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# Chapter 4 - Engine characteristics - 2 Notes | EduRev

## : Chapter 4 - Engine characteristics - 2 Notes | EduRev

``` Page 1

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 1
Chapter 4
Lecture 14

Engine characteristics – 2

Topics

4.2.8 Parameters for describing propeller performance and typical
propeller characteristics
4.2.9 Selection of propeller diameter for chosen application
4.2.8 Parameters for describing propeller performance and typical propeller
characteristics
As pointed out at the end of the previous subsection, the momentum
theory of propeller has limitations. Though the refined theories are helpful in
design of propeller blades, the propeller characteristics obtained from the wind
tunnel tests are used for estimation of airplane performance. These
characteristics are presented in terms of certain parameters. First these
parameters are defined and then typical characteristics of propellers are
presented. The procedures for (a) selection of the propeller diameter and (b)
obtaining the propeller efficiency for given h, v, BHP and N, are given in the next
two subsections.
Following Ref.4.1 and Ref.3.7 chapter 16, the propeller performance is
expressed in terms of the following coefficients. It may be pointed out that FPS
units are used in these references whereas SI units are used here.
Advance ratio : J = V/nd                                                                        (4.14)
Power coefficient:
P
C = P/?n
3
d
5
; P in Watts                                          (4.15)
Thrust coefficient: C
T
= T/?n
2
d
4
(4.16)
Speed power coefficient: C
s
= V (?/ Pn
2
)
1/5
=
5
P
J/ C                          (4.17)
Propeller efficiency:
p
? =TV / P; P in Watts
= J (C
T
/
P
C )                                                       (4.18)
Page 2

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 1
Chapter 4
Lecture 14

Engine characteristics – 2

Topics

4.2.8 Parameters for describing propeller performance and typical
propeller characteristics
4.2.9 Selection of propeller diameter for chosen application
4.2.8 Parameters for describing propeller performance and typical propeller
characteristics
As pointed out at the end of the previous subsection, the momentum
theory of propeller has limitations. Though the refined theories are helpful in
design of propeller blades, the propeller characteristics obtained from the wind
tunnel tests are used for estimation of airplane performance. These
characteristics are presented in terms of certain parameters. First these
parameters are defined and then typical characteristics of propellers are
presented. The procedures for (a) selection of the propeller diameter and (b)
obtaining the propeller efficiency for given h, v, BHP and N, are given in the next
two subsections.
Following Ref.4.1 and Ref.3.7 chapter 16, the propeller performance is
expressed in terms of the following coefficients. It may be pointed out that FPS
units are used in these references whereas SI units are used here.
Advance ratio : J = V/nd                                                                        (4.14)
Power coefficient:
P
C = P/?n
3
d
5
; P in Watts                                          (4.15)
Thrust coefficient: C
T
= T/?n
2
d
4
(4.16)
Speed power coefficient: C
s
= V (?/ Pn
2
)
1/5
=
5
P
J/ C                          (4.17)
Propeller efficiency:
p
? =TV / P; P in Watts
= J (C
T
/
P
C )                                                       (4.18)
Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 2
Torque coefficient:
25
Q
Q
=
?n d
C                                                                (4.19)
Torque speed coefficient:
3
SQ
Q = J/ C = V ?d /Q                                  (4.20)
Where, P = Power in watts, T = thrust (N); V = flight velocity (m/s), n = rotational
speed (rev/s),
d = diameter of propeller (m)
Q = Torque (Nm) = P/ 2 n ?
In FPS units:
T = thrust (lbs); P = power (ft lbs/s) = 550 BHP
V = velocity (ft / s), BHP = brake horse power
The performance of a propeller is indicated by thrust coefficient (C
T
), power
coefficient (
P
C ) and efficiency (
p
? ). These quantities depend on advance ratio
(J) and pitch angle ? ? ß . Based on Ref.4.1, the experimental characteristics of a
two bladed propeller are presented in Figs. 4.5a to d.
Figure 4.5a presents the variation of
p
? vs J with ß as parameter. It is seen that
p
? is zero when V is zero; J is also zero in this case by virtue of its
definition(Eq.4.14). Equation (4.2) also indicates that
p
? is zero when V is zero.
This is because even though the engine is working and producing thrust, no
useful work is done when V is zero. This is like a person pressing an immovable
wall. He spends muscular energy to push the wall but the output and hence the
efficiency is zero as the wall does not move and no useful work is done.

Page 3

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 1
Chapter 4
Lecture 14

Engine characteristics – 2

Topics

4.2.8 Parameters for describing propeller performance and typical
propeller characteristics
4.2.9 Selection of propeller diameter for chosen application
4.2.8 Parameters for describing propeller performance and typical propeller
characteristics
As pointed out at the end of the previous subsection, the momentum
theory of propeller has limitations. Though the refined theories are helpful in
design of propeller blades, the propeller characteristics obtained from the wind
tunnel tests are used for estimation of airplane performance. These
characteristics are presented in terms of certain parameters. First these
parameters are defined and then typical characteristics of propellers are
presented. The procedures for (a) selection of the propeller diameter and (b)
obtaining the propeller efficiency for given h, v, BHP and N, are given in the next
two subsections.
Following Ref.4.1 and Ref.3.7 chapter 16, the propeller performance is
expressed in terms of the following coefficients. It may be pointed out that FPS
units are used in these references whereas SI units are used here.
Advance ratio : J = V/nd                                                                        (4.14)
Power coefficient:
P
C = P/?n
3
d
5
; P in Watts                                          (4.15)
Thrust coefficient: C
T
= T/?n
2
d
4
(4.16)
Speed power coefficient: C
s
= V (?/ Pn
2
)
1/5
=
5
P
J/ C                          (4.17)
Propeller efficiency:
p
? =TV / P; P in Watts
= J (C
T
/
P
C )                                                       (4.18)
Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 2
Torque coefficient:
25
Q
Q
=
?n d
C                                                                (4.19)
Torque speed coefficient:
3
SQ
Q = J/ C = V ?d /Q                                  (4.20)
Where, P = Power in watts, T = thrust (N); V = flight velocity (m/s), n = rotational
speed (rev/s),
d = diameter of propeller (m)
Q = Torque (Nm) = P/ 2 n ?
In FPS units:
T = thrust (lbs); P = power (ft lbs/s) = 550 BHP
V = velocity (ft / s), BHP = brake horse power
The performance of a propeller is indicated by thrust coefficient (C
T
), power
coefficient (
P
C ) and efficiency (
p
? ). These quantities depend on advance ratio
(J) and pitch angle ? ? ß . Based on Ref.4.1, the experimental characteristics of a
two bladed propeller are presented in Figs. 4.5a to d.
Figure 4.5a presents the variation of
p
? vs J with ß as parameter. It is seen that
p
? is zero when V is zero; J is also zero in this case by virtue of its
definition(Eq.4.14). Equation (4.2) also indicates that
p
? is zero when V is zero.
This is because even though the engine is working and producing thrust, no
useful work is done when V is zero. This is like a person pressing an immovable
wall. He spends muscular energy to push the wall but the output and hence the
efficiency is zero as the wall does not move and no useful work is done.

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 3

Fig 4.5a Propeller efficiency  (
p
? ) vs advance ratio (J) with pitch angle (ß) as
parameter.

For a chosen value of ß , the efficiency (
p
? ) increases as J increases. It reaches
a maximum for a certain value of J and then decreases (Fig. 4.5a). The
maximum value of
p
? is seen to be around 80 to 85%. However, the value of J at
which the maximum of
p
? occurs, depends on the pitch angleß . This indicates
that for a single pitch or fixed pitch propeller, the efficiency is high (80 to 85%)
only over a narrow range of flight speeds (Fig. 4.5a). Keeping this behaviour in
view, the commercial airplanes use a variable pitch propeller. In such a propeller
the entire blade is rotated through a chosen angle during the flight and the pitch
of all blade elements changes. Such propellers have high efficiency over a wide
range of speeds. However, propellers with variable pitch arrangements are
expensive and heavy. Hence, personal airplanes, where cost of the airplane is an
important consideration, employ a fixed pitch propeller. As a compromise, in
some designs, propellers with two or three pitch settings are employed.
Figure 4.5b presents the variation of power coefficient (
P
C ) vs J with ß and C
T
as parameters. This chart is useful to obtain
p
? for given values of altitude,
velocity, RPM and BHP (see subsection 4.2.10).
Page 4

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 1
Chapter 4
Lecture 14

Engine characteristics – 2

Topics

4.2.8 Parameters for describing propeller performance and typical
propeller characteristics
4.2.9 Selection of propeller diameter for chosen application
4.2.8 Parameters for describing propeller performance and typical propeller
characteristics
As pointed out at the end of the previous subsection, the momentum
theory of propeller has limitations. Though the refined theories are helpful in
design of propeller blades, the propeller characteristics obtained from the wind
tunnel tests are used for estimation of airplane performance. These
characteristics are presented in terms of certain parameters. First these
parameters are defined and then typical characteristics of propellers are
presented. The procedures for (a) selection of the propeller diameter and (b)
obtaining the propeller efficiency for given h, v, BHP and N, are given in the next
two subsections.
Following Ref.4.1 and Ref.3.7 chapter 16, the propeller performance is
expressed in terms of the following coefficients. It may be pointed out that FPS
units are used in these references whereas SI units are used here.
Advance ratio : J = V/nd                                                                        (4.14)
Power coefficient:
P
C = P/?n
3
d
5
; P in Watts                                          (4.15)
Thrust coefficient: C
T
= T/?n
2
d
4
(4.16)
Speed power coefficient: C
s
= V (?/ Pn
2
)
1/5
=
5
P
J/ C                          (4.17)
Propeller efficiency:
p
? =TV / P; P in Watts
= J (C
T
/
P
C )                                                       (4.18)
Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 2
Torque coefficient:
25
Q
Q
=
?n d
C                                                                (4.19)
Torque speed coefficient:
3
SQ
Q = J/ C = V ?d /Q                                  (4.20)
Where, P = Power in watts, T = thrust (N); V = flight velocity (m/s), n = rotational
speed (rev/s),
d = diameter of propeller (m)
Q = Torque (Nm) = P/ 2 n ?
In FPS units:
T = thrust (lbs); P = power (ft lbs/s) = 550 BHP
V = velocity (ft / s), BHP = brake horse power
The performance of a propeller is indicated by thrust coefficient (C
T
), power
coefficient (
P
C ) and efficiency (
p
? ). These quantities depend on advance ratio
(J) and pitch angle ? ? ß . Based on Ref.4.1, the experimental characteristics of a
two bladed propeller are presented in Figs. 4.5a to d.
Figure 4.5a presents the variation of
p
? vs J with ß as parameter. It is seen that
p
? is zero when V is zero; J is also zero in this case by virtue of its
definition(Eq.4.14). Equation (4.2) also indicates that
p
? is zero when V is zero.
This is because even though the engine is working and producing thrust, no
useful work is done when V is zero. This is like a person pressing an immovable
wall. He spends muscular energy to push the wall but the output and hence the
efficiency is zero as the wall does not move and no useful work is done.

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 3

Fig 4.5a Propeller efficiency  (
p
? ) vs advance ratio (J) with pitch angle (ß) as
parameter.

For a chosen value of ß , the efficiency (
p
? ) increases as J increases. It reaches
a maximum for a certain value of J and then decreases (Fig. 4.5a). The
maximum value of
p
? is seen to be around 80 to 85%. However, the value of J at
which the maximum of
p
? occurs, depends on the pitch angleß . This indicates
that for a single pitch or fixed pitch propeller, the efficiency is high (80 to 85%)
only over a narrow range of flight speeds (Fig. 4.5a). Keeping this behaviour in
view, the commercial airplanes use a variable pitch propeller. In such a propeller
the entire blade is rotated through a chosen angle during the flight and the pitch
of all blade elements changes. Such propellers have high efficiency over a wide
range of speeds. However, propellers with variable pitch arrangements are
expensive and heavy. Hence, personal airplanes, where cost of the airplane is an
important consideration, employ a fixed pitch propeller. As a compromise, in
some designs, propellers with two or three pitch settings are employed.
Figure 4.5b presents the variation of power coefficient (
P
C ) vs J with ß and C
T
as parameters. This chart is useful to obtain
p
? for given values of altitude,
velocity, RPM and BHP (see subsection 4.2.10).
Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 4

Fig 4.5b Power coefficient (
P
C ) vs advance ratio (J) with pitch angle (ß) and
thrust coefficient (C
T
) as parameters.

Figure 4.5c presents the variations of C
S
vs J and C
S
vs
p
? with ß as parameter.
This figure is designated as ‘Design chart’ and is used for selection of the
diameter of the propeller. A brief explanatory note on this topic is as follows.
Using defintions of J and
P
C , the parameter
s
C , defined below, is obtained. It is
observed that this parameter does not involve the diameter (d) of the propeller.

2 1/5
1/5
P
s
J
C = = V (?/ Pn )
C
(4.21)
Page 5

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 1
Chapter 4
Lecture 14

Engine characteristics – 2

Topics

4.2.8 Parameters for describing propeller performance and typical
propeller characteristics
4.2.9 Selection of propeller diameter for chosen application
4.2.8 Parameters for describing propeller performance and typical propeller
characteristics
As pointed out at the end of the previous subsection, the momentum
theory of propeller has limitations. Though the refined theories are helpful in
design of propeller blades, the propeller characteristics obtained from the wind
tunnel tests are used for estimation of airplane performance. These
characteristics are presented in terms of certain parameters. First these
parameters are defined and then typical characteristics of propellers are
presented. The procedures for (a) selection of the propeller diameter and (b)
obtaining the propeller efficiency for given h, v, BHP and N, are given in the next
two subsections.
Following Ref.4.1 and Ref.3.7 chapter 16, the propeller performance is
expressed in terms of the following coefficients. It may be pointed out that FPS
units are used in these references whereas SI units are used here.
Advance ratio : J = V/nd                                                                        (4.14)
Power coefficient:
P
C = P/?n
3
d
5
; P in Watts                                          (4.15)
Thrust coefficient: C
T
= T/?n
2
d
4
(4.16)
Speed power coefficient: C
s
= V (?/ Pn
2
)
1/5
=
5
P
J/ C                          (4.17)
Propeller efficiency:
p
? =TV / P; P in Watts
= J (C
T
/
P
C )                                                       (4.18)
Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 2
Torque coefficient:
25
Q
Q
=
?n d
C                                                                (4.19)
Torque speed coefficient:
3
SQ
Q = J/ C = V ?d /Q                                  (4.20)
Where, P = Power in watts, T = thrust (N); V = flight velocity (m/s), n = rotational
speed (rev/s),
d = diameter of propeller (m)
Q = Torque (Nm) = P/ 2 n ?
In FPS units:
T = thrust (lbs); P = power (ft lbs/s) = 550 BHP
V = velocity (ft / s), BHP = brake horse power
The performance of a propeller is indicated by thrust coefficient (C
T
), power
coefficient (
P
C ) and efficiency (
p
? ). These quantities depend on advance ratio
(J) and pitch angle ? ? ß . Based on Ref.4.1, the experimental characteristics of a
two bladed propeller are presented in Figs. 4.5a to d.
Figure 4.5a presents the variation of
p
? vs J with ß as parameter. It is seen that
p
? is zero when V is zero; J is also zero in this case by virtue of its
definition(Eq.4.14). Equation (4.2) also indicates that
p
? is zero when V is zero.
This is because even though the engine is working and producing thrust, no
useful work is done when V is zero. This is like a person pressing an immovable
wall. He spends muscular energy to push the wall but the output and hence the
efficiency is zero as the wall does not move and no useful work is done.

Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 3

Fig 4.5a Propeller efficiency  (
p
? ) vs advance ratio (J) with pitch angle (ß) as
parameter.

For a chosen value of ß , the efficiency (
p
? ) increases as J increases. It reaches
a maximum for a certain value of J and then decreases (Fig. 4.5a). The
maximum value of
p
? is seen to be around 80 to 85%. However, the value of J at
which the maximum of
p
? occurs, depends on the pitch angleß . This indicates
that for a single pitch or fixed pitch propeller, the efficiency is high (80 to 85%)
only over a narrow range of flight speeds (Fig. 4.5a). Keeping this behaviour in
view, the commercial airplanes use a variable pitch propeller. In such a propeller
the entire blade is rotated through a chosen angle during the flight and the pitch
of all blade elements changes. Such propellers have high efficiency over a wide
range of speeds. However, propellers with variable pitch arrangements are
expensive and heavy. Hence, personal airplanes, where cost of the airplane is an
important consideration, employ a fixed pitch propeller. As a compromise, in
some designs, propellers with two or three pitch settings are employed.
Figure 4.5b presents the variation of power coefficient (
P
C ) vs J with ß and C
T
as parameters. This chart is useful to obtain
p
? for given values of altitude,
velocity, RPM and BHP (see subsection 4.2.10).
Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 4

Fig 4.5b Power coefficient (
P
C ) vs advance ratio (J) with pitch angle (ß) and
thrust coefficient (C
T
) as parameters.

Figure 4.5c presents the variations of C
S
vs J and C
S
vs
p
? with ß as parameter.
This figure is designated as ‘Design chart’ and is used for selection of the
diameter of the propeller. A brief explanatory note on this topic is as follows.
Using defintions of J and
P
C , the parameter
s
C , defined below, is obtained. It is
observed that this parameter does not involve the diameter (d) of the propeller.

2 1/5
1/5
P
s
J
C = = V (?/ Pn )
C
(4.21)
Flight dynamics-I  Prof. E.G.Tulapurkara
Chapter IV
Indian Institute of Technology, Madras 5
It is also observed that the parameter
s
C depends on V, ? , P and N.
Consequently, this parameter can be evaluated when the power output (P),
engine RPM(N) and flight condition viz. V and h are specified.
The design problem involves obtaining the value of J which would give the
maximum value of
p
? for a specified value of
s
C . This is arrived at in the
following manner.

Fig 4.5c Design chart
Using the data in Figs 4.5b & a , the values of
s
C can be obtained for constant
values of J or ß . For example, for ß = 15
o
the values given in  table 4.1 are
obtained.

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