference 5. distance from the blade, and blade chord. These comparatively rapid increments in lift, caused by vortex interaction, are very efficient noise radiators. It appears that a very large part of the observed noise from a helicopter can be attributed to these vortex effects. A particularly severe case of this is well known in helicopter operations under the name "blade slap". It is found that under various conditions, for instance during low power descent, the helicopter produces a particularly loud slapping or banging noise, which occurs at the blade passage frequency. Narrow band analysis of blade slap noise reveals it to be harmonic in nature with the fundamental equal to the blade passage frequency and a large number of significant harmonic components. Blade slap occurs at precisely those conditions where the vortex wake can be expected to pass very close to the rotor, and can be particularly severe on a tandem rotor aircraft where the wake from the first rotor can pass through the second. In fact, the sharpest banging case will occur when the vortex wake interactions cause the flow over a rotor blade to go locally supersonic, and blade slap is thus most severe for high speed rotors. A second form of blade slap can occur on high speed rotors, which correlates with the appearance of supersonic flow on the blades. It may be noted that the description of both these blade slap phenomena is fairly straightforward acoustically and the effects mentioned above can be readily predicted from the theory, as will be shown later. Reference can also be made to the interesting studies by Leverton and Taylor [8].

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M.V. LOWSON AND J. B. OLLERHEAD

However, even in the absence of blade slap the rotor is always undergoing some form of wake interaction, which is generally less severe. The resulting "rotational noise" is still attributable to fluctuating forces acting on the blades and exhibits the same discrete frequency characteristics. But in this case the acoustic harmonic amplitudes decrease more rapidly with increasing frequency (as is shown in Figure 1). The same mechanisms also apply at the tail rotor, which operates in an extremely non-symmetric flow field. It will he observed that the harmonic spectrum shape of the tail rotor noise in Figure 1 is not very different from that of the main rotor, thus suggesting that basically similar mechanisms are at work. The third aerodynamic noise source which has been generally associated with the main rotor is its "vortex noise". Several authors [6, 7, 15] have studied this source, generally assuming it to have a broad-band spectrum and to be basically due to some form of boundary layer phenomenon on the blade. These studies developed from a report by Yudin [19] on the noise radiation by spinning rods. In fact, it appear that the "vortex" noise component, as generally defined for the helicopter case, really represents some of the higher harmonics of the main rotor rotational noise. Figure 2 shows a narrow-band (2 Hz) analysis of the noise from a UH 1B helicopter [9], basically the same helicopter as is analyzed in Figure 1. Figure 2 shows that broadened harmonic peaks at multiples of the fundamental frequency are clearly visible out at least as far as 400 Hz. Thus the spectrum over the range described as vortex noise in Figure 1 is basically a collection of discrete frequencies rather than being broad-band in nature. It may be assumed to arise from the higher harmonics of the rotational noise spectrum. Thus each of the three sources, blade slap, rotational noise, and vortex noise, which are generally considered to occur separately on the main rotor can be regarded as the result of a single cause, the rotor blade/wake interactions. Since the wake is assumed to be periodic the resulting radiated noise is a series of discrete frequency tones at the fundamental and its harmonics. It is this discrete frequency noise radiation from the rotor which is considered in detail in this paper. The basic source for the noise is the fluctuating forces on the blades, and these forces rotate with the blades. Because of the rotation the blades are moving successively towards and away from the observer, and this introduces effects due to a varying Doppler frequency shift. The forces on the blades can be broken down into a series of Fourier components. But, because of the modulated Doppler effect, each loading harmonic can produce more than one sound harmonic, in the same way as strongly frequency-modulated radio signals. Thus the level in each sound harmonic can be expected to be the result of contributions from many loading harmonics. All these effects will be observed in the mathematical analysis presented in the next section. Before commencing the theoretical analysis of the discrete frequency case it is of interest to discuss the actual broad-band noise which must be radiated from the rotor. Figure 2 suggests that its levels are 3 to 5 dB below the frequency peaks out to about 500 Hz. There are three possible causes of the broad-band noise, boundary layer turbulence on the blades, random vortex shedding at the trailing edge, and the interaction of the blade with turbulence in the wake of previous blades. The probable comparative magnitudes of these have been demonstrated convincingly by Sharland [20] from both theoretical and experimental considerations. In a fan noise case studied by Sharland the noise radiation from boundary layer turbulence was roughly 20 dB below that due to the random vortex shedding, which was in turn 20 dB below the noise due to interactions of a blade with oncoming stream turbulence. It is the random vortex shedding at the trailing edge which has generally been assumed to be the predominant source of broad-band noise on the rotor (hence the name vortex noise). However Sharland's analysis clearly suggests that it is the interaction of the shed wake turbulence with the oncoming blade which will be the basic source of broad-band noise for a helicopter rotor, at least at low disc loadings.

HELICOPTER ROTOR NOISE

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202

M.V. LOWSONAND J. B. OLLERHEAD

It is possible to perform analyses of the broad-band case. This is done in reference 1 and also, from a slightly different point of view, by Ffowcs Williams and Hawkings [21]. Both these analyses show how taking account of the Doppler frequency shift, due to the rotation of the rotor, causes a substantial broadening of the input spectrum. Using the results it is also possible to make estimates of the broad-band noise output of the rotor once the statistical characteristics, such as spectrum and cross-spectrum, of the random fluctuating forces on the blades are known. 3. THEORY A detailed description of the theoretical analysis is given in reference 1. Here a more summary approach will be followed. The theory is based on the Lighthill [22] formulation of the wave equation, which can be written ~2 ~

'2 ~2 P

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where T u -- pvt vj + Plj - a02PSu (the acoustic stress), 8u = 1, i = J i = 0, i # j (the Kronecker 5) F~ is the force per unit volume acting on the fluid, Q is the mass source strength per unit volume, and x ~ ( i = 1,2,3) are Cartesian co-ordinates. The usual tensor notation and summation convention are assumed. The right-hand side of equation (1) gives the various possible sources of sound present. In our case, we are interested in the effect of fluctuating forces F~. Now the solution to the wave equation is well known. If the right-hand side of equation (1) is written as g(y), the solution to equation (1) is 1 where p = a fluctuating density, r = the distance from source to observer, and y = the coordinate of the source position; y is bold face implying it is a vector quantity. The square brackets around the g / r term are of extreme importance, since they imply evaluation of their contents at retarded time r = t - r / a o . Also, the solution for the case of the force distribution Fl can be written as [1, 19] -1 0 F, p= Ox, f [T]dy (3) Comparing equations (2) and (3) we see that the solution for the force case may be found from the solution to the simple source case [equation (2)] by differentiation after an integration of a simple source strength F~ over the appropriate retarded co-ordinates. This approach is particularly convenient in the present case. Consider now the case of radiation from a point force rotating at angular velocity ~, radius R, as defined by the co-ordinate system in Figure 3. We use Cartesian co-ordinates x, y, z, with x along the rotor axis. The observer is located a distance Yfrom the x axis, so that the reference angle between the observer ( Y axis) and the y axis is ¢ (see also Figure 2). Vee wish first of all to define the Fourier coefficients of the sound radiation due to a rotating simple source, which requires multiplication by exp(inOt) and integration at the observer's time t. Since the source is moving we can transform to appropriate source co-ordinates r/ using, as first shown by Lighthill [22] (see also reference 1), vI = y + Mr, d~ --- (1-Mr) dy where Mr is the component of convection Mach number in the direction of the observer. We also transform to source time ~- by ~ = t - r / a o and dt = Or (1 - M r ) . These two co-ordinate transformations have cancelling effects so that the final result for the complex magnitude of the nth sound harmonic is

2~r On= 47r21.]1"[g] exp in(O+ £2r/ao)dO o

(4)

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HELICOPTER ROTOR NOISE

where 12r has been replaced by 0. Then, defining the source term g by a complex Fourier series +o0

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Since the integral applies over any interval 27r it can be expressed in Bessel function form, using formula 42 in McLachlan [23], so that c,=~

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Equation (7) gives, in complex form, the sound harmonics from a point simple source describing a circular path. The equation could be applied directly to the calculation of rotating mass

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Circumferential:

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(8)

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M . V . LOWSON AND J. B. OLLERHEAD

The prime on the Bessel function in the radial expression denotes differentiation, M ~- QR/ao is the rotational Mach number of the point force. Negative signs must be applied in the first two equations because differentials are based on observer co-ordinates whereas the differential on the last equation is on a source co-ordinate. Notation in equations (8) must now be changed to specify the forces acting. Defining the three components by simple Fourier series

T(O) = a0r + ~ aarcosA0 + bar sin2t0,

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D(O) = aoo + ~ aao cos )tO + bao sin)t0,

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Outward components: C(O) = aoc + ~ aac cos)t0 + bac sin 2t0. A=I

The thrust, drag, and outward components of force are assumed to act in the axial, circumferential, and radial directions, respectively. In conversion to thrust, a minus sign must be incorporated because the force on the air is in the negative x direction. Equations (8) are converted to the required form using equation (9). Note that terms for both plus and minus 2tin the summations in equations (8) contribute to the result for any given loading harmonic. Thus, the final result for the complex magnitude of the sound harmonic is

c, = a, + ib,,

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nOx (+taar(Jn_ . a + (-1) aL+a) - bar(Jn-a - (-1)aJ~+a)}

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ng2Y{aac(J~-a + (-1)aZ+a)+ tbac(J;_a" ' - (-1)aJ,~+a)}} . ' + aorj

(I0)

The argument of all the Bessel functions is nMy]r~. Equation (10) gives the desired result for the sound radiation by a rotating three component fluctuating point force. Putting 2t = 0 in the above equation gives the result for the steady loading only as

(i)-n+In~IXTo~}Jn(nm,]

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i-nnO YCo{ [nMy~ j (nM,~] 2rraor 1. 2r I Jn-,~-~l ] - ,+i\ r, /1"

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The first term in the above equation is identical with the classical propeller noise solution due to Gutin [15] while the second, radial component term, is the same as that derived in reference 12. The general solution [equation (10)] also agrees with results obtained by different methods by Morse and Ingard [24], Arnold et al. [25] and Lowson [26]. One important effect not explicitly given in equation (11) is the effect of blade number. IfB blades are present, harmonics which are not integral multiples orB will cancel out. Those harmonics which are multiples of B will add. Thus the effect of blade number may be included in equations (10) and (11) by replacing n by roB. In this ease the coefficients of the force harmonics must be taken as the values for the complete rotor, which are B times the values for the individual blades. The effect of forward velocity is also of considerable interest. In reference 11 it was pointed out how the equations for constant velocity convection of the hub could be obtained from

HELICOPTER ROTOR NOISE

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those for the stationary case by replacing the term rl in the stationary case by rt(1 - Mot) where M0, is the component of the hub convection Mach number in the direction of the observer. In utilizing this transformation it is important to note that it applies to the retarded position of the helicopter. In other words the dimension r t used must be taken as the distance from the observer to the position of the helicopter when it emitted the sound. Relation of the results to the instantaneous position of the helicopter requires another transformation, discussed in reference 1 and 2. Also, in reference 26 it was shown that the above (1 - M0t) correction term gave the Garrick and Watkins [18] moving propeller result directly from that of Gutin [17] for the stationary case. 4. AERODYNAMICS In order to estimate the noise radiation from a helicopter using equation (10), it is necessary to define the magnitudes of the fluctuating force harmonics which act on the rotor blade. As was discussed above, these fluctuating loads are dominated by the effects of the vortex wake interactions. Unfortunately, it is extremely difficult to make any realistic estimate of the wake dynamics, and consequently almost impossible to predict the resulting fluctuating forces on the blades. In reference 1 a detailed study of the basic performance equations was made, and it was shown that even predictions of the second harmonic airloads were seriously in error when compared to experiment. Several workers have attempted to construct detailed computer solutions of the blade/wake system. Although such approaches have given some of the same trends as experiment, it is certainly true to say that no sufficiently detailed prediction of the airloads is yet possible via the computer. Furthermore, such approaches are found to require excessive computer time. A discussion of some of the problems associated with this approach is given by White [27]. Thus, in the present work a simpler method was sought. Experimental data on the first ten harmonics of the fluctuating airloads are available in reports by Schieman [28] and Burpo and Lynn [29]. Some of these data are shown here in Figures 4 and 5. Figure 4 shows harmonic sectional lift as a function of harmonic number, based on Scheiman's data. The data are shown on a log-log plot, and the mean (steady) sectional lift is also shown plotted at ?~-- 1. The remarkable thing about the data in Figure 4 is that advance ratio/~ (the forward speed divided by the tip speed) makes so little difference. The general trend in each plot is the same. Simple arguments based on basic rotor aerodynamic theory suggest that harmonic levels should increase with advance ratio. It is clear that this does not occur to any marked degree although there is some evidence of increased higher harmonic loadings for small advance ratios (/~ ~ 0.05). Thus, even in hover, the helicopter rotor is very far from acting like a propeller. One possible reason for this is the predicted instability of the helical vortex wake for axial advance ratios below 0.3 [30]. From the present viewpoint the data offer a useful simplification, in that effects of forward velocity may apparently be ignored in estimating the harmonic airloads. Available experimental data include harmonic amplitudes up to the tenth. In order to extrapolate these results to higher frequencies, "power laws" based on some harmonic are very helpful. That is, a relationship is assumed for the harmonic amplitude La of the ~th harmonic of the form L~ = LA(~ -- A) -~ where LA is the amplitude of the Ath harmonic (A _<)~).Two possible laws are shown in Figure 4. The dashed line gives a power law based on the second harmonic loading (A -~ 2), and the solid line one based on the steady loading, plotted at the ~t-- 1 point. It will be observed that the second harmonic power law gives some variation in slope, while the law based on the steady loading gives a fairly constant result, close to a "6 dB per octave" fall off. Thus an inverse square power law based on the steady loading has been chosen in the present paper to give the predicted noise levels. Figure 4 shows

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/,!. V. L O W S O N A N D J. B. O L L E R H E A D

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Figure 4. Rotor loading harmonic laws at various advance ratios. Data from Scheiman [28]. (a) Hover (V=0, / z - 0 ) (Table 4); (b) V=42 kt, F =0.112 (Table 8); (c) V=66 kt, F=0.20 (Table 11); (d) V= 112 kt,/~ = 0.3 (Table 2). that such a law is in reasonable agreement with the data for clean flow cases, except for the = 1 case which is consistently overestimated. Since the ~t = 1 loading does not contribute significantly to the more important higher harmonic levels, no modification to the simple basic power law was thought to be justified at this time. Figure 4 gave some further loading results plotted in the same way. Figure 4 gives results for a four bladed CH-34 helicopter, from Scheiman [28]. Figure 5(a) and (b) gives results for I00

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Figure5. Further data on rotor loading harmonic laws. Clean flow data from Burpo and Lynn [29]; rough running data from Scheiman [28]. (a) V=92 kt, tz=0-216; (b) V= 111 kt, /z=0.260; (c) level flight in ground effect V= 27 kt (Table 27); (d) partial power descent VD= 80 ft/min (Table 8).

HELICOPTER ROTOR NOISE

207

a two bladed UH-1A helicopter from Burpo and Lynn [29]. It will be noted that the basic power law trends noted in Scheiman's data are repeated here. This enables a little more confidence to be placed in the power law as a general prediction method for all helicopters. Figure 5(c) and (d) shows some rough running cases, again from Scheiman. It will be observed that the levels of the higher loading harmonics have definitely increased here compared with the steady cases described above. Thus, the power laws based on the second harmonic substantially increase in order. Possibly an inverse first power based on the steady would be an adequate description, although it is clear that no accurate general prediction method is feasible at the present time. Even for the steady cases in Figure 4 it will be observed how, for instance, the third harmonic in Figure 4(b) and the sixth in Figure 4(c) are much higher than expected. These small differences in loading harmonics must be reflected in small differences in the sound field in a real case. In fact, it is very probable that these instantaneous loadings vary considerably along the blade span. Peak loads are basically due to the close proximity of a wake vortex. As the blade passes over a vortex the intersection point will also move along the span. This is discussed in more detail in reference 1. One possibility of particular interest is that the intersection point velocity, and thus the velocity of the major pressure disturbance on the blade, can move across the span at supersonic speeds, and could thus be a particularly efficient radiator of sound. Such an effect is not included in the present work. In reference 1 the harmonic levels along the span were studied, and it was found that levels of the higher loading harmonics were greater at the tip than at the root. However, it seems that the inverse square law for loading harmonics still gives the best single approximation for this overall blade. A further important effect is that of phase. Consider first the effect of the phase between the loading harmonics. Referring back to equation (10) note that the phase is dependent on the parameter i-~"-a). Thus the same phase input (i.e. ratio of aa to b~) of the load coefficients will result in acoustic outputs which are 180° shifted for every two loading harmonics. Now at the high values of A there will be little difference in magnitude between successive odd or even harmonics, and their acoustic effect would therefore cancel if they had the same phase. Unfortunately available data do not give any useful information in the loading phase. Clearly the effect described above is unrealistic, and it is more appropriate to assume a random phase angle between harmonics. If this is done then the sums of the squares for each loading harmonic input may be added directly to give the observed intensity. An equivalent effect occurs with respect to the loading along the span, again discussed in more detail in reference 1. In view of the vortex intersection effects discussed above, it would not be correct to assume that the higher harmonic loads were in phase across the whole blade span. Thus, it becomes necessary to incorporate a correlation length in the loading specification to enable the acoustic predictions to be made. It seems probable that correlation length will be inversely proportional to loading harmonic order (A). It will be assumed that the nondimensional spanwise correlation lengthis numerically equal to ?~-x.Recalling that the acoustic intensity is proportional to the pressure squared, and thus to the force input squared, it will be seen that this correlation assumption amounts to an additional -0.5 power in the harmonic loading law. Thus if the local loadings are falling in magnitude as A-2, then the effective loading law including random effects is )~-2 5. 5. R E S U L T S A N D D I S C U S S I O N

Computations have been made based on equation (10), and Figures 6 to 8 show results for the effect of single loading harmonic of the same amplitude at various input frequencies. In all the present work the ratio of thrust:drag:outward components has been taken as 10:1:1. This is representative. Figure 6 gives the effect of the various loading harmonics on the sound

208

M . V . LOWSON A N D

J. B. OLLERHEAD

for a four-bladed (B = 4) rotor at a point 10 ° below the rotor disc at a rotational Mach number M - 0.5. The same general features may be observed in each of the harmonics plotted. Only a limited range of loading harmonics contribute. Take, for instance, the fourth sound harmonic (m = 4) in Figure 6. Loading harmonics below the eighth can be seen to produce little noise. Between the eighth and twenty-fourth the sound produced varies, but is of roughly

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the same order of magnitude, while beyond the twenty-fourth loading harmonic the sound radiation falls away rapidly. Thus, it may be concluded that on a real helicopter rotor, when all loading harmonics can contribute to the observed noise, loading harmonics between the eighth and twenty-fourth must be included to obtain an accurate calculation of the fourth harmonic. I10~

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Figure 7. Effect of field position on contribution of loading harmonics to fourth harmonic sound. , 0 ° from rotor disc; ,10 ° from rotor disc; . . . . . ,60 ° f~llm rotor disc; . . . . . . ,80 ° from rotor axis; e, rotor axis. This effect may be understood by reference to equation (10). There are two basic terms in this equation, the J , - a and the J,+a. F o r values typical of the helicopter problem, the J,+a terms can be ignored (except perhaps for the low harmonic noise). N o w n = m B where m is the harmonic order and B is the number of blades. Thus as the loading harmonic ~ increases, the order of the Bessel function n - ~ will decrease, eventually becoming negative. For example, for m = 4, B = 4; n - )t -- 6 for)~ = 10 (the tenth loading harmonic) and n - ~ = - 6 for )t = 22. Since the absolute value of a Bessel function with a negative order is equal to the value of the Bessel function with positive order, we expect the results for the ~ = 10 and 22 cases to be the

209

HELICOPTER ROTOR NOISE

same for the fourth harmonic case. Inspection of Figure 6 will show this to be so. Indeed it will be observed that each curve in Figure 6 is symmetrical about A = mB, which corresponds to A = 16 for the fourth harmonic. Figure 7 shows the effect of the loading harmonics as a function of field position. Figure 6 applied 10° from the plane of the disc. Figure 7 shows how, as the point of observation is moved away from the disc plane towards the rotor axis, the number of loading harmonics contributing to a specific acoustic harmonic reduces. Indeed, in the limit immediately under the rotor disc only the single loading harmonic A = m B contributes. The effect may again be understood by reference to equation (10). The argument of the Bessel function terms includes the factor y/r. Thus moving away from the rotor disc reduces the magnitude of the argument and hence the range of effectiveness of the loading harmonics. In the limit when y/r = 0, then only the Jo term has a finite value, equal to unity. The increase in amplitude of the loading harmonics on moving toward the rotor axis may also be understood by reference to equation (10). The thrust term, which dominates the results, is multiplied by x/r. Moving towards the rotor axis gives increasing values of x/r, and accounts for about a 51 dB increase between the 10° and 80° cases. The remaining increment comes from the increasing peak magnitude of

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Figure 8. Effect of Mach number on contribution of loading harmonics to fourth harmonic sound. the lower order Bessel functions. The fact that sound radiation immediately under the helicopter rotor is dependent on a very limited range of loading harmonics may be of some potential significance in naval applications. However, it should also be noted that, immediatelyunder the helicopter, the refractive effects of the downwash can also be important. The key requirement now is to be able to predict which loading harmonics are necessary for the acoustic calculation of any given sound harmonic. From considerations of the basic features of Bessel functions, it is possible to show that the range of interest of loading harmonics is roughly roB(1 - M ) < )t < roB(1 + M )

(12)

where M is the rotational Mach number. The accuracy of this equation may be checked on Figure 6 where M = 0.5. The equation will be found to be conservative when applied to Figure 7 for points removed from the rotor disc. In fact here the formula roB(1 -- My/r) < )t < mB(1 + My/r) can be used if desired. However, for general purpose calculations, equation (12) is appropriate. Figure 8 shows the effect of rotational Mach number on the noise radiation. It will be observed that the range of loading harmonics which contribute to the noise is substantially increased as Mach number increases. Again the effects are those given by equation (12). Figure 9 gives a plot of equation (12) and may be used to determine the range of 15

210

M. V. L O W S O N A N D J. B. OLLERHEAD

loading harmonics necessary for accurate calculation of any given noise harmonic. Previous studies [ 13 to 15] necessarily used very limited ranges of input harmonics, and this clearly goes a considerable way to explaining the low values of the higher sound harmonics computed in these investigations. I°°1

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Figure 9. Range of effective contribution of loading harmonics to sound radiation. Figure 10 shows the contribution of the three force components to the overall sound pressure. The proportions of components used in this and all the other calculations of the parameter study is thrust: drag: outward component = 10:1:1. It will be observed that in the inefficient region of radiation (well down the shoulders of Figure 10) the effects of all three components are about equal. However, over the efficient radiation range the thrust dominates.

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Figure 10. Contribution of force components to fourth harmonic noise 10° below rotor disc at rotational Mach number M = 0.5. - - - , Total; - - - , thrust; . . . . . . , drag; . . . . , outward. The substantial movement of the plots between successive harmonic levels corresponds to moving past lobes in the sound patterns, as will be discussed in more detail later. Note how the T a n d D terms move together, but in antiphase to C. Thus the curve for overall level shows less magnitude of excursion. The drag term is very inefficient in the central region. This is the effect of the (n - ;~) multiplier in equation (10). For most practical purposes it would appear to be a good approximation to consider the thrust term only. The other terms only contribute

HELICOPTER ROTOR NOISE

211

significantly directly in the plane of the rotor disc and in the inefficient radiation region, for instance, the steady loading contributions at low rotational Mach numbers. In reality, of course, the observed sound field is composed of the contributions of many loading harmonics. The key problem is, therefore, to estimate the magnitude and phase of these. In section 4 it was concluded that the amplitude of the loading harmonics should be taken to vary as an inverse power of the harmonic number. Random phase was also assumed together with a correlation length. In order to study the effects of various harmonic loading laws, Figure 11 has been prepared. The figure corresponds to a summation of the results like those presented in Figure 6 with an appropriate weighting according to the harmonic loading inverse power law applied. The first 60 loading harmonics are summed for each point. The results apply for a four-bladed rotor 10° below the rotor disc. Figure 11(a) gives the results of the zeroth power law case, which corresponds to the direct summation of all the harmonic levels with equal weighting. Note how the noise is predicted to go up with harmonic order, actually rising at 6 dB per octave. Because of the limited number (60) of loading harmonics used, the present calculation loses accuracy above a sufficiently high sound harmonic. Referring to Figure 9, it may be predicted that accuracy will be lost beyond about the eighth, ninth and tenth harmonics for M = 1.0, 0.75 and 0.5, respectively. Figure 11(a) shows how this is indeed true. The effect of Mach number is also shown in Figure 7(a). It will be observed that the effect of Mach number is small for this zeroth power case. This is consistent with the effects noted in Figure 8, where increase in Mach number gave an increased range of loading harmonics, but not a major increase in amplitude of the typical sound radiated by a single harmonic. Figure 1l(a) also gives the results of assuming only a steady loading. This corresponds to the classic propeller noise calculation [17]. Note how the increase in Math number has a very pronounced effect on the noise radiation by the steady loading. The same effect may be observed by studying the intercepts of the various curves in Figure 8 with the vertical axis. Figure 1l(b) to (d) gives the results of assuming other loading harmonic power laws. In each case the loading harmonics have been derived from the zeroth by using the appropriate inverse power law, as shown. (The first and zeroth loading harmonics always have equal magnitude.) In each figure the result for steady loading only is also shown. This may be considered as the result for the minus infinity power law for loading harmonics. The inverse first power law case is shown in Figure 1l(b). For M = 0.5 and 0.75 the result is very closely a constant sound level for all harmonics. This would correspond to an impulsive type of noise (blade slap). Since an inverse first power law was suggested in section 4 for the rough running cases it can be seen that blade slap is predicted acoustically for those cases where it would probably occur. For M = 1.0, the sound rises with frequency. Thus, for transonic flow cases, an impulsive type of noise corresponding to a blade slap condition is again predicted. In this way blade slap due to either vortex interaction or to compressibility effects is predicted by the theory. It appears that the observed levels in Figure 1l(b) at M = 1.0 are basically due to steady loading effects, with fluctuating forces playing a minor role. Figure 1l(c) shows the inverse squaer law loading results. Here the curves drop off more rapidly with increase in sound harmonic and rotational Mach number has a more significant effect. Also, it can be seen that the M = 0.75 case is governed by the steady loading for the first five harmonics, and only above this is there any significant effect of the fluctuating loads. It may be noted that, because of the markedly reduced effect of the higher loading harmonics in this inverse square loading law, the inaccuracies introduced by the limitation to 60 loading harmonics disappear, and Figure 11(b) is probably accurate out to the sixteenth sound harmonic. The inverse third power law results given in Figure 1l(d) shows all these effects to an even greater degree, with the steady loading dominating the M = 0.75 ease out to about the twelfth harmonic and the M = 0.5 case out to the fourth. It should be noted that even in this M = 0.5 ease the fluctuating

212

M.V. LOWSONAND J. B. OLLERHEAD

loads still dominate the subjective response since the first few sound harmonics are below the range of hearing. The same general effects as shown in Figure 11 occur at all positions in the helicopter disc, although the effects of the lower loading harmonics are markedly reduced nearer the rotor axis. The limiting law for the higher harmonics is given by an approximate argument [1] as p2 ~(mB)2+2k where k is the exponent of the loading law. Thus, for 0, -1, - 2 and - 3 power laws, the sound in the higher harmonics falls off at the +2, 0, - 2 and - 4 power, respectively. This may be observed at the higher harmonics shown in Figure 11. These laws may be used to extrapolate to the highest harmonics as necessary. Figure 12 shows the effects of forward velocity on the sound output. Its effects have been calculated via the method suggested at the end of section 3, multiplying all r terms by (1 - M0,) where M0, is the component of the hub convection Mach number in the direction of the observer. The results also include a transformation to give the sound in relation to the instantaneous rather than the retarded position of the helicopter. Because of the (1 - M0,) 120,

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Figure 11. Effect of loading power laws on sound radiation 10° below rotor disc in hover. , M = 1.0; - - - , M = 0.75; • ., M = 0.5. (a)Zeroth power law for loading harmonics; (b) inverse first power law for loading harmonics; (c) inverse square power law for loading harmonics, (d) inverse cube power for loading harmonics. term the maximum effect of velocity is observed when the helicopter is flying toward or away from the observer while, when the helicopter is flying at right angles to the observer's line of sight, the convection Mach number component is negligible. In Figure 12 both forward and aft radiation cases are given, together with the zero velocity condition which thus also corresponds to the sideways radiation. As before the effect of steady loading only is given in each case as a reference. In each case the forward radiation is higher than the aft. For the zeroth loading law [Figure 12(a)] little change is noticeable, but for the steady loading alone the forward velocity has a substantial effect. For the 0.25 forward Mach number case, the sound due to the steady loading alone is increased by over 50 dB in the forward direction compared to the aft. Plots of the other loading law cases in Figure 12 show that in each the sound is increased in the forward and reduced in the aft directions. Similar plots for other rotational and forward Mach number cases show the same general effects (see reference 1). The effects of forward velocity noted on Figure 12 are very similar to the effects observed simply due to change in rotational M a t h number (compare with' Figure 11). This suggests that it may be possible to estimate the effects of forward velocity simply by choosing an effective rotational Mach number for the forward speed case.

213

HELICOPTER ROTOR NOISE

It is shown in reference 1 that if instead of replacing r by r (1 - Mar), the rotational Mach number M is replaced by an "effective Mach n u m b e r " M/(1 - Mo,), which can be calculated for any particular field point, the true effects of forward speed are approximated to within 1 dB near the plane of the rotor disc. This technique leads to several simplifications in noise prediction methods and also suggests a possible method for comparing experimental data. The direction in which the sound radiates is important in determining its significance. Under the randomizing approximations used in this paper, no variation in sound pressure around the azimuth occurs. Little variation is actually observed in practice. The small differences in sound pressure measured could easily be due to experimental error or the effect of the tail rotor. Azimuthal variations would be predicted if a definite phase for the various loading harmonics was introduced into the calculation, and equation (10) could be used here. But under the random phase condition assumed in the present case such variations are not possible, and the sound field is circularly symmetric. On the other hand distinct variations in sound level are predicted on passing above or below the helicopter disc. Figure 13 shows the directionality patterns due to various individual 120 I

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Figure 12. Effect of forward velocity (Mr = 0-25) on sound radiation 10° below rotor disc. Rotational Mach number M = 0.5. ~ , Hover; . . . . . , forward; . . . . . . , aft. (a) Zeroth power law for loading harmonics; (b) inverse first power for loading harmonics; (c) inverse-square power law for loading harmonics (d) inverse-cube power law for loading harmonics. force components. All plots are based on a single point loading, with the observer a constant radius from the hub and have been non-dimensionalized so that rotational Mach number effects only enter through the frequency parameter mBM. The zero dB line on all plots corresponds to the average sound power radiated, so that the plotted curves give the correction factor (directivity index) to be added to the spherical spreading law to give the sound in any direction. The dotted lines on the plots correspond to contours of equal ground noise. As the helicopter flies over the ground the sound radiated fore or aft has to travel much further before striking the ground than the sound radiated immediately downward. Over this additional distance the sound will attenuate according to the inverse square law. The dotted lines on the figure allow for this spherical spreading, assuming that the rotor disc is parallel to the ground. Thus sound levels lying on the same dotted lines will be observed as the same level at the ground. The plots in Figure 13 are given in the first quadrant, but are entirely symmetrical so that sound radiated up equals sound radiated down in magnitude. In each of the plots the same general effects can be observed. For large values of m B - 2, and low frequencies (mBM) the sound radiation pattern is substantially outwards, in the plane of the disc. This is, of course, particularly disadvantageous, but it should be noted that the overall sound efficiency in these cases is poor, with sound levels well down the shoulders of

214

M.V. LOWSONAND J. B. OLLERHEAD

the curves in Figure 6. On the other hand, these cases essentially correspond to the effect of low harmonics of the loading, which are generally of greater magnitude. As frequency is increased, or as m B - A is decreased, the peak of the directionality pattern moves around towards the axis of rotation, and the patterns have a stronger and stronger lobe structure. All the cases with a lobed structure correspond to efficient acoustic radiation, with levels across the top of the curves in Figure 6. It m a y be noted that increase in rotational Mach number M corresponds to a movement from left to right in each directivity matrix given. mBM=2

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- 3°-zo-I° o +10-~SZ'0-100+tO-30-26100 ÷10-~ZO-~00+~0 Figure 13. Directionality patterns of various loading components. However, an increase in harmonic order m or blade number B corresponds to a movement both across and down (at least for the lower loading harmonics A) since mB occurs as a parameter on both axes. Individual comparison of the plots in Figure 13 shows that all the thrust terms go to zero along the rotor disc. This is the effect of the x/r term on the thrust in equation (10) and x - 0 at the rotor disc. Note also that all harmonics of all force components go to zero at the rotor axis except for one case. That is the thrust component for rnB - A = 0 which has a maximum there. Thus only the single loading mode ;t = rnB contributes immediately under the helicopter. This was also observed in Figure 7. The drag terms shown in Figure 13 have the opposite effect. All m B - A = 0 cases are virtually zero. This can also be seen in Figure 10. This occurs

HELICOPTER ROTOR NOISE

215

because of the m B - A multiplication factor in the drag term of equation (10). Note that there is also an m B + A term which does not go to zero, but this is so small as to be negligible in virtually all cases. Also its relative magnitude is a function of roB and A separately rather than the single term m B - A. Thus no case corresponding to m B - A = 0 has been plotted on Figure 13 for the drag component. The m B - A multiplication factor has another effect. When )~ is greater than m B it goes negative. The amplitude of the negative cases is the same as the equivalent positive case, but the phase has been shifted 180° with respect to the thrust. Hence, the drag terms add to the thrust terms below the rotor for positive m B - ~ and subtract for negative. Since the thrust is dominant the effect is of little practical importance, but this does explain the asymmetries near the plane of the rotor disc in Figure 14, to be discussed later. The same general effects can be observed on the outward components of force terms. These terms become significant slightly nearer the rotor axis than the thrust and drag terms for any given harmonic. Note that all the zeros in the thrust and drag terms are matched by maxima in the outward terms, and vice versa. This is due to the outward terms containing the differential of the Bessel function term used in the thrust and drag expressions. The lobed sound patterns given in Figure 13 are idealizations, and are unlikely to occur in practice for two reasons. First, the random effects discussed before will rarely allow such an ordered pattern to occur. Second, and far more important, the observed sound level is, of course, the sum of the contributions from all loading harmonics. The effects of any one harmonic will usually be lost in the overall pattern. Figure 14 gives a polar plot of the overall sound radiation field. It is based on a 2.5 inverse power law for the loading harmonics as was suggested in section 4. Figure 14(a) gives the hover case. Here the sound field is symmetric on both sides of the rotor axis, with a maximum at about 20 ° below the rotor disc. A minimum occurs above the rotor disc which is at about 10° for the first harmonic, and moves towards the rotor disc for the higher harmonics. The minimum is basically due to the cancellation between the thrust and drag terms above the disc as familiar in propeller noise theory [17, 18]. Below the rotor disc, away from the minimum, the sound field is fairly uniform, and in the higher harmonics, only varies a few dB from a spherical distribution. The results shown on Figure 14 are, of course, very dependent on the randomization and harmonic loading laws assumed. On a real helicopter rotor it must be expected that particular combinations of loading harmonics will occur depending on the flight condition. This will be reflected in a much stronger lobe structure. Furthermore, particular phasings of these loading combinations can give azimuthal variations in sound level. However, Figure 14(a) should reflect the basic trends. Figure 14(b) and (c) gives results for forward flight cases. Sound is given relative to the position of the helicopter when the sound is heard, as before. The two parts of the figure show how forward flight causes a general swelling forward of the sound field. Details of the minimum also vary somewhat with forward speed, but this is of comparatively little significance. In both forward flight cases the maximum effect is observed in the plane of the disc, and also for the second and third harmonics plotted. For a forward Mach number of 0.125 [Figure 14(b)] the difference between the forward and aft radiation amounts to about 5 dB for both the first harmonic and for the higher harmonics, but up to 10 dB for the second and third. At a forward Mach number of 0-25 [Figure 14(c)] the corresponding figures are 10 dB and 20 dB, respectively. For harmonics higher than the tenth (not shown here) the differences are slightly less. The results discussed so far are all based on the far-field approximation of equation (10). As was mentioned in the introduction, a comprehensive computer program [2] has also been written for direct computation of the sound field. It is interesting to compare the results from the computational and analytic solution. Figure 15 gives the results calculated at 25 and 1 diameter for the first harmonic sound from a four-bladed rotor with point steady lift

216

M.V. LOWSONANDJ. B. OLLERHEAD

and drag loading at 0.8 span. The levels for the two cases have been normalized using the spherical spreading law. The far-field results (25 diameters) agreed with those calculated using Gutin's equation to within a fraction of a dB at all points which verifies the accuracy o f the program. At one diameter it can be seen that the biggest influence of the near-field effects occur above the rotor although the absolute levels are still slightly less than those which occur below the rotor. It seems that in addition to smoothing out the lobes the near-field pressures are more evenly distributed about the rotor plane than is the radiated sound. In (a)

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120~ ~ / _ 60 105 90 75 Flight d i r e c t i o n :) Figure 14. Sound patterns beneath rotor for various harmonics. (a) Hover; (b) forward speed Mach number = 0.125; (c) forward speed Mach number = 0-25. this case the maximum amplification in the near field occurs 10 ° above the disc and is equal to 27 dB. This corresponds to the position where the thrust and drag components cancel in the radiation field. However, below the disc the maximum difference is approximately 4 dB. Figure 16 illustrates the decay of the near field effects with increasing distance for the first three harmonics. Three curves are shown in each case. The first is the radiation field which can be seen to decay at 6 dB per distance doubling. The second includes geometric near field effects; i.e. the effects caused by the spatial distribution of the source at distances of the order o f the extent of the source. The third includes both geometric and acoustic near field effects. It should be noted that the latter effects actually mitigate some of those of source geometry for

217

HELICOPTER ROTOR NOISE

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218

M.V.

LOWSON

A N D J . B. O L L E R H E A D

Further computations were performed to evaluate directly the effects of the point loading approximation used elsewhere in this study. Figure 17 shows the results. It is particularly interesting that the errors introduced at high frequencies are small, and even for the second harmonic are only 2 dB. Previous studies have always investigated the effect of spanwise distribution on loads which are in phase across the blade, and found more significant effects. However, in the present case it seems that the randomizing assumptions used have removed any justification for using more than a point loading approximation, particularly when it is recalled that it is the higher harmonics which are of principal importance in helicopter audibility. Additional computational and analytic studies were performed on the effects of blade motion, but these were found to be very small (less than I dB).

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6. COMPARISON OF THEORY AND EXPERIMENT Little reliable data on helicopter noise is available, so that comparison with experiment has necessarily been limited. However, in general, agreement with experimental trends has been found. As discussed in section 4, an appropriate loading harmonic power law for a helicopter rotor in clean flight, including correlation effects, is -2" 5. Using this approximation, the rotational noise spectrum for the Bell UH-1 helicopter has been calculated for comparison with available measurements [5, 9]. The random phase assumption was used and 60 loading harmonics were included. The comparison is shown in Figure 18. The experimental data were obtained on three separate occasions under very different conditions and show remarkable consistency. Because of uncertainties regarding the overall levels, they have been normalized on the basis of the third and higher harmonics. This step reduces the probability of error due to the low-frequency response of the microphones and tape recorders which is certainly poor at the fundamental frequency (around 10 Hz). Although for this reason nothing can be said about overall levels, the agreement, insofar as spectral shape is concerned, is good right up to the 30th harmonic. Note particularly that this includes frequencies well out into what is usually described as its "vortex noise" regime. Stuckey and Goddard [7] recently presented new acoustic data on a rotor tower test. Their 50 ft diameter rotor was only 20 ft from the ground, and vortex reingestion with consequent increases in noise level is to be expected. Their data are unlikely to be representative of hover out of ground effect, but may be applicable to lift-off maneuvers. The harmonic level varies

HELICOPTER ROTOR NOISE

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220

M . V . LOWSON AND J. B. OLLERHEAD

rotor). Thus a significant change in spectral shape is predicted at going from low to high tip speeds with lower harmonics becoming more important, as was observed in Figure 19. The theory also predicts a favorable effect of blade number increase on noise for a single-rotor vehicle. This possibly explains the lower "vortex" noise levels predicted by Schlegel et al. [15] and compared to Davidson and Hargest [6]. See reference 1 for discussion. A comparison between theory and experiment in the hover is shown in Figure 20, which gives data (and also theory) from Schlegel et al. [15]. Fairly good agreement is achieved, at least for the first three harmonics. The fourth harmonic is a little low. It will be observed that the present results are higher than Schlegel's theory. This is partly due to the inclusion of a higher number of loading harmonics in the present calculations. Figure 9 shows that for the present case (rob = 16, M = 0.5) to up to 24 loading harmonics are required for accurate calculations. Schlegel et aL used Scheiman's data [28] which is limited to the first ten loading harmonics. Results at higher harmonics would be very significantly lower in Schlegel's calculations. IOOi "1o £k/ O O

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Figure 20. Comparison of theory and experiment for H-34 helicopter at 80 knots. I = Measured data [15]; [] = theory--Gutin [16]; o = theory--Schlegel [15]; zx = present theory. 250 ft range, 500 ft altitude. A further comparison between the present theory and the experimental results of reference 15, this time for a forward flight condition, is shown in Figure 21. This applies to the same S-58 (CH-34) helicopter in level flight at an altitude of 200 ft and a velocity of 80 knots. The microphone was located 250 ft to starboard of the aircraft line of flight. The theoretical results were calculated using the simplified technique, mentioned previously, in which forward speed effects are accommodated through the use of an effective rotational Math number. This approach in fact enables the results to be calculated by hand from a set of normalized curves generated by the computer program. For comparison the computed results of Schlegel et aL [15] are also included in Figure 21, and it can be seen that the present theory gives good agreement for the first three harmonics. For the fourth harmonic the present theoretical curve, although still somewhat low, is substantially nearer to the experimental results; again almost certainly because of the inclusion of a much greater number of loading harmonics. Thus, the theory has been fairly successful in predicting experimentally observed trends. Perhaps it should be noted that other overall level comparisons made during the study were not always as successful as those shown in Figures 20 and 21. However, predictions of experimental trends and spectral shapes were generally good in "clean flow" cases. The most interesting finding is that the use of somewhat idealized blade loading laws has led to close comparisons with previous theoretical work for the lower harmonics. At the higher harmonics, where previous predictions have been deficient due to the omission of important loading

HELICOPTERROTORNOISE

221

harmonics, the technique led to very substantial improvements and available data suggest that the approach is valid at least up to 400 Hz or so. Perhaps more important from a practical viewpoint is that the random phase assumptions result in a much less sensitive dependence on field point location. IO0

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d a t a [15];

In conclusion, it appears that significant improvement in prediction accuracy will require an order of magnitude improvement in present knowledge of the fluctuating airload distributions. Nevertheless, the present methods appear to be of considerable value for predicting helicopter rotor noise, and can be used directly in trade-off studies to minimize noise during design. ACKNOWLEDGMENTS The authors would like to thank R. B. Taylor and Mrs. M. R. Setter for their programming work in this study. The investigation was partially supported under Contract DAAJ02-67-C-0023 by the U.S. Army Aviation Materiel Laboratories, Fort Estis, Virginia. REFERENCES 1. M. V. LOWSONand J. B. OLLERHEAD1968 Wyle Laboratories Research Staff WR 68-9. Studies of helicopter rotor noise. 2. J.B. OLLERHEADand R. B. TAYLOR1968 WyleLaboratories Research StaffWR 68-10. Description of a computer program for helicopter noise calculation. 3. H. H. HUBBARDand D. J. MAGLIERI1960 J. acoust. Soc. Am. 32, 1105. Noise characteristics of helicopter rotors at tip speed up to 900 feet per second. 4. H. STERNnELD,JR., R. H. SPENCERand E. G. SCHAErFER1961 TREC Technical Report 61-72, U.S. Army Transportation Command, Fort Eustis, Virginia. Study to establish realistic acoustic design criteria for future Army aircraft. 5. C. R. Cox and R. R. LY~,~ 1962 TCREC Technical Report 62-73, U.S. Army Transportation Research Command, Fort Eustis, Virginia. A study of the origin and means of reducing helicopter noise.

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6. I. M. DAVIDSONand T. J. HARGEST1965 Jl. R. aeronaut. Soc. 69, 653. Helicopter noise. 7. T. J. STUCKEYand J. O. GODDARD1967 J. Sound Vib. 5, 50. Investigation and prediction of helicopter rotor noise: 1 Wessex whirl tower results. 8. J. W. LEVERTONand F. W. TAYLOR1966 J. Sound Vib. 4, 345. Helicopter blade slap. 9. J. B. OLLERrlEADWyle Laboratories Research Staff WR 68-8, (to be published). 10. M. V. LowsoN 1964 Institute of Soundand Vibration Research, Southampton. Some observations on the noise from helicopters. 11. M. V. LowsoN 1965 Proc. R. Soc. Series A 286, 559. The sound field for singularities in motion. 12. M. V. LowsoN 1966 J. Sound Vib. 3, 454. Basic mechanisms of noise generation by helicopters, V/STOL aircraft, and ground effect machines. 13. R. G. LOEWYand L. R. SUTTON1966 USAA VLABS TechnicaIReport 65-85, U.S. Army Aviation Materiel Laboratories, Fort Eustis, Virginia. A theory for predicting the rotational noise of lifting rotors in forward flight, including a comparison with experiment. 14. R. G. LOEWYand L. R. SUTTON1966 J. Sound Vib. 4, 305. A theory for predicting the rotational noise of lifting rotors in forward flight including a comparison with experiment. 15. R. G. SCHLEGEL,R. J. KING and H. R. MULL 1966 USAA VLABS Tech. Report 66-4, U.S. Army Aviation Materiel Laboratories, Fort Eustis, Virginia. Helicopter rotor noise generation and propagation. 16. R. G. LoEwY 1963 d. Am. Helicopter Soc., 36. Aural detectability of helicopters in tactical situations. 17. L. YA GtrriN 1936 Phys.Z. Sowjn., Band A Heft 1, 57. Translated as NACA TM-1195, National Advisory Committee for Aeronautics. On the sound field of a rotating propeller (1948). 18. I. E. GARRICKand C. E. WATKINS1954 NACA Report 1198, NationalAdvisory Committee for Aeronautics. A theoretical study of the effect of forward speed on the free space sound pressure field around propellers. 19. E. Y. YUDIN1944Z. Tekh. Fiz. 14, 561. Translated as NACA TMl136. On the vortex noise from rotating rods (1947). 20. I. J. SHARLAND1964J. Sound Vib. 1, 302. Sources of noise in axial flow fans. 21. J. E. FFowcs WILLIAMSand D. L. HAWKINGS1968 A R C 29, 821. Theory relating to the noise of rotating machinery. 22. M. J. LIGHTHILL1952 Proc. R. Soc. Series A., 211,564. On sound generated aerodynamically. I. General theory. 23. N. W. McLACnLAN 1961 Bessel Functions for Engineers. Oxford: Oxford University Press, second edition. 24. P. M. MORSEand K. U. INGARO1968 Theoretical Acoustics. New York: McGraw-Hill. 25. I. ARNOLD,F. LANEand S. SLtrrSKY1961 General Applied Science Laboratories TR-221, Westbury, New York. Propeller singing analysis. 26. M.V. LowsoN 1968 WyleLaboratoriesReseareh StaffWR 68-5. Theoretical studies of compressor noise. 27. R. P. WHITE 1966 J. Sound Vib. 4, 305. VTOL periodic areodynamic loadings: the problems, what is being done and what needs to be done. 28. J. SCHEIMAN1964 NASA TM-X-952, Washington, D.C. A tabulation of helicopter rotor-blade differential pressures, stresses, and motions, as measured in-flight. 29. F. B. BURPO and R. R. LYNN 1962 TCREC Tech. Report 62-42, U.S. Army Transportation Research Command, Fort Eustis, Virginia. Measurement of dynamic airloads on a full scale semi-rigid rotor. 30. H. LEVIand A. G. FORSDYKE1928 Proc. R. Soe. Series A. 120, 670. Steady motion and stability of a helical vortex.