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.Read More

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