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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