High Speed Large Aircraft Propeller Design

AE 658

Ajinkya Kadu

HIGH SPEED LARGE AIRCRAFT PROPELLER DESIGN

Ajinkya Kadu

Saket Guddeti

Abhiram M

Keshav Agarwal

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Table of Contents

1 Introduction

1.1 Overview of Turboprop

1.2 High Speed Large Passenger Aircraft

2 Literature Review

2.1 Airfoil Characteristics

2.2 Actuator Disk Theory

2.3 Blade Element Theory

2.4 Advanced Blade Element Theory

2.5 Engine Characteristics

3 Selection of Machine

3.1 Aircraft Specifications

3.2 Engine Selections

3.3 Performance Matching

4 Propeller Design Concept

4.1 Constraints and Requirements to Design

4.2 Theoretical Background of Propeller Design

4.3 Propeller Design Process

5 Designing High Speed Large Aircraft Propeller

5.1 Airfoil Determination at 0.75R

5.2 Analysis for 2 Blades


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5.7 Design Output

6 Design of Propeller in Solidworks and Catia

6.1 Airfoil Coordinates

6.2 Steps to Design

6.3 Final Design

7 References

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INTRODUCTION

Overview of Turboprop

Aircraft propellers convert rotary motion from piston engines or turboprops to provide

propulsive force. They may be fixed or variable pitch. There are various kinds of engines

currently in use in civil aviation sector, military, transportation sector etc. To name a few there

are turboprops, turbofans, turbojets and turbo shafts. All of these classified based on the

mechanism they achieve thrust.

Turbojet engine derives its thrust by highly accelerating a mass of air, all of which goes

through the engine. The turbine of turbo jet is designed to extract only enough power from

the hot gas stream to drive the compressor and accessories.

Turboprop engine derives its propulsion by the conversion of the majority of gas stream

energy into mechanical power to drive the compressor, accessories, and the propeller load.

The shaft on which the turbine is mounted drives the propeller through the propeller

reduction gear system. Approximately 90% of thrust comes from propeller and about only

10% comes from exhaust gas.

Turbofan engine has a duct enclosed fan mounted at the front of the engine and driven either

mechanically at the same speed as the compressor, or by an independent turbine located to

the rear of the compressor drive turbine. The fan air can exit separately from the primary

engine air, or it can be ducted back to mix with the primary's air at the rear. Approximately

more than 75% of thrust comes from fan and less than 25% comes from exhaust gas.

Turbo shaft engine derives its propulsion by the conversion of the majority of gas stream

energy into mechanical power to drive the compressor, accessories, just like the turboprop

engine but the shaft on which the turbine is mounted drives something other than an aircraft

propeller such as the rotor of a helicopter through the reduction gearbox. The engine is called

turbo shaft.

Among these, propellers are used in turboprop engines, Turbo shaft engines, turbofan engines.

These engines have gained wide range popularity in recent decades and have been able to

compete with the high speed jet engines. Propeller driven engines though slow and higher

maintenance have many advantages over the jet engines.

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Some of the factors include short field performance, range, and fuel used during a climb.

Many of the regional airports have shorter runways than the major international airports. As

stall speeds are lower for propeller driven aircraft, the speed at take-off is consequently lower.

Therefore shorter take-off runs are possible.

The maximum climb angle for a power producing aircraft is the stall speed, unlike thrust

producing aircraft where maximum climb angle is at maximum lift/drag (L/D) ratio. For this

reason airports with significant obstacles in the climb-out path are only suitable for propeller

aircraft.

For the jet, the power required is unaffected by increasing altitude, and yet the efficiency

greatly increases. On the other hand, the power required curve shifts to the right for propeller

driven aircraft with increasing altitude. In short, propeller aircraft fly lower and slower than

their jet counterparts.

Consider the time and distance to height for either aircraft to climb to the most economical or

best range height. All other factors being ignored, the extra fuel burned to climb higher by the

jet will make it less efficient over shorter range, where cruise may only be possible at height

before it is time to descend for landing. As the propeller aircraft cruises more efficiently at

lower altitude, less time and fuel will be consumed, and consequently more time at cruise

altitude will be the norm.

The propeller is usually attached to the crankshaft of a piston engine, either directly or

through a reduction unit. Light aircraft engines often do not require the complexity of gearing

but on larger engines and turboprop aircraft it is essential.

Choice of aircraft for particular routes is a complex and involved process. Many factors are

involved. However, the basic premise is that propeller aircraft are more cost effective over

short range.

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Traditionally, propeller aircraft have been used for short-range flights and turbine engine

aircraft for long-range flights.

High Speed Large Passenger aircraft:

Turboprop engines are generally used on small subsonic aircraft, but some aircraft outfitted

with turboprops have cruising speeds in excess of 926 km/h. large military and civil aircraft,

such as the Lockheed L-188 Electra and the Tupolev Tu-95, have also used turboprop power

Turboprops are very efficient at flight speeds below 725 km/h (450 mph; 390 knots) because the

jet velocity of the propeller (and exhaust) is relatively low. Due to the high price of turboprop

engines, they are mostly used where high-performance short take-off and landing (STOL)

capability and efficiency at modest flight speeds are required. The most common application of

turboprop engines in civilian aviation is in small commuter aircraft, where their greater

reliability than reciprocating engines offsets their higher initial cost.

Turboprop airliners now operate at near the same speed as small turbofan-powered aircraft but

burn two-thirds of the fuel per passenger. However, compared to a turbojet (which can fly at

high altitude for enhanced speed and fuel efficiency) a propeller aircraft has a much lower

ceiling. Turboprop-powered aircraft have become popular for bush airplanes such as the Cessna

Caravan and Quest Kodiak as jet fuel is easier to obtain in remote areas than is aviation-grade

gasoline.

Large passenger or military aircrafts which fly at cruise Mach numbers 0.5 to 0.6 can have a

take-off weight of around 10,000 kg to 15,000 kg with cruise speed ranging from 500-900

Kmph and having a service ceiling at about 10,000 m. These propeller driven aircrafts have a

typical range of around 1800-2000 km.

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Comparing the turboprops with the traditional jet engine aircrafts in the large size range.

Turboprops score easily over their counterparts in efficiency in short runs even though they are

slower.

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But from the above charts, it has to be noted that the percentage maintenance cost for turboprop

aircraft is 20.5% as compared to 15.8% for Regional Jet’s and 7.5% for large jets. For this reason

an increasing use of Regional Jet’s has had a major impact on the cost efficiencies of short-range

transportation.

Regional aircraft are 40% to 60% less fuel efficient than their larger narrow- and wide-body

counterparts, while regional jets are 10% to 60% less fuel efficient than turboprops. Fuel

efficiency differences can be explained largely by differences in aircraft operations, not

technology. Direct operating costs per revenue passenger kilometer are 2.5 to 6 times higher for

regional aircraft because they operate at lower load factors and perform fewer miles over which

to spread fixed costs. Further, despite incurring higher fuel costs, regional jets are shown to have

operating costs similar to turboprops when flown over comparable stage lengths.

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LITERATURE REVIEW

Airfoil Characteristics

The lift on an airfoil is primarily the result of its angle of attack and shape. When

oriented at a suitable angle, the airfoil deflects the oncoming air, resulting in a force on the

airfoil in the direction opposite to the deflection. This force is known as aerodynamic force and

can be resolved into two components: Lift and drag. Most foil shapes require a positive angle of

attack to generate lift, but cambered airfoils can generate lift at zero angle of attack. This

"turning" of the air in the vicinity of the airfoil creates curved streamlines which results in lower

pressure on one side and higher pressure on the other. This pressure difference is accompanied

by a velocity difference, via Bernoulli's principle, so the resulting flow field about the airfoil has a

higher average velocity on the upper surface than on the lower surface. The lift force can be

related directly to the average top/bottom velocity difference without computing the pressure by

using the concept of circulation and the Kutta-Joukowski theorem.

Airfoils are also found in propellers, fans, compressors and turbines. Any object with an angle of

attack in a moving fluid, such as a flat plate etc. will generate an aerodynamic force but airfoils

are more efficient lifting shapes, able to generate more lift (up to a point), and to generate lift

with less drag.

Airfoil design is a major facet of aerodynamics. Various airfoils serve different flight regimes.

Asymmetric airfoils can generate lift at zero angle of attack, while a symmetric airfoil may better

suit frequent inverted flight as in an aerobatic airplane. In the region of the ailerons and near

a wingtip a symmetric airfoil can be used to increase the range of angles of attack to avoid spin-

stall. Thus a large range of angles can be used without boundary layer separation. Subsonic

airfoils have a round leading edge, which is naturally insensitive to the angle of attack. The cross

section is not strictly circular, however: the radius of curvature is increased before the wing

achieves maximum thickness to minimize the chance of boundary layer separation. This

elongates the wing and moves the point of maximum thickness back from the leading edge.

Supersonic airfoils are much more angular in shape and can have a very sharp leading edge,

which is very sensitive to angle of attack. A supercritical airfoil has its maximum thickness close

to the leading edge to have a lot of length to slowly shock the supersonic flow back to subsonic

speeds.

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A lift and drag curve represents an aerofoil’s characteristics which are reflected by lift vs. angle

of attack and drag vs. angle of attack graphs. With increased angle of attack, lift increases in a

roughly linear relation, called the slope of the lift curve. At some angle this airfoil stalls, and lift

falls off quickly beyond that. The drop in lift can be explained by the action of the upper-

surface boundary layer, which separates and greatly thickens over the upper surface at and past

the stall angle. The thicker boundary layer also causes a large increase in pressure drag, so that

the overall drag increases sharply near and past the stall point.

Airfoil Nomenclature

The various terms related to airfoils are defined below:

The suction surface (a.k.a. upper surface) is generally associated with higher velocity and lower

static pressure.

The pressure surface (a.k.a. lower surface) has a comparatively higher static pressure than the

suction surface. The pressure gradient between these two surfaces contributes to the lift force

generated for a given airfoil.

The geometry of the airfoil is described with a variety of terms.

We thus define the following concepts:

The leading edge is the point at the front of the airfoil that has maximum curvature.

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The trailing edge is defined similarly as the point of maximum curvature at the rear of the

airfoil.

The chord line is a straight line connecting the leading and trailing edges of the airfoil.

The chord length, or simply chord, is the length of the chord line and is the characteristic

dimension of the airfoil section.

The shape of the airfoil is defined using the following concepts:

The mean camber line is the locus of point’s midway between the upper and lower surfaces. Its

exact shape depends on how the thickness is defined;

The thickness of an airfoil varies along the chord. It may be measured in either of two ways:

Thickness measured perpendicular to the camber line.

Thickness measured perpendicular to the chord line.

Two key parameters to describe an airfoil’s shape are its maximum thickness (expressed as a

percentage of the chord), and the location of the maximum thickness point (also expressed as a

percentage of the chord).

Finally, important concepts used to describe the airfoil’s behavior when moving through a fluid

are:

The aerodynamic center, which is the chord-wise length about which the pitching moment is

independent of the lift coefficient and the angle of attack.

The center of pressure, which is the chord-wise location about which the pitching moment is

zero.

Actuator Disk Theory

Actuator Disk Theory, also known as Momentum Theory, is based upon consideration of

whole propeller as an element of pressure increase (flow energizer) which is denoted by disk.

Flow through the disk is assumed to have constant velocity. Hence, phenomenon like transonic

region on blade, flow separation, flow blocking are neglected.

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Figure 2: Flow Analysis around Propeller

Mass Flow through the disk = ρAV1

Thrust Produced by the disk = ṁ (Ve - V∞)

Thrust can also be derived from pressure distribution = A (P2 – P1)

Bernoulli’s Equation: P2 – P1 = 0.5 ρ (Ve2

- V∞2)

Air Flow Velocity, V1 = Ve + V∞

Thrust, T = 0.5 ρ (Ve2

- V∞2) A

V1 = V∞ + v Ve = V∞ + 2v

Where v = induced velocity = √𝑻

2ρA for V∞ = 0

Power Input for Static Thrust Production, Pin = 𝑇3

2√2ρ𝐴

Power Output, Pout = T V∞

Induced Efficiency, ηi = 1/ [1 + (v/ V∞)]

Induced Efficiency cannot be realized due to following reasons

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1) Loss because of interaction of blades

2) Loss due to propeller drag

3) Loss due to non – uniformity of thrust loading

4) Loss of Energy in rotational motion

Blade Element Theory

This theory is based upon assumption of each

element of blade have its share of power and torque

component and they contribute in generating thrust

for the propeller.

Consider the propeller shown in figure 2. Cut the

propeller blade at radius r from the axis. Flow

entering this element with an axial velocity V.

Propeller rotates at angular velocity of ω rad/s.

The blade element is assumed to be made of airfoil

shape of known lift Cl and drag Cd Characteristics.

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The thrust and Torque of an element of radial length dr is made from an airfoil of lift dL and

drag dD.

Thrust Produced, dT = 𝑞 𝑐 𝑑𝑟

𝑠𝑖𝑛2𝜙(Cl

cos 𝜙 – Cd sin 𝜙 )

Torque Supplied, dQ =

𝑞 𝑐 𝑟 𝑑𝑟

𝑠𝑖𝑛2𝜙(Cl sin 𝜙 – Cd cos 𝜙)

Net Torque = B

∫𝑞 𝑐 𝑑𝑟

𝑠𝑖𝑛2𝜙(Cl cos 𝜙 – Cd sin 𝜙 )

𝑅

0

Net Torque = B

∫𝑞 𝑐 𝑟 𝑑𝑟

𝑠𝑖𝑛2𝜙(Cl sin 𝜙 – Cd cos 𝜙)

𝑅

0

The blade Element Efficiency,

ηel = Thrust power produced /

Torque power Supplied

ηel =(Cl cos 𝜙 – Cd sin 𝜙 )

(Cl sin 𝜙 – Cd cos 𝜙) tan 𝜙

Maximum efficiency occurs at ϕ = 𝜋

4−

𝐶𝑑

2 𝐶𝑙

Advanced Blade Element Theory

This theory is based upon the inclusion of downwash in simple blade element theory.

Downwash is an effect at trailing edge due to which induction of flows is seen. Induced flow

particularly changes angle of attack which then reduces lifting force L and hence circulation

around the airfoil.

We will quickly look into induced angle of attack (difference between airfoil angle of

attack and effective angle of attack), elemental as well as total thrust and elemental torque

coefficients and efficiency.

Induced angle of attack on element in generalized form,

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αi = 1

2[ − (

𝜆

𝑥+

𝜎𝑎𝑉𝑟

8𝑥2𝑉𝑇) + √((

𝜆

𝑥+

𝜎𝑎𝑉𝑟

8𝑥2𝑉𝑇)

2) + (

𝜎𝑎𝑉𝑟

2𝑥2𝑉𝑇 ) (𝛽 − 𝜙) ]

Where, λ = V/ωR Vr = VT √𝑥2 + λ2 σ = B c/ 𝜋 R x = r/R tan αi

Elemental Thrust Coefficient 𝑑𝐶𝑇

𝑑𝑥= 3.88 𝑥2 𝜎 𝜓𝑇

Elemental Torque Coefficient 𝑑𝐶𝑄

𝑑𝑥 = 1.94 𝑥3 𝜎 𝜓𝑄

Where 𝜓𝑇 = (cos 𝛼𝑖

cos 𝜙0)2(Cl cos 𝜙0 – Cd sin 𝜙0 )

𝜓𝑄 = (cos 𝛼𝑖

cos 𝜙0)

2(Cd cos 𝜙0 + Cl sin 𝜙0 )

Propeller Thrust Coefficient, CT = ∫𝑑𝐶𝑇

𝑑𝑥𝑑𝑥

1

0

Propeller Torque Coefficient, CQ = ∫𝑑𝐶𝑄

𝑑𝑥𝑑𝑥

1

0

Propeller Efficiency, η = 𝐽𝐶𝑇

𝐶𝑃

Engine Characteristics

Overall Efficiency:

Thermal Efficiency:

ƞ𝑡ℎ𝑒𝑟𝑚𝑎𝑙 =𝑢𝑒

2− 𝑢𝑜

2

2𝑚𝑓ℎ

Propulsive Efficiency:

ƞ𝑝𝑟𝑜𝑝𝑢𝑙𝑠𝑖𝑣𝑒 =T𝑢𝑜

𝑢𝑒2/2− 𝑢𝑜

2

/2

Overall Efficiency:

ƞ𝑜𝑣𝑒𝑟𝑎𝑙𝑙 = ƞ𝑡ℎ𝑒𝑟𝑚𝑎𝑙ƞ𝑝𝑟𝑜𝑝𝑢𝑙𝑠𝑖𝑣𝑒

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Specific Impulse (𝐼𝑠𝑝):

ƞ𝑝𝑟𝑜𝑝𝑢𝑙𝑠𝑖𝑣𝑒 =F

fg

Specific Fuel Consumption:

Propeller Performance Parameters:

Propeller Efficiency:

ƞ𝑃𝑟𝑜𝑝 =2

1 + 𝑢𝑒/𝑢𝑜

Propulsive Efficiency:

ƞ𝑃𝑟𝑜𝑝𝑢𝑙𝑠𝑖𝑣𝑒 =2

1 + (1 +2T

𝐴𝑑𝑖𝑠𝑘𝑢𝑜2 𝜌)

Power Coefficient:

𝑃𝑖𝑛 = 2𝜋𝑛𝑄

𝑃𝑜𝑢𝑡 = 𝑇𝑢𝑜

ƞ𝑃𝑟𝑜𝑝 =

12π

𝐾𝑇𝐽

𝐾𝑄

𝑃𝑖𝑛 = 2𝜋𝜌𝐾𝑄𝑛3𝐷5

𝑆𝐹𝐶 =mass flow rate

thrust

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Selection of Machine

The basic need to design a propeller is to choose an aircraft and an engine so as to get the

initial parameters like Power Input, Thrust required, and rotational speed. From literature

survey, we found out that Fairchild Dornier 328 produced by Fairchild Aircraft, an aircraft and

aerospace manufacturing company based at Farmingdale, New York, is suitable for our topic,

i.e., High speed large aircraft (M = 0.6). The engine for this particular aircraft is PW 119, a

turboprop engine produced by Pratt & Whitney, a U.S. based aerospace manufacturer. But we

choose PW 127E to have a room for adjustment of power.

Aircraft Specifications:

Dornier 328 is turboprop – powered commuter airliner. It was initially produced by

Dornier Luftfahrt GmBH. In 1996, the firm was acquired by Fairchild Aircraft resulting in firm

named Fairchild – Dornier. First flight was flown on 6 December, 1991. 217 Dornier – 328 were

produced from period of 1991 – 2000. Following are the variants of Dornier – 328

328-100 - Initial 328.

328-110 - Standard 328 with greater range and weights

328-120 - 328 with improved STOL performance.

328-130 - 328 with progressive rudder authority reduction at higher airspeeds.

328JET - Turbofan-powered variant, formerly the 328-300.

C-146A - Designation of 328s operated by the United States Air Force's Air Force Special

Operations Command.

On 25 February 1999, Minerva Airlines Flight 1553 on a flight from Cagliari-Elmas

Airport to Genoa Cristoforo Colombo Airport in Italy. When on landing on runway 29 the

aircraft ran off the end of the runway and crashed into the sea. Four of the 31 passengers and

crew died in the accident.

General characteristics

Crew: Three (2 Pilots, 1 Flight Attendant)

Capacity: 30 to 33 (14 in First Class Config) passengers

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Length: 21.11 m (69 ft 7 in)

Wingspan: 20.98 m (68 ft 10 in)

Height: 7.24 m (23 ft 9 in)

Wing area: 40 m² (431 ft²)

Empty weight: 8,920 kg (19,670 lb)

Useful load: 3,450 kg (7,606 lb)

Max. takeoff weight: 13,990 kg (30,840 lb)

Performance

Cruise speed: 620 km/h (335 kts)

Range: 1,850 km (1,000 nm, 1,150 mi)

Service ceiling: 9,455 m (31,020 ft)

Powerplant/Propeller

Engine Manufacturer / Model: Pratt & Whitney Canada / PW 119B

Takeoff Power: 2x 2,180 SHP = 2x 1,626 kW

Propeller Manufacturer / Type Hartzell / 6 Blades Composite

Propeller Diameter: 3.6 m

Avionics

Honeywell PRIMUS 2000

Engine Specifications

The PW100 turboprop engine is the proven airline benchmark for low fuel consumption

on the shorter routes of 350 miles or less. PW100 powered airline turboprops consume 25 to 40

per cent less fuel and produce up to 50 per cent fewer CO2 emissions than similar-sized regional

jets. As a result, many airlines are renewing their fleets with PW100-powered aircraft. With a

range of 1,800 to over 5,000 shaft horsepower, the PW100 has demonstrated its versatility in

powering aircraft applications spanning the airlines, coastal surveillance, firefighting and cargo

transport. From this series, we chose PW 127E as our engine to provide a power for propeller.

PW127E

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Specifications:

Power: 2400 SHP = 1876 kW

Length: 84 ''

Width: 26 ''

Height: 33 ''

RPM: 1200

Certification: 1994-12-16

Features:

Two-spool, two-stage centrifugal compressors

All rotors integrally bladed

Each driven independently by low pressure and high pressure compressor turbines

No variable geometry

Easy electric start – no APU required

Reverse flow combustor

Low emissions, high stability, easy starting, durable

Single-stage low pressure and high pressure turbines

Advanced materials and cooling technology for long life

Two-stage power turbine

Free turbine, shrouded blades

Off-set reduction gearbox

Rugged design for high durability

1,200 to 1,300 rpm output speed for low propeller noise

Electronic engine control

Ease of operation, reduced workload

Security of mechanical back-up

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Performance Matching

In this section, we will study the analysis of thrust requirement. The general principle to

follow here is that thrust produced by a propeller must be greater than or equal to thrust

required to fly an aircraft. There are two cases here to analyze.

Case 1 : Aircraft at cruising condition

When a/c cruises at M = 0.6, Net Acceleration of a/c in horizontal and vertical

direction is zero. And hence, lift produced by wing nullifies weight force. Thrust produced by

propeller equals drag force.

Thrust = Drag T = D

Lift = Weight L = W

Typical L/D ratio for this type of a/c is 15. And hence

Thrust = Weight/15 T = W/15

At cruising condition, typical weight of a/c ranges from 9,000 – 12,000 kg

Hence maximum thrust required = 7840 N

Thrust provided by PW 127E can be calculated from propeller efficiency which is

a relation between power input and thrust produced

Power Input = 1500 x 2 kW = 3000 kW (2 Engines required to drive the a/c)

Propeller Efficiency = 𝑇𝑉∞

𝑃 = 0.75 (assumed value)

Cruising Speed = 172.2 m/s

Thrust Produced = 13066 N

By comparing thrust produced by engine and thrust required to drive the a/c, PW 127E engine

provides enough power to cruise Dornier – 328 at mach 0.6.

Case 2 : Aircraft at take – off

When a/c takes off, equations changes in horizontal and vertical directions. There

is no net acceleration component in Vertical direction but in horizontal direction, there is a

acceleration component which increases speed of a/c from zero. The following are equations in

horizontal and vertical direction.

Vertical Direction: W – L = R

Horizontal Direction: T – D – μ (W – L) = 𝑊

𝑔

𝑑𝑉

𝑑𝑡

The lift-off distance SLO is defined as a take – off parameter. Ignoring D and R compared to T,

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SLO = 1.44 𝑊2

𝑔 𝜌 𝑆 𝐶𝐿𝑚𝑎𝑥𝑇

SLO = 1088 m (from Dornier Datasheet)

W = 13990 kg (from Dornier Datasheet)

g = 9.8 m/s2

ρ = 1.225 kg/m3

S = 40 m²

CLmax = 1.5

Hence, max thrust required = 34,500 N

To produce this much amount of thrust at static condition, we need to find out

induced velocity from Actuator Disk Theory.

Induced Velocity: v = Pin / T = 87 m/s

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Propeller Design

The propeller theory which began with Rankine and Froude gives an overall description

of the fluid motion where the propeller is treated as an actuator disk that imparts a certain

momentum to the fluid passing through it. The simple momentum theory gives a good

indication of the efficiency of a propeller but fails to furnish the required design data for the

propeller blades.

It was realized that the induced velocities along the blades had to be determined in order

to solve the basic propeller problem. A certain optimum loading exists for each propeller

configuration in analogy with the case of elliptical loading on a wing. Bertz formulated the

theorem of rigid vortex sheet, tactically referring to light loading; and Prandtl devised the

method of calculating the loading function on the basis on an infinite number of blades and then

applying a tip correction that was obtained by a simple two dimensional treatment. Betz proved

that the most efficient loading along the propeller balse corresponds to the requirements of rigid

vortex behind the propeller.

The velocity of the flow is such that all the vortex lines move rearward as if attached to a

perfectly rigid sheet. This solid spiral moves with a velocity that is referred to as a displacement

velocity. The vortex surface is in fact unstable and will not maintain its ideal shape for any

length of time. With the wake specified thrust torque and efficiency can be calculated.

Constraints and requirements to the design

The engine produces a power of 1500 kW each and having rotational speed of 1200 RPM

max. The propeller design was proposed with the given engine specifications. The cruise speed

of a/c is 172.2 m/s and static induced velocity is 87 m/s. In order to get the most efficient

propeller the Cl/Cd is taken to be constant (approx. value) to find the design point for each of the

blade section and corresponding airfoil that was selected.

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Theoretical Background of Propeller Design

Propeller Design is a relatively simple program, which is based on the blade element

theory. The blade is divided into small sections, which are handled independently from each

other. Each segment has a chord and a blade angle and associated airfoil characteristics. The

theory makes no provision for three dimensional effects, like sweep angle or cross flow. But it is

able to find the additional axial and circumferential velocity added to the incoming flow by each

blade segment. This additional velocity results in an acceleration of the flow and thus thrust.

Usually this simplified model works very well, when the power and thrust loading of the

propeller (power per disk area) is relatively small, as it is the case for most aircraft propellers.

Propeller Design Process

We need to design propeller blades by inputting the constraints and varying the variables

among the rpm, power, airfoil characteristics and Flow velocity at propeller.

The design process is based on the formulas in comparison to Adkins vs. Larrabee. Based on the

theory of the optimum propeller (as developed by Betz, Prandtl, Glauert), only a small number

of design parameters must be specified. These are

The number of blades B,

The axial velocity v of the flow (flight speed or boat speed),

The chord distribution c/D of the propeller,

The selected distribution of airfoil lift and drag coefficients CL and CD along the radius,

The desired thrust T or the available shaft power P,

The density rho of the medium (air: ~1.22 kg/m³)

The design procedure creates the blade geometry in terms of the chord distribution along the

radius as well as the distribution of the blade angle. The local chord length c depends mainly on

the prescribed lift coefficient CL to have wider blades, having to choose a smaller design lift

coefficient (resp. angle of attack) and vice versa. It should be noted, that the design procedure

23 | P a g e

does not work accurately for high thrust

loadings as they occur under static

conditions. If the power coefficient Pc is

less than 1.5, otherwise the theory is not

fully applicable and may lead to errors.

Figure 3 shows the flowchart of the

design process.

A propeller shows a strong variation of the twist distribution along the radius. The local inflow,

seen by a segment of the propeller consists of two parts:

The axial velocity component v due to the movement of the aircraft and

The circumferential component caused by the rotation of the propeller.

The rotational component depends on the rotation speed and the radial position, where the blade

section is located; at the axis this component is zero, whereas at the wing tip (r = D/2) it reaches

its maximum value. The total velocity is the sum of the axial and the rotational component:

The following equations are basic equations while carrying out the analysis of the geometry to

check if it meets the design criteria. From these equations the design point can be selected.

Thrust CT

CT = 𝑇

𝜌 𝑛2 𝐷4

Power CP CP = 𝑃

𝜌 𝑛3 𝐷5

Advance Ratio V/nD V/nD

Efficiency ηp ηp = J 𝐶𝑇

𝐶𝑃

24 | P a g e

Selection of Airfoil

Airfoil Characteristics at 0.75R Calculation of blade pitch angle, diameter of propeller and Cl/Cd characteristics of an airfoil is

done at station 0.75R.

. The given parameters are power input ‘P’, rotational speed

in rpm ‘n’, density of air and cruse

speed ‘V’

calculate Cs the speed power coefficient

From Cs versus J graph find out B and J which

is the advanced ratio

Calculate flow angle 'phi'

Find out angle of attack which is the difference

blade pitch angle and flow

angle

For maximum efficiency find out Cl/Cd ratio

for obtained flow angle

Select an airfoil having

aprroxiamately same Cl/Cd

ratio as obtained for

given angle of attack

25 | P a g e

Density of Air (ρ) = 1.225 kg/m3

Cruise Speed (V∞) = 172.2 m/s

Power Input (P) = 2 x 1500 = 3000 kW

Speed (n) = 1200 RPM = 20 RPS

Speed Power Coefficient = 2.74

Blade Angle (β) = 40.500

Advance Ratio (J) = 1.86

Propeller Diameter (D) = 4.6m

Air Flow Angle (Φ) = 38.4600

Angle of Attack (α) = 2.0400

For Max. Efficiency, Φ= π/4 –0.5*CD/CL

Hence, CL/Cd= 4.38

Airfoil Selection at 0.75R

Due to the high Mach number, compressibility effects (recompression shocks, causing

additional drag) reduce the efficiency of the propeller. A practical way to keep the drag of an

airfoil at acceptable levels is the use of thinner and less cambered airfoils. To avoid excessive

drag, a certain critical camber and thickness should not be exceeded. The Mach number, at

which the flow reaches supersonic speed at some point on the airfoil, is called the critical Mach

number. Sometimes it might be acceptable to have a small supersonic region at the propeller tip,

because a reduction of the diameter (to avoid supersonic tips) also decreases the performance.

But in general, a propeller should be designed to avoid supersonic flow by choosing the right

airfoil thickness and the right diameter. The analysis of compressibility effects on propeller

performance is a very complex matter, and cannot be handled here, but, concluding from

experimental data, it is possible to develop a rule of thumb. The different airfoils were being

selected based on their maximum allowable thickness and camber for a given Mach number and

vice versa. Comparing all of them, we choose Trainer60 airfoil

Trainer 60

Thickness: 18.3% Camber: 0.2%

Trailing edge angle: 16.9o Lower flatness: 5.6%

26 | P a g e

Leading edge radius: 3.8% Max CL: 1.064

Max CL angle 15.0 Max L/D: 16.861

Max L/D angle: 10.50 Max L/D CL: 0.917

Stall angle: 13.50 Zero-lift angle: 0.50

AoA Cl Cd Cm 0.25 T.U. T.L. S.U. S.L. L/D A.C. C.P.

-1.5 -0.201 0.0704 0.023 0.404 0.338 0.908 0.903 -2.851 0.279 0.365

-1 -0.141 0.07148 0.021 0.384 0.346 0.906 0.907 -1.977 0.278 0.401

-0.5 -0.081 0.07116 0.02 0.37 0.356 0.903 0.91 -1.139 0.29 0.493

0 -0.057 0.07126 0.018 0.36 0.364 0.901 0.913 -0.804 0.289 0.565

0.5 0.006 0.07127 0.016 0.35 0.375 0.897 0.916 0.082 0.287 -2.55

1 0.037 0.07035 0.015 0.341 0.403 0.893 0.918 0.532 0.29 -0.139

1.5 0.096 0.06723 0.013 0.333 0.452 0.889 0.916 1.435 0.281 0.118

2 0.156 0.06672 0.011 0.326 0.467 0.886 0.917 2.333 0.283 0.18

2.5 0.214 0.06618 0.009 0.32 0.481 0.88 0.92 3.228 0.285 0.208

3 0.27 0.06506 0.007 0.313 0.494 0.873 0.921 4.154 0.287 0.225

3.5 0.327 0.06429 0.005 0.307 0.5 0.866 0.924 5.081 0.289 0.236

4 0.382 0.06404 0.002 0.297 0.506 0.858 0.927 5.969 0.282 0.244

4.5 0.447 0.06978 0.001 0.169 0.513 0.866 0.929 6.406 0.282 0.248

5 0.503 0.06152 -0.001 0.159 0.519 0.859 0.998 8.17 0.294 0.253

5.5 0.556 0.06069 -0.004 0.15 0.526 0.849 0.998 9.162 0.303 0.257

6 0.606 0.05987 -0.007 0.143 0.534 0.834 0.998 10.121 0.319 0.261

6.5 0.65 0.0579 -0.01 0.137 0.54 0.812 0.998 11.228 0.373 0.266

7 0.678 0.05665 -0.016 0.133 0.545 0.765 0.998 11.961 0.461 0.273

7.5 0.702 0.05592 -0.021 0.129 0.552 0.715 0.998 12.547 0.456 0.28

8 0.73 0.05545 -0.026 0.125 0.559 0.674 0.998 13.157 0.427 0.286

8.5 0.758 0.05439 -0.031 0.121 0.567 0.638 0.998 13.945 0.349 0.291

9 0.81 0.05512 -0.034 0.036 0.855 0.636 0.887 14.702 0.336 0.292

9.5 0.845 0.05531 -0.039 0.024 0.858 0.611 0.888 15.274 0.371 0.296

10 0.882 0.05554 -0.043 0.023 0.859 0.592 0.89 15.877 0.368 0.299

10.5 0.916 0.05547 -0.047 0.021 0.862 0.571 0.89 16.52 0.383 0.302

11 0.948 0.05784 -0.052 0.02 0.863 0.547 0.891 16.386 0.403 0.305

11.5 0.976 0.0613 -0.056 0.02 0.865 0.521 0.892 15.917 0.453 0.308

12 0.995 0.06548 -0.061 0.019 0.866 0.486 0.893 15.202 0.542 0.312

12.5 1.011 0.07027 -0.067 0.018 0.868 0.445 0.894 14.382 0.624 0.316

13 1.023 0.07577 -0.072 0.017 0.869 0.402 0.894 13.496 0.741 0.32

13.5 1.031 0.08199 -0.076 0.017 0.871 0.353 0.894 12.571 0.114 0.324

14 0.993 0.09722 -0.076 0.017 0.873 0.037 0.895 10.211 -1.372 0.326

27 | P a g e

Trainer60 Airfoil Coordinates

Calculation of Section Quantities:

% Program to produce propeller design Table

% AE 658 - Design of PowerPlant % Group 11 : High Speed Large Aircraft Propeller (Ducted / Unducted) % The table is based on Advanced blade Element Theory

clc; clear all %-------------------------------------------------------------------------- % Selection of blade sections

x = [0.3 0.45 0.6 0.7 0.75 0.8 0.85 0.9 0.95 1.00]; e1 = x; e2 = x.^2; e3 = x.^3;

%-------------------------------------------------------------------------- %Defining Given Qunatities

R = 2.3; % Radius of blade B = 2; % No. of Blades n = 20; % rotational speed in rps omega = 2*pi*n; % rotational speed in rad/s V = 172.2; % Velocity of flow at blade cl = 0.139; % Fixed value of lift coefficient a0 = 5; % Cl - alpha curve slope

%-------------------------------------------------------------------------- % Calculation of chord and solidity b = -0.5591*x.^2 + 0.6681*x + 0.09807; % Chord distribution evaluated % from c/d vs x typical graph e4 = b;

sigma = (B*b)/(pi*R); % Solidity

14.5 1.029 0.10063 -0.079 0.016 0.874 0.034 0.896 10.228 0.338 0.327

15 1.064 0.10436 -0.082 0.016 0.876 0.032 0.896 10.192 0.342 0.327

28 | P a g e

e5 = sigma;

%-------------------------------------------------------------------------- % Calculations of angles

e7= omega*R*x; % Tangential velocity component at blade section

phi = atan(V./e7); % flow angle phi e8 = phi;

q = (8*x.*sin(phi))./(sigma*a0); beta = (cl/a0)*((1+q)./q) + phi; % blade pitch angle e6 = beta;

e9 = sin(phi);

%-------------------------------------------------------------------------- % Cl - alpha slope, induced AoA and effective AoA

e10 =[5 5 5 5 5 5 5 5 5 5]; % Cl - alpha slope in /rad

e11 = beta - phi; % gap between flow and blade angle

alpha_i = e11./(1 + (8*x.*sin(phi)./(sigma*a0))); % Induced AoA e12 = alpha_i;

phi_0 = phi + alpha_i; % Effective flow angle e13 = phi_0;

alpha_0 = beta - phi_0; % Effective AoA e14 = alpha_0;

%-------------------------------------------------------------------------- % Lift and Drag Coefficient

Cl = a0*alpha_0; % lift coefficient e15 = Cl;

Cd = 0.066; % Drag Coefficient e16 =[0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066];

%-------------------------------------------------------------------------- % Computation of lambdaT

e17 = cos(alpha_i).*cos(alpha_i); e18 = cos(phi).*cos(phi); e19 = cos(phi_0); e20 = sin(phi_0); e21 = Cl.*cos(phi_0); e22 = Cd.*sin(phi_0);

lambda_T = (e17.*( e21 - e22 ))./e18;

29 | P a g e

e23 = lambda_T;

%-------------------------------------------------------------------------- % Computation of lambdaQ

e24 = Cl.*sin(phi_0); e25 = Cd.*cos(phi_0);

lambda_Q = (e17.*( e24 + e25 ))./e18; e26 = lambda_Q;

%-------------------------------------------------------------------------- % Computation of elemental thrust and torque coefficient

dCtbydx = 3.88*(x.^2).*(sigma.*lambda_T); e27 = dCtbydx;

dCqbydx = 2.94*(x.^3).*(sigma.*lambda_Q); e28 = dCqbydx;

%-------------------------------------------------------------------------- % Importing all values in a table

e =

[e1;e2;e3;e4;e5;e6;e7;e8;e9;e10;e11;e12;e13;e14;e15;e16;e17;e18;e19;e20;e21;e

22;e23;e24;e25;e26;e27;e28];

%-------------------------------------------------------------------------- % Plots

figure(); plot(x,b); xlabel('Blade Section(r/R) --->'); ylabel('Chord(c) ---->'); title('Chord Distribution');

figure(); plot(x, dCtbydx); xlabel('Blade Section(r/R) --->'); ylabel('Chord(c) ---->'); title('Elemental Thrust Coefficient Distribution');

figure(); plot(x, dCqbydx); xlabel('Blade Section(r/R) --->'); ylabel('Chord(c) ---->'); title('Elemental Torque Coefficient Distribution');

This code was used for different number of blades and then, thrust and torque coefficient is

calculated from elemental thrust coefficient distribution (𝑑𝐶𝑡

𝑑𝑥 𝑣𝑠 𝑥) and elemental torque

coefficient distribution (𝑑𝐶𝑞

𝑑𝑥 𝑣𝑠 𝑥) .

30 | P a g e

Analysis for Two Blades:

Station(X) 0.3 0.45 0.6 0.7 0.75 0.8 0.85 0.9 0.95 1

X2 0.09 0.2025 0.36 0.49 0.5625 0.64 0.7225 0.81 0.9025 1

X3 0.027 0.091125

0.216 0.343 0.421875

0.512 0.614125

0.729 0.857375

1

Chord(b) 0.248181

0.285497

0.297654

0.291781

0.284651

0.274726

0.262005

0.246489

0.228177

0.20707

Solidity 0.068694

0.079023

0.082388

0.080762

0.078789

0.076042

0.072521

0.068226

0.063157

0.057315

Pitch Angle 1.136583

0.955538

0.813066

0.736044

0.702046

0.670692

0.641735

0.614946

0.590118

0.567066

Ωr 86.70796

130.0619

173.4159

202.3186

216.7699

231.2212

245.6725

260.1239

274.5752

289.0265

Air Flow Angle 1.104328

0.923915

0.78188

0.705151

0.671311

0.640127

0.611352

0.58476

0.560144

0.53732

sin(Φ) 0.893162

0.797967

0.704615

0.648149

0.622013

0.597297

0.573975

0.551999

0.531308

0.511836

Lift Curve Slope(a0)

5 5 5 5 5 5 5 5 5 5

β - Φ 0.032254

0.031624

0.031186

0.030893

0.030734

0.030565

0.030383

0.030186

0.029974

0.029746

Induced AoA(αi)

0.004454

0.003824

0.003386

0.003093

0.002934

0.002765

0.002583

0.002386

0.002174

0.001946

Φ0 1.108783

0.927738

0.785266

0.708244

0.674246

0.642892

0.613935

0.587146

0.562318

0.539266

α0 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278

Lift Coefficient(Cl)

0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139

Drag Coefficient(Cd)

0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066

cos^2(αi) 0.99998

0.999985

0.999989

0.99999

0.999991

0.999992

0.999993

0.999994

0.999995

0.999996

cos2 (Φ) 0.202261

0.363249

0.503518

0.579903

0.613099

0.643236

0.670553

0.695297

0.717711

0.738024

cos2 (Φ0) 0.445751

0.599646

0.7072 0.759505

0.781178

0.800365

0.817388

0.832525

0.846021

0.858086

sin(Φ0) 0.895157

0.800266

0.707013

0.650501

0.624308

0.599513

0.576088

0.553987

0.533149

0.513506

31 | P a g e

Cl*cos(Φ0) 0.061959

0.083351

0.098301

0.105571

0.108584

0.111251

0.113617

0.115721

0.117597

0.119274

Cd*sin(Φ0) 0.05908

0.052818

0.046663

0.042933

0.041204

0.039568

0.038022

0.036563

0.035188

0.033891

ΨT 0.014234

0.084055

0.102553

0.108014

0.109899

0.11144 0.112735

0.113847

0.114822

0.11569

Cl*sin(Φ0) 0.124427

0.111237

0.098275

0.09042

0.086779

0.083332

0.080076

0.077004

0.074108

0.071377

Cd*sin(Φ0) 0.02942

0.039577

0.046675

0.050127

0.051558

0.052824

0.053948

0.054947

0.055837

0.056634

ΨQ 0.760617

0.415174

0.287871

0.242361

0.225633

0.211672

0.199869

0.189775

0.181054

0.17345

Elemental Thrust

Coefficient(dCt/dx)

0.000341

0.005219

0.011802

0.016585

0.018898

0.021043

0.022919

0.024411

0.025394

0.025728

Elemental Torque

Coefficient(dCq/dx)

0.004148

0.00879

0.015061

0.019738

0.02205

0.024229

0.026171

0.02775

0.028824

0.029228

dCT/dx from interpolation

f(x) = p1*x^9 + p2*x^8 + p3*x^7 + p4*x^6 + p5*x^5 + p6*x^4 + p7*x^3 + p8*x^2 + p9*x +

p10

Coefficients:

p1 = -0.002646 p2 = 0.02219 p3 = -0.08452 p4 = 0.1927

p5 = -0.2918 p6 = 0.2228 p7 = -0.0989 p8 = 0.0775

p9 = -0.008995 p10 = -0.002483

dCq/dx from interpolation

F(x) = p1*x^9 + p2*x^8 + p3*x^7 + p4*x^6 + p5*x^5 + p6*x^4 + p7*x^3 + p8*x^2 + p9*x +

p10

Coefficients:

p1 = -0.000593 p2 = 0.00521 p3 = -0.02046 p4 = 0.04846

p9 = 0.003342 p10 = 3.305e-005

Therefore CT and CQ can be calculated from distributions

32 | P a g e

CT = 0.0092 CQ = 0.0126

33 | P a g e

Analysis of 3 Blades

Station(X) 0.3 0.45 0.6 0.7 0.75 0.8 0.85 0.9 0.95 1

X^2 0.09 0.2025 0.36 0.49 0.5625 0.64 0.7225 0.81 0.9025 1

X^3 0.027 0.091125

0.216 0.343 0.421875

0.512 0.614125

0.729 0.857375

1

Chord(b) 0.248181

0.285497

0.297654

0.291781

0.284651

0.274726

0.262005

0.246489

0.228177

0.20707

Solidity 0.103041

0.118535

0.123582

0.121144

0.118183

0.114063

0.108781

0.102339

0.094736

0.085973

Pitch Angle 1.13881 0.95745

0.814759

0.737591

0.703513

0.672075

0.643026

0.616139

0.591205

0.568039

Ωr 86.70796

130.0619

173.4159

202.3186

216.7699

231.2212

245.6725

260.1239

274.5752

289.0265


0.923915

0.78188

0.705151

0.671311

0.640127

0.611352

0.58476

0.560144

0.53732

sin(Φ) 0.893162

0.797967

0.704615

0.648149

0.622013

0.597297

0.573975

0.551999

0.531308

0.511836


5 5 5 5 5 5 5 5 5 5

β - Φ 0.034482

0.033536

0.032879

0.032439

0.032202

0.031948

0.031674

0.031379

0.031061

0.030718

Induced AoA(αi)

0.006682

0.005736

0.005079

0.004639

0.004402

0.004148

0.003874

0.003579

0.003261

0.002918

Φ0 1.11101 0.92965

0.786959

0.709791

0.675713

0.644275

0.615226

0.588339

0.563405

0.540239

α0 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278


0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139

Drag Coefficient(Cd

)

0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066

cos^2(αi) 0.999955

0.999967

0.999974

0.999978

0.999981

0.999983

0.999985

0.999987

0.999989

0.999991

34 | P a g e

cos^2(Φ) 0.202261

0.363249

0.503518

0.579903

0.613099

0.643236

0.670553

0.695297

0.717711

0.738024

cos(Φ0) 0.443757

0.598114

0.706002

0.758498

0.780261

0.799536

0.816643

0.831864

0.845441

0.857586

sin(Φ0) 0.896147

0.801411

0.70821

0.651675

0.625454

0.600619

0.577143

0.55498

0.534068

0.514341

Cl*cos(Φ0) 0.061682

0.083138

0.098134

0.105431

0.108456

0.111135

0.113513

0.115629

0.117516

0.119204

Cd*sin(Φ0) 0.059146

0.052893

0.046742

0.043011

0.04128

0.039641

0.038091

0.036629

0.035249

0.033946

ΨT 0.01254

0.083259

0.102064

0.107638

0.109566

0.111146

0.112476

0.11362

0.114624

0.115521

Cl*sin(Φ0) 0.124564

0.111396

0.098441

0.090583

0.086938

0.083486

0.080223

0.077142

0.074236

0.071493

Cd*sin(Φ0) 0.029288

0.039476

0.046596

0.050061

0.051497

0.052769

0.053898

0.054903

0.055799

0.056601

ΨQ 0.760628

0.415326

0.28804

0.242525

0.225791

0.211824

0.200013

0.189909

0.181178

0.173562

Elemental Thrust

Coefficient(dCt/dx)

0.000451

0.007754

0.017618

0.024791

0.028261

0.031481

0.034299

0.036544

0.038025

0.038535

Elemental Torque

Coefficient(dCq/dx)

0.006222

0.013189

0.022605

0.029628

0.033098

0.036369

0.039284

0.041655

0.043265

0.04387



p10

p1 = -0.00389 p2 = 0.03276 p3 = -0.125 p4 = 0.2856

p5 = -0.4335 p6 = 0.3309 p7 = -0.1466 p8 = 0.1155

p9 = -0.01339 p10 = -0.003779

dCq/dx from interpolation

F(x) = p1*x^9 + p2*x^8 + p3*x^7 + p4*x^6 + p5*x^5 + p6*x^4 + p7*x^3 + p8*x^2 + p9*x +

p10

p1 = -0.0008877 p2 = 0.007817 p3 = -0.03048 p4 = 0.07212

p5 = -0.1592 p6 = 0.1208 p7 = -0.02298 p8 = 0.05171

p9 = 0.005006 p10 = 4.883e-005

CT = 0.0137 CQ = 0.0189

35 | P a g e


Station(X) 0.3 0.45 0.6 0.7 0.75 0.8 0.85 0.9 0.95 1

X^2 0.09 0.2025 0.36 0.49 0.5625 0.64 0.7225 0.81 0.9025 1

X^3 0.027 0.091125

0.216 0.343 0.421875

0.512 0.614125

0.729 0.857375

1

36 | P a g e

Chord(b) 0.248181

0.285497

0.297654

0.291781

0.284651

0.274726

0.262005

0.246489

0.228177

0.20707

Solidity 0.137389

0.158046

0.164776

0.161525

0.157578

0.152083

0.145041

0.136452

0.126315

0.11463

Pitch Angle 1.141037

0.959362

0.816452

0.739137

0.70498

0.673457

0.644317

0.617332

0.592293

0.569012

Ωr 86.70796

130.0619

173.4159

202.3186

216.7699

231.2212

245.6725

260.1239

274.5752

289.0265


0.923915

0.78188

0.705151

0.671311

0.640127

0.611352

0.58476

0.560144

0.53732

sin(Φ) 0.893162

0.797967

0.704615

0.648149

0.622013

0.597297

0.573975

0.551999

0.531308

0.511836


5 5 5 5 5 5 5 5 5 5

β - Φ 0.036709

0.035447

0.034572

0.033986

0.033669

0.03333

0.032965

0.032572

0.032148

0.031691

Induced AoA(αi)

0.008909

0.007647

0.006772

0.006186

0.005869

0.00553

0.005165

0.004772

0.004348

0.003891

Φ0 1.113237

0.931562

0.788652

0.711337

0.67718

0.645657

0.616517

0.589532

0.564493

0.541212

α0 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278


0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139


0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066

cos^2(αi) 0.999921

0.999942

0.999954

0.999962

0.999966

0.999969

0.999973

0.999977

0.999981

0.999985

cos^2(Φ) 0.202261

0.363249

0.503518

0.579903

0.613099

0.643236

0.670553

0.695297

0.717711

0.738024

cos(Φ0) 0.44176 0.596581

0.704802

0.75749

0.779343

0.798705

0.815897

0.831201

0.84486

0.857085

sin(Φ0) 0.897133

0.802553

0.709404

0.652847

0.626598

0.601723

0.578197

0.555972

0.534987

0.515175

Cl*cos(Φ0) 0.061405

0.082925

0.097968

0.105291

0.108329

0.11102 0.11341 0.115537

0.117436

0.119135

Cd*sin(Φ0) 0.059211

0.052968

0.046821

0.043088

0.041355

0.039714

0.038161

0.036694

0.035309

0.034002

ΨT 0.010845

0.082463

0.101574

0.107261

0.109233

0.110852

0.112216

0.113392

0.114426

0.115351

Cl*sin(Φ0) 0.124702

0.111555

0.098607

0.090746

0.087097

0.08364

0.080369

0.07728

0.074363

0.071609

Cd*sin(Φ0) 0.029156

0.039374

0.046517

0.049994

0.051437

0.052715

0.053849

0.054859

0.055761

0.056568

ΨQ 0.760628

0.415474

0.288207

0.242687

0.225949

0.211975

0.200156

0.190043

0.181301

0.173673

Elemental Thrust Coefficient(dCt/dx)

0.00052

0.01024

0.023378

0.032939

0.037567

0.041864

0.045626

0.048627

0.050613

0.051304

37 | P a g e

Elemental Torque Coefficient(dCq/dx)

0.008295

0.017592

0.030158

0.03953

0.044161

0.048527

0.052416

0.055578

0.057726

0.05853


38 | P a g e


p10

p1 = -0.005099 p2 = 0.04299 p3 = -0.1645 p4 = 0.3763

p5 = -0.5725 p6 = 0.437 p7 = -0.1931 p8 = 0.153

p9 = -0.01772 p10 = -0.005111

dCQ/dx from interpolation


p10

p1 = -0.00118 p2 = 0.01041 p3 = -0.04035 p4 = 0.0954

p5 = -0.2117 p6 = 0.1608 p7 = -0.03049 p8 = 0.06895

p9 = 0.006665 p10 = 6.406e-005

CT = 0.0182 CQ = 0.0253


Station(X) 0.3 0.45 0.6 0.7 0.75 0.8 0.85 0.9 0.95 1

X^2 0.09 0.2025 0.36 0.49 0.5625 0.64 0.7225 0.81 0.9025 1

X^3 0.027 0.091125 0.216 0.343 0.421875 0.512 0.614125 0.729 0.857375 1

Chord(b) 0.248181 0.285497 0.297654 0.291781 0.284651 0.274726 0.262005 0.246489 0.228177 0.20707

Solidity 0.171736 0.197558 0.20597 0.201906 0.196972 0.190104 0.181302 0.170565 0.157894 0.143288

Pitch Angle 1.143264 0.961274 0.818145 0.740684 0.706447 0.67484 0.645609 0.618525 0.59338 0.569985

Ωr 86.70796 130.0619 173.4159 202.3186 216.7699 231.2212 245.6725 260.1239 274.5752 289.0265

Air Flow Angle 1.104328 0.923915 0.78188 0.705151 0.671311 0.640127 0.611352 0.58476 0.560144 0.53732

sin(Φ) 0.893162 0.797967 0.704615 0.648149 0.622013 0.597297 0.573975 0.551999 0.531308 0.511836


5 5 5 5 5 5 5 5 5 5

β - Φ 0.038936 0.037359 0.036265 0.035532 0.035136 0.034713 0.034257 0.033765 0.033235 0.032664

Induced AoA(αi) 0.011136 0.009559 0.008465 0.007732 0.007336 0.006913 0.006457 0.005965 0.005435 0.004864

39 | P a g e

Φ0 1.115464 0.933474 0.790345 0.712884 0.678647 0.64704 0.617809 0.590725 0.56558 0.542185

α0 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278 0.0278

Lift Coefficient(Cl) 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139


0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066

cos^2(αi) 0.999876 0.999909 0.999928 0.99994 0.999946 0.999952 0.999958 0.999964 0.99997 0.999976

cos^2(Φ) 0.202261 0.363249 0.503518 0.579903 0.613099 0.643236 0.670553 0.695297 0.717711 0.738024

cos(Φ0) 0.43976 0.595046 0.7036 0.756479 0.778422 0.797872 0.81515 0.830537 0.844278 0.856583

sin(Φ0) 0.898115 0.803692 0.710596 0.654018 0.627741 0.602827 0.57925 0.556963 0.535905 0.516008

Cl*cos(Φ0) 0.061127 0.082711 0.0978 0.105151 0.108201 0.110904 0.113306 0.115445 0.117355 0.119065

Cd*sin(Φ0) 0.059276 0.053044 0.046899 0.043165 0.041431 0.039787 0.038231 0.03676 0.03537 0.034057

ΨT 0.009151 0.081666 0.101084 0.106883 0.1089 0.110557 0.111956 0.113164 0.114228 0.115181

Cl*sin(Φ0) 0.124838 0.111713 0.098773 0.090908 0.087256 0.083793 0.080516 0.077418 0.074491 0.071725

Cd*sin(Φ0) 0.029024 0.039273 0.046438 0.049928 0.051376 0.05266 0.0538 0.054815 0.055722 0.056535

ΨQ 0.760616 0.415617 0.288371 0.242847 0.226104 0.212124 0.200298 0.190176 0.181423 0.173784

Elemental Thrust Coefficient(dCt/dx)

0.000549 0.012676 0.029082 0.041028 0.046815 0.05219 0.056901 0.060661 0.063156 0.064036

Elemental Torque Coefficient(dCq/dx)

0.010369 0.021997 0.037719 0.049445 0.055239 0.060702 0.065567 0.069522 0.072206 0.073209

40 | P a g e



p10

p1 = -0.006256 p2 = 0.05289 p3 = -0.2029 p4 = 0.4649

p5 = -0.7088 p6 = 0.5411 p7 = -0.2385 p8 = 0.1901

p9 = -0.02199 p10 = -0.006479

41 | P a g e



p10

p1 = -0.00147 p2 = 0.01301 p3 = -0.05008 p4 = 0.1183

p5 = -0.2639 p6 = 0.2007 p7 = -0.03792 p8 = 0.0862

p9 = 0.00832 p10 = 7.872e-005

CT = 0.0227 CQ = 0.0316


Station(X) 0.3 0.45 0.6 0.7 0.75 0.8 0.85 0.9 0.95 1

X^2 0.09 0.2025 0.36 0.49 0.5625 0.64 0.7225 0.81 0.902

5 1

X^3 0.027 0.0911

25 0.216 0.343

0.421875

0.512 0.6141

25 0.729

0.857375

1

Chord(b) 0.2481

81 0.2854

97 0.2976

54 0.2917

81 0.2846

51 0.2747

26 0.262005

0.246489

0.228177

0.20707

Solidity 0.206083

0.237069

0.247164

0.242287

0.236367

0.228125

0.217562

0.204678

0.189472

0.171945

Pitch Angle 1.1454

92 0.9631

86 0.8198

38 0.7422

3 0.7079

15 0.6762

22 0.6469

0.619718

0.594467

0.570957

Ωr 86.707

96 130.06

19 173.41

59 202.31

86 216.76

99 231.22

12 245.67

25 260.12

39 274.57

52 289.0265

Air Flow Angle

1.104328

0.923915

0.78188

0.705151

0.671311

0.640127

0.611352

0.58476

0.560144

0.53732

sin(Φ) 0.8931

62 0.7979

67 0.7046

15 0.6481

49 0.6220

13 0.5972

97 0.5739

75 0.5519

99 0.5313

08 0.5118

36


5 5 5 5 5 5 5 5 5 5

β - Φ 0.0411

63 0.0392

71 0.0379

58 0.037079

0.036603

0.036095

0.035548

0.034958

0.034322

0.033637

Induced AoA(αi)

0.013363

0.011471

0.010158

0.009279

0.008803

0.008295

0.007748

0.007158

0.006522

0.005837

Φ0 1.1176

92 0.9353

86 0.7920

38 0.7144

3 0.6801

15 0.648422

0.6191 0.5919

18 0.5666

67 0.5431

57

α0 0.0278 0.0278 0.027

8 0.027

8 0.0278

0.0278

0.0278

0.0278

0.0278

0.0278

42 | P a g e

Lift Coefficient(Cl

) 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139 0.139

Drag Coefficient(C

d) 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066 0.066

cos^2(αi) 0.999

821 0.9998

68 0.999897

0.999914

0.999923

0.999931

0.99994

0.999949

0.999957

0.999966

cos^2(Φ) 0.202

261 0.3632

49 0.5035

18 0.5799

03 0.6130

99 0.643236

0.670553

0.695297

0.717711

0.738024

cos(Φ0) 0.4377

59 0.5935

08 0.7023

96 0.7554

67 0.7775

01 0.7970

38 0.8144

01 0.829872

0.843695

0.856081

sin(Φ0) 0.899092

0.804828

0.711786

0.655187

0.628882

0.603929

0.580302

0.557954

0.536823

0.516842

Cl*cos(Φ0) 0.060849

0.082498

0.097633

0.10501

0.108073

0.110788

0.113202

0.115352

0.117274

0.118995

Cd*sin(Φ0) 0.0593

4 0.0531

19 0.046978

0.043242

0.041506

0.039859

0.0383

0.036825

0.03543

0.034112

ΨT 0.007456

0.080868

0.100592

0.106504

0.108565

0.110261

0.111695

0.112935

0.114029

0.115011

Cl*sin(Φ0) 0.1249

74 0.1118

71 0.098938

0.091071

0.087415

0.083946

0.080662

0.077556

0.074618

0.071841

Cd*sin(Φ0) 0.028892

0.039172

0.046358

0.049861

0.051315

0.052604

0.05375

0.054772

0.055684

0.056501

ΨQ 0.7605

93 0.4157

56 0.288

533 0.243006

0.226258

0.212273

0.200438

0.190308

0.181545

0.173894

Elemental Thrust

Coefficient(dCt/dx)

0.000537

0.015063

0.034728

0.04906

0.056006

0.062461

0.068122

0.072647

0.075655

0.076729

Elemental Torque

Coefficient(dCq/dx)

0.012442

0.026406

0.045288

0.059373

0.066332

0.072893

0.078735

0.083484

0.086706

0.087907

43 | P a g e

44 | P a g e



p10

p1 = -0.007367 p2 = 0.06247 p3 = -0.2403 p4 = 0.5514

p5 = -0.8425 p6 = 0.6432 p7 = -0.2828 p8 = 0.2266

p9 = -0.0262 p10 = -0.007881



p10

p1 = -0.00147 p2 = 0.01301 p3 = -0.05008 p4 = 0.1183

p5 = -0.2639 p6 = 0.2007 p7 = -0.03792 p8 = 0.0862

p9 = 0.00832 p10 = 7.872e-005

CT = 0.0270 CQ = 0.0379

Selection of No. of Blades

We’ve done the analysis for 2 blades, 3 blades, 4 blades, 5 blades, 6 blades respectively.

To select one of this, we need to compare them and select the appropriate.

2 Blades 3 Blades 4 Blades 5 Blades 6 Blades

Thrust Coefficient 0.0184 0.0274 0.0364 0.0454 0.054

Torque Coefficient 0.0252 0.0378 0.0506 0.0632 0.0758

Power Coefficient 0.15833627 0.237504405 0.317929177 0.397097311 0.476265446

Thrust(N) 4036.87433 6011.432426 7985.990522 9960.548618 11847.34858

Torque(Nm) 25432.30828 38148.46241 51066.46027 63782.61441 76498.76855

Power(W) 1195918.114 1793877.171 2417200.657 2015159.714 2613118.771

Advance Ratio 1.86 1.86 1.86 1.86 1.86

τ 0.013543535 0.020168091 0.026792646 0.033417202 0.039747332

σ 0.062658745 0.093988117 0.125814781 0.157144154 0.188473526

45 | P a g e

Induced Exit

Swirl(ω)

0.02188995 0.032781268 0.043810442 0.054631206 0.065422017

Induced Velocity(Vi) 1.162176641 1.727804478 2.291598799 2.853577319 3.388898525

Induced

Efficiency(ηi)

0.71614757 0.724581284 0.729953088 0.742653165 0.760890798

From the comparison chart, we find that propeller with 6 blades have highest efficiency. It

produces 11,847 N thrust for power input of 2613 kW.

Design Output

Propeller with

No. of Blades : 6

Airfoil : Trainer60

Diameter : 4.6 m

Blade Pitch Angle: 32 - 700

Chord Distribution: 0.1 m at hub

0.21 m at tip

max of 0.295 m at 0.6R

46 | P a g e

Design of Propeller in Solidworks

Airfoil Coordinates

The airfoils coordinates were imported from an airfoil database the lower and upper surface were imported into the software.

Steps to Design

Get the airfoil coordinates from any airfoil database and then save the file as .DAT file.0

Use any software to convert the .DAT file to .txt file and open the file in Solidworks.

Join the Coordinates in the front plane to form an airfoil shape and convert it into an entity so that it is usable for editing.

Join the leading edge point and the trailing edge point with a centerline so as to form a chord line.

Now form a reference plane parallel to the front plane and copy paste the airfoil entity into the corresponding planes and use features rotate entity and scale entity to get the desired chord length and Pitch angle.

Repeat the above step for as many planes as you want say 10, ranging from 0.2R to R, radius of the propeller and adjust the chord and pitch angle of the airfoil. More the number of sections more is the accurate representation of the blade.

Now use the lofted base feature to join the existing sections with a solid structure. This forms a blade structure.

47 | P a g e

Final Design:

Now make a circle in the centre and extrude it on the either sides so that 0.2-0.3R of the blade is inside the hub. This forms our hub.

Use the circular pattern feature in the solidworks to copy the blades and space them equally around the hub.

Make a dome on the hub which corresponds to the front of the propeller so that one can identify the front.

48 | P a g e

Front View

Side View

49 | P a g e

Back View

50 | P a g e

References

http://www.worldofkrauss.com/

http://www.ae.illinois.edu/m-selig/ads/coord_database.html

http://en.wikipedia.org/wiki/Dornier_328


http://www.328support.de/en/index.php

http://www.pwc.ca/en/engines/pw100

Introduction to Flight by J D Anderdson

http://www.worldofkrauss.com/

http://www.ae.illinois.edu/m-selig/ads/coord_database.html



http://www.328support.de/en/index.php

http://www.pwc.ca/en/engines/pw100

High Speed Large Aircraft Propeller Design

Documents

boundary layer

gas stream

thickness

propeller

blade pitch

maximum climb

leading edge

139 drag coefficient