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# Brief Tutorial on Aircraft

Propulsion
GMU SYST 460/560
Fall semester, Nov. 5, 2012
Prof. George Donohue

Overview
One of the most sophisticated of modern
engineering designs
Requires an understanding of
Thermodynamics, Heat Transfer, Fluid
Mechanics, Mechanics of Materials
Designs have evolved from Prop to Jet, to
Turbojet, Turboprop, High Bypass Ratio
Fan Jet engines

Archimedes of Syracuse
(c.287-212 BCE)

## Sum of the Forces F = 0

Sum of the Moments (F x L) = 0
Buoyancy force = weight of displaced fluid
First Description of the Screw Propeller
Foundation for Lighter than Air Flight in 18th cent.
Pi: The ratio of the circumference of any circle to its
diameter is less than 3 1/7 but greater than 3 10/71.
calculus like derivation
Great Mathematician and Military Engineer killed
in 2nd Punic War

Leonardo da Vinci
(c. 1452-1519 CE)
Self Educated
Continuity Equation
A1v1=A2v2.

## Precursor to Conservation of Mass and

Bernoulli Equation in the 18th century
Artist and Military Engineer
Designs poorly documented
Art works better known
Conceptual Designs of Winged Gliders

## Robert Boyle (1627-1691 CE)

pV= constant
addition of temperature (T) in Charles's law
pV/T=constant (Gas Law)

## Thermodynamic Equation of State

Used in Mechanical , Aerospace and Chemical
Engineering

## Fundamental to understanding Brayton Cycle

Foundation for Lighter than Air flight in 18th
century

## Isaac Newton (1642-1727 CE)

Great Mathematician, Physicist
Vector Calculus

Law of Gravity
Vector Relationships
Conservation of Momentum
mv = constant
F = ma = d(mv)/dt
Sigma F = 0
If I have seen further, it is by standing on the
shoulders of Giants

## Gottfried Wilhelm Leibniz

(1646-1716 CE)
Great Statesman, Mathematician, Physicist
Calculus

## Altitude + Vis Viva (mv^2) = Constant

Today, we state this as the:
Law of Conservation of Energy for solid
bodies:
Potential Energy + Kinetic Energy = Constant

## Daniel Bernoulli (1700-1782 CE)

Recognized Leibniz vis vita applied to fluid
motion as well
Medical experimentalist and Mathematician
Pressure + rho v2 = Constant
Where rho is the fluid density and v is the fluid
velocity magnitude (along a streamline).

## Simple Equation to calculate both Airfoil

Lift and Propeller/Fan Thrust

## Rudolf Julius Emanuel Clausius

(1822-1888)
The net change in the total energy of the universe is zero
1st Law of Thermodynamics
For a thermodynamic cycle, the net heat supplied to the
system equals the net work done by the system.
Carnot efficiency = 1 Low Absolute Temperature/High
Absolute Temperature <100%
The net change in the total entropy of the universe is
always greater than zero 2nd Law of Thermodynamics
Temperature is a Measure of Entropy in a Heat Engine
d (Q) = T d(S)

## Perpetual Motion Machine is impossible and the Universe

is running down, Information order decays

## John Barber (1734-1801)

George Brayton (1830-1892)
Frank Whittle (1907-1996)
John Barber- UK pat. No. 1833 gas turbine engine
Materials inadequate to construction & operation

## George Brayton US pat. (1872) constant

pressure combustion thermodynamic cycle
Lost ground trans. Competition to Otto Cycle

## Air Commodore Sir Frank Whittle (RAF)

pat. (1930) Turbojet engine
Ranked by BBC poll #42 of 100 Greatest Britons

## Fundamental Attributes of All

Aircraft Designs
Aero 101:
If it Flys, It weights TOO MUCH!

## Wright Bros Major Accomplishment:

Designed a System with Adequate Thrust to
Drag ratio, Low weight with Adequate
Structural Strength, Wings with Adequate Lift
to Weight ratio and a Stable Flight Control
system

## Some Energy Density Comps

Energy Storage Medium

0.016

CNG (CH4)

1.3

Gasoline (C8H18)

5.3

5.8

TNT =0.34

## Natural Gas = CH4 can be chained as (CnH2n+2)

2*C8H18 + 25*O2 = 18*H2O + 16*CO2 + ENERGY

## Prediction: Renewables grow rapidly, but under current

policies fossil fuels still provide 78% of U.S. energy use in 2035
Shares of total U.S. energy

## U.S. primary energy consumption

History

Projections
2009
Renewables (excluding liquid biofuels)

125

10%

7%

100

Coal

21%

75

Natural gas

25%

50

21%

24%

3%
1%

25

Liquid biofuels

37%

## Oil and other liquid fuels

9%

33%
8%

Nuclear
0
1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035
13

## Shale gas offsets declines in other U.S. supply to meet

consumption growth and lower import needs
U.S. dry gas
trillion cubic feet per year
History

Projections

2009

30

1%

25

Net imports
11%

20

14%

15

45%

Shale gas

20%
Non-associated onshore

9%

8%
8%

Non-associated offshore

10
28%

Tight gas

8%
9%

Coalbed methane
Associated with oil

22%

5
0
1990
14

2%

1995

2000

2005

2010

2015

2020

2025

7%

2030

2035

## Oil prices in the AEO2011 Report Reference Case

annual average price of low sulfur crude oil
real 2009 dollars per barrel
History

225

2009

Projections
High oil price

200
175
150
125

AEO2011 Reference

100
75
50

## Low oil price

25

0
1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035
15

## Turbo Jet Fundamental Operating

Principles

Suck
-Air Intake
Squeeze -Cool Axial Compression (Work In)
Bang -Fuel + Combustion (Heat In)
Blow -Hot Turbine to Extract (work Out)

Thrust = d(mv)/dt

## Basic Axial Flow Turbo Jet Engine

Low Mass Flow, High Exit velocity (~3:1)
Low Efficiency

## Brayton Cycle Thermodynamics

Actual Brayton cycle:
isobaric process - heat rejection.

## Idealized Brayton cycle

Carnot Eff. = 1 T low / T high

## Fan/Prop. Thrust & Power

Conservation of Energy Bernoulli Equ. To find Pressure
and Velocity Before & After Prop or Fan
Thrust Force = d(mv)/dt
Useful Power = FThrust * Velocity=d(mv)/dt * v
Power Input = dm/dt*v*dv [ 1 dv/2v ]

Pressure
dv
dv

dP
Fuel + Heat = Work + Waste Heat

## Est. of Max efficiency

Brayton Cycle Thermal (Carnot) Efficiency
= 1-T low/T high = 1-300K(80F)/1500K(2240F) ~ 80% max
Increase Turbine Inlet Temp to Increase efficiency
Material Properties Limitation

## Fan (Prop) Propulsive Efficiency = Power Out/Power In

= 1 dv/2v ~ 80% max
Where Advance ratio (J) = v/nD ~ 0.9
D = Prop Disc Diameter
Bernoulli Equation (const. energy analysis along an accel. streamline)

## Max Thrust at High dv

Max Efficiency at LOW dv
Increase Mass Flow at Minimum dv to Increase Thrust @ min.
Wake Loss
Combined Efficiency = Prop Eff. X Thermal Eff.
~ 0.8 X 0.8 ~ 0.64 MAX

Constraints
Prop/Fan Diameter
Tip Speed less than M1.0 (Noise/Drag)

## Turbine Inlet Temperature

Active Cooling, Titanium, Ceramics

## Specific fuel Consumption

Lb Fuel/Hr/ Lb. Thrust
Turboprop = SFC ~ 0.5 * v/550* prop. Eff (per shp)
Prop. Eff. ~ 0.8
V (ft/sec)
dv~1.5:1
SFC @ 550 ft/sec ~ 0.40 / Hr. @~M0.7
Jets @ cruise = SFC ~ 0.9e^(-0.05BPR) : 0 <BPR<6.0
Turbojet (dv~3:1) ~ 0.9 lb fuel/hr / lb Thrust
LBPR Turbofan (BPR ~6)~ 0.67 lb fuel/hr / lb Thrust
HBPR Turbofan (~BPR 9:1) ~ 0.57 lb fuel/hr/ lb Thrust

## Max Combustion Efficiency @ stoichiometric

Air/fuel 15:1 Turbine Inlet Temp TOO HIGH for Material
strength
Air/fuel @ 60:1 Turbine Inlet temps ( 2,00 0 to 2,500 deg. F)

## Turbo Prop Vel <M0.75

with Controllable Pitch Propellers

A/C

Engine

TO rating
(KW)

Weight (Kg)

Power/Weight

ATR-72-200

PW 127

2,051

481

4.3

C-130J

RR AE 2100

3,424

702

4.9

Dash 8 (Q400)

PW 150A

3,781

690

5.5

8,203

1,900

4.4

11,033

1,900

5.8

TU-95 Bear

NK-12MV

## Tu-95 w/ NK-12MV & (2) AV-6H CR

Controllable Pitch Props

## TU-95 Bear Bomber (1952-present)

TU-114 Pax Aircraft (1961-1991)

## Max Speed = 470 Kn

Cruise Speed = 415 Kn
Range = 3,300 nm
Cruise Altitude = 26,000 ft.
Service Ceiling = 39,000 ft.
High Reliability
224 PAX
Pwr/Wt = 5.8 Kw/Kg
Contra-Rotation Prop ~ 10% increased Efficiency
4 X 4 Props Noisy (5X3 Scimitar would be a better
combination)

Dash 8 (Q400)

Bombardier Aerospace
Production (1983-pres)
1,054 (Oct. 2011)
\$27M price
PW 150A engines
Pwr/Wt = 5.5 Kw/Kg
78 PAX
360 Knot Cruise
27,000 Max Alt.
1,500 nmi. Range
Active Noise& Vibration Reduction (ANVS)

## GE-Dowty R391, Prop (Q400)

P&W150A
3,781 KW Take Off Pwr
Carbon Fiber
Controllable pitch
Scimitar Propellers

Antonov An-70
Progress D-27 Propfan w/ SV27
Contra-Rotation Scimitar Propellers

## Dev. ~ 1992 - 1994

14,000 shp
Prop. Dia. 4.2m (165 in.)
Wt. 1,650 Kg (3,600 lb.)
Pwr/Wt = 6.3 Kw/Kg
Never entered production
Competitor to A400M
High efficiency
Noise Concerns

A400M

IOC ~ 2012?
TP400-D6
CR 8 Bld composite props
Composite Wings & Emp
Cruise M0.72 (300Kt)
Ceiling > 37,000 ft.
Range ~ 3000 nmi.

TP-400-D6

## 11,000 shp (8,200 Kw)

1,900 Kg
TIT = 1500K
8 Bld CP composite prop
Scimitar Propellers
SFC = 0.4 lb/shp-hr
Pwr/Wt = 4.4 Kw/Kg
FOC 2009

## Basic Turbofan Engine

High BPR increases Thrust Efficiency
Large Air flow Mass at Low dv

High-bypass Turbofan

GE CF6-6

## Some Typ. Long Range

Turbo Fan Jets
A/C

Engine

Thrust
(KN)

Weight
(Kg)

BPR

B 737-500/A320,A340

CFM 56

100

1,950

6:1

B 777-200LR

GE 90

417

7,550

9:1

B 787,B747-8

GEnx

300

5,816

9.5:1

B787

RR Trent 1000

330

5,765

11:1

B747-400,767,A300,A310

CF6-80C2

280

4,100

5.2

A/C

Engine

Thrust
(KN)

Weight
(Kg)

BPR

A318

PW6000

100

2,289

5:1

CRJ100/440

GE CF 34-3

41

760

6.2:1

E190/195,ARJ21

GE CF34-10

89

1,700

5.1:1

B717-200

BR 715

83-95

2,800

4:1?

GV

BR 710

66

2,100

## BR 715 has a 58 inch fan diameter

GE CF34-10 has a 57 inch total diameter

## Some Final Thoughts

BPR on Commuter Jets have been ~ 4 to 6:1
Long Range, high efficiency engines have moved
BPR ~ 9 to 11:1
Q400 may be the future of Hub feeder routes
Jet A fuel can be replaced by Synfuel at a cost of
over ~\$60/bl
Electric Propulsion is not in the future due to low
energy density of source and high weight of
engines
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