1

ISABE-2015-20196

COUNTER ROTATING PROPELLER DESIGN USING BLADE ELEMENT MOMENTUM THEORY

Kiran Siddappaji and Mark G. Turner

Gas Turbine Simulation Laboratory

University of Cincinnati

Cincinnati, Ohio 45221 USA

Abstract

Counter rotating propellers (CRProp) have many

advantages over single propeller systems. Rotational

energy lost in the slipstream is recovered by the aft

rotor, smaller diameter and lower loading per blade

and total torque is balanced due to the opposite

rotation of the rotors. A design method is presented

using Blade Element Momentum Theory (BEMT)

combining Blade Momentum (BMT) and Blade

Element (BET) theories. The tip loss effect

(Prandtl's) and the wake rotation due to the front rotor

is also accounted. The non-linear relationship

between the flow angle and the axial and angular

induction factors is converted to a linear equation and

is solved using Brent’s method with appropriate

boundary conditions. The axial gap between the

rotors is also accounted in all the calculations.

Spanwise distribution of chord, stagger angles and

airfoil type is utilized as initial geometry and a 3D

blade shape is created using an in-house 3D geometry

generator (3DBGB). Appropriate airfoil lift and drag

properties are obtained from a look-up table as a

function of angle of attack for a wide range of

Reynolds number (REYN) as it varies spanwise. A

design optimization is performed with a single

objective function using genetic algorithm to obtain a

blade design with maximum efficiency for the

counter rotating propeller configuration for a

specified thrust. The robust implementation of

Brent’s method and BEMT makes the design process

fast, computationally cheaper and quicker

optimization cycles.

Nomenclature

A Intermediate term for a' calculation

a Axial Induction factor

a' Angular Induction factor

C Coefficient of lift/drag/axial/normal forces

c(r) Chord at a radial location

dQ Incremental Torque

dr Incremental radius

dT Incremental Thrust

dP Incremental Power

e Mathematical Constant: 2.71828

F Total Loss factor, Axial Force

f Prandtl loss factor

n Revolutions per second

P Power

Q Torque

R Radius at hub and tip

r Radius at any location

T Thrust

V Velocity of the fluid

x Rotor axial gap coefficient

Z Blade count

Greek Symbols

α Angle of Attack

κ Intermediate term for a calculation

λ Tip speed ratio

Ω Rotor rotational speed

ω Wake rotational speed

φ Flow Angle

π Circumference to diameter ratio for circle

ρ Fluid density

σ Blade solidity

θ Twist angle

Subscripts

1 Rotor 1 or Front Rotor

1-7 Axial stations 1 to 7

12 Influence on rotor 2 due to rotor 1

2 Rotor 2 or Aft Rotor

a Axial

d Drag

l Lift

local Local twist

n Normal

p Propeller

r Radial

total Total

z Axial direction or Free stream

2

Abbreviations

3D Three Dimensional

3DBGB 3D Blade Geometry Builder

AoA Angle of Attack

BEMT Blade Element Momentum Theory

BET Blade Element Theory

BMT Blade Momentum Theory

CFD Computational Fluid Dynamics

CRProp Counter Rotating Propeller

REYN Reynolds Number

RPM Revolutions Per Minute

TSR Tip Speed Ratio

Introduction

Counter rotating propeller systems have a front and

aft propeller spinning in opposite directions. The exit

swirl coming out of the front rotor is utilized by the

aft rotor and the rotational energy which is normally

lost in the slipstream is recovered. The other benefits

of this configuration are torque balance due to the

counter rotation, higher efficiency for a given disk

area due to lower loading per blade and smaller

optimum diameter. The challenges are the complex

shafting and gear systems. The electrical propulsion

systems have made it easier for application of these

devices in multicopter. Multicopters are beginning to

gain popularity in a variety of fields and an efficient

propulsion system is essential along with smart

control systems for adopting this technology.

There are several propeller theories which analyze

the aerodynamic performance and the behavior of the

slipstream. Lock et al. (1941) developed a method for

calculating the performance of a pair of contra-

rotating airscrews including the interference

velocities between the rotors through a blade force

analysis with some assumptions and appropriate

velocity diagram. Chen et al. (1990) developed a

design system for contra-rotating propellers using

momentum, mass and circulation conservation

through lifting-line theory for calculating propeller

loadings and rotor interaction velocities. Three

dimensional viscous flow models are also

implemented but cannot be included in an iterative

geometry manipulation process because of high

computational cost and longer solution time. A low

fidelity approach is widely incorporated in the design

process which uses a combination (BEMT) of blade

momentum theory (BMT), a derivative of actuator

disk theory to relate the flow momentum at the

propeller to that of the far wake and the blade

element theory to predict the propeller forces (M.K.

Rwigema, 2010). Ernesto Benini (2004) implemented

the combined momentum-blade element theory for

marine propellers using a panel/integral boundary

layer method for calculating the properties of each

blade profile. Furthermore, he demonstrated that the

performance prediction with this approach is accurate

for a certain range of the advance ratio and deviates

from the 3D CFD results outside this range due to 3D

effects. Hence, application of BEMT is simple, fast,

computationally inexpensive and accurate within a

certain range.

QPROP and XROTOR (Mark Drela, 2006) are

design and analysis programs for predicting the

performance of propeller-motor combinations and

minimum induced loss rotor for free-tip propellers

along with structural and acoustic analysis

respectively which use an extension of the classical

blade-element/vortex formulation. BEMT is used to

calculate the axial and angular induction factors in

order to calculate the spanwise distribution of

geometric and aerodynamic properties. Typically,

numerical methods used to solve the equations to

calculate the induction factors are either fixed point

iteration or variations of newton’s method. Ning

(2013) converted the non-linear relationship between

the induction factors and the flow angle to a linear

equation and used Brent’s method for obtaining the

flow angles with guaranteed convergence

implementing proper boundary conditions.

The assumptions made in BMT are homogenous;

incompressible; steady state flow; no frictional drag;

uniform thrust over the ideal propeller (disk); a non-

rotating wake and the static pressure far upstream and

downstream is equal to the ambient static pressure.

BET divides the rotor blade into discrete span-wise

elements with an incremental radius and assumes no

fluid interaction between the airfoil elements which

makes the flow completely two dimensional. The lift

and drag properties of the airfoil are usually obtained

by running XFOIL (Mark Drela, 2013) on the chosen

geometry at a specific Reynolds number for a chosen

angle of attack.

3

Application

An unducted CRProp is designed for a multicopter

with 150 pounds (667.24 N) of thrust per pod,

suitable for rescue and relief operations in natural

disaster areas. A 10 cm hub diameter is assumed. The

number of pods for the multicopter can be chosen

based on the total thrust requirement.

Methodology

A process flowchart describing the design steps are

shown in Figure 1.

Figure 1: Process Flowchart for CRProp design

using BEMT.

Airfoil Selection

The lift and drag properties of an airfoil depend on

the Reynolds number and the angle of attack. Clark Y

airfoil was chosen with 11.71% thickness, 28%

maximum thickness position, 3.43% maximum

camber and 42% maximum camber position for the

design and analysis. A vast library of the airfoil lift

and drag properties as a function of angle of attack

(-10.00 to 10.00 degrees) for a wide range of

Reynolds number (10.0E4 – 11.6E6) is created using

XFLR5 (Deperrois, A., 2009) as shown in Figure 2.

This library is used as a look-up table to obtain the

airfoil properties spanwise at corresponding Reynolds

number. The BEMT code is a unified approach for

both wind or hydrokinetic turbines and propellers. In

order to use the same set of equations for both cases,

the chosen convention for propeller is negative

induction factors, thrust, power and angle of attack

whereas for turbines they are taken as positive. The

Cl-AoA curve shown in Figure 2 is taken as a mirror

image about the origin to obtain lift and drag

coefficients for negative angle of attack since a

propeller blade is an upside down wind turbine blade.

Figure 2: Airfoil lift and drag coefficients for

Clark Y airfoil for a range of REYN (10.0E4 –

11.6E6) as a function of angle of attacks (-10.00 to

10.00) using XFLR5 (Deperrois, A., 2009).

tiphubtotal

tip

tip

hubhub

f

FFF

r

rRZf

r

RrZf

eF

sin2

)(

sin2

)(

)(cos2 1

(1)

Blade Element Momentum Theory

The CRProp configuration and the streamtubes are

shown in Figure 3. The streamtube contraction is

exactly opposite to the streamtube expansion in a

wind turbine case as shown by Sairam et al. (2014).

The axial gap between the 2 rotors also affects the

performance as shown by Pundhir et al. (1992). It is

assumed that the 2 rotors are very close to each other.

Tip losses are accounted by using a Prandtl tip loss

4

factor (Shen et al., 2005) as shown in equation (1).

Applying Bernoulli’s principle upstream and

downstream of the front rotor, we get

)(2

1

2

1

2

1

2

1

2

1

2

4

2

132

2

44

2

33

2

22

2

11

VVPP

VPVP

VPVP

ss

ss

ss

(2)

The mass flow rate is conserved in the streamtube

and the axial force (thrust) is given as

)()(2

1

)()(

)(

)(

22

4

2

1

2

32

41

2

2

rVV

rPPThrust

VVmF

rVm

ss

A

(3)

)1(

)1(

0

2

)(2

1)(

114

23

112

1

12

1

21

1

41

2

2

4

2

141

xaVV

VV

aVV

a

VV

V

VVa

VVV

VVVVm

(4)

Equating the axial force and the thrust, an expression

for the velocity at the rotor is obtained. Axial

induction factor is defined as the ratio of the

difference of free stream velocity and velocity at the

rotor to the free stream velocity as shown in equation

(4) and is negative because the velocity increases

axially due to the streamtube contraction. Velocities

at other axial locations are also calculated and can be

extended to the aft rotor as well. x is the rotor axial

gap coefficient ranging from 1 to 2.

Blade momentum and blade element theories are

combined to calculate the induction factors and other

performance parameters. The velocity triangles are

shown in Figure 4. Angular induction factor is the

ratio of the wake rotational speed to the rotor

rotational speed as shown in equation (5). Axial and

angular momentum conservation across the rotors

give the incremental thrust and torque for the front

(dT1, dQ1) and aft rotor (dT2, dQ2) as shown in

equation (5), where Ftotal is the total loss factor.

drrVaaaFdQ

rdrVaaFdT

drrVaaFdQ

rrardrVdQ

rrmddQ

a

rdrVxaxaFdT

rdrVxaxadT

rdrPPdT

total

total

ztotal

ztotal

z

ss

3

2421222

2

4222

3

1111

121

1

1

11

22

111

22

111

321

)1)(''(4

)1(4

)1('4

)'2(2

)(

2'

)2(4

)2(4

2)(

(5)

In equation (6), a’12 is the angular induction factor

due to the wake rotation at the inlet of the aft rotor

exiting from the front rotor, ω12 is the wake rotation

speed and Ω2 is the aft rotor rotation speed.

Figure 3: CRProp configuration and axial

velocities at different axial stations. (Sairam et al,

2014)

)'1(')1(

4112

1'

2'

222

2

22

12

2

1212

aaaa

A

Aa

a

r

p

p

(6)

Similarly, according to the BET for the front rotor,

we have,

5

z

tip

tip

r

r

dln

dla

nz

az

V

R

R

r

a

a

CCC

CCC

drrCaV

dQ

rdrCaV

dT

11

1

1

11

11

11

11111

11111

2

1

1

2

2

1

2

11

1

1

2

2

1

2

11

)'1(

1tan

cossin

sincos

sin

)1(

sin

)1(

(7)

and for the aft rotor,

4

22

2

2

22

22

22

22222

22222

2

2

2

2

2

2

2

422

2

2

2

2

2

2

422

)'1(

1tan

cossin

sincos

sin

)1(

sin

)1(

V

R

R

r

a

a

CCC

CCC

drrCaV

dQ

rdrCaV

dT

tip

tip

r

r

dln

dla

n

a

(8)

where,

222

111

14

]2,1[

)1(

local

local

z

x

xaVV

(9)

Figure 4: Velocity triangles for CRProp. (Su et al,

2012)

σ1, σ2 are the solidities for respective rotors. The

relationship between advance ratio and the tip speed

ratio is given in equation (10).

J

nD

VJ

tip

z

(10)

Spanwise definition of chord, AoA and REYN

The spanwise chord is given and can be scaled

smoothly using chord multipliers defined as several

control points which create a smooth parametric

cubic B-spline (Vince, J., 2006). The angle of attack

can also be varied spanwise using B-spline control

points. The Reynolds number varies across the blade

span and the corresponding airfoil properties can be

obtained using a REYN based library of Cl and Cd

values for a range of AoAs.

Calculation of Induction Factors

The relationship between axial and angular induction

factors and the flow angle is non-linear and reducing

it to a linear equation is very beneficial in terms of

numerical convergence and obtaining a unique

solution. The reduced single equations for both rotors

are shown in equations (11) and (12).

0)'1(

cos)1(sin

0)'1(

cos

1

sin

2

22

11

1

1

1

r

r aa

(11)

22

22

2

2

22

cossin4'

sin4

total

n

total

a

F

C

F

C

(12)

The roots of equation (11) are obtained using Brent’s

method with proper boundary conditions (Brent,

1971 and Ning, 2013). The relationship of a and a’ is

given in equation (13) and (14) for the front and aft

rotors. The axial gap coefficient (x) affects the axial

induction factor for the front rotor. The spanwise

distribution of incremental thrust, torque, power,

flow, metal and stagger angles are calculated once all

6

the necessary variables are obtained. The total thrust

and the torque is the summation of the dT and dQ for

all elemental airfoils spanwise and the power is

obtained as shown in equation (15).

1cossin4

1'

sin4

1

)1()1(1

11

11

1

11

1

2

2

22

1

n

total

a

total

p

p

ppp

C

Fa

C

F

x

xxxa

(13)

1cossin4

1'

1sin4

1

22

222

22

2

22

n

total

a

total

C

Fa

C

Fa

(14)

tip

hub

tip

hub

tip

hub

R

R

R

R

R

R

drdr

dQP

dQdP

drdr

dTT

drdr

dQQ

)(

)(

)(

(15)

The coefficient of power, thrust and the CRProp

efficiency are calculated using equation (16).

AftFront

zAftFront

opCR

P

T

tip

zop

tip

T

tip

P

PP

VTT

C

C

Rn

V

Rn

TC

Rn

PC

)(

)2(

)2(

)2(

Pr

Pr

42

53

(16)

3D Parametric Geometry

The spanwise chord, stagger angles and the airfoil

type obtained from the BEMT code is used to create

a 3D blade geometry using an in-house parametric

3D blade geometry builder (Siddappaji et al., 2012).

A variety of parameters can be modified in 3DBGB

to create blade shapes for a wide range of operating

conditions. Several types of airfoils can be imported

at different spanwise locations. This 3D geometry

serves as an initial step in 3D CFD analysis,

structural analysis and design optimization, hence

bridging the low fidelity with the high fidelity

system. Figure 5 shows a 3D geometry of a counter

rotating propeller model using the initial parameters

from the BEMT code.

Figure 5: Counter rotating propeller 3D model for

the baseline design with constant REYN.

Design Optimization using BEMT code

The optimization was performed for maximum

efficiency as a single objective function using

DAKOTA (http://dakota.sandia.gov.) and the BEMT

code for the counter rotating propeller.

Genetic Algorithm was utilized which is based on

the natural selection process and evolution in nature.

Single-Objective Genetic Algorithm (SOGA) from

the John Eddy Genetic Algorithm (JEGA) library of

DAKOTA is used in the optimization. DAKOTA

controls the optimization as shown in Figure 6. The

optimization is done in serial due to the fast

convergence of the BEMT code and the details of the

DAKOTA optimization process is explained by

Siddappaji et al. (2015).

Figure 6: DAKOTA Optimization flowchart.

7

Optimization parameters

The goal was to obtain a design with optimum

efficiency. The single objective function to be

minimized was set to (1-η). No mechanical constraint

was enforced in order to obtain the universal

optimum and to understand the behavior of the

design parameters. Fixed design parameters for

counter rotating propeller design optimization are

1. Reynolds Number = 50000 ; α = -4°

2. Airfoil type = Clark Y ; Vz = 15 m/s

3. Rhub = 0.05 m

4. Number of spanwise airfoil sections : 21

5. Axial gap between the rotors.

Variable design parameters (total 16) for the counter

rotating propeller are given in Table 1.

Variables Front Aft

Rtip [m] 0.55-0.85 0.45-0.85

Z 3-6 3-6

TSR, RPM 7.0-12.0 -3500 to -1000

5 chord

multipliers

0-75% 1.0-3.0

>75% 1.0-4.0

0-75% 1.0-4.0

>75% 1.0-5.0

Table 1: Varying parameters for the CRProp

optimization.

Results

Air is used as the fluid with a density of 1.225 kg/m3,

kinematic viscosity of 15.68E-6 m2/s at 20

°C.

Constant REYN and constant AoA

The baseline design details are given in Table 2. The

optimization was performed by varying 16

parameters using DAKOTA which took 14 minutes

and 8 seconds to be completed using 1438 function

evaluations on a single core of an Intel I7 processor.

The optimized design has an improved total

efficiency of 66.49% from the baseline efficiency of

53.09% with a total thrust of 166.25 pounds.

Furthermore, the front rotor is 3 bladed and the

efficiency is improved to 67.40% from 60.09% and

the aft rotor is 4 bladed and the efficiency is

improved to 65.42% from 47.82%. The optimized

design characteristics are tabulated in Table 3. Figure

7a shows the spanwise distribution of induction

factors and the velocity distribution at various axial

locations for the baseline design cases of constant

and varying REYN. The power and thrust

coefficients for a range of advance ratios for both

baseline cases are shown in Figure 7b. Figure 10

shows the spanwise distribution of chord, stagger

angles for both baseline and optimized cases in

addition to the induction factors and axial velocities.

a1, a’1 are the axial and angular induction factors for

the front rotor and a2, a’2 for the aft rotor; a’12 is the

angular induction factor due to the exit wake from the

front rotor interacting with the aft rotor. The span is

calculated with respect to the front rotor tip radius

which results in shorter spans for the aft rotor as

shown in the radial plots. Vz_R1 is the inlet velocity

for the front rotor; V_LE_R1 is the velocity at the

front rotor leading edge and is equal to V_TE_R1,

velocity at the front rotor trailing edge. Vz_R2 is the

inlet velocity for the aft rotor and is equal to the

velocity at the front rotor trailing edge as the 2 rotors

are very close to each other.

Properties Units FRONT AFT

Hub Dia. cm 10.00 10.00

Tip Dia. cm 130.00 127.50

Vz m/s 15.0 16.79-19.03

Z - 3 3

TSR - 9.18 -8.26

RPM - 2023.20 -2300.00

Chord m specified specified

Thrust N

(lbf)

-335.80

(-75.49)

-354.70

(-79.74)

Torque Nm -39.56 46.19

Power kW -8.38 -11.13

Rotor Eff. % 60.09 47.82

ηCRProp % 53.09

Table 2: Design properties of the baseline CRProp

design for constant REYN spanwise.

Properties Units FRONT AFT

Hub Dia. cm 10.00 10.00

Tip Dia. cm 165.61 91.55

Vz m/s 15.0 15.71-18.56

Z - 3 4

TSR - 7.06 -3.23

RPM - 1220.88 -1223.36

Chord m specified specified

Thrust N

(lbf)

-403.21

(-90.65)

-336.30

(-75.60)

Torque Nm -70.19 60.19

Power kW -8.97 -7.71

Rotor Eff. % 67.40 65.42

ηCRProp % 66.49

Table 3: Optimized design properties with

constant REYN along the span.

8

Figure 7a: a, a’ and Vz for constant (left) and varying REYN (right) baseline cases.

Figure 7b: Thrust (top) and power (bottom) coefficients for a range of advance ratio for constant (left) and

varying REYN (right) baseline cases.

9

It can be clearly seen that the inlet velocity for the

aft rotor is no longer a constant. V_LE_R2 is the

velocity at the aft rotor leading edge and is equal to

the velocity at the aft rotor trailing edge, V_TE_R2.

Vexit is the exit velocity.

Varying REYN and constant AoA

The Reynolds number varies along the blade span for

both rotors as shown in Figure 8a for the baseline

case and the baseline design details are shown in

Table 4. In this optimization, appropriate lift and drag

coefficients were calculated along the span, obtained

from a look-up table of the coefficients and Reynolds

number for a constant AoA. The Reynolds number

variation for the optimized case is shown in Figure 8b

for both front and aft rotors. The optimization was

performed by varying 16 parameters using DAKOTA

which took 26 minutes and 8 seconds to be

completed using 2502 function evaluations on a

single core of an Intel I7 processor.

Properties Units FRONT AFT

Hub Dia. cm 10.00 10.00

Tip Dia. cm 130.00 110.00

Vz m/s 15.0 16.63-19.52

Z - 3 3

TSR - 9.18 -7.61

RPM - 2023.2 -2200.00

Chord m specified specified

Thrust N

(lbf)

-386.32

(-86.85)

-266.30

(-59.87)

Torque Nm -42.05 31.82

Power kW -8.91 -7.33

Rotor Eff. % 65.04 54.49

ηCRProp % 60.28

Table 4: Design properties of the baseline CRProp

design for REYN varying spanwise.

The optimized design has an improved total

efficiency of 73.87% from the baseline efficiency of

60.28% with a total thrust of 153.03 pounds.

Furthermore, the front rotor is 3 bladed and the

efficiency is improved to 72.18% from 65.04% and

the aft rotor is 5 bladed and the efficiency is

improved to 75.75% from 54.49%. The optimized

design characteristics are tabulated in Table 5. Figure

10 shows the comparison of spanwise distribution of

chord, stagger, induction factors and axial velocities

at various axial locations for the varying REYN and

constant REYN optimization cases. The AoA is

constant for both cases. The 3D geometries for both

optimum cases are shown in Figure 9.

Figure 8a: Spanwise variation of REYN (10

5) for

the baseline case.

Figure 8b: Spanwise variation of REYN (10

5) for

the optimized case.

Properties Units FRONT AFT

Hub Dia. cm 10.00 10.00

Tip Dia. cm 142.87 94.54

Vz m/s 15.0 16.49-18.82

Z - 3 5

TSR - 7.05 -2.88

RPM - 1413.25 -1069.03

Chord m specified specified

Thrust N

(lbf)

-351.04

(-78.92)

-329.68

(-74.11)

Torque Nm -49.29 58.32

Power kW -7.29 -6.53

Rotor Eff. % 72.18 75.75

ηCRProp % 73.87

Table 5: Optimized design properties with REYN

varying along the span.

10

Conclusions and Future Work

A robust design system for counter rotating

propellers is created using blade element momentum

theory. Counter rotating propellers are advantageous

over single row propellers due to the fact that an

additional amount of power is extracted from the

front rotor exit swirl by the counter rotating aft rotor.

The axial gap between the rotors is also accounted in

the formulation and the rotors are assumed to be very

close to each other. The low fidelity design tool takes

into account the tip losses using a Prandtl’s tip loss

model. The non-linear relationship between induction

factors and flow angle is linearized and solved using

Brent’s method with appropriate boundary conditions

which ensures convergence. Appropriate airfoil lift

and drag properties are obtained as a function of

AoAs for a wide range of Reynolds number. The

design is also optimized for maximum total

efficiency using genetic algorithm. The optimization

was performed with no mechanical constraints to

study the optimum design space.

Future work includes optimization with varying

AoA and airfoil spanwise, 3D CFD and structural

analysis. A suitable wake model needs to be added to

account for wakes. Entropy minimization is essential

to improve the efficiency. Blade-to-blade interaction

is necessary for designs with more blades. Design

exploration with swept and leaned blades, novel

features like rotor winglets and split tips will be

conducted. A study of radius ratios and nose effect on

velocity at the hub for smaller size propellers will

also be investigated.

In conclusion, the robust implementation of Brent’s

method and BEMT makes the design process fast,

computationally cheaper and quicker optimization

cycles. It is demonstrated that BEMT combined with

optimization is a great tool for obtaining efficient

designs rapidly for counter rotating propellers and

when coupled with a parametric 3D blade geometry

tool, it can function as a preprocess to high fidelity

design and analysis.

Figure 9: 3D geometry lofted in a CAD package (NX) for the CRProp optimized design case with constant

(top) and varying REYN (bottom).

11

Figure 10: Comparison of spanwise distribution of chord, stagger, induction factors and Vz at various axial

locations for the constant REYN (left) and varying REYN (right) optimization cases of CRProp.

12

References

Lock, C. N. H., July 1941. “Interference velocity for

a close pair of contra-rotating airscrews”, Tech. Rep.

No. 2084, Aerodynamics Division, NPL, London,

UK.

Chen, B. Y. H., and Reed, A. M., January 1990. “A

design method and an application for contra rotating

propellers”, Tech. Rep. AD-A218625, David Taylor

Research Center, Bethesda, MD 20084-5000,

Rwigema, M. K., September 2010, “Propeller Blade

Element Momentum Theory with Vortex Wake

Deflection”, 27th

International Congress of the

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