NASA/CR–2012-216039

Determination of HART I Blade Structural Properties 

by Laboratory Testing

Sung N. Jung

Konkuk University

Seoul, South Korea

Benton H. Lau

Ames Research Center

Moffett Field, California

August 2012
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NASA/CR–2012-216039

Determination of HART I Blade Structural Properties by 

Laboratory Testing

Sung N. Jung

Konkuk University

Seoul, South Korea

Benton H. Lau

Ames Research Center

Moffett Field, California

August 2012

National Aeronautics and

Space Administration

Ames Research Center

Moffett Field, California 94035-1000
Available from:

NASA Center for AeroSpace Information National Technical Information Service

7115 Standard Drive 5285 Port Royal Road

Hanover, MD 21076-1320 Springfield, VA 22161

(301) 621-0390 (703) 487-4650

Acknowledgments

The measurement of HART I blade properties began by Benton Lau in late 2005 under U.S.–German MOU 

(Memorandum of Understanding). Much of the measurements were finished, but the study was never 

completed due to a serious health issue for Benton Lau. He passed away in 2010. Later, Professor Sung 

Jung at Konkuk University of South Korea proposed research on HART I- and HART II-related activities 

using his sabbatical leave for one year. He joined Ames Research Center in September 2011 and 

resumed the blade property measurement, leading to the successful documentation of the test data. He 

was supported by a leading foreign research institute recruitment program through the National Research 

Foundation of Korea (NRF), funded by the Ministry of Education, Science, and Technology (MEST) 

(K2060100001). The authors wish to thank Berend van der Wall of the German Aerospace Center 

(DLR) for providing HART I blades, Brandon Hagerty for doing preliminary measurements, Wayne 

Johnson and William Warmbrodt of Ames Research Center, Joon Lim and Thomas Maier of AFDD 

(U.S. Army Aeroflightdynamics Directorate) for valuable comments and support, and Eduardo Solis of 

Ames Research Center for artwork on figures.
iii 

TABLE OF CONTENTS 

LIST OF FIGURES ............................................................................................................................. iv 

LIST OF TABLES ................................................................................................................................ v 

NOMENCLATURE ............................................................................................................................ vi

SUMMARY .......................................................................................................................................... 1

INTRODUCTION ................................................................................................................................ 1

HART I ROTOR ................................................................................................................................... 2

HART I BLADE PROPERTY MEASUREMENT .............................................................................. 2

Mass and Inertia Properties .............................................................................................................. 4

Elastic Axis ....................................................................................................................................... 8

Section Stiffness ............................................................................................................................... 9

Chord Bending ............................................................................................................................ 11

Flap Bending ............................................................................................................................... 14

Torsion Stiffness ......................................................................................................................... 14

Comparison With Estimated DEI Values ....................................................................................... 19

Expanded Blade Property Data ....................................................................................................... 24

COMPARISON OF ROTOR NATURAL FREQUENCIES ............................................................. 24

CONCLUSIONS ................................................................................................................................ 27

REFERENCES ................................................................................................................................... 28
iv 

LIST OF FIGURES 

Figure 1. Geometric dimensions measured for the HART I blade. .................................................... 3

Figure 2. Configuration of the HART I rotor hub. ............................................................................. 4

Figure 3. Schematic view for cut-out sections of H1B (blade 3). ...................................................... 4

Figure 4. Measurement of the chordwise center of gravity. ............................................................... 5

Figure 5. Measurement of the polar mass moment of inertia for a cut-out section using 

the trifilar pendulum. .......................................................................................................... 6

Figure 6. Measurement setup for the determination of elastic axis. .................................................. 8

Figure 7. The mirror method for a blade in bending. ......................................................................... 9

Figure 8. Geometry of the mirror method. ....................................................................................... 10

Figure 9. The simply supported blade in bending (3-point bending method). ................................. 11

Figure 10. Measurement of the lag bending using a 3-point bending method. .................................. 12

Figure 11. Linear regression of the load-deflection curve for the lead bending 

(data from table 5)............................................................................................................. 13

Figure 12. Linear regression of the load-deflection curve for the lag bending 

(data from table 6)............................................................................................................. 13

Figure 13. Measurement of the flap bending for H1S blade using a 3-point bending method. ......... 15

Figure 14. Linear regression of the load-deflection curve for the flap bending 

(data from table 8)............................................................................................................. 15

Figure 15. Measurement of the flap bending for H1B cut section using a 3-point bending 

method. ............................................................................................................................. 16

Figure 16. Measurement of the flap bending with the mirror method. ............................................... 16

Figure 17. Measurement of the torsion stiffness with the mirror method. ......................................... 17

Figure 18. Comparison of the center of gravity offset from the elastic axis. ..................................... 20

Figure 19. Comparison of the elastic axis offset from the quarter chord axis. ................................... 20

Figure 20. Comparison of flap bending stiffness along the blade length. .......................................... 21

Figure 21. Comparison of chordwise bending stiffness along the blade length. ................................ 21

Figure 22. Comparison of torsion stiffness along the blade length. ................................................... 22

Figure 23. Comparison of mass distribution along the blade length. ................................................. 22

Figure 24. Comparison of polar mass moment of inertia along the blade length. .............................. 23

Figure 25. Comparison of section radius of gyration along the blade length. .................................... 23

Figure 26. Comparison of rotor natural frequencies. .......................................................................... 27
v 

LIST OF TABLES 

Table 1. General Properties of the HART I Blade ............................................................................ 3 

Table 2. HART I Blade Names ......................................................................................................... 3 

Table 3. Mass Properties of H1B Cut Sections ................................................................................ 5

Table 4. Time Period of Oscillations Measured for H1B Cut Sections ............................................ 7 

Table 5. Measured Deflections at the Blade Central Position for the Lead Bending ..................... 12 

Table 6. Measured Deflections at the Blade Central Position for the Lag Bending ....................... 12 

Table 7. Slopes of the Load-Deflection Curve for the Lead-Lag Bending ..................................... 13 

Table 8. Measured Deflections at the Blade Central Position for the Flap Bending ...................... 17 

Table 9. Slopes of the Load-Deflection Curve for the Flap Bending ............................................. 17 

Table 10. The Traverse Distance of Laser Dots on the Wall for Each Mirror (Flap Bending) ........ 18 

Table 11. Measured Flap Bending for Blade Root Region ............................................................... 18 

Table 12. The Traverse Distance of Laser Dots on the Wall for Each Mirror (Torsion Stiffness) .. 18 

Table 13. Comparison of Blade Structural Properties of HART I Uniform Section ....................... 19 

Table 14. Summary of HART I Blade Properties ............................................................................. 25 
vi 

NOMENCLATURE 

BVI = blade-vortex interaction 

c = blade chord 

CAMRAD = Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics 

CG = center of gravity 

DEI = Dynamic Engineering, Inc. 

DLR = German Aerospace Center 

DNW = German–Dutch wind tunnel 

EA = elastic axis 

EICHD = chord bending stiffness 

EIFLAP = flap bending stiffness 

GJ = torsion stiffness 

HART = Higher Harmonic Control Aeroacoustic Rotor Test 

HHC = higher harmonic control 

IP, Iθ = polar mass moment of inertia 

kP = polar radius of gyration 

MOI = moment of inertia 

ONERA = Office National d'Études et de Recherches Aérospatiales 

QC = quarter chord 

R = rotor radius 

RPM = revolutions per minute 

SI = International System of Units 

Y, Z = blade section coordinates 

Ω = rotor speed 

Ω0 = rotor nominal speed 

 
1 

DETERMINATION OF HART I BLADE STRUCTURAL PROPERTIES BY 

LABORATORY TESTING 

Sung N. Jung1 and Benton H. Lau 

Ames Research Center 

SUMMARY 

The structural properties of Higher Harmonic Control Aeroacoustic Rotor Test (HART I) blades 

were measured using the original set of blades tested in the German–Dutch wind tunnel (DNW) in 

1994. The measurements include bending and torsion stiffness, geometric offsets, and mass and 

inertia properties of the blade. The measured properties were compared to the estimated values 

obtained initially from the blade manufacturer. The previously estimated blade properties showed 

consistently higher stiffness, up to 30 percent for the flap bending in the blade inboard root section. 

The measured offset between the center of gravity and the elastic axis is larger by about 5 percent 

chord length, compared to the estimated value. The complete structural properties of HART I blades 

were obtained using the present measured data along with the previously available data provided by 

the blade manufacturer. The rotor structural dynamics analysis in vacuum condition was also carried 

out to examine the validity of the measured blade properties. 

INTRODUCTION 

In 1994, the Higher Harmonic Control Aeroacoustic Rotor Test (HART I) was conducted in an 

open-jet anechoic test chamber of the German–Dutch wind tunnel (DNW) by a joint research team 

from the German Aerospace Center (DLR), the French Office National d'Études et de Recherches 

Aérospatiales (ONERA), NASA Langley, DNW, and the U.S. Army (ref. 1). The main focus of the 

task was to measure the noise level, airloads, vortex wake, and blade motions of a rotor in various 

flight conditions, with and without higher harmonic control (HHC) pitch inputs, with objectives to 

improve the physical understanding of the blade-vortex interaction (BVI) phenomena and to 

promote the HHC techniques for active rotor control. The test data included extensive acoustic and 

vortex flow measurements that resulted in a milestone accomplishment in rotorcraft aeromechanics 

(ref. 2). 

The HART I rotor is a four-bladed, Mach-scaled model of the BO-105 hingeless main rotor. The 

blades are composed of E-glass spar and honeycomb materials and were manufactured by Dynamic 

Engineering, Inc. (DEI) in the early 1990s. Even though some of the measured properties such as the 

nonrotating blade frequencies are available, the actual blade properties were never measured as a 

complete set. Previous studies on the validation of the HART I rotor (refs. 3–6) indicate that the 

predicted airloads are reasonably matched with the measured data, whereas the structural load results 

 

1

 Department of Aerospace Information Engineering, Konkuk University, Seoul, South Korea
2 

exhibit poor correlation with the wind tunnel test data, in terms of both magnitude and phase. 

In some investigations, good correlation was obtained by adjusting the blade stiffness and inertia 

(refs. 5, 6). This suggests uncertainty in the blade property set, and there is a need for reliable HART 

I blade properties that can only be achieved by a careful measurement process. Furthermore, it is 

known that up to four different sets of blade property data for HART I have been in use, and there is 

a clear need for a unified version of the blade properties. 

In an attempt to resolve the uncertainty issue associated with the HART I blade properties and to 

provide the required data set to the rotorcraft community, the blades used in the wind tunnel test in 

1994 were delivered to NASA Ames Research Center in 2005 from the DLR. Since then, a series of 

laboratory tests have been conducted to experimentally determine the structural properties of HART 

I blades. The measurements include geometric offsets, bending and torsion stiffness, and mass and 

inertia properties. In order to ensure the reliability of the measured data, multiple testing techniques 

were introduced for specific blade properties. These test techniques include the mirror method 

(ref. 7) and 3-point bending (ref. 8) for stiffness properties, as well as the trifilar (ref. 9) and 

pendulum methods (ref. 10) for inertia properties. 

This report documents the measurement of the blade properties and provides a complete set of 

measurement data for HART I blades. The measurement methods and test procedures adopted for 

specific properties are described along with the detailed measured records. 

HART I ROTOR 

The HART I rotor is a four-bladed, 40-percent Mach-scaled hingeless BO-105 model with 2 m 

radius and 0.121 m chord length. The geometric properties of HART I blades are summarized in 

table 1. Figure 1 shows the detailed dimensions measured for the HART I blade, which has an 

overall span length of 1.873 m from root to tip. The reference blade (blade 1) is heavily equipped 

with pressure transducers and strain gauges distributed along the span and chord. Because of these 

sensors, the weight of blade 1 is about 6 percent heavier than the other blades. The weights of 

individual HART I blades are documented in the test report (ref. 11). Most of the pressure sensors 

are installed at three radial stations (r/R = 0.75, 0.87, 0.97) to obtain the complete pressure 

distribution along the chordwise direction. A total of 32 strain gauges, distributed between r/R = 

0.14 and 0.83, are attached on the blade surface to measure the structural loads and the elastic 

deflections of the blade. Figure 2 shows the configuration of the HART I rotor hub. All four HART I 

blades are identified with different colors. For instance, the instrumented blade is identified with 

yellow ribbons taped in the blade root region and named briefly as H1Y. The rest of the blades are 

named in a similar manner as shown in table 2. The additional blade H1S (spare) is also available for 

the structural test. 

HART I BLADE PROPERTY MEASUREMENT 

Ideally, the instrumented blade (blade 1) would be used to measure the blade structural properties 

because most of the wind tunnel measurements were carried out using blade 1. However, blade 1 

was severely damaged during a separate test after HART I and, consequently, could not be used for 
3 

further structural tests. The other blades also suffer from partial damage concentrating mostly near 

the trailing edge of the blades’ inboard region. In general, they appear appropriate for structural tests 

because the primary load carrying parts remain relatively healthy despite the accident. Therefore, 

measurements were made using the remaining set of blades. In addition, a spare HART I blade 

(H1S), which remains clean and intact, is available for the structural tests. One of the HART I blades 

(blade 3, H1B) was cut into several pieces to obtain the mass and inertia properties of the blade cross 

sections. As is shown in figure 1, the airfoil section of the HART I blade with constant chord starts 

at 22 percent radial station (0.22R) up to the tip of the blade. For convenience, inboard of 0.22R is 

called the blade root section, and the outboard portion is called the blade uniform section. Specific 

testing methods and procedures for the measurement of HART I blade properties are described in 

the following section. 

TABLE 1. GENERAL PROPERTIES OF THE HART I BLADE 

Rotor radius, m 

Blade chord, m 

Airfoil 

Blade root cutout, m 

Blade twist, deg 

Blade twist at the tip, deg 

Position of zero twist, m 

Airfoil tab length, m 

Airfoil tab thickness, m 

2.0 

0.121 

NACA 23012mod 

0.44 

–8.0 

–2.4 

1.4 

0.0054 

0.0008 

TABLE 2. HART I BLADE NAMES 

Blade No. Nickname 

Blade 1 

Blade 2 

Blade 3 

Blade 4 

Spare blade 1 

H1Y (yellow) 

H1G (green) 

H1B (blue) 

H1R (red) 

H1S (spare) 

1.873 m

0.373 m 1.56 m

y

x

0.22R

R = 2 m

Figure 1. Geometric dimensions measured for the HART I blade. 
4 

Figure 2. Configuration of the HART I rotor hub. 

Mass and Inertia Properties 

Blade 3 (H1B) was cut into six small pieces to measure the mass and inertia properties of the blade 

uniform section. Figure 3 shows the schematic view of the cut-out sections. The region of the cut 

sections is about 994 mm (39.125 in.) long, starting from the blade tip. As shown in figure 3, they 

consist of three 12.7-mm-wide sections (A, B, E), two 25.4-mm-wide sections (C, F), and one 

905-mm-wide section (D). The actual dimensions of the cut-out sections indicate some scatter due to 

imperfections in the blade cuts. The weights of each blade section segment were measured using a 

mechanical balance. Table 3 shows the mass properties of individual sections. The blade tip sections 

(A, B) have a large piece of metal near the leading edge resulting in about twice as much weight 

compared to the other sections. The chordwise center of gravity (CG) is measured by placing the 

blade section segments on a needle top, as shown in figure 4. The stable position of a section is 

marked by the painted tip of the needle top and then the distance from the leading edge is measured. 

This process is repeated several times to reduce the measurement error. The position of CG in the 

chordwise direction varies between the sections because of the differences in the internal layouts 

(e.g., balancing weights and internal cables), as well as the uncertainty in the cuts. The mid-section 

D has relatively uniform properties with significantly less uncertainty in geometries and layouts. It is 

finally determined that the measured CG of the blade uniform section is located at 26.5 percent 

chord from the leading edge of the blade section. 

Figure 3. Schematic view for cut-out sections of H1B (blade 3). 
5 

TABLE 3. MASS PROPERTIES OF H1B CUT SECTIONS 

Section Actual Width, mm Weight, kg Polar MOI at QC, 

kg-m

A 12.7 0.0260 0.000670 

B 13.5 0.0349 – 

C 25.9 0.0311 0.000534 

D 905 0.8677 0.000572 

E 13.1 0.0135 – 

F 26.2 0.0269 0.000697 

Figure 4. Measurement of the chordwise center of gravity. 

The polar mass moment of inertia (MOI) is obtained using a trifilar pendulum method (ref. 9). In 

this method, a circular disk with known weight and inertia is suspended by three thin cables having 

equal lengths (see fig. 5). The polar MOI Iθ is obtained using the relationship given by (ref. 9): 

cl

W r t

b

I 2

2 2

4

1

π

θ = (1) 

where W is the weight of the suspended object, r is the radial distance of the cable attachment from 

the disk center, t is the time period, lc is the length of the cable, and b is the length of the blade 

segment. The measurement is carried out in the following sequence: 1) place the blade uniform 

section on the suspended disk; 2) start a pendulum motion with a small initial angle; 3) obtain the 

period of oscillations after sufficient number of cycles; and 4) repeat the above procedures for an 
6 

averaged response. Figure 5 shows a photograph taken for the actual measurement on the polar MOI 

of a blade uniform section. The circular disk has a weight of 0.476 kg with a diameter of 0.3048 m. 

The disk is supported by three cables having the dimension of 0.5733 m and the radius of 0.146 m 

from the center. A laser sensor and a frequency counter (HP 5334B) are used to measure the period 

of oscillations. About 40 cycles are repeated for each section to obtain the frequency response. 

Table 4 shows the raw data on measured periods of oscillations for sections A, C, D, and F. The 

actual inertia component is obtained using Eq. (1) after subtracting the contribution of the circular 

disk. The measured polar MOI for each section is presented in table 3. It is noted that the 

measurement is made at the quarter chord (QC) axis of the blade sections. The polar MOI at CG and 

EA (elastic axis) is evaluated respectively using the parallel axis theorem as given by, 

( )

2

2

2

, , 1

2

, , 1

I I m d d

I I md

EA QC

CG QC

= − −

= −

θ θ

θ θ

 (2) 

where m denotes the mass of the sections, d1 is the chordwise offset between CG and QC, and d2 is 

the chordwise offset between CG and EA. 

Figure 5. Measurement of the polar mass moment of inertia for a cut-out section using 

the trifilar pendulum. 
7 

TABLE 4. TIME PERIOD OF OSCILLATIONS MEASURED FOR H1B CUT SECTIONS 

No. of Scans Time Period, sec 

Section A Section C Section D Section F 

1 0.718436 0.712524 0.502541 0.73254 

2 0.719181 0.712324 0.502345 0.732435 

3 0.719112 0.712413 0.502469 0.73253 

4 0.718821 0.712195 0.502389 0.732582 

5 0.718636 0.712533 0.502481 0.732452 

6 0.718726 0.712146 0.502159 0.732679 

7 0.718763 0.712191 0.502104 0.732534 

8 0.718793 0.712063 0.502197 0.73246 

9 0.718981 0.711984 0.502379 0.732387 

10 0.718743 0.712082 0.501984 0.732499 

11 0.718735 0.71205 0.501794 0.732381 

12 0.718767 0.712218 0.501049 0.732295 

13 0.718551 0.712115 0.501465 0.73238 

14 0.718893 0.712226 0.50257 0.732237 

15 0.718945 0.711916 0.502309 0.732193 

16 0.718696 0.712135 0.502521 0.732358 

17 0.718612 0.71191 0.50091 0.732311 

18 0.71878 0.711974 0.500445 0.732394 

19 0.718642 0.712116 0.501305 0.732439 

20 0.718654 0.711971 0.502081 0.732327 

21 0.718564 0.712094 0.501819 0.732278 

22 0.718696 0.711716 0.501369 0.732307 

23 0.718555 0.712128 0.500848 0.732384 

24 0.71854 0.711951 0.502235 0.732168 

25 0.718852 0.711876 0.501618 0.732365 

26 0.718811 0.711900 0.500377 0.732361 

27 0.718600 0.711799 0.500963 0.732363 

28 0.718447 0.712151 0.500901 0.732261 

29 0.718033 0.711635 0.501374 0.732319 

30 0.719321 0.711901 0.501516 0.732197 

31 0.7189791 0.7115144 0.5015562 0.7322398 

32 0.7188179 0.7116963 0.5012538 0.7321769 

33 0.7187343 0.7119638 0.5011115 0.7322537 

34 0.7189463 0.7117866 0.5010785 0.732542 

35 0.7187833 0.7120377 0.5013631 0.7319772 

36 0.718413 0.7114913 0.5008766 0.732253 

37 0.7187677 0.7116729 0.5018594 0.7322524 

38 0.7187611 0.7118541 0.4994735 0.7322852 

39 0.7185838 0.711904 0.4986774 0.7318549 

40 0.7184031 0.712002 – 0.7322085 
8 

Elastic Axis 

The elastic axis (EA) is defined as the chordwise position of the blade where the vertical bending 

introduces no tosional motion. Figure 6 shows the measurement setup for the determination of the 

EA. A clamped-free blade, having effective length of about 946 mm, with a 76.2-mm-wide steel root 

fixture with a loading fixture at the tip, is constructed for this purpose. The number 4 blade (H1R) is 

used for the test. The position of loading along the chord can be varied using a sliding table attached 

to the loading fixture, and the amount of loading is measured by an interface load-cell. To measure 

the angular displacements, both dial gauges and an auto-collimator are installed near the root and the 

tip of the cantilevered blade, respectively. Two dial guages separated by 91 mm along the blade 

chord are used to measure the rotational angle with the resolution of 11.5 arcsecond. A third dial 

gauge is set to measure the chordwise travel of the sliding table. Two optical mirrors are mounted on 

the blade leading edge near the blade tip, and they are aligned with the auto-collimator to measure 

the angular displacement as indicated in figure 6. Once the measurement setup is completed, the 

load is applied first at the quarter chord position, and the angle of twist is determined by reading the 

collimator angle as well as the dial gauges. The loads are applied up to 11.2 N, which corresponds to 

the limit of the collimator reading. Next, the chordwise position of loading is moved toward leading 

edge or trailing edge until the relative twist angle becomes nearly zero, which represents the 

EA position. The measured EA of the blade uniform section is positioned at 20.5 mm (0.169 c) from 

the leading edge. The measurement error is within 0.5 deg by the collimator limit. 

Figure 6. Measurement setup for the determination of elastic axis. 
9 

Section Stiffness 

The stiffness measurements are made based on two techniques: the mirror method (ref. 11) and the 

3-point bending technique (ref. 12). The first one uses a pair of mirrors attached on the blade surface 

while laser lights are beamed onto the mirrors. It is assumed that the section properties are uniform 

between the mirror pair. Figure 7 shows the schematic view of the mirror method for a fixed-free 

blade in bending. The laser lights are reflected from the mirrors onto the wall, separated at a distance 

D (see fig. 8). In the initial unloaded state, the laser beam is reflected at an angle 2θ and is 

positioned on the wall at a distance δ 0 , as shown in figure 8. When the blade is under bending, the 

mirrors are rotated further to have an inclination angle 2β, and the laser reflection on the wall 

traverses to a distant location δ. The laser path angle β is determined using the geometric 

relationship shown in figure 7: 





 



 − + = − θ δ δ β D

1 0 tan

2

1 (3) 

By increasing the loads applied to the blade and the movement of laser reflections on the wall, the 

effective blade stiffness in bending is obtained between each mirror pair as: 

( ) 2

2

2

1 2

1

a a

P

EI = − β (4) 

where P is the applied force, and a1 and a2 denote the distances between the mirrors and the position 

of load (see fig. 7), respectively. In the actual measurements, the load is increasingly applied, and 

the slope of the laser reflection angle versus the applied load (2β/P) is obtained accordingly. A 

number of cycles are preceded using the same setup to ensure repeatability. 

Figure 7. The mirror method for a blade in bending. 
10 

Figure 8. Geometry of the mirror method. 

The torsion stiffness is obtained by measuring the angle of twist under a torque and is given by the 

relation: 

T

l GJ

φ

1 = (5) 

where l1 is the effective length of the blade between the end supports, φ is the angle of rotation, and 

T denotes the applied torque. The mirror method is again applied to determine the angle of twist 

between specified radial stations of the blade. 

For the 3-point bending, the blade is placed on roller supports to simulate a simply supported 

boundary condition while the load is applied at the center (see fig. 9). Uniformity of blade properties 

between the end supports is assumed to obtain the blade elastic property. The bending stiffness is 

evaluated using the relation: 

( ) P

l EI

c 48 /

3

2

⋅ δ = (6) 
11 

where l2 is the length between the end supports, δ c denotes the deflection at the center, and 

δ c / P represents the slope of the deflection-load curve. The deflection is measured using a pair of 

dial gauges having a resolution of 0.0001 inch each. The slope of the deflection-load curve is 

determined by averaging the measured records. This rather simple technique has proven efficient to 

determine the bending stiffness of the blade uniform section. In the following subsections, the 

measurement details of the flap bending, chord bending, and torsion stiffness are described. 

Chord Bending 

The 3-point bending method is used to determine the chord bending stiffness of the blade uniform 

section. Special fixtures and loading blocks were built for the boundary supports at the ends and at 

the application of the load, respectively. In addition, tilt platforms having ±2.86 deg adjustable range 

were placed underneath the end supports to accommodate the built-in twist angle of the HART I 

blade and to ensure that the loading axis remains perpendicular to the blade axis. Both lead bending 

(leading-edge down) and lag bending (trailing-edge down) tests were performed and then averaged 

for the chord bending stiffness. Figure 10 shows the measurement setup for the lag bending stiffness 

using the 3-point bending method. The length of the blade between the end supports, l2, is 1.381 m, 

and the load (weight) P is increased from 5.528 kg up to 16.79 kg. The deflection is measured at the 

central station of the blade using a dial gauge having a resolution of 0.0001 inch (0.0254 mm). A 

total of 10 different measurements were made for either lead bending or lag bending. Tables 5 and 6 

show the measurement records for the deflections at the center for lead bending and lag bending, 

respectively, with the increase of the weights. Figures 11 and 12 show the linear regressions of the 

load-deflection curves for 10 different measurements on lead bending and lag bending cases, 

respectively. The measured slopes indicate some scatter between the different cases. The standard 

deviation of the slopes in reference to the mean value is 2.16 percent for the lag bending and 

2.51 percent for the lead bending. The slopes of each load-deflection curve in the dimension of N/m 

are shown in table 7. Inserting the averaged values of the load-deflection curves into Eq. (6), the lead 

bending or the lag bending stiffness can be obtained. The averaged values are 3,833 N-m2

 for the 

lead bending and 4,232 N-m2 for the lag bending. The chord bending stiffness, which is determined 

by averaging the lead bending and the lag bending stiffness, is 4,032 N-m2

. The estimated chord 

bending stiffness by DEI is 4,706 N-m2

, 17 percent higher than the measured value. 

 

Figure 9. The simply supported blade in bending (3-point bending method). 
12 

Figure 10. Measurement of the lag bending using a 3-point bending method. 

TABLE 5. MEASURED DEFLECTIONS AT THE BLADE CENTRAL POSITION FOR THE 

LEAD BENDING 

Load P

kg Deflections at the Center δc, mm 

0 0 0 0 0 0 0 0 0 0 0 

5.528 0.742 0.712 0.730 0.687 0.687 0.707 0.681 0.694 0.687 0.697 

9.528 1.371 1.269 1.318 1.239 1.267 1.262 1.234 1.247 1.242 1.244 

12.25 1.790 1.693 1.721 1.658 1.678 1.670 1.635 1.645 1.635 1.647 

14.97 2.201 2.102 2.140 2.000 2.074 2.076 2.028 2.036 2.033 2.036 

16.79 2.480 2.371 2.406 2.312 2.350 2.330 2.294 2.294 2.292 2.297 

TABLE 6. MEASURED DEFLECTIONS AT THE BLADE CENTRAL POSITION FOR THE 

LAG BENDING 

Load P

kg Deflections at the Center δc, mm 

0 0 0 0 0 0 0 0 0 0 0 

5.528 0.669 0.633 0.636 0.656 0.666 0.692 0.679 0.681 0.687 0.676 

9.528 1.239 1.234 1.188 1.191 1.191 1.196 1.178 1.183 1.191 1.183 

12.25 1.599 1.586 1.551 1.536 1.551 1.541 1.518 1.515 1.515 1.513 

14.97 1.959 1.936 1.893 1.888 1.891 1.909 1.858 1.860 1.860 1.860 

16.79 2.203 2.172 2.124 2.124 2.119 2.137 2.094 2.086 2.117 2.094 
13 

TABLE 7. SLOPES OF THE LOAD-DEFLECTION CURVE FOR THE LEAD-LAG BENDING 

Case Slopes of P/δc Curve, N/m 

Lead 65809 68926 67946 71194 69440 70065 71242 71261 71299 71222 

Lag 74101 74625 76572 77075 77177 76942 78699 78889 78271 78663 

Figure 11. Linear regression of the load-deflection curve for the lead bending 

(data from table 5). 

Figure 12. Linear regression of the load-deflection curve for the lag bending 

(data from table 6). 
14 

Flap Bending 

The flap bending of the blade uniform section is obtained using the 3-point bending technique while 

the mirror method is used for the root section. Figure 13 shows the measurement setup for the 

3-point bending to determine the flap bending stiffness of the HART I blade. The full span of the 

H1S blade is used for this property. The length between the supports at end is 1.214 m, and the 

weights applied at the center are increased up to 2.34 kg. At the maximum loading, the deflections at 

the center reach around 4.6 mm. The deflections are measured using a dial gauge installed at the 

center of the blade (see table 8). Figure 14 shows the linear regression of the load-deflection curves 

for 10 different measurements. As can be seen in the plot, the linearity is a good approximation for 

the elastic behavior of the blade. Most of the measured deflections form nearly identical curves with 

a few exceptions. Table 9 presents the slopes of the load-deflection curve P/δc for the 10 different 

measurements. The standard deviation of the data is about 1.2 percent in reference to the mean value 

of the load-deflection curve. Overall, the flap bending tests demonstrate reasonably good 

repeatability as compared with the chord bending tests. The flap bending stiffness is obtained by 

inserting the load-deflection curve P/δc into Eq. (6), which gives about 188.4 N-m2

 for the uniform 

section of the H1S blade. Similar tests were also performed for the cut-down section of H1B (blade 

3), as shown in figure 15. In this case, the length between the end supports is 0.902 m. The measured 

flap bending obtained using the load-deflection curves is 182.9 N-m2

. The final value for the 

measured flap bending of the uniform portion of the HART I blade is obtained by averaging the 

values between the H1S and H1B cut-down sections, which result in 185.6 N-m2. 

The flap bending for the root portion of the HART I blade is determined using the mirror method. 

Figure 16 shows the actual measurement scene for the flap bending via the mirror method. The blade 

(H1S) is clamped at the root using the L-bracket made of stainless steel and hung vertically. The 

load is applied near the tip in the flap-up direction using a pulley connected with a series of weights. 

The load remains perpendicular to the blade chord at the tip. A total of six mirrors are attached on 

the blade surface: four of them are for the blade root and two are for the uniform blade. The mirrors 

from the top to the lower end of the root region are placed at 1.796 m, 1.758 m, 1.692 m, 1.662 m, 

and 1.557 m, measured from the blade tip, respectively. It is noted that the bracket itself is used as a 

top mirror. The direct distance between the mirror and the laser on the wall is about 7.3 m. The 

vertical distances (δ0) from the ideally leveled laser to the undeflected laser for the mirrors are 

–1.39 m, 0.19 m, –0.69 m, 0.11 m, and –0.205 m, respectively. The load is increased from 0.199 kg 

to 1.69 kg. Table 10 shows the measured records for the traverse distance of laser reflections on the 

wall for each mirror. The mirrors are designated M1 to M5 located from the top. At each mirror pair, 

the delta slope (2β/P) is evaluated by measuring the traverse distance of the laser reflections on the 

wall, and these are inserted in Eq. (4) for the flap bending stiffness between the mirror pair. The 

measurement is conducted for both H1R (blade 4) and H1S (spare). The flap bending stiffness 

between each mirror pair is averaged for H1R and H1S, and the results are presented in table 11. 

Torsion Stiffness 

The blade torsion stiffness is obtained using Eq. (5). The mirror method is again introduced to 

determine the ratio of the twist angle to the torque (φ/T). Figure 17 shows the setup for the 

measurement of the torsion stiffness. Three mirrors are attached on the blade surface at 0.782 m, 

0.4 m, and 0.0534 m, relative to the blade tip. The mirrors are designated M1, M2, and M3, 
15 

respectively. The nose-down torque up to 15.8 N-m is applied at the EA location. The amount of 

torque is measured by a torque cell with an excitation voltage of 5.014 V and a conversion factor of 

2733.2 N-m/V. The distance between the mirror and the wall is approximately 4.76 m. The vertical 

distances from the laser sources to the reflections are 0.422 m, 0.273 m, and 0.603 m, respectively. 

Table 12 shows the measurement records for the traverse distance of laser reflections marked on the 

wall for each mirror. The measurements are made for the H1R blade (blade 4) with either pitch-up or 

pitch-down position, and they are averaged for about six different measurements. The final 

measured torsion stiffness is determined to be 128.5 N-m2 for the uniform section. 

Figure 13. Measurement of the flap bending for H1S blade using a 3-point bending method. 

0 

1 

2 

3 

4 

5 

6 

0.00 0.05 0.10 0.15 

Weights, lb

Deflection, in

Weights, kg

Figure 14. Linear regression of the load-deflection curve for the flap bending (data from table 8). 
16 

Figure 15. Measurement of the flap bending for H1B cut section using a 3-point bending method. 

Figure 16. Measurement of the flap bending with the mirror method. 
17 

Figure 17. Measurement of the torsion stiffness with the mirror method. 

TABLE 8. MEASURED DEFLECTIONS AT THE BLADE CENTRAL POSITION FOR THE 

FLAP BENDING 

Load P

kg Deflections at the Center δc, mm 

0 0 0 0 0 0 0 0 0 0 0 

1.161 0.0359 0.036 0.0344 0.0369 0.0437 0.0346 0.0352 0.0355 0.0339 0.0358

3.161 0.1073 0.107 0.1051 0.1073 0.1142 0.1049 0.106 0.1066 0.1051 0.1053

5.161 0.1782 0.1781 0.1759 0.1765 0.1856 0.1764 0.1774 0.1772 0.1749 0.1766

TABLE 9. SLOPES OF THE LOAD-DEFLECTION CURVE FOR THE FLAP BENDING 

Case Slopes of P/δc Curve, N/m 

Flap 5035.0 5041.0 5093.2 5093.0 4886.2 5083.6 5056.6 5061.7 5113.9 5090.7
18 

TABLE 10. THE TRAVERSE DISTANCE OF LASER DOTS ON THE WALL FOR EACH MIRROR 

(FLAP BENDING) 

Load, kg Traverse Distance of Laser, mm 

M1 M2 M3 M4 M5 

0 0 0 0 0 0 

0.199 1.5 4 10 15.5 36 

0.398 3 8 21 31.5 72 

0.597 5.5 13 32 47.5 108.5 

0.795 7.5 18 43 64 145.5 

0.994 10 22 54 80 183 

1.193 12 27.5 65 96 220 

1.392 14.5 32 76 112 257 

1.591 17 37 87 128.5 294 

1.690 N/A 39.5 92.5 136.5 312 

TABLE 11. MEASURED FLAP BENDING FOR BLADE ROOT REGION 

Station Flap Bending Stiffness, N-m2

1.796 m – 1.758 m 

1.758 m – 1.692 m 

1. 692 m – 1.662 m 

1.662 m – 1.557 m 

656.1 

528.3 

270.1 

219.4 

TABLE 12. THE TRAVERSE DISTANCE OF LASER DOTS ON THE WALL FOR EACH MIRROR 

(TORSION STIFFNESS) 

Load, kg Traverse Distance of Laser, mm 

M1 M2 M3 

2.26 0 100 100 

4.54 38.5 203 267 

6.79 76 304.5 433.4 

9.06 115.5 408.5 605 

11.31 155 516 784 

13.56 196.5 631 977.5 

14.69 217 687 1074 
19 

TABLE 13. COMPARISON OF BLADE STRUCTURAL PROPERTIES OF HART I 

UNIFORM SECTION 

Property Measured DEI % Difference 

Flap bending 190.1 N-m2 185.6 N-m2 2.37% 

Chord bending 4706 N-m2 4032 N-m2 14.3% 

Torsion stiffness 134 N-m2 128.5 N-m2 4.10% 

Center of gravity 0.245 c 0.265 c 8.16% 

Elastic axis 0.20 c 0.169 c 15.5% 

Polar MOI at CG 0.000623 kg-m 0.000569 kg-m 8.67% 

Comparison With Estimated DEI Values 

The present measured structural property data obtained for the uniform portion of the HART I blade 

are compared against the estimated values obtained by DEI, the manufacturer of HART I blades. 

Table 13 shows the comparison results. A significant change is seen in the blade structural properties. 

Generally, the measured data indicate more flexible blade stiffness compared to the DEI values. The 

maximum difference is about 14.3 percent for the chord bending stiffness. DEI predictions indicate 

that the chordwise CG is located very close to the QC axis and shifted in the direction of the leading 

edge. On the contrary, the measured CG indicates a shifting to the trailing edge. In addition, the 

measured EA is positioned far to the leading edge compared to the DEI predictions. Overall, the 

measured offset between CG and EA is larger by about 5 percent chord length than the estimated 

value by DEI. These differences in measured blade properties (i.e., softening of blade stiffness 

combined with increased offsets) are expected to introduce larger couplings between aerodynamics 

and structures of HART I blades than DEI values, which will make the rotor aeroelastic analysis 

more complex. 

Almost all of the blade properties are measured for the blade uniform portion. Only the flap bending 

is considered for the measurement of the blade root section. The lack of data in this region of blade 

is overcome by introducing the DEI values and combining them with the present measured property 

data results in the complete set of HART I structural properties. Figures 18 through 25 show the 

comparison between the present measured data and the DEI values. The blade properties are 

presented as a function of the blade span coordinates. It is observed that the DEI values generally 

overestimate the blade section stiffness by up to 30 percent in the flap bending of the blade root 

section. 
20 

Figure 18. Comparison of the center of gravity offset from the elastic axis. 

Figure 19. Comparison of the elastic axis offset from the quarter chord axis. 
21 

Figure 20. Comparison of flap bending stiffness along the blade length. 

Figure 21. Comparison of chordwise bending stiffness along the blade length. 
22 

(c) Torsion 

Figure 22. Comparison of torsion stiffness along the blade length. 

Figure 23. Comparison of mass distribution along the blade length. 
23 

Figure 24. Comparison of polar mass moment of inertia along the blade length. 

Figure 25. Comparison of section radius of gyration along the blade length. 
24 

Expanded Blade Property Data 

The complete set of structural property data for the HART I blade in Comprehensive Analytical 

Model of Rotorcraft Aerodynamics and Dynamics II (CAMRAD II) input format (ref. 13) is 

summarized in table 14. The first column (r/R) denotes the blade coordinates nondimensionalized by 

the blade radius (R = 2 m). YEA and ZEA denote the location of the EA parallel and perpendicular to 

the chord line of the blade from the QC axis, respectively. The sign convention for Y and Z axes is 

defined as positive when moved toward the trailing edge and the vertical direction, respectively. The 

next two columns describe the position of CG from the EA in the Y and Z coordinates. It is remarked 

that the position of tension center is not measured and assumed to coincide with the EA location. 

Twist and Mass, appearing after the CG offsets, denote the blade pretwist angle and the mass 

distribution, respectively. The blade flap bending, EIFLAP, chord bending, EICHD, and torsion stiffness, 

GJ, follow next. The next column is the cross-sectional radius of gyration in polar coordinates, 

Kp polar radius of gyration. The final two columns represent the polar moment of inertia at CG for Iθ

and IP, respectively. All the values presented in table 14 are given in the International System of 

Units (SI). 

COMPARISON OF ROTOR NATURAL FREQUENCIES 

In figure 26, predicted natural frequencies of the HART I rotor using the measured properties are 

compared against the test data (ref. 11), as well as those obtained using DEI property data. The 

predicted results are obtained in vacuum condition using CAMRAD II (ref. 13). The frequency 

values are nondimensionalized by the rotor nominal speed (Ω0 = 1040 RPM). It should be noted that 

the measured frequencies are obtained for the instrumented blade (blade 1) and only available at 

nonrotating condition. For the control system modeling, a linear pitch link model with the spring 

constant of 0.43 million N/m is adopted, which is equivalent to a pitch bearing stiffness of 1706 

N-m/rad, to match the first torsion frequency of the instrumented blade. In general, the DEI data 

result in higher bending and torsion frequencies than the measured values. It is observed that the 

present predictions indicate reasonable agreements for lead-lag bending and torsion frequencies but 

show slightly higher frequencies in flap bending compared to the measured data. The main reason is 

because the measured frequencies are taken from the instrumented blade while the present structural 

properties are obtained from the rest of the blades (i.e., uninstrumented blades). Considering the fact 

that the instrumented blade is heavier than the other blades by about 6 percent (ref. 11), the present 

frequencies appear to have a reasonable correlation with the test data. 

Further investigation was made in Jung et al. (ref. 14) for the correlation of airloads and structural 

loads of the HART I rotor in descending flight condition, with and without higher harmonic pitch 

control inputs, using the measured blade properties. It was observed that, in general, more improved 

predictions were achieved with the measured data. 
TABLE 14. SUMMARY OF HART I BLADE PROPERTIES 

r/R YEA, 

m 

ZEA, m YCG, m ZCG, m Twist deg Mass kg/m EIFLAP N-m2 EICHD N-m2 GJ N-m2 kP, m Iθ_CG kg-m IP_CG kg-m 

0 0 0 0 0.0001 3.84 10.706 25482.82 25482.82 10000.65 0.0056 0.000356 0.000311

0.025 0 0 0 0.0001 3.84 10.706 25482.82 25482.82 10000.65 0.0056 0.000356 0.000311

0.0251 0 0 0 0.0001 3.84 10.529 41237.32 41237.32 10000.65 0.0056 0.000356 0.000311

0.05 0 0 0 0.0001 3.84 10.529 41237.32 41237.32 10000.65 0.0056 0.000356 0.000311

0.0501 0 0 0 0.0001 3.84 9.633 39486.87 61984.91 10000.65 0.0192 0.003559 0.0035140.0699 0 0 0 0.0001 3.84 9.633 39486.87 61984.91 10000.65 0.0192 0.003559 0.003514

0.07 0 0 0 0.0001 3.84 10.706 1004.57 6600.15 438.03 0.0266 0.007562 0.007517

0.095 0 0 0 0.0001 3.84 10.706 1004.57 6600.15 438.03 0.0266 0.007562 0.007517

0.0951 0 0 0 0.0001 3.84 1.321 656.1 5767.9 166.45 0.0124 0.000222 0.000178

0.12 0 0 0 0 3.84 1.321 656.1 5767.9 166.45 0.013 0.000222 0.000178

0.1201 0 0 0 0 3.84 1.25 528.3 4961.69 146.37 0.013 0.000222 0.000178

0.135 0 0 0 -0.00002 3.84 1.25 528.3 4961.69 146.37 0.0136 0.000222 0.000178

0.1351 0 0 0 -0.00002 3.84 1.068 528.3 4318.7 195.42 0.0136 0.000178 0.000133

0.15 0 0 0 -0.00002 3.84 1.068 528.3 4318.7 195.42 0.0138 0.000178 0.000133

0.1501 0 0 0 -0.00002 3.84 1.02 528.3 3340.16 214.92 0.0138 0.000178 0.000133

0.155 0 0 0 0.00002 3.84 1.02 528.3 3340.16 214.92 0.017 0.000178 0.000133

0.1551 0 0 0 0.00002 3.84 1.02 270.1 3340.16 214.92 0.017 0.000178 0.000133

0.17 0 0 0 0.00002 3.84 1.02 270.1 3340.16 214.92 0.022 0.000178 0.000133

0.1701 0 0 0 0.00002 3.84 0.828 219.4 2849.65 189.96 0.022 0.000222 0.000178

0.19 0 0 0 0 3.84 0.828 219.4 2849.65 189.96 0.022 0.000222 0.000178

0.1901 0 0 0 0 3.84 0.8 219.4 2875.27 172.48 0.022 0.0004 0.000356

0.20225 -0.00606 0.00118 0.003322 -0.0007 3.84 0.8 219.4 2875.27 172.48 0.0232 0.0004 0.0003560.20226 -0.00606 0.00118 0.003322 -0.0007 3.84 0.8 219.4 2875.27 172.48 0.0232 0.0004 0.000356

25 
TABLE 14. SUMMARY OF HART I BLADE PROPERTIES (CONTINUED) 

r/R 

XEA, m ZEA, m XCG, m ZCG, m Twist deg Mass kg/m EIFLAP N-m2 EICHD N-m2 GJ N-m2 kP, m Iθ_CG kg-m 

IP_CG

kg-m 

0.21 -0.0098 0.00118 0.01161 -0.00114 3.84 0.8 219.4 2875.27 172.48 0.0252 0.0004 0.000356

0.2101 -0.0098 0.00118 0.01161 -0.00114 3.84 0.996 219.4 3825.3 128.5 0.0252 0.000534 0.000489

0.22 -0.0098 0.00118 0.01161 -0.00022 3.84 0.996 219.4 3825.3 128.5 0.027 0.000534 0.000489

0.2201 -0.0098 0.00118 0.01161 -0.00022 3.8392 0.996 185.6 3825.3 128.5 0.027 0.000534 0.000489

0.23 -0.0098 0.00118 0.01161 -0.00022 3.76 0.996 185.6 3825.3 128.5 0.027 0.000534 0.000489

0.2301 -0.0098 0.00118 0.01161 -0.00022 3.7592 0.982 185.6 4032 128.5 0.027 0.0006 0.000556

0.25 -0.0098 0.00118 0.01161 -0.00022 3.6 0.982 185.6 4032 128.5 0.027 0.0006 0.000556

0.2501 -0.0098 0.00118 0.01161 -0.00022 3.5992 0.958 185.6 4032 128.5 0.027 0.0006 0.000556

0.3 -0.0098 0.00118 0.01161 -0.00022 3.2 0.958 185.6 4032 128.5 0.027 0.0006 0.000556

0.3001 -0.0098 0.00118 0.01161 -0.00022 3.1992 0.948 185.6 4032 128.5 0.027 0.0006 0.0005560.3714 -0.0098 0.00118 0.01161 -0.00022 2.6288 0.948 185.6 4032 128.5 0.027 0.0006 0.0005560.3715 -0.0098 0.00118 0.0098 -0.00022 2.628 2.212 185.6 4032 128.5 0.027 0.000603 0.00056 

0.397 -0.0098 0.00118 0.0098 -0.00022 2.424 2.212 185.6 4032 128.5 0.027 0.000603 0.00056 

0.3971 -0.0098 0.00118 0.01161 -0.00022 2.4232 0.948 185.6 4032 128.5 0.027 0.0006 0.000556

0.503 -0.0098 0.00118 0.01161 -0.00022 1.576 0.948 185.6 4032 128.5 0.027 0.0006 0.000556

0.5031 -0.0098 0.00118 0.01161 -0.00022 1.5752 1.027 185.6 4032 128.5 0.027 0.000694 0.000643

0.522 -0.0098 0.00118 0.01161 -0.00022 1.424 1.027 185.6 4032 128.5 0.027 0.000694 0.000643

0.5221 -0.0098 0.00118 0.01161 -0.00022 1.4232 0.958 185.6 4032 128.5 0.027 0.000569 0.000528

0.974 -0.0098 0.00118 0.01161 -0.00022 -2.192 0.958 185.6 4032 128.5 0.027 0.000569 0.000528

0.9741 -0.0098 0.00118 0.01161 -0.00022 -2.1928 1.2 185.6 4032 128.5 0.027 0.00053 0.000492

0.987 -0.0098 0.00118 0.01161 -0.00022 -2.296 1.2 185.6 4032 128.5 0.027 0.00053 0.000492

0.9871 -0.0098 0.00118 0.0098 -0.00022 -2.2968 2.342 185.6 4032 128.5 0.027 0.00067 0.000622

0.994 -0.0098 0.00118 0.0098 -0.00022 -2.352 2.342 185.6 4032 128.5 0.027 0.00067 0.000622

0.9941 -0.0098 0.00118 0.0114 -0.00022 -2.3528 2.342 185.6 4032 128.5 0.027 0.000664 0.000616

1 -0.0098 0.00118 0.0114 -0.00022 -2.4 2.342 185.6 4032 128.5 0.027 0.000664 0.000616

26 
27 

0 0.2 0.4 0.6 0.8 1 1.2

0

1

2

3

4

5

6

7

8

9

10

11

12

1F

1L

2F

3F

2L

1T

4F

Non-dimensional Rotor Speed, / 0

Natural Frequency, /rev

Present with measured data

Present with DEI data 

Test [12]

5F

3L

3T

Figure 26. Comparison of rotor natural frequencies. 

CONCLUSIONS 

The elastic properties of HART I blades were measured using well-established test techniques. The 

following conclusions were drawn from this study. 

1) The blade properties were measured using several test techniques. Both flap and chordwise 

bending stiffness in the blade uniform sections were measured using the 3-point bending method, 

while the flap bending in the inboard root section and the torsion stiffness in the blade uniform 

section were measured using the mirror method. The inertia properties were measured using the 

trifilar pendulum technique. 
28 

2) The measured blade properties were compared to the estimated values provided by DEI, the 

company that designed and built the HART I blades. It was found that the deviation was up to 

30 percent for the flap bending over the blade root sections and 14.3 percent for the chord bending 

over the blade uniform section. As compared with the DEI estimations, the measured elastic axis 

(EA) was located more toward the leading edge and the center of gravity (CG) was shifted aft 

toward the trailing edge, resulting in larger offsets between CG and EA. 

3) The comparison of rotor natural frequencies indicated that the present predictions with measured 

blade properties were in reasonable agreement with the test data, as compared with the predictions 

using DEI data. 

REFERENCES 

1. Yu, Y. H.; Gmelin, B.; Heller, H.; Philippe, J. J.; Mercker, E.; and Preisser, J. S.: HHC 

Aeroacoustics Rotor Test at the DNW—The Joint German/French/US HART Project. 20th 

European Rotorcraft Forum, Amsterdam, Netherlands, 1994. 

2. Johnson, W.: Milestones in Rotorcraft Aeromechanics. NASA TP-2011-215971, 2011. 

3. Tung, C.; Gallman, J. M.; Kube, R.; Wagner, W.; van der Wall, B.; Brooks, T. F.; Burley, C. L.; 

Boyd, Jr., D. D.; Rahier, G.; and Beaumier, P.: Prediction and Measurement of Blade-Vortex 

Interaction Loading. CEAS/AIAA Aeroacoustics Conference, Munich, Germany, June 12–15, 

1995. 

4. Lim, J. W.; Yu, Y. H.; and Johnson, W.: Calculation of Rotor Blade-Vortex Interaction Airloads 

Using a Multiple-Trailer Free-Wake Model. J. of Aircraft, vol. 40, no. 6, Nov.–Dec. 2003, 

pp. 1123–130. 

5. Yeo, H., and Johnson, W.: Assessment of Comprehensive Analysis Calculation of Airloads on 

Helicopter Rotors. J. of Aircraft, vol. 42, no. 5, 2005, pp. 1218–1228. 

6. Yeo, H., and Johnson, W.: Prediction of Rotor Structural Loads With Comprehensive Analysis. 

J. of the American Helicopter Society, vol. 53, no. 2, 2008, pp. 193-209. 

7. Shekoski, T., and Tram L. H.: Blade Qualification and Accepatance Data Report, and 

Instrumentation and Calibration Report. ATI Document no. 167, Advanced Technologies, Inc., 

July 1996. 

8. Ogorkiewicz, R. M., and Mucc, P. E. R.: Testing of Fibre-Plastics Composites in Three-Point 

Bending. Composites, vol. 2, no. 3, 1971, pp. 139–145. 

9. Hughes, G. W.: The Trifilar Pendulum and Its Application to the Experimental Determination of 

Moments of Inertia. ASME Paper 57-SA-51, 1957. 

10. Sharpe, D. L.: An Experimental Investigation of the Flap-Lag-Torsion Aeroelastic Stability of a 

Small-Scale Hingeless Helicopter Rotor in Hover. NASA TP-2546 (AVSCOM TR 85-A-9), Jan. 

1986. 
29 

11. Splettstoesser, W. R.; Kube, R.; Seelhorst, U.; Wagner, W.; Boutier, A.; Micheli, F.; Mercker, 

E.; and Pengel, K.: Higher Harmonic Control Aeroacoustic Rotor Test (HART)–Test 

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