Analytical Calculation of Helicopter Main Rotor Blade 

Flight Loads in Hover and Forward Flight 

by Ki C. Kim 

ARL-TR-3180 April 2004 

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Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5068 

ARL-TR-3180 April 2004 

Analytical Calculation of Helicopter Main Rotor Blade 

Flight Loads in Hover and Forward Flight 

Ki C. Kim 

Survivability/Lethality Analysis Directorate, ARL 

Approved for public release; distribution is unlimited. 
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Analytical Calculation of Helicopter Main Rotor Blade Flight Loads in Hover and 

Forward Flight 

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14. ABSTRACT 

An aeroelastic analysis was conducted to calculate flight loads on the OH-58D Kiowa Warrior main rotor blade at hover and 

forward flight conditions. Centrifugal force and flap and chord bending moments were calculated with the University of 

Maryland Advanced Rotorcraft Code (UMARC) comprehensive helicopter aeroelastic analysis code. The calculated loads were 

correlated with available flight data for the Bell model 406LM helicopter (model 406T rotor blade) to validate the analytical 

model. After the correlation study, UMARC was used to calculate blade loads at the ballistic test section radial stations. These 

baseline loads were represented during the ballistic tests. This report presents the methods and results of the aeroelastic 

analysis. 

15. SUBJECT TERMS

flight loads, aeroelastic analysis, dynamic response 

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Ki C. Kim 

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iii

Contents 

List of Figures iv

List of Tables iv

1. Introduction 1

2. Helicopter Aeroelastic Model 1

2.1 UMARC Helicopter Aeroelastic Analysis Code.............................................................2 

2.2 Vehicle Trim....................................................................................................................3 

2.3 Rotor Steady Response....................................................................................................3 

2.4 Rotor Wake Modeling.....................................................................................................4 

2.5 Solution Procedure for Blade Load Calculations............................................................4 

3. Results and Discussion 5

3.1 Correlation Study ............................................................................................................7 

3.2 Blade Flight Load Calculations for Hover and 100-kn Forward Speed........................10 

4. Summary 12

5. References 13

List of Abbreviations and Symbols 14

Distribution List 15 
iv

List of Figures 

Figure 1. Local and global degrees of freedom of KW main rotor blade.......................................6 

Figure 2. Correlation of main rotor blade natural frequencies........................................................7 

Figure 3. Correlation of CFs along the blade span. ........................................................................8 

Figure 4. Correlation of flap bending moment along blade span (μ = 0.28). .................................9 

Figure 5. Correlation of lag bending moments along blade span (μ = 0.28)................................10 

Figure 6. Correlation of torsional moments along blade span (μ = 0.28).....................................11 

List of Tables 

Table 1. Aerodynamic characteristics of KW helicopter................................................................5 

Table 2. FE beam model input for OH-58D KW main rotor blade. ...............................................5 

Table 3. Flap bending moments of Bell model 406T helicopter main rotor blade.........................9 

Table 4. Reference blade loads and moments for test phase I-B..................................................11 
1

1. Introduction 

In support of Kiowa Warrior (KW) main rotor blade ballistic vulnerability tests under the Live 

Fire Test and Evaluation program (1), a comprehensive helicopter aeroelastic analysis was 

conducted to calculate flight loads on the OH-58D KW main rotor blade at hover and forward 

flight conditions. Centrifugal force (CF) and flap and chord bending moments were calculated 

with the University of Maryland Advanced Rotorcraft Code (UMARC) comprehensive 

helicopter aeroelastic analysis code (2). 

The calculated loads were first correlated with available flight data for the Bell Model 406LM 

helicopter to validate the analytical model. After the correlation study, UMARC was used to 

calculate blade loads at the ballistic test section radial stations. These baseline loads were 

represented during the ballistic tests (1). 

The UMARC helicopter aeroelastic model used in the present study is a nonlinear representation 

of elastic rotor blades coupled to a rigid fuselage. The key feature in UMARC is the use of a 

finite element (FE) methodology, which can accurately model the kinematics and elastic 

behavior of the rotating blade. The rotor blade is assumed to be an elastic beam undergoing flap 

bending, lag bending, elastic twist, and axial deflections. The helicopter fuselage is assumed to 

be a rigid body undergoing six degrees of freedom. Each blade is modeled as a number of beam 

FEs. The formulation for the blade and fuselage equations of motion is based on Hamilton’s 

energy principle. The analysis is developed for helicopters with nonuniform rotor blades having 

pretwist, precone, and chord-wise offsets of the center of mass, aerodynamic center, and tension 

center, from the elastic axis. 

This report presents the methods and results of the aeroelastic analysis. Definitions of symbols 

used in the report are given in the List of Abbreviations and Symbols. In section 2, the 

formulation details and aerodynamic model used in UMARC helicopter aeroelastic analysis code 

are presented. Numerical results are shown and compared with available flight data in section 3. 

The summary and recommendations for future work are presented in section 4. 

2. Helicopter Aeroelastic Model 

The calculation of rotor loads is a difficult task because of the complex interactions of structural, 

inertial, and aerodynamic forces acting on the rotary wing. Basically, it is necessary to calculate 

the periodic aerodynamic and inertial forces of the blade, and thus the resulting motion of 

structural components. Since the higher harmonic blade loading is the principal source of high 

loads, an accurate analysis of the rotor aerodynamics is required, including the effects of the 
2

rotor wake, stall, and compressibility. The high frequencies involved and the importance of 

resonance excitation also require good inertial and structural models. 

2.1 UMARC Helicopter Aeroelastic Analysis Code 

The UMARC helicopter aeroelastic model used in this study is a nonlinear representation of 

elastic rotor blades coupled to a rigid helicopter fuselage. The key feature in UMARC is the use 

of an FE methodology, which can accurately model the kinematics and elastic behavior of the 

rotating blade. The rotor blade is assumed to be an elastic beam undergoing flap bending, lag 

bending, elastic twist, and axial deflections. The helicopter fuselage is assumed to be a rigid 

body undergoing six degrees of freedom. Each blade is modeled as a number of beam FEs. The 

formulation for the blade and fuselage equations of motion is based on Hamilton's energy 

principle. The analysis is developed for helicopters with nonuniform rotor blades having 

pretwist, precone, and chord-wise offsets of the center of mass, aerodynamic center, and tension 

center from the elastic axis. This code is the current state-of-the-art rotorcraft engineering 

analysis code and is widely used by U.S. Army Research Laboratory researchers and other 

Government/industry researchers (e.g., NASA Ames and Boeing and Sikorsky). 

In UMARC, aerodynamic loads acting on the rotor blade are calculated using quasi-steady strip 

aerodynamic theory. Noncirculatory aerodynamic forces are also included. To include the effect 

of high angle-of-attack flows on the retreating blade, a dynamic stall model is incorporated. 

Dynamic stall characterizes the delay in flow separation because of unsteady angle of attack and 

the shedding of a vortex from the leading edge of the airfoil when it gets into a deep stall 

condition. These effects are introduced in the calculation of section lift and drag and pitching 

moment. The first step to calculate blade loads and moment is to determine the trim state of the 

helicopter for given flight conditions (i.e., gross weight, ambient conditions, and forward speed). 

The UMARC utilizes the coupled trim solution procedure to calculate the helicopter trim in 

hover and forward flight. 

The coupled trim analysis consists of two phases, vehicle trim and steady response, calculated as 

one coupled solution using a modified Newton’s method. For a given flight condition, the 

control settings and the blade steady response must satisfy both the blade and the vehicle 

equilibrium conditions. The method of solving simultaneously the blade responses and the trim 

control settings is referred to as the coupled trim analysis. An uncoupled trim solution based on 

the rigid flapping blade assumption is used as an initial estimate for the coupled trim analysis. 

With the trim control settings, the blade steady responses are calculated. Using the blade 

responses, the rotor hub loads and a new vehicle equilibrium position are recomputed. The 

control settings are then updated based on the new equilibrium condition (3). 
3

2.2 Vehicle Trim 

Propulsive trim, which simulates an aircraft free-flight condition, is used to calculate the initial 

rotor control settings. The solution is determined from the overall equilibrium—three force 

(vertical, longitudinal, and lateral) and three moment (pitch, roll, and yaw) equations. (See Kim 

[4] for more details.) 

For a specified helicopter weight coefficient, Cw, and a forward speed, μ, the unknown quantities 

to be determined from the vehicle equilibrium equations are as follows: 

[ ] s s c s tail

T u = α ,φ ,θ .75 ,θ 1 ,θ 1 ,θ . (1) 

These values are recalculated iteratively using the modified hub forces and moments, including 

the blade elastic responses. The solution technique is based on a modified Newton’s method. 

The rotor controls, which are updated at the ith iteration, can be expressed in a canonical form as 

follows: 

ui+1 ≅ ui + ∆ui , (2) 

in which 

| ( ) 0 i u u F ui

u

F

u = ∂

∂ ∆ = − , (3) 

where uo is the trim control settings obtained initially using the rigid flapping blade solution and 

the Jacobian 

u

F

∂

∂ is calculated using the finite difference approach. For computational 

efficiency, the Jacobian is computed only once initially and used for subsequent iterations. 

2.3 Rotor Steady Response 

The rotor dynamic response involves the determination of time-dependent blade positions at 

different azimuth locations for one rotor revolution. To reduce computational time, the FE 

equations are transformed into modal space as a few normal mode equations using the coupled 

natural vibration characteristics of the blade. These nonlinear periodic coupled equations are 

solved for steady response using an FE in time procedure based on Hamilton’s principle in weak 

form. 

One rotor revolution is divided into a number of azimuthal (time) elements, and then periodicity 

of response is used to join the motions of the first and last elements. The assembly of elements 

results in nonlinear algebraic equations that are solved using the Newton-Raphson procedure. 

After the blade response is obtained, hub forces and moments are calculated using the force 

summation method. These values are finally used to recalculate the coupled trim control values, 

as described in section 2.2. 
4

2.4 Rotor Wake Modeling 

For the induced in-flow distribution on the rotor disk, a free-wake model is fully coupled in the 

rotor aeroelastic analysis. The model can account for wake self-distortion by updating its 

geometry according to newly calculated in-flow and blade circulation distributions. The 

geometry of the free wake is divided into the following three regions: (1) near wake, (2) rolling 

up wake, and (3) far wake. The near wake consists of a series of radial panels, each with linear 

circulation distributions. The rolling-up wake consists of an inboard linear circulation 

distribution panel, and a tip panel that represents the rolling up of the tip vortex. The far wake is 

modeled as one panel with a linear circulation distribution and a concentrated tip vortex whose 

strength is proportional to the maximum circulation value on the rotor blade. The helical 

geometry of the concentrated tip vortex is updated, while the inboard wake portions are not 

changed. 

The free-wake analysis is implemented in three stages. First, blade motion and loading are 

calculated using a linear in-flow model. Next, wake-induced coefficients are calculated for 

undistorted wake geometry. The nonuniform inflow is calculated and used to obtain blade 

motion and loading. Finally, the free-wake geometry is calculated. For this, the influence 

coefficients are reevaluated, and blade motion and loading are again obtained using nonuniform 

in-flow values. For subsequent iterations, the free-wake geometry is generally held fixed, and 

only the strength of vortices is updated. This comprehensive rotor wake model is used in the 

present blade flight loads calculation. 

2.5 Solution Procedure for Blade Load Calculations 

The following procedures were used to calculate blade loads and moments on selected blade 

stations in hover and forward flight conditions. 

1. With prescribed input data, vehicle trim equations are calculated using rigid blade flapping 

(a starting point). 

2. Using control inputs from the vehicle trim solution of step 1, the blade nonlinear steady 

response is calculated. The results give detailed individual blade responses at different 

span-wise and azimuthal positions. 

3. Hub loads and moments are calculated using elastic rotor responses. Then, the vehicle trim 

values and blade responses are recalculated iteratively using the modified hub forces and 

moments. This step is repeated until a converged solution is obtained. 

4. Blade loads and moments at selected blade stations are calculated using the force 

summation method. 
5

3. Results and Discussion 

Numerical results are first calculated for the OH-58D KW helicopter at the gross weight of 

4500 lb with the forward speed of 120 kn (equivalent advance ratio, μ, of 0.28). This flight 

condition is selected for the benchmark correlation with the available test data obtained on the 

Bell Model 406T rotor blade (5, 6). The 406T rotor blade is also used on the OH-58D KW. 

Following the correlation, blade loads were calculated for the KW at a gross weight of 4086 lb 

for hover and a cruising forward speed of 100 kn (μ = 0.23). 

The KW helicopter is equipped with a four-bladed, soft in-plane, advanced geometry, hingeless 

main rotor system. Some important aerodynamic characteristics of this helicopter rotor are given 

in table 1. In the present study, an effort was made to model the helicopter main rotor blade 

characteristics as accurately as possible. The rotor blade structural properties data obtained from 

manufacture (7, 8) were used to create a finite element model (FEM) (see table 2). Figure 1 

shows the global and local degrees of freedom of the FE blade model for the whole rotor blade. 

Nonlinear twist distribution of the blade was also modeled in the blade FEs. 

Table 1. Aerodynamic characteristics of KW helicopter. 

Air Density, 

ρ 

(slug/ft3

) 

No. of 

Blades 

in 

Main 

Rotor, 

Nb

Helicopter 

Gross 

Weight(s), 

W 

(lb) 

Main 

Rotor 

Blade 

Radius, 

R 

(ft) 

Blade 

Tip 

Speed, 

ΩR 

(ft/s) 

Blade 

Mean 

Chord, 

cm

(ft) 

Main 

Rotor 

Solidity 

Ratio, 

σ

Blade 

Twist, 

θtw

(degree) 

Rotor 

Shaft 

Tilt, 

αs

(degree)a 

Blade 

Precone, 

βp

(degree) 

Rotor 

Disk 

Area, 

A 

(ft2

) 

.002378(ρSL) 4 4500, 4086 17.5 723.88 0.786 0.057 –12 5 2 962 a Positive for forward tilt.

Table 2. FE beam model input for OH-58D KW main rotor blade. 

Element No. 

Flap-Wise 

Bending Stiffness 

















Ω2 4

m R

EI

o

Y

Lag-Wise Bending 

Stiffness 

















Ω2 4

m R

EI

o

z

Torsional Stiffness 

















Ω2 4

m R

GJ

o

Element Length 







 







R

li

1(tip) 0.00581 0.02316 0.00522 0.025 

2 0.00623 0.04324 0.00634 0.106 

3 0.00934 0.06237 0.00935 0.169 

4 0.00823 0.05762 0.00843 0.100 

5 0.01420 0.08321 0.01743 0.152 

6 0.02342 0.16342 0.02654 0.162 

7 0.03429 0.32143 0.03021 0.086 

8 (root) 0.22840 0.72342 0.06443 0.084 
6

For the calculation of blade dynamic response, each rotor blade is discretized into eight beam 

elements, and each beam element consists of 15 nodal degrees of freedom (see figure 1). For 

normal mode reduction, five coupled rotating natural modes comprised of two flaps, two lags, 

and one torsion mode are used. For periodic response, one cycle of time is discretized into eight 

time elements, and each time element represents a fifth-order polynomial distribution of motion. 

Figure 1. Local and global degrees of freedom of KW main rotor blade. 

Figure 2 shows the correlation of the blade rotating natural frequencies. The UMARC calculated 

values are compared with the experimental data (7) obtained on the Bell 406 helicopter rotor 

blade. The UMARC results are calculated with the nominal operating rotational value of 

395 rpm. There is a good correlation between the analytical UMARC results and the 

experimental data, especially for the lower modes. It is also seen that UMARC slightly 

underpredicts the torsional frequency. 
7

Figure 2. Correlation of main rotor blade natural frequencies. 

3.1 Correlation Study 

To validate the current blade load analysis, the calculated blade centrifugal loads and bending 

moments were compared with available flight test data. The correlation study will not only serve 

as an analysis check, but also as a guideline for further UMARC model improvement efforts. 

Figure 3 shows the correlation of the centrifugal force acting on the blade stations. The UMARC 

calculated values are compared with the flight test data obtained on the Bell 406 helicopter. The 

centrifugal forces measured during the flight test are available at the two blade stations— 

26,600 lb at inboard blade station 24.25 (r/R = 0.116) (5) and 20,600 lb at outboard blade station 

96 (r/R = 0.457) (6). Comparing the UMARC results obtained using nonuniform FE beam 

model with the flight test data, we observe an excellent correlation. Also shown in the figure is 

the analytical result obtained with a simple uniform blade assumption. As expected, the result 

obtained using the uniform blade shows a poor correlation. This is most likely due to the high 

nonuniformity of the helicopter blade; rotor analysis with a simple uniform blade model can 

generate erroneous results. Blade Natural Frequency ( per rev.)

0

1

2

3

4

5

6

7

Model 406 Experimental Data

UMARC Code Prediction

First

Lag

First Flap Second

Flap

Second

Lag

Torsion

Correlation of Rotor Blade Natural Frequencies

Ω = 395 r.p.m.
8

Figure 3. Correlation of CFs along the blade span. 

The computed blade bending moments were also correlated with the flight test data. In reference 

(5), three flap bending moment values are given at three inboard blade stations—stations 31 

(r/R = 0.148), 40 (r/R = 0.191), and 50 (r/R = 0.238), respectively. In reference (6), only one 

bending value is given at the outboard blade station 96 (r/R = 0.457). These flight values were 

replicated and shown in table 3. Also, shown in the fourth column of the table are the peak-topeak values of the moments. The peak-to-peak value is a good indication of loading on the 

structural component. It is seen that the bending moment is largest inboard and decreases 

outboard. 

Figure 4 shows the correlation of the UMARC flap-bending moments with the flight test data. 

There are some discrepancies between the UMARC results and the flight test data. However, 

considering the complexities associated with rotor loads and vibration analysis, a reasonably 

good agreement is observed. In particular, the general trend and the peak-to-peak magnitude of 

the moments are well correlated with flight test data, especially at inboard blade stations. 

Blade Station (r/R)

Centrifugal Force (lbf

)

0 0.2 0.4 0.6 0.8 1 0

10000

20000

30000

40000

50000

Uniform Blade Assumption

UMARC Code Prediction (Non-Uniform Blade FEM Model)

Flight Test Data (Model 406LM)

Correlation of Axial Blade Loads on OH-58D KW Blade

Blade Root Blade Tip

VN = 120 knots, GW = 4500 lbs
9

Table 3. Flap bending moments of Bell model 406T helicopter main rotor blade. 

Blade Station 

 (r/R) 

Mean 

Value 

(in-lbf) 

Oscillatory Value 

(in-lbf) 

Peak-to-peak 

Value 

(in-lbf) 

0.148 2125 ±2725 5450 

0.191 1725 ±2360 4720 

0.238 1275 ±2000 4000 

0.457 –180 ±780 1560 

Figure 4. Correlation of flap bending moment along blade span (μ = 0.28). 

Figure 5 shows the correlation of UMARC lag bending moments with flight test data. Again, 

there are some discrepancies between the analytical results and the test data. A comparison 

reveals that the UMARC values are slightly greater than the test data values. However, a 

reasonable correlation with the test data is observed, and the general trend is especially well 

correlated. 

Blade Station (r/R)

Flap Bending Moment (in - lbf

)

0.2 0.4 0.6 0.8 1 -10000

-5000

0

5000

10000

MODEL 406 DATA (Flapping Up)

MODEL 406 DATA (Flapping Down)

UMARC-120knots

Flap Bending Moment Variation Along Blade Span

(Envelope Curves)

Blade Root Blade Tip
10

Figure 5. Correlation of lag bending moments along blade span (μ = 0.28). 

Next, the UMARC calculated blade torsional moments were correlated with the flight test data in 

Figure 6. There are only two blade stations where the flight torsional data are available—the 

inboard blade station 24.25 (r/R = 0.116) (5) and the outboard blade station 96 (r/R = 0.457) (6). 

The inboard station (r/R=0.116) is where the main rotor blade is connected with the pitch link. 

Again, there are some discrepancies between the two results. However, a reasonable correlation 

is observed. 

3.2 Blade Flight Load Calculations for Hover and 100-kn Forward Speed 

From the correlation study, it was determined that the UMARC code adequately calculated flight 

loads. Excellent agreement with test dada was observed for the most dominant loading (i.e., the 

axial load), giving a certain confidence in the helicopter rotor subsystem model. Next, a new set 

of bending moments was calculated for the ballistic test flight conditions—the gross weight of 

4086 lb at hover and a cruising forward speed of 100 kn (μ = 0.23) for three blade radial 

Blade Station (r/R)

Lag (Chord-wise) Bending Moment (in- lbf

)

0.2 0.4 0.6 0.8 1 -30000

-15000

0

15000

30000

MODEL 406 Flight Data (Lagwise Direction)

MODEL 406 Flight Data (Lead-Lagging)

UMARC-120knots

Lag Bending Moment Variation Along Blade Span (Envelope Curves)

Blade Root Blade Tip
11

Figure 6. Correlation of torsional moments along blade span (μ = 0.28). 

stations. Since the new flight conditions had a negligible influence on the centrifugal force on 

the blade, the previous calculated values were used for the axial loading. These loads and 

moments (peak values) were used as baseline loads during the ballistic test events. The results 

are summarized in table 4. 

Table 4. Reference blade loads and moments for test phase I-B. 

Blade 

Station 

(r/R)

CF 

(lb)

FB 

Hover 

GW = 4086 lb 

 (lb-in) 

FB 

100 kn 

GW = 4086 lb

(lb-in) 

FB 

120 kn 

GW =4500 lb

(lb-in) 

LB 

Hover 

GW = 4086 lb 

(lb-in) 

LB 

100 kn 

GW = 4086 lb 

(lb-in) 

LB 

120 kn 

GW = 4500 lb 

(lb-in) 

0.286 22374 2020 2219 2691 6860 7605 8284 

0.614 16220 564 795 872 1416 1743 2169 

0.843 8264 202 242 379 684 690 1112 

Notes: FB = flap bending moment, positive flapping up; LB = lag (chord-wise) bending, positive lagging back. 

Blade Station (r/R)

Torsional Moment (in- lbf

)

0.2 0.4 0.6 0.8 1 -1500

-1000

-500

0

500

1000

1500

MODEL 406 Flight Data (Pitch Up)

MODEL 406 Flight Data (Pitch Down)

UMARC-120knots

Torsional Moment Variation Along Blade Span (Envelope Curves)

Blade Root Blade Tip
12

4. Summary 

An aeroelastic analysis was conducted to calculate flight loads on the OH-58D KW main rotor 

blade for hover and cruise forward-flight conditions. Centrifugal force and flap and lag bending 

moments were calculated using the UMARC code. The calculated loads were correlated with 

flight test data for the Bell model 406LM helicopter to validate the analysis. The correlation 

showed good general agreement between the test data and analytical results. After the 

correlation study, blade loads were calculated for the desired ballistic test conditions. 

In the present study, the UMARC comprehensive helicopter aeroelastic analysis, based on FE 

methodology in both space and time coordinates, was conducted to analytically calculate the 

flight loads. In spite of it being computer-intensive, its benefit must be appreciated as a powerful 

analytical tool to validate simple design-oriented analysis. 
13

5. References 

1. Polyak, S. F. Detailed Test Plan for U.S. Army OH-58D Kiowa Warrior Live Fire Test and 

Evaluation: Main Rotor Blade Ballistic Vulnerability Test Phase I-B (Quasi-Static); ARLMR-0549, U.S. Army Research Laboratory: Aberdeen Proving Ground, MD, March 2003. 

2. Bir, G. S.; Chopra, I.; Kim, K. C.; Wang, J.; Smith, E.; Vellaichamy, S.; Ganguli, R.; 

Nixon, M; Torok, S. University of Maryland Advanced Rotorcraft Code (UMARC) Theory 

Manual; AERO report no. 94-18; University of Maryland, College Park, MD, July 1994. 

3. Kim, K. C. Helicopter Trim Calculation in Forward Flight. Proceedings of the 1993 

Summer Computer Simulation Conference, ISBN:1-5655-057-9, Boston, MA, July 1993, 

pp 374–379. 

4. Kim, K. C. Analytical Investigation Into the Helicopter Vibration Resulting From Main 

Rotor Blade (MRB) Ballistic Damage; ARL-TR-1985; U.S. Army Research Laboratory: 

Aberdeen Proving Ground, MD, June 1999. 

5. Bell Helicopter TEXTRON. Fatigue Test of The Model 406T Main Rotor Blade, Inboard 

Section, PART No 406-015-001, PART I –Test Plan & PART II – Test Results; report no. 

406-998-001; Fort Worth, TX, February 1986. 

6. Bell Helicopter TEXTRON. Fatigue Test of The Model 406T Main Rotor Blade, Outboard 

Section, PART No 406-015-001, Part II – Test Results; report no. 406-998-002; Fort Worth, 

TX, March 1986. 

7. Bell Helicopter TEXTRON. OH-58D Air Vehicle Technical Description Data; report no. 

406-099-026; Fort Worth, TX, May 1984. 

8. Bell Helicopter TEXTRON. Model 406 Performance Analysis; report no. 406-099-080; Fort 

Worth, TX, August 1983. 
14

List of Abbreviations and Symbols 

A Rotor disk area, πR2

cm Mean blade chord length 

CW Helicopter weight coefficient, 2 A( R)

W

ρ Ω

E Young’s modulus 

EIy Effective flap bending stiffness 

EIz Effective lag (chord) bending stiffness 

G Shear modulus 

GJ Effective sectional torsion stiffness 

Iy, Iz Blade cross-sectional moment of inertia about y and z axis, respectively 

J Polar moment of inertia 

li Length of the ith beam element 

mo Reference blade section mass 

Nb Number of rotor blades 

R Blade radius 

u

T

 Row vector of unknowns in vehicle trim equations 

u Blade displacement in the axial direction 

V Helicopter forward speed 

v Blade displacement in the lead-lag direction 

W Helicopter weight 

w Blade displacement in the flap-wise direction 

αs Longitudinal shaft tilt 

θ.75 Main rotor collective pitch angle at 75% blade radius 

θ1c, θ1s Lateral and longitudinal cyclic trim pitch angles, respectively 

θtail Tail rotor collective pitch angle at root 

μ Advance ratio, R

V

Ω

σ Rotor solidity ratio, R

N c b m

π

φ Elastic blade twist about the elastic axis 

φs Lateral shaft tilt 

ρ Air density 

Ω Rotor rotational speed 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

15

 1 DEFENSE TECHNICAL 

 (PDF INFORMATION CENTER 

 Only) DTIC OCA 

 8725 JOHN J KINGMAN RD 

 STE 0944 

 FT BELVOIR VA 22060-6218 

 1 COMMANDING GENERAL 

 US ARMY MATERIEL CMD 

 AMCRDA TF 

 5001 EISENHOWER AVE 

 ALEXANDRIA VA 22333-0001 

 1 INST FOR ADVNCD TCHNLGY 

 THE UNIV OF TEXAS 

 AT AUSTIN 

 3925 W BRAKER LN STE 400 

 AUSTIN TX 78759-5316 

 1 US MILITARY ACADEMY 

 MATH SCI CTR EXCELLENCE 

 MADN MATH 

 THAYER HALL 

 WEST POINT NY 10996-1786 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL D 

 DR D SMITH 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 1 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL CS IS R 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 3 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL CI OK TL 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

 3 DIRECTOR 

 US ARMY RESEARCH LAB 

 AMSRD ARL CS IS T 

 2800 POWDER MILL RD 

 ADELPHI MD 20783-1197 

ABERDEEN PROVING GROUND

 1 DIR USARL 

 AMSRD ARL CI OK TP (BLDG 4600) 
NO. OF NO. OF 

COPIES ORGANIZATION COPIES ORGANIZATION

16

 1 OASD C3I 

 J BUCHHEISTER 

 RM 3D174 

 6000 DEFENSE PENTAGON 

 WASHINGTON DC 20301-6000 

 1 OUSD(AT)/S&T AIR WARFARE 

 R MUTZELBURG 

 RM 3E139 

 3090 DEFENSE PENTAGON 

 WASHINGTON DC 20301-3090 

 1 OUSD(AT)/S&T LAND WARFARE 

 A VIILU 

 RM 3B1060 

 3090 DEFENSE PENTAGON 

 WASHINGTON DC 20310-3090 

 1 UNDER SECY OF THE ARMY 

 DUSA OR 

 RM 2E660 

 102 ARMY PENTAGON 

 WASHINGTON DC 20310-0102 

 1 ASST SECY ARMY 

 ACQSTN LOGISTICS & TECH 

 SAAL ZP RM 2E661 

 103 ARMY PENTAGON 

 WASHINGTON DC 20310-0103 

 1 ASST SECY ARMY 

 ACQSTN LOGISTICS & TECH 

 SAAL ZS RM 3E448 

 103 ARMY PENTAGON 

 WASHINGTON DC 20310-0103 

 1 DIRECTOR FORCE DEV 

 DAPR FDZ 

 RM 3A522 

 460 ARMY PENTAGON 

 WASHINGTON DC 20310-0460 

 1 US ARMY TRADOC ANL CTR 

 ATRC W 

 A KEINTZ 

 WSMR NM 88002-5502 

 1 USARL 

 AMSRD ARL SL M 

 J PALOMO 

 WSMR NM 88002-5513 

 1 USARL 

 AMSRD ARL SL EA 

 R FLORES 

 WSMR NM 88002-5513 

 1 USARL 

 AMSRD ARL SL EI 

 J NOWAK 

 FT MONMOUTH NJ 07703-5601 

ABERDEEN PROVING GROUND

 1 US ARMY DEV TEST COM 

 CSTE DTC TT T 

 APG MD 21005-5055 

 1 US ARMY EVALUATION CTR 

 CSTE AEC SVE 

 R BOWEN 

 4120 SUSQUEHANNA AVE 

 APG MD 21005-3013 

 1 US ARMY EVALUATION CTR 

 CSTE AEC SVE S 

 R POLIMADEI 

 4120 SUSQUEHANNA AVE 

 APG MD 21005-3013 

 1 US ARMY EVALUATION CTR 

 CSTE AEC SV L 

 R LAUGHMAN 

 4120 SUSQUEHANNA AVE 

 APG MD 21005-3013 

 13 DIR USARL 

 AMSRD ARL SL 

 J BEILFUSS 

 P DEITZ 

 AMSRD ARL SL B 

 J FRANZ 

 M PERRY 

 P TANENBAUM 

 AMSRD ARL SL BB 

 D BELY 

 D FARENWALD 

 S JUARASCIO 

 M RITONDO 

 AMSRD ARL SL BD 

 R GROTE 
NO. OF 

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 AMSRD ARL SL BE 

 L ROACH 

 AMSRD ARL SL E 

 M STARKS 

 AMSRD ARL SL EC 

 J FEENEY 

 E PANUSKA 
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18

1 NASA LANGLEY RESCH CTR 

 VEHICLE TECH DIR 

 M NIXON MS 266 

 HAMPTON VA 23665 

 1 US ARMY EVALUATION CTR 

 CSTE AEC SV LF 

 4120 SUSQUEHANNA AVE 

 APG MD 21005 

ABERDEEN PROVING GROUND

 20 DIR USARL 

 AMSRD ARL SL B 

 AMSRD ARL SL BB 

 D JORDAN 

 M KUNKEL 

 S MOULSDALE 

 B WALTHER 

 AMSRD ARL SL BD 

 S POLYAK 

 B SMITH 

 J FRIES 

 D TEN BROECK 

 K KIM (10 CPS) 

 AMSRD ARL SL BE 

 E FIORAVANTE