Toward Understanding the Aerodynamic Efficiency of a Hovering Micro-Rotor

Manikandan Ramasamy∗ Bradley Johnson† J. Gordon Leishman‡

Department of Aerospace EngineeringGlenn L. Martin Institute of Technology

University of Maryland, College Park, MD 20742

Abstract

The velocity field of a micro-rotor was measured usingdigital particle image velocimetry (DPIV) to help iden-tify the pertinent flow features and the various sources ofpotential aerodynamic losses. These flow measurementswere complemented by balance measurements of rotorthrust and power. Several rotor blades were used with dif-ferent planforms, twist distributions, and airfoil profiles.In each case, the operating blade tip Reynolds numberwas nominally 35,000. A unique aspect of the work wasthe use of advanced DPIV correlation algorithms, whichallowed for high-resolution flow measurements. This al-lowed for the accurate estimation of the spanwise lift anddrag along the blade from sectional circulation measure-ments and wake velocity deficiency characteristics, re-spectively. Sharpening the leading- and trailing-edges ofthe blade was shown to reduce the wake thickness and pro-file losses, resulting in improved rotor performance. Thetwisted blades also showed improved levels of rotor per-formance. The evolutionary characteristics of the tip vor-tices, including the growth rate of the vortex cores andthe peak swirl velocities, were also measured. The vortexcontained a circulation that was found to be about 80%of the maximum sectional bound circulation, and showedslow dissipative characteristics with increasing wake age.The circulation contained within the viscous core wasabout 50% of the total circulation at early wake ages, andcontinued to increase with wake age.

Nomenclature

A rotor disk areac blade chordCd drag coefficientCd0 minimum (profile) drag coefficient

∗Assistant Research Scientist. mani@glue.umd.edu†Minta Martin Intern. bjo212@glue.umd.edu‡Minta Martin Professor. leishman@umd.edu

Presented at the American Helicopter Society InternationalSpecialists Meeting on Unmanned Rotorcraft, January 23–25,2007, Phoenix, AZ. c©2007 by M. Ramasamy et al. Publishedby the AHS International with permission.

Cl lift coefficientCT rotor thrust coefficient, = T/ρAΩ2R2

CP rotor power coefficient, = P/ρAΩ3R3

D rotor blade sectional drag/unit spanDL disk loading, = T/AFM figure of meritL rotor blade sectional lift/unit spanPL power loading, = T/Pr radial distancer0 initial core radius of the tip vortexrc core radius of the tip vortexR radius of the bladeRev vortex Reynolds number, = Γv/ν

t timeS perimeter of the loop integralT rotor thrustVr radial velocityVθ swirl velocityVz axial velocityu, v, w velocities along x, y, z directions, respectivelyx, y, z rotor coordinate systemα Lamb’s constant, = 1.25643Γ circulation, = 2πrVθ

Γb bound circulationΓc circulation at the core radiusΓv circulation at large distancesδ ratio of apparent to actual kinematic viscosityζ wake ageν kinematic viscosityρ air densityσ rotor solidityψ azimuthal position of bladeΩ rotational speed of the rotor2-C two-component3-C three-component2-D two-dimensional3-D three-dimensional

Introduction

While many types of manned aircraft play a role in themilitary mission, military planners foresee a day in thenear future when swarms of micro air vehicles (or MAVs)

1

can be used to augment combat effectiveness and reducecasualties. A MAV has been defined variously as an air-craft having a maximum dimension of 15 cm (≈6 in) to asmuch as 40 cm (≈16 in), with the requirement that theyare small and light enough so that they can be backpackedby single soldiers into the battlefield. MAVs have the ob-vious advantage of small scale and correspondingly lowradar cross-section and stealthiness. They can give goodreconnaissance capability with rapid deployment and, inmany cases, real-time data acquisition capability such asimaging. It is expected that in the future MAVs will takeon larger roles, and will support missions that are cur-rently performed by manned aircraft.

MAVs are usually required to hover, and previousMAV designs have encompassed rotating-wings of vari-ous types, including ducted and unducted rotor concepts.But existing designs fall well short of the desired pay-load and endurance objectives because they have not yetshown sufficiently good aerodynamic efficiency. Severalexperiments have clearly shown that their aerodynamic ef-ficiency is substantially lower than their higher Reynoldsnumber rotor counterparts (Refs. 1–3). One main issueaffecting efficiency is that rotating-wing MAVs operate atblade chord Reynolds numbers that may be three ordersof magnitude lower than full-scale helicopters. This pro-duces thick boundary layers on the blades, which resultsin large values of profile drag. The resulting poor lift-to-drag ratios of the blade sections (which may be 5 or lower)substantially decrease the overall operating efficiency ofthe rotor system. In concert with this effect, is the rela-tively higher induced power requirements of MAV-scalerotors, as well as higher rotational and turbulent losses inthe wakes downstream of the rotating blades.

While a number of approaches have been examined totry to improve rotor performance (Refs. 2–5), only mod-est gains have been attained. One key to improved per-formance obviously lies within understanding the viscousdominated wake structure and the need to reduce inducedlosses not just profile losses. In fact, there is reason tobelieve that induced (wake) and profile (blade airfoils) ef-fects are strongly interdependent at this small scale, andthat induced and viscous effects cannot be isolated andexamined separately to the same degree as they can onfull-scale rotor systems. For example, we should not for-get that the nature of the MAV rotor flow probably violatesmost, if not all, of the assumptions made in the develop-ment of the fundamental theories of rotor analyses. Whatwe lack for now are methods that allow for small-scalerotor design, and until such methods become established,MAVs will continue to demonstrate much lower levels ofperformance capability than is desired.

To this end, the objective of the present study wasto perform several performance (i.e., thrust and power)and high-fidelity flow field measurements of a micro-rotor

with different rotor blade planforms. This includes ap-proaches towards understanding methods of reducing theprofile losses (by varying the airfoil shape, nose sharp-ness, and blade thickness distribution) and induced losses(by varying blade planform and twist shapes). The ob-jective was to help further understand the flow field char-acteristics of micro-rotors that, in turn, may help in thefuture validate mathematical models, and to develop de-sign strategies to improve upon their performance. Simul-taneous measurement of rotor performance and flow fieldanalysis is required to more clearly understand their aero-dynamics. Also, it is necessary to estimate the sectionalperformance across the blades, which is critical to developstrategies aimed at improving the aerodynamic efficiencyof micro-rotors. It is not yet clear whether conventionalrotor design strategies can be used effectively to this end.

Sources of Rotor LossesIncreasing the flight performance of a rotating-wing MAV(i.e., their speed, range, endurance, etc.) directly dependson improving their aerodynamic efficiency. One measureof hovering performance is the figure of merit (FM ). Fig-ure 1 shows current performance levels of micro-rotors interms of their measured FM as well as the intended de-sign efficiency goal of 0.8 or possibly higher. Figure 1shows that for a given level of induced losses progres-sively smaller improvements in the FM can be achievedby improving upon the efficiency of the airfoils throughhigher values of C3/2

l /Cd (i.e., the lift-to drag) after a cer-tain FM threshold is reached. Also, it shows that unlessthe the values of C3/2

l /Cd can exceed at least 10, whichappears high for low Reynolds number airfoils (Ref. 5),there is no possibility of increasing FM much above 0.6.Induced and rotational losses must be reduced in unisonwith profile losses to produce any real improvement inoverall hovering efficiency. However, at low Reynoldsnumbers profile and induced losses have likely interde-pendent influences, and improving one over the other isno guarantee that improved rotor efficiency levels will, infact, be obtained.

Even though FM can give one measure the relative hov-ering performance of MAVs, it is the power loading thatdefines the overall hovering performance in terms of thrustproduced for the energy expended. The power loading isdefined as

PL =TP

=CT

CPΩR(1)

Rewiting Eq. 1 in terms of FM using simple momentumtheory considerations gives

PL =√

2ρ FM√DL

(2)

2

Figure 1: Rotor FM variations and goals in terms in-duced losses and blade section aerodynamic efficiency.

Figure 2: Power loading versus effective disk loading.

It is apparent from Eq. 2 that the power loading improveswith an increase in FM and a reduction in disk loading.Figure 2 shows the values of power loading versus equiv-alent disk loading for different scale hover-capable air-craft and biological mechanisms, which also operate overa wide range of Reynolds numbers based on blade or wingchord. Notice the logarithmic scale on both axes. Thefundamental momentum theory given by Eq. 2 seems tohold good at all scales, including insects and humming-birds, as it should bearing in mind it is simply a state-ment of the theoretical ideal limit as given by Newton’s2nd Law. Clearly the key to improved hovering efficiency(best power loading) is to operate at a low disk loadingand at as high a figure of merit as possible at that diskloading.

It is convenient to idealize total rotor losses into theconstituents of induced (i), profile (0), and “other” (o)losses losses. The other losses have their source in therotational and turbulent flow inside the rotor wake, andare difficult to quantify a priori because these are inter-dependent functions of profile and induced losses. On arotor operating at full-scale Reynolds numbers, rotationaland turbulent losses are low when the rotor is operating in

Figure 3: Relationship between rotor power loadingand FM versus blade loading coefficient.

its normal working state. Rewriting Eq. 1 gives

PL =CT

ΩR(CP0 +CPi +CPo)

=CT

ΩR

(κ

C3/2T√2

+σCd0

8+CPo

) (3)

In the first instance, it is convenient to group the other in-duced and rotational losses into an average induced powerfactor κ. Differentiating Eq. 3 with respect to CT andequating it to zero results in a maximum PL at a FM of2/(3κ). But κ is always greater than one because thereare always non-ideal induced losses, and so the maximumpower loading for the rotor system will be achieved whenwhen the FM is smaller than 2/3, as shown in Fig. 3. Inthis particular case, κ is assumed to be 1.8, which is con-sistent with the measured levels of performance (as givenby the data points) for a micro-rotor. Because other lossesare involved, this is a value that is considerably higherthan those typically found with rotors operating at highertip chord Reynolds numbers.

It will be seen from Fig. 3 that the required blade load-ing coefficient at the most efficient or “optimum” hover-ing condition is extremely low, and this requires a largerotor disk area. Because of overall maximum allowablerotor size and weight constraints for a MAV, the rotor mustgenerally operate at a higher disk loadings and CT valuesthan its optimum value. However, Fig. 3 also shows thatthe power loading curve is relatively flat after the best op-erating point is reached, suggesting that the performancelosses associated with operating at slightly higher diskloadings are modest. Nevertheless, the design point forthe most efficient rotor operation is clear.

Even though Fig. 1 assumes that effect of the profile andinduced losses on the FM of the rotor system operate as in-dependent parameters, these two effects actually have in-terdependent influences, especially at low blade Reynolds

3

Tip vortexζ = 10 deg

Tipvortices

Tip vortexζ = 190 deg

Turbulentvortex sheet

Rotor shaft

Figure 4: Representative laser light sheet flow visualization image in the flow field of a rotating-wing MAV.

Rotor blade

Tipvortices

Mergingboundary

layers(vortex sheet)

Figure 5: A close up view of the flow field immediately behind the blade revealing the presence of thick turbulentwake sheet with strong streamwise vorticity.

numbers. For example, κ will vary with CT , and rotationaland turbulent losses become a function of blade sectioncharacteristics (profile losses).

There is evidence to support this hypothesis. Figure 4shows a laser sheet flow visualization image of the flowfield of a hovering micro-rotor (Ref. 1). Several flow fea-tures can be identified. One distinctive feature in the wakeof a micro-rotor is that the thicker boundary layers fromthe top and bottom surfaces of the blades merge to resultin a relatively thick, turbulent wake sheets.

This can be more clearly seen in Fig. 5, which is theimage of the wake immediately behind the rotor blade.Clearly organized streamwise vorticity (wake sheets) thatresult from the merging of the thick boundary layers fromtop and bottom surface of the blade can be noticed. Thesewake sheets are a source of rotational and turbulent losses.It is known that an increase in the boundary layer thick-ness increases profile drag at the lower chord Reynoldsnumbers below 50,000—see Fig. 6. Notice from Fig. 4that at the outer edges of the sheets are rolled-up tip vor-tices, which seem to have relatively large viscous corescompared to the rotor dimensions.

Figure 6: Variation of two-dimensional profile drag co-efficient versus chord Reynolds number.

Experimental Setup

The current experiments involved the following: 1. Ro-tor thrust and torque measurements using a mass balanceand a torque sensor; 2. Two-component (2-C) DPIV mea-surements for estimating the sectional lift and drag com-ponents along the blade span; 3. Three-component (3-C)

4

DPIV for measuring the overall rotor flow field.Eight blade shapes were used in the study. All of the

blades were made of composite carbon fiber, and had cam-bered, circular arc airfoil sections. The blades included:

1. Baseline rectangular blade, as shown in Fig. 7a.

2. Baseline blade with sharpened leading edge (SLE).

3. Baseline blade with sharpened leading edge andtrailing-edge (SLT).

4. Tapered blade (Type-1), as shown in Fig. 7b.

5. Tapered blade (Type-2), as shown in Fig. 7c.

6. Inverse tapered blade, as shown in Fig. 7d.

7. −9 linearly twisted blade.

8. −24 linearly twisted blade.

The rotor had a radius of 86 mm and was operated in atwo-bladed configuration. The baseline blade had a uni-form chord of 19 mm, giving a blade aspect ratio of 3.7and it had no twist or taper. The general dimensions of theother blades are shown in Fig. 7. Each rotor system hadan effective thrust weighted solidity, σe, of 0.14 as givenby

σe = (σr−σt)y13 +(

σt −σr

1− y1

)[− 1

4+ y1

3− 34

y14]+σt

(4)where the suffixes r and t represent the values at the rootand tip of the blade, respectively, and y1 represents thepoint at which the taper starts. For the sharpened leading-and trailing-edge blades, the blades were sharpened fromthe 15% and 85% chord locations by linearly reducingtheir thickness towards the leading- and trailing-edges, re-spectively.

Thrust and Torque MeasurementsThe rotor stand was rigidly attached to a linear reactiontorque sensor, which in turn was mounted on a micro massbalance capable of measuring the rotor thrust at a pre-cision of ±0.1 grams—see Fig. 8. The torque cell wascalibrated by using weights applied at a precisely knownarm. The analog signal from the torque sensor was ap-propriately signal-conditioned and read into a digital dataacquisition system. The rotational speed of the rotor wasmeasured with a Hall-effect sensor mounted adjacent tothe rotor shaft.

A digital inclinometer was used to precisely set thepitch angle of the blades at 75% span location. The ro-tor system was positioned to thrust vertically downwards(wake directed upward) to prevent ground effect interfer-ence. The measurement of rotor thrust and torque were

Figure 7: Schematics showing the different rotor bladeconfiguration used for the measurements.

made at rotational frequencies of 20, 30, 40, 50 and 60Hz, and at collective pitch angles (measured at 75% ra-dius) of 8, 12, 16, and 20. At each rotational speed,torque and thrust data were collected over a 5 second pe-riod. The final data was ensemble averaged and used tofind the the coefficients of thrust and power and the FMof each rotor at the different pitch angles and blade tipReynolds numbers. The rotor was also tested at all con-ditions without the blades attached to the hub to deter-mine tares. These tares were subtracted from the thrustand torque measurements taken with the blades attached.To guarantee measurement precision and repeatability ofthe experiment, multiple tests were made on each rotor atthe same pitch angles and rotational speeds. The measuredthrust was found to be within the instrument precision ofthe mass balance, while the measured torque had an un-certainty of ±3% of the mean value.

5

Figure 8: Schematic showing the experimental setupused in measuring the performance of the micro-rotor.

Flow Field Measurements

The flow field analysis using the 2-C DPIV was limitedto five blade configurations: (1) The baseline blade; (2)The baseline blade with sharp leading- and trailing-edges;(3) The tapered blade (Type-1); (4) The inverse taperedblade; (5) The −9 linearly twisted blade. The evolution-ary characteristics of the wake and tip vortices were mea-sured using 3-C DPIV only for the baseline case, althoughother measurements are in progress. For all the flow fieldanalyses, the rotor was operated at 50 Hz, with a tip speedof 27 m/s. The nominal operating tip Mach number andReynolds number based on chord were 0.082 and 35,000,respectively.

The flow at the rotor was seeded with a thermally pro-duced mineral oil fog. The average size of the seed parti-cles were between 0.20 to 0.22 microns in diameter. Forthe PIV experiments, the entire test area was uniformlyseeded before each sequence of measurements. For theflow visualization, judicious adjustment of the seeder wasrequired to introduce concentrations of fog at the locationsneeded to clearly identify specific types of flow structures.

The PIV system included dual Nd:YAG lasers that wereoperated in phase synchronization with the rotor, the op-tical arm to transmit the laser light into the region of in-terrogation, a digital CCD camera with 1 mega-pixel res-olution placed orthogonally to the laser light sheet for 2-C measurements (see Fig. 9a), a high-speed digital frame

DPIV camera

ND-Yag laser sheet

Z

X

Y

r

(a) 2-C DPIV

ND-YAG Laser sheet

DPIV Cameras

z

y

x

(b) 3-C DPIV

Figure 9: Experimental set for 2-component and 3-component PIV measurements.

grabber, and DPIV analysis software. For the 3-C mea-surements, two digital CCD cameras with 2 mega-pixelresolution were placed at an angle to satisfy the Scheim-plfug criteria—see Fig. 9b. The lasers could be fired atany blade phase angle around the azimuth, enabling flowfield measurements to be made at any required wake age.The two lasers were fired with a pulse separation time of2µs; this corresponded to less than 0.02 of blade motion.

Image Processing

For the 2-C DPIV measurements, a simple adaptive gridwas used to correlate the images to obtain the velocity vec-tors. The details of this correlation technique have beenexplained in Ref. 8. The entire region of focus was di-vided in to 64× 64 nodes. An interrogation window of24 pixels on either side with a 50% overlap was used forcorrelation. The number of allowed interpolated vectorswas restricted to less than 1% of the total number vectorsin any one image.

6

Figure 10: Schematic explaining the DPIV image processing technique used in the current study.

For the 3-C DPIV measurements, a new recursivetechnique called deformation grid correlation was used(Ref. 14). This procedure is similar to that of the sim-ple recursive technique, however, the second window isdeformed in that it is both sheared and translated insteadof just using the simple translation—see Fig. 10. The pro-cedure starts with the correlation of an interrogation win-dow of a defined size (say, 64-by-64), which is the firstiteration. After the mean displacement of that region isestimated, the interrogation window of the displaced im-age is moved by integer pixel values for better correla-tion in the second iteration. This third iteration starts bymoving the interrogation window of the displaced imageby sub-pixel values based on the displacement estimatedfrom second iteration. Following this, the interrogationwindow is sheared twice (for integer and sub-pixel val-ues) based on the velocity magnitudes from the neighbor-ing nodes before performing a fourth and fifth iteration,respectively.

Once the velocity is estimated after these five itera-tions, the window is split into four equal windows (ofsize 32× 32). These windows are moved by the averagedisplacement estimated from the final iteration (using awindow size of 64× 64) before starting the first iterationat this resolution. This procedure can be continued untilthe resolution required to properly resolve the flow fieldis reached. The second interrogation window is deformeduntil the particles remain at the same location after thecorrelation. This technique, especially the introduction ofshear, has been shown in Ref. 15 to be appropriate formeasuring the high velocity gradients found inside rotor

wake flows. Detailed analysis on the uncertainty associ-ated with the process has also been made in Ref. 15.

ResultsThe observed results have been analyzed in the followingcategories: (1) Performance of the micro-rotor estimatedfrom mass balance and torque sensors; (2) Sectional liftand drag estimation from the flow field analysis; (3) Evo-lutionary characteristics of the tip vortices.

PerformanceFigures 11a through 11c show the performance spolarsfor the various blade configurations. All the plots includemeasurements obtained at the four collective pitch anglesand five rotational speeds. The theoretical results weremade using the simple momentum theory and by estimat-ing average values of κ and Cd0 in a least-squares sensefrom the measured data. It should be understood that inthis context momentum theory may not be applicable be-cause of its assumptions, especially at these low operatingReynolds numbers. However, the results can still be usedas a baseline for comparative analysis; this is the purposehere and it is not meant to be an endorsement of the appli-cability of this theory.

Figure 11a shows the measurement made for three rect-angular blade planforms: (1) The simple baseline; (2) Thebaseline with sharpened leading edge (SLE); (3) The base-line with sharpened leading- and trailing-edges (SLT). Itis apparent that the modified baseline cases (i.e., the SLE

7

(a) Rectangular blade configurations

(b) Tapered blade configurations

(c) Twisted blade configurations

Figure 11: Power polars for the various rotor bladeconfigurations.

and SLT blades) perform better than the baseline. Thismeans that the amount of power consumed to produce thesame amount of thrust is smaller for the modified baselinecases. It can be seen that CP0, which represents the min-imum power consumed (essentially at non-lifting or zeroCT ) is also smaller for the modified baseline cases. Thissuggests that reducing the profile losses by sharpening theleading-edge (or both the leading- and trailing-edges) iseffective for increasing rotor performance.

The improved performance in terms of FM are shown

(a) Rectangular blade configurations

(b) Tapered blade configurations

(c) Twisted blade configurations

Figure 12: Figure of merit for the various rotor bladeconfigurations.

in Fig. 12a. It can be seen that the measured FM wasimproved by about 10% for the modified baseline cases.Because all the three blades have identical rectangulartip shapes and were operated under identical conditions,the induced losses among these blades should also befairly similar, unless the modified boundary layer (fromthe sharpening of the blades) altered the roll-up and evolu-tionary characteristics of the wake and tip vortices. There

8

was some evidence of this, although only preliminary re-sults have been measured thus far. Between the SLE andSLT cases, the SLT blade showed a slightly better perfor-mance than for the SLE blade.

Figure 11b shows the performance characteristics ofthe tapered blade configurations. One immediate observa-tion is that the inverse taper configuration performs poorlywhen compared with the conventional tapered blades. In-verse taper was designed to increase the operating tipReynolds number, which initially was felt that it may helpto reduce the profile losses (see Fig. 6). However, it isapparent that the value of CP0 is actually higher for theinverse tapered blade. On the other hand, at the samepitch angle and at the same rotor tip speed, the inversetapered blade produced significantly higher thrust than forthe other two blades.

Even though no substantial difference in the polarscould be observed between the two linearly taperedblades, plotting their FM revealed some differences. Be-cause the Taper-2 blade configuration produces substan-tially lower thrust at lower pitch angles for the samepower, the FM values are also lower. Also, there is nosubstantial increase in the lift characteristics of the taperedblade when compared with the baseline case. This is con-sistent with the observation made in Ref. 4.

Both of the twisted blades exhibited better performancecompared with the baseline (untwisted) case. It can beseen that the twisted blades produced slightly higher val-ues of CT for the same power when compared to the base-line case. This is expected because the inflow distribu-tion across the twisted blade should be more uniform (seelater), resulting in lower induced losses and better rotorperformance.

Figures 13a through 13c show the measured powerloading for all the rotor blade configurations with respectto disk loading. It can be seen that the operating diskloadings are substantially lower than for large scale rotors.Consequently, their power loading is much better. This isexpected based on Eq. 1. However, hovering efficiencies(the FM) are still relatively low at these disk loadings. Be-cause rotor power varies with the cube power of rpm whilethrust increases by the square of rpm, operating the rotorat a lower rotational speed and at higher pitch angles willreduce the profile losses (Ref. 4).

Bound Circulation & Sectional Lift

Measuring the sectional lift across the blade span is es-sential to understand the aerodynamic performance of therotating-wing system. This is because the formation (roll-up) and evolutional characteristics of tip vortices directlydepends upon the distribution of bound circulation acrossthe wing span (Refs. 16, 17). The distribution of liftcan be measured using static pressure taps. However, for

(a) Rectangular blade configurations

(b) Tapered blade configurations

(c) Twisted blade configurations

Figure 13: Variation of measured power loading ver-sus disk loading.

micro-scale rotors with such small, thin blades, estimatingthe spanwise lift distribution using pressure sensors is notpossible. In such cases where direct measurement of pres-sure is not possible, the concept of “bound” circulationhas been used successfully (Refs. 22–24, 17).

The concept of estimating the sectional lift per unit span(from the bound circulation) at a specified span locationcan be obtained from the Kutta—Joukowski theorem, as

9

Figure 14: Integration around the blade to estimatethe sectional “bound” circulation at a spanwise loca-tion.

given byL = ρ(Ωr)Γb (5)

The challenges involved in estimating a unique valueof circulation that can be related to the sectional lift of theblade are discussed in Ref. 17. Care must be taken to en-sure that the circulation contained within the integrationloop contains only the “bound” part. The shed and trailedvorticity from the wake must be avoided, which otherwise,would result in an incorrect estimation of the circulation.In the case of a fixed-wing, this process is relatively eas-ier because of the simpler downstream wake structure, ex-cept near the wing tip. In the case of rotating-wings, thepresence of the returning wake makes the estimation of“bound” circulation much more difficult. As suggested byTaylor (Ref. 25), which was later confirmed by Bhagwat& Leishman (Ref. 17), the integration loops must be mod-ified to prevent the inclusion of any shed vorticity; this canbe achieved by keeping the appropriate branches of the in-tegration contours perpendicular to the streamwise axis ofthe shed wake.

The schematic in Fig. 14 shows the procedure followedin estimating the sectional bound circulation along theblade. The first loop completely encloses the rotor blade,i.e., the diagonal of this primary integration loop connectsthe leading- and trailing-edge of the blade section. In thesecond step, the length of the integration loop is increasedby ∆x along all four sides. Subsequent integral loops in-crease their path length in a similar manner by increasing∆x on all four sides from the previous integral loop. Esti-mates of the bound circulation, Γb were then made by nu-merically evaluating the closed loop integral of the mea-sured velocity field around a counterclockwise contour,and fully encompassing the blade section without extra-neous vorticity, i.e., by using

Γb =I

cV. ds

¯= ∑UT i(∆x)+WT i(∆z) (6)

Figure 15a shows the results of this closed loop in-tegration process for three representative spanwise loca-tions. It can be seen that the estimated circulation us-ing the primary integral loop is smaller. However, withan increase in the integration path length, the sectionalcirculation increases significantly before asymptoting toa constant value. Similar results were seen at all span-wise locations, except for very close to the blade tip. Theblade lift loading can then be determined from this asymp-totic value of sectional circulation through the applicationof the Kutta—Joukouski theorem (Eq. 5). The measuredpeak bound circulation and the associated lift value perunit span are given in Table 1.

Figures 15b to 15f show the estimated lift distributionacross the blade span for the five different blade configu-rations. The figures also include the distribution of drag,the estimation of which is detailed in a later section of thispaper. It can be seen that the lift is nearly linearly dis-tributed in the baseline case and is also heavily tip loaded.The value of sectional lift can be seen to reach its peakvalue at approximately the 88.5% span location. It shouldbe appreciated that the experiment was performed with afinite spatial resolution, especially along the spanwise di-rection of the blade. As a result, the spanwise location atwhich the maximum value of sectional lift was observedmay only be approximate. The reduction in sectional liftobserved near the tip is from the tip vortex, which inducesa downwash velocity that reduces the effective angle ofattack to nearly zero.

The lift distribution across the blade for the SLT casesappears similar to that of the simple baseline case. How-ever, the point of maximum lift appears slightly closer to-wards the blade tip. The baseline blade with sharpenedleading edge (SLE) and the baseline blade with the SLTwere designed to reduce the profile losses. However, asmentioned earlier, profile and induced losses are likelyto be interdependent at this scale, so reducing one is noguarantee of better rotor performance As expected, theoverall thrust produced by the SLT blade (obtained fromthe integration of the spanwise distribution of lift) ap-pears slightly higher than for the baseline case—see Ta-ble 2. The table also includes the performance values mea-sured by the balance for comparison; good correlation wasfound between the two techniques.

The lift distribution for the tapered blade was differentfrom all other blades because it had a double lift peak nearthe tip. This is likely a result of a secondary trailed vortex(other than the tip vortex), which results from the suddenchange in the circulation gradient at the point where thetaper starts. This secondary vortex has the same directionof rotation as that of the conventional tip vortex. As a re-sult, there is an upwash from a trailed vortex (between thepoint of origination and the blade tip) which counters thedownwash induced by tip vortex. This limits the reduction

10

Blade Span Maximum sectional Maximum sectionalconfiguration location (y/R) bound circulation, (Γb/ΩRc) lift (lbs/ft)Baseline 0.884 0.355 0.36282Baseline–sharp l.e. & t.e. 0.912 0.313 0.32672Taper 0.855 0.411 0.40242Inverse taper 0.912 0.3255 0.33974Twist (−9 linear) 0.825 0.336 0.31763

Table 1: Measured values of maximum sectional bound circulation, maximum lift per unit span, and their corre-sponding span locations: θ = 12, ΩR = 27 m/s.

Blade configuration CT CP CT CP0 CPi CP

(Technique (Mass (Torque (Bound (Wake C3/2T /√

2 CP0 +CPiused) balance) sensor) circulation) integral)Baseline 0.015992 0.0030651 0.014678 0.0021507 0.0012574 0.0034081Baseline - SLT 0.017223 0.0024482 0.015316 0.0016715 0.0013402 0.0030118Taper 0.014586 0.0024443 0.013748 0.0020448 0.0011399 0.0031847Inverse taper 0.016702 0.0036304 0.011909 0.0019163 0.0009189 0.0028352Twist (−9 linear) 0.014814 0.0025662 0.016683 0.0018024 0.0015238 0.0033261

Table 2: Comparison of the coefficient of thrust and torque measured using different techniques: θ = 12, ΩR = 27m/s.

in angle of attack induced by the tip vortex. Consequently,the lift produced at the blade span locations between thetwo vortices shows higher values than for any other blade.However, the overall integrated lift values produced by thetapered blades is still lower than for the baseline case.

The intent of the blade with inverse taper was to op-erate the tip region at higher chord Reynolds numbers.Even though the maximum thrust produced by the in-verse taper blade was found to be higher than any otherblade, partially satisfying the intended goal of producingmore thrust, the thrust estimated from the bound circula-tion concept seems to be substantially lower. Unlike thetapered blade, the blade with inverse taper did not showa double lift peak. The presence of a secondary trailedvortex with the tapered blade could have been identifiedby making measurements in the spanwise plane, however,this is left for future work.

The linearly twisted blade shows a lift distribution simi-lar to that of baseline case. Here, as mentioned earlier, theintent of the twisted blade is to try to produce a more uni-form inflow distribution across the disk, and thereby helpto minimize induced power losses. This can be achievedby operating the inboard part of the blade at higher anglesof attack. Again, even though the lift distribution appearssimilar to that of baseline case, the overall thrust producedby the twisted blade is higher than for any other bladeconfiguration—see Table 2.

The importance of the inflow spanwise distribution canbe better understood by reverting back to simple rotor the-ory, which suggests that a rotating-wing will have maxi-mum aerodynamic performance if the inflow is uniform

across the entire blade (Ref. 26). The more the devia-tion from uniform values of inflow, the poorer the aero-dynamic performance would be. In the experiments, thevalue of inflow was measured just above the 1/4-chord ofthe blade. It can be seen from Fig. 16b, that as expectedthe twisted blades have more uniform inflow across theentire blade span, while the profile losses are similar invalue to the baseline blade case (see Fig. 11c).

The results for SLT blade were found to be similar tothe baseline case. As a result, the induced losses can beassumed to be almost similar to that for the simple base-line case as it has essentially a similar linear inflow—seeFig. 16a. However, sharpening the leading- and trailing-edges of the blades significantly reduced the profile losses.

Wake Integration & Profile Drag

Unlike the difficulties in the estimation of the sectionallift distribution across the blades using the bound circula-tion approach, measuring the distribution of profile drag isslightly easier (Refs. 27–31). The momentum deficit ap-proach, defined by Betz (Ref. 16), can be used to estimatethe sectional drag by comparing the momentum upstreamand downstream of the airfoil (wing section) (Ref. 30).Wu et al. (Ref. 32) and Hackett & Sugavanam (Ref. 33)further developed this equation for finite wings to separateout the components of drag (induced and profile). A fur-ther explanation of this approach is also given by McAlis-ter (Ref. 34).

In the case of two-dimensional airfoils (infinite wings),there is no induced drag because of the absence of a trailed

11

(a) Inverse taper (b) Baseline

(c) Baseline–sharp l.e.& t.e. (d) Taper

(e) Twist (f) Inverse taper

Figure 15: Performance measurement for various rotor blade configurations (solid line – lift, dashed line – drag).

wake and tip vortices. For finite wings, the tip vorticesare the predominant flow features and they primarily in-duce two components of velocity: 1. A spanwise velocityfrom tip of the wing towards the root (VT ); 2. A veloc-ity component normal to the wing resulting from the swirlvelocity component of the tip vortex (WT ). This can bebetter understood from Fig. 17. The resulting inducedvelocity field inclines the lift vector aft, which upon re-solving introduces a component of drag (induced drag).By tilting the lift vector back, i.e, by having VT 1 = VT 2and WT 1 = WT 2, it is possible to measure the profile dragalone.

In reference to the rotating blade, a momentum balance

upstream and downstream of the blade section gives

D =Z

∞

−∞

(p1 +ρU12)dS−

Z∞

−∞

(p2 +ρU22)dS (7)

By introducing total pressure, which is given by

P = p+12

ρ(U2 +V 2 +W 2) (8)

the momentum balance in Eq. 7 (for an incompressibleflow) reduces to

D =Z

∞

−∞

(P1−P2)dS +12

ρ

Z∞

−∞

(UT 12−UT 2

2)dS(9)

− 12

ρ

Z∞

−∞

((VT 12 +WT 1

2)− (VT 22 +WT 2

2))dS(10)

12

Figure 17: Difference between 2-D and 3-D flow showing the source of induced drag.

(a) Baseline & twisted blade configurations

(b) Tapered blade configurations

Figure 16: Measured inflow distribution across thespan for various blade configurations.

where the subscripts 1 and 2 denote the upstream anddownstream locations relative to the blade section, re-spectively. The first two integrals represent the profiledrag, and the third integral represents the induced drag(Ref. 34).

In the present study, the profile drag was estimated us-

Figure 18: Measurement of profile drag per unitspan—velocity deficit behind the blade at the 94%span location.

ing

D =Z

∞

−∞

(P1−P2)dS +12

ρ

Z∞

−∞

(UT 12−UT 2

2)dS (11)

Here, the integralR

∞

−∞(P1−P2)dS can be assumed to be

negligible because of there is a very small reduction ofpressure inside the rotor wake downstream of the blade.Using continuity gives

ρUT 1 = ρUT 2 (12)

and substituting this in Eq. 11 gives the expression fordrag as

D =12

ρ

Z∞

−∞

UT 2(UT 1−UT 2)dS (13)

Here UT 1 −UT 2 is the decrease in flow velocity, whichwhen multiplied by the mass flux ρUT 2, gives the decre-ment in momentum per unit time in the drag direction.

Figure 18 shows the reduction in flow velocity behindthe rotor blade obtained from the measurements and the

13

Figure 19: Measured lift-to-drag ratio for variousblade configurations.

process outlined above. The drag per unit span measuredat different span locations for the various blades is shownin Figs. 15. One immediate observation is that the drag isapproximately one-fifth of the estimated lift at that loca-tion for all of the blades. This is consistent with the obser-vations made by Laitone (Ref. 28) and Mueller (Ref. 29)for low Reynolds number wing and airfoil flows. The sec-tional drag is also linearly distributed from the root of theblade to until approximately 85% of the blade radius, andthe drag then falls off rapidly towards the tip because ofthe influence of the tip vortex.

Operating the blade sections at or close to their bestvalues of C3/2

l /Cd is known improve the aerodynamic ef-ficiency of a rotor system. This can be understood by writ-ing the FM in terms of Cl/Cd , i.e,

FM =1

κ+2.6√

σ

(C3/2

LCD

)−1 (14)

after assuming that the overall average lift coefficientCL = Cl = 6(CT /σ) and all the blade sections operate atthe same sectional drag coefficient Cd = CD. Figures 19aand b show the sectional lift-to-drag ratio obtained at var-

Figure 20: Example of phase-averaged velocity mea-surements in the flow field of the micro-rotor.

ious blade sections for the different blades. It is apparentthat the baseline blade with the SLT configuration and thetwisted blades have a better L/D ratio than any of the otherblades. Consequently, the overall performance of the ro-tors with these blades is also better.

Tip Vortex Measurements

Understanding the formation and evolutionary character-istics of the blade tip vortices is critical. This is becauseof their influence on the induced inflow and overall per-formance of any rotating wing system, irrespective of thesize or the operating Reynolds number (Refs. 1, 6–8).In the case of MAVs, this is more critical because the tipvortices are larger in size relative to the dimensions of therotor blade (Ref. 1). Figure 15 clearly demonstrates theimportance of the tip vortices, where the loss of circula-tion (or lift) near the tip of the blade is primarily a resultof the downwash velocity induced by the tip vortices.

To understand the relationship between the tip vor-tex and the rotor performance, DPIV measurements weremade in the wake of the baseline blade to measure all threecomponents of the flow velocities. The acquired instanta-neous velocity maps were conditionally phase-averaged tocorrect for the effects of aperiodicity in the flow (Ref. 35).The resulting mean velocity across the region of interestis shown in Fig. 20.

Betz (Ref. 16) developed a mathematical model torelate the roll-up of the tip vortices with the maximumsectional bound circulation found across the span of theblade. Assuming that the tip vortex is responsible for theloss of circulation near the tip, it was hypothesized that thecirculation contained within the vortex should be equal to

14

Figure 21: Ratio of total vortex circulation in the tipvortex to the maximum measured bound circulation.

the maximum sectional bound circulation, i.e., all the vor-ticity beyond the point of maximum sectional circulationshould roll up into the tip vortex. In the present study,the maximum sectional bound circulation for the baselineblade was measured to be 0.1820 m2s−1.

Figure 21 shows the circulation contained within the to-tal vortex normalized by the peak sectional bound circu-lation at various wake ages. Two key observations shouldbe made here: (1) the peak value of this ratio, and (2) thewake age (or time) at which this ratio reached its peakvalue. The maximum value of this ratio can be seen to beapproximately 0.8. This means that only 80% of vortic-ity beyond the point of maximum circulation has rolledup in to the tip vortex, which is smaller than that pre-dicted by the Betz model. Also, it can be observed that thepeak value is attained at 60 wake age, i.e., the tip vortexroll up is complete over a time that is substantially longerthan for rotor blades operated at higher Reynolds numbers(Refs. 6, 17). The observed increase in roll-up time wasalso found to reflect in the evolutionary properties of tipvortices—see Fig. 22—and is consistent with the observa-tion made in Ref. 1. The ratio of total vortex circulationto the maximum sectional bound circulation can be seento decrease slowly with time, suggesting the dissipation ofenergy through turbulent mechanisms.

The ratio of circulation contained within the viscousvortex core to that of the total vortex circulation and itsvariation with Reynolds number is given in Fig. 23. Itcan be seen that approximately 50–70% of the total vor-tex circulation is contained within the vortex core. Thisfigure also includes measurements from another (but sim-ilar) micro-rotor experiment (Ref. 1), as well as measure-ments obtained from rotors operated at higher Reynoldsnumbers. The small difference between the current mea-surements and those shown in Ref. 1 can be attributed tothe difference in the experimental and data processing pro-cedures used to estimate the core and total vortex circula-tion. In the present study, mean values estimated from

(a) Growth of the tip vortex core

(b) Reduction in the peak swirl velocity with time

Figure 22: Measured sizes of the tip vortex cores andtheir associated peak swirl velocities at various wakeages.

both horizontal and vertical cuts through the vortex corehave been used instead of horizontal cuts only in the caseof Ref. 1. Also, the spatial resolution is much higher inthe present study compared with the other experiment.

Figure 23 is also plotted with an theoretical solution tothe N–S equations as obtained by Iversen (Ref. 36). Alarger value of the circulation ratio basically means thatthe diffusion of vorticity will be very slow similar to thosefound in a laminar flow at very low vortex Reynolds num-bers. Despite operating at a lower vortex Reynolds num-ber, the value of this ratio for the current set of measure-ments is similar to those found at higher vortex Reynoldsnumbers. This implies then that the growth properties oftip vortices should also be similar to that of tip vorticesgenerated at higher vortex Reynolds numbers.

Core size and Peak Swirl VelocityThe variation of the measured core size (half the distancebetween the swirl velocity peaks) with respect to wake age(or time) is given in Table 3. The table lists the dimensions

15

Wake age rc/c Vtip/ΩR rc/c Vtip/ΩR rc/c Vtip/ΩRζ H-cut H-cut V-cut V-cut Mean Mean6 0.0804 0.2888 0.1088 0.2303 0.0946 0.259630 0.0520 0.3327 0.05216 0.3106 0.0521 0.316360 0.0804 0.2735 0.0994 0.2264 0.0899 0.250090 0.1041 0.2316 0.1041 0.2095 0.1041 0.2205120 0.0946 0.2114 0.1183 0.2055 0.1065 0.2085150 0.1135 0.2043 0.1278 0.1940 0.1207 0.1991180 0.0994 0.2180 0.0899 0.2102 0.0946 0.2141210 0.1372 0.1963 0.1325 0.1700 0.1349 0.1831240 0.1183 0.2163 0.1325 0.1748 0.1254 0.1956

Table 3: Evolutionary characteristics of the tip vortices: (H-cut – Horizontal cut, V-cut – Vertical cut).

Figure 23: Ratio of circulation contained within thevortex core to the total vortex circulation.

of the vortex cores and the estimated peak swirl velocitiesthat were obtained by making two orthogonal (horizon-tal and vertical) cuts through the vortex, along with theirmean values. It can be observed that the vortex core isnot axisymmetric because the peak swirl velocity occursat different radial distances between the two cuts. Thissuggests that a complete characterization of the tip vor-tex properties is not possible using a measurement gridthat passes along a horizontal or vertical line through thecenter of the vortex, as is usually assumed in most laserDoppler velocimeter (LDV) measurements.

Figure 24 shows the measured mean swirl velocitiesacross the tip vortex at 60 wake age. By convention, thevelocities and the radial distances were normalized by thetip speed of the rotor and the blade radius. Notice that thepeak swirl velocity is not symmetrical on either side of thevortex, mainly because of its non-zero convection veloc-ity through the flow. The maximum average peak swirlvelocity was estimated to be 25% of the tip speed of therotor. The difference between the two peaks on each sideof the core can be assumed to be its average convectionvelocity, which is also a measure of the induced velocityinside the slipstream boundary of the rotor wake.

One of the complexities in understanding the evolu-

Figure 24: Measured non-dimensionalized velocities inthe tip vortex at ζ = 60 wake age.

tionary properties of tip vortices is identifying the char-acteristic variables. Usually, core size of the tip vortexis non-dimensionalized using a characteristic length suchas chord or radius of the blade. Swirl velocity is normal-ized using the tip speed of the rotor. However, analyzingthe evolutionary properties of tip vortices also requires acharacteristic time scale. The use of absolute time is notappropriate because the diffusion of vorticity (and hencethe growth of the vortex core) is not only a function oftime, but also a function vortex Reynolds number (or to-tal vortex circulation). As a result, vortex circulation mustbe taken into account to properly understand the growthproperties of the blade tip vortices.

In the present study, following Refs 36 and 1, the non-dimensionalized mean core size and the peak swirl veloc-ity were plotted in Fig. 22 against non-dimensionalizedtime. It can be seen from Fig. 22 that the core size ini-tially decreases before starting to increase, which is a di-rect result of the action of viscous and turbulent diffusion.The initial reduction in the core size of the tip vortex, asmentioned earlier, can be attributed to its delayed roll up(Ref. 1) at these low Reynolds numbers. Also, the nor-malized initial core size of the tip vortex was found to belarger than those found on larger scale rotors (Ref. 7). In

16

the present study, the initial core size, r0, was found to beapproximately 5% of the mean blade chord.

The curve fit in Fig. 22a is obtained using a variation ofSquire’s core growth model, which is given by

rc =

√r2

0 +4ανδζ

Ω(15)

where α is Lamb’s constant and δ is the ratio of appar-ent to actual viscosity. A value of δ = 6.4 seems to fit thegrowth rate of the vortex core estimated from the measure-ments. This observation is consistent with Fig. 23, whichsuggested that the rate of core growth of the tip vorticesshould be similar to those observed using larger scale ro-tors, despite operating at lower vortex Reynolds numbers.The measured peak swirl velocity for increasing time isshown in Fig. 22b. This, as expected, can be seen to de-crease inversely with t1/2 to conserve circulation.

Conclusions

To identify and measure the various sources of profileand induced losses, measurements of the performance andthe wake characteristics of a small MAV-scale or “micro-rotor” was performed. Several rotor blade configurationshave been tested over a range of pitch angles and rota-tional speed combinations. Several new observations havebeen found that help in understanding the nature of suchsmall-scale rotor performance. The following are conclu-sions derived from this study:

1. Conventional rotor design strategies for reducing in-duced and profile losses by altering the blade shapeseem applicable to MAV-scale rotor systems. The ef-fects of blade twist were shown to reduce losses andimprove performance. It is not yet clear, however, ifthere is an optimum blade twist that can help to max-imize rotor efficiency, although linear twist seems tobe a good start.

2. Reducing profile losses through blade section (airfoilshape) changes (albeit non-traditional changes) isan effective means of improving rotor performance.In the present case, modified rectangular bladeswith circular-arc airfoil sections that have sharpenedleading- and trailing-edges showed improved perfor-mance compared to the other rotor blades that weretested. The primary issues for the future are in bet-ter understanding the airfoil shapes that can give bestaerodynamic performance in the rotating-wing flowenvironment at low chord Reynolds numbers below50,000. To this end, further spanwise loads measure-ments are necessary.

3. DPIV was found to be a powerful technique for in-terrogating the flow near the rotor. Good correla-tions were found between the balance measurementsagainst the estimated thrust and torque values basedon integration of section properties. Estimating thelift and drag distributions along the blade span usingflow field measurements with the circulation and mo-mentum deficiency techniques gave good insight intothe performance of the rotor system.

4. The tip vortex seems to plays a more important rolein influencing the performance of a MAV-scale ro-tor because of its larger overall size relative to theradius and chord dimensions of the rotor. The roll-up process of the tip vortex was measured to take arelatively longer time when compared to tip vortexdevelopments that have been measured higher vortexReynolds numbers.

5. Despite the much lower vortex Reynolds numbersfound on MAV-scale rotors, the tip vortices exhibitedgrowth properties (viscous and turbulent diffusion)similar to that observed at higher Reynolds numbers.But the evolutionary characteristics of tip vortices,when analyzed in the appropriate time scales, con-firmed a higher growth rate than that would be ex-pected based on the vortex Reynolds number. About50% of the total vortex circulation was found to beinside the viscous vortex core, the circulation whichincreased with time.

AcknowledgmentsThis research was supported, in part, by the Multi-University Research Initiative under Grant ARMYW911NF0410176. Dr. Tom Doligalski is the technicalmonitor. The authors also wish to acknowledge TylerHuismann for his contributions in this work.

References1Ramasamy, M., Leishman, J. G., and Lee, T. E.., “Flow

Field of a Rotating Wing MAV,” American Helicopter So-ciety 62th Annual National Forum Proceedings, Phoenix,AZ, May 7–9, 2006.

2Bohorquez, F., Samuel, P., Sirohi, J., Pines, D., Rudd,L., and Perel, R., “Design Analysis and Hover Perfor-mance of a Rotating Wing Micro Air Vehicle,” The Jour-nal of American Helicopter Society, Vol. 48, No. 2, April2003, pp. 80–90.

3Hein, B., and Chopra, I., “Hover Performance of a Mi-cro Air Vehicle: Rotor at Low Reynolds Number,” AHS

17

International Specialists’ Meeting on Unmanned Rotor-craft: Design, Control and Testing, Phoenix, AZ, January2005.

4Gray, N., Kim, J., and Koratkar, N., “AerodynamicDesign Considerations for Micro-Rotorcraft,” AmericanHelicopter Society 58th Annual National Forum Proceed-ings, Montreal, Canada, June 11–13, 2002.

5Kim, J., and Koratkar, N., “Effect of Surface Tempera-ture and Heat Transfer on the Aerodynamic Performanceof Micro-Rotorcraft” American Helicopter Society 59thAnnual National Forum Proceedings, Phoenix, AZ, May6–8, 2003.

6Martin, P. B., Pugliese, G., and Leishman, J. G., “HighResolution Trailing Vortex Measurements in the Wake ofa Hovering Rotor,” Journal of the American HelicopterSociety, Vol. 49, No. 1, January 2004, pp. 39–52.

7Ramasamy, M., and Leishman, J. G., “Interdependenceof Diffusion and Straining of Helicopter Blade Tip Vor-tices,” Journal of Aircraft, Vol. 41, No. 5, September2004, pp. 1014–1024.

8McAlister, K., “Rotor Wake Development During theFirst Revolution,” Journal of the American Helicopter So-ciety, Vol. 49, No. 4, October 2004, pp. 371–390.

9Yu., Y. H., and Tung, C., “The HART-II Test: Ro-tor Wakes and Aeroacoustics with Higher Harmonic PitchControl (HHC) Inputs,” American Helicopter Society58th Annual National Forum, Montreal, Canada, June 11–13, 2002.

10Mahalingam, R., and Komerath, N. M., “Measure-ments of the Near Wake of a Rotor in Forward Flight,”AIAA Paper No. 98-0692, 36th Aerospace SciencesMeeting & Exhibit, Reno, NV, January 12–15, 1998.

11Tung, C., Pucci, S. L., Caradonna, F. X., and Morse,H. A., “The Structure of Trailing Vortices Generatedby Model Helicopter Rotor Blades,” NASA TM 81316,1981.

12Cook, C. V., “The Structure of the Rotor Blade Tip Vor-tex,” Paper 3, Aerodynamics of Rotary Wings, AGARDCP-111, September 13–15, 1972.

13Leishman, J. G., “Seed Particle Dynamics in Tip Vor-tex Flows,” Journal of Aircraft, Vol. 33, No. 4, 1996,pp. 823–825.

14Scarano, F., “Iterative Image Deformation Methodsin PIV,” Measurement Science and Technology, Vol. 12,2002, pp. R1–R19.

15Ramasamy, M., and Leishman, J. G., “BenchmarkingPIV with LDV for Rotor Wake Vortex Flows,” AIAA pa-per 2006-3479, 24th Applied Aerodynamics conferenceProceedings, San Francisco, CA, June 6–8, 2006.

16Betz, A., “Behavior of Vortex Systems,” NACATM 713, 1935.

17Bhagwat, M., and Leishman, J. G., “Measurementsof Bound and Wake Circulation on a Helicopter Rotor,”Journal of Aircraft, Vol. 37, No. 2, pp. 227–234, March2000.

18Fage, A., and Simmons, L. F., “An Investigat ion of theAir-Flow Pattern in the Wake an Aerofoil of Finite Span,Philosophical Transactions of the Royal Society, Series A,Vol . 225, 1925, pp. 303–330, 1925.

19Bryant, L. W., and Williams, D. H., “An Investiga-tion of the Flow of the Flow of Air Around an Aerofoilof Infinite Span,” Philosophical Transactions of the RoyalSociety, Series A, Vol . 225, pp. 199–237, 1925.

20McAlister, K. W., and Takahashi, R. K., “NACA0015 Wing Pressure and Trailing Vortex Measurements,”NASA TR 3151 AVSCOM TR 91-A-003, November1991.

21Kitapliouglu, C., and Caradonna, F. W., “Aerodynam-ics and Acoustics of Blade-Vortex Interaction using Inde-pendantly Generated Vortex,” American Helicopter So-ciety Aeromechanics Specialists Meeting, January 19–21,San Francisco, CA, 1994

22Orloff, K. L., “The Spanwise Lift Dist ribut ion on aWing from Flowfield Velocity Survey,” Proceedings of theAIAA 11th Fluid and Plasma Conference, Seattle, WA,July 1978.

23Felker, F. F., Piziali, R. A., and Gall, J. K., “Spanwise Loading Distribution and Wake Velocity Surveys of aSemi-Span Wing,” NASA TM 84213 USAARADCOMTR 82-A-1, Feb. 1982.

24Desabrais, K. J., and Johar i, H., “Direct CirculationMeasurement of a Wing Tip Vortex Using Ultrasound,”Proceedings of 36th Aerospace Sciences Meet ing and Ex-hibit, AIAA Paper 98-0609, Reno, NV, 1998.

25Taylor, G. I., “Note on the Connection Between theLift on an Aerofoil in a Wind Tunnel and the CirculationRound It , Philosophical Transactions of t he Royal Soci-ety, Series A, Vol . 225, pp. 238–245, 1925.

26Leishman, J. G., Principles of Helicopter Aerody-namics, Cambridge University Press, New York, 2000,Chap. 3, pp. 96–98.

18

27Schmitz, F. W., “Aerodynamics of the Model Air-plane,” Redstone Arsenal Translation, N70-39001, RSIC-721, Nov. 22, 1967

28Laitone, E. V., “ Wind Tunnel Tests of Wings atReynolds Numbers Below 70,000,” Experiments in Flu-ids, Vol. 23, pp. 405–409, 1997.

29Mueller, T. J., and Batill, S. M., Experimental Stud-ies of Separation on a Two-Dimensional Airfoil at LowReynolds Numbers,” Journal of Aircraft, Vol. 20, pp. 457–463, 1982.

30Kusunose, K., “Drag Prediction Based on a Wake-Integral Method,” 16th Applied Aerodynamics Confer-ence, Albuquerque, NM, June 15–18, 1998. pp. 501–514.

31Maskell, E. C., “Progress Towards a Method of Mea-surement of the Components of Drag of a Wing of Fi-nite Span,” Royal Aeronautical Establishment, RAE-TR-72232, 1979

32Wu, J. C., Hackett, J. E., and Liley, D. E., “A Gener-alized Wake-Integral Approach for Drag Determination inThree-Dimensional Flows,” American Institute of Aero-nautics and Astronautics, 17th Aerospace Sciences Meet-ing, New Orleans, La, 15–17 January 1979.

33Hackett, J. E., and Sugavanam, A., “Recent Develop-ments in Three-Dimensional Wake Analysis,” AGARDReport 723, Aircraft Drag Prediction and Reduction,1985.

34McAlister, K. W., Schuler, C. A., Branum, L., and Wu,J. C., “3-D Wake Measurements Near a Hovering Rotorfor Determining Profile and Induced Drag,” NASA TP3577 ATCOM TR 95-A-006, August 1995.

35Leishman, J. G., “Measurements of the AperiodicWake of a Hovering Rotor,” Experiments in Fluids,Vol. 25, 1998, pp. 352–361.

36Iversen, J. D., “Correlation of Turbulent Trailing Vor-tex Decay Data,” Journal of Aircraft, Vol. 13, (5), May1976, pp. 338–342.

19