This document provides an introduction to jet propulsion, including: 1. It discusses concepts like momentum analysis, Newton's second law of motion, and how thrust is generated through the acceleration of mass. 2. It covers topics such as the generation of thrust through jet velocity, specific thrust, thrust specific fuel consumption, and propulsion efficiency. 3. It describes characteristics of jet engines and velocities of different propulsion systems like turbojets, ramjets, and rockets.

1. Introduction to Jet Propulsion
P MV Subbarao
Professor
Mechanical Engineering Department
Strong and Reliable Muscles for the Aircraft……

2. Global Momentum Analysis

3. Momentum Equation
pinlet
pexit
Vac Vjet
∑ =
dt
dM
F cm
surface
Reynolds Transport Theorem:
inletexit
cvcm
MM
dt
dM
dt
dM  −+=
Newton’s Second Law of Motion

4. inletexit
cv
surface MM
dt
dM
F  −+=∑
For a frictionless flight, pressure forces are only the
surface forces…
inletexit
cv
ductwallexitexitinletinlet MM
dt
dM
FApAp  −+=−− ∑∑
Steady state steady flow
inletexitductwallexitexitinletinlet MMFApAp  −=−− ∑∑
airairjetjetductwallexitexitinletinlet VmVmFApAp  −=−− ∑∑
airairjetjetexitexitinletinletductwall VmVmApApF  +−−= ∑∑

5. airairjetjetexitexitinletinletductwall VmVmApApF  +−−= ∑∑
Pressure Thrust Momentum Thrust
At design cruising conditions : Pressure thrust is zero.
airairjetjetthrust VmVmF  −=
atmexitinlet ppp ==

6. Generation of Thrust : The Capacity
acairjetjetT VmVmF  −=
Thrust
( ) acairjetfuelairT VmVmmF  −+=
( ){ }acjetairT VVfmF −+= 1
f : Fuel-air ratio

7. Dynamic Equilibrium : Cruising Vehicle
For a cruising vehicle:
( ){ } Vehicleon1 dragVVfmF acjetairT =−+= 
( ){ }
2
1
2
air
ac
acdragacjetair
V
ACVVfm ρ=−+

8. Drag on Aircraft

9. Generation of Lift

10. Drag Coefficient of an Air Craft

11. Generation of Lift

12. Drag Coefficient of an Air Craft

13. Lift - to - Drag Ratio
Flight article Scenario L/D ratio
Virgin Atlantic
GlobalFlyer
Cruise 37[
Lockheed U-2 Cruise ~28
Rutan Voyager Cruise[4]
27
Albatross 20
Boeing 747 Cruise 17
Common tern 12
Herring gull 10
Concorde M2 Cruise 7.14
Cessna 150 Cruise 7
Concorde Approach 4.35
House sparrow 4

14. Minimum Drag Coefficients
Aircraft Type Aspect Ratio CDmin
RQ-2 Pioneer Single piston-engine UAV 9.39 0.0600
North American Navion Single piston-engine general aviation 6.20 0.0510
Cessna 172/182 Single piston-engine general aviation 7.40 0.0270
Cessna 310 Twin piston-engine general aviation 7.78 0.0270
Marchetti S-211 Single jet-engine military trainer 5.09 0.0205
Cessna T-37 Twin jet-engine military trainer 6.28 0.0200
Beech 99 Twin turboprop commuter 7.56 0.0270
Cessna 620 Four piston-engine transport 8.93 0.0322
Learjet 24 Twin jet-engine business jet 5.03 0.0216
Lockheed Jetstar Four jet-engine business jet 5.33 0.0126
F-104 Starfighter Single jet-engine fighter 2.45 0.0480
F-4 Phantom II Twin jet-engine fighter 2.83 0.0205 (subsonic)
0.0439 (supersonic)
Lightning Twin jet-engine fighter 2.52 0.0200
Convair 880 Four jet-engine airliner 7.20 0.0240
Douglas DC-8 Four jet-engine airliner 7.79 0.0188
Boeing 747 Four jet-engine airliner 6.98 0.0305
X-15 Hypersonic research plane 2.50 0.0950

15. Propulsive Power or Thrust Power:
( ){ }acjetairacacTp VVfmVVFP −+== 1
Specific Thrust S
( ) acjet
air
T
VVf
m
F
S −+== 1

Measure of compactness of a jet engine:

16. Thrust Specific Fuel Consumption TSFC
( ){ } ( ){ }acjetacjetair
fuel
T
fuel
VVf
f
VVfm
m
F
m
TSFC
−+
=
−+
==
11

Measure of fuel economy:

17. Aviation Appreciation
Propulsion Efficiency
JettheofPowerKineticAvailable
PowerThrust
propulsion =η
( ){ }22
1
2
acjet
air
acT
propulsion
VVf
m
VF
−+
=

η
( )( )
{ }22
)1(
2
1
acjet
air
acacjetair
propulsion
VVf
m
VVVfm
−+
−+
=


η

18. Jet Characteristics
• Quantities defining a jet are:
– cross-sectional area;
– composition;
– velocity.
jetjetjetjet VAm ρ=
acairjetjetjetT VmVAF −=
2
ρ
acairjetjetT VmVmF  −=
Of these, only the velocity is a truly characteristic feature and is of
considerable quantitative significance.

19. Jet Characteristics of Practical Propulsion Systems
System Jet Velocity (m/s)
Turbofan 200 - 600
Turbojet (sea-level, static) 350 - 600
Turbojet (Mach 2 at 36000 ft) 900 - 1200
Ramjet (Mach 2 at 36000 ft) 900 - 1200
Ramjet (Mach 4 at 36000 ft) 1800 - 2400
Solid Rocket 1500 – 2600
Liquid Rocket 2000 – 3500

20. Nozzle : Steady State Steady Flow
First Law :
No heat transfer and no work transfer & No Change in potential
energy.
in jet
cv
jetin
cv Wgz
V
hmgz
V
hmQ  +





++=





+++
22
22
jetin
V
h
V
h 





+=





+
22
22

21. Combined analysis of conservation of mass and first law
22








+=






+
jetjet
jet
inin
in
A
m
h
A
m
h
ρρ

A SSSF of gas through variable area duct can interchange the
enthalpy and kinetic energy as per above equation.
Consider gas as an ideal and calorically perfect.
0
22
22
Tc
c
V
Tc
c
V
Tc p
p
jet
jetp
p
in
inp =








+=








+

22. γ
γ 1−








=
jet
in
jet
in
p
p
T
T
Isentropic expansion of an ideal and calorically perfect gas.