Page 1 Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 1 Chapter 4 Lecture 15 Engine characteristics – 3 Topics 4.2.10 Procedure for obtaining propeller efficiency for given h,V, BHP and N 4.2.11 Variations of THP and BSFC with flight velocity and altitude 4.2.12 Loss of propeller efficiency at high speeds 4.3 Gas turbine engines 4.3.1 Propulsive efficiency 4.3.2 Why turboprop, turbo fan and turbojet engines? 4.2.10 Procedure for obtaining THP for given h, V, BHP and N For calculating the performance of the airplane, the thrust horse power (THP) is needed at different values of engine RPM(N), break horse power (BHP), flight speed (V) and flight altitude (h). In this context the following may be noted. (a) The engine output (BHP) depends on the altitude, the RPM (N) and the manifold air pressure (MAP). (b) The propeller absorbs the engine power and delivers THP; p THP = ? BHP ? (c) The propeller efficiency depends, in general, on BHP, V, N and ß. (d) The three quantities viz. d, V and n can be combined as advance ratio (J = V/nd). (e) Once p ? is known : THP = p ? x BHP and T = THP×1000/ V . The steps required to obtain p ? depend on the type of propeller viz. variable pitch propeller, constant speed propeller and fixed pitch propeller. The steps in the three cases are presented below. Page 2 Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 1 Chapter 4 Lecture 15 Engine characteristics – 3 Topics 4.2.10 Procedure for obtaining propeller efficiency for given h,V, BHP and N 4.2.11 Variations of THP and BSFC with flight velocity and altitude 4.2.12 Loss of propeller efficiency at high speeds 4.3 Gas turbine engines 4.3.1 Propulsive efficiency 4.3.2 Why turboprop, turbo fan and turbojet engines? 4.2.10 Procedure for obtaining THP for given h, V, BHP and N For calculating the performance of the airplane, the thrust horse power (THP) is needed at different values of engine RPM(N), break horse power (BHP), flight speed (V) and flight altitude (h). In this context the following may be noted. (a) The engine output (BHP) depends on the altitude, the RPM (N) and the manifold air pressure (MAP). (b) The propeller absorbs the engine power and delivers THP; p THP = ? BHP ? (c) The propeller efficiency depends, in general, on BHP, V, N and ß. (d) The three quantities viz. d, V and n can be combined as advance ratio (J = V/nd). (e) Once p ? is known : THP = p ? x BHP and T = THP×1000/ V . The steps required to obtain p ? depend on the type of propeller viz. variable pitch propeller, constant speed propeller and fixed pitch propeller. The steps in the three cases are presented below. Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 2 I) Variable pitch propeller In this type of propeller the pitch of the propeller is changed during the flight so that the maximum value of p ? is obtained in various phases of flight. The steps are as follows. (a) Obtain the ambient density ? ? ? for the chosen altitude. Also obtain engine BHP at chosen V and N. (b) Obtain ? ? 35 P C = P/ ? n d ; P is BHP in watts (c) Obtain J = V/nd (d) Calculate 1/5 P S C = J/C (e) From the design chart for the chosen propeller (e.g. Fig 4.5c for a two bladed propeller), obtain ß which will give maximum efficiency. Obtain corresponding p ? . Consequently, THP = p ? x BHP and T = THP x 1000 / V ; note V ? 0 (f) To get the thrust (T) at V = 0, obtain BHP of the engine at V = 0 at the chosen altitude and RPM. Calculate P C . From P C vs J plot (e.g. Fig 4.5b for a two bladed propeller) obtain C T and ß at this value of P C and J = 0. Having known C T , the thrust(T) is given by : T = 2 T 4 ? n d C II) Constant speed propeller The variable pitch propellers were introduced in 1930’s. However, it was noticed that as the pilot changed the pitch of the propeller, the engine torque changed and consequently the engine RPM deviated from its optimum value. This rendered, the performance of the engine-propeller combination, somewhat suboptimal. To overcome this problem, the constant speed propeller was introduced. In this case, a governor mechanism alters the fuel flow rate so that the required THP is obtained even as rpm remains same. The value of ß is adjusted to give maximum possible p ? . The steps to obtain p ? are the same as mentioned in the previous case. Page 3 Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 1 Chapter 4 Lecture 15 Engine characteristics – 3 Topics 4.2.10 Procedure for obtaining propeller efficiency for given h,V, BHP and N 4.2.11 Variations of THP and BSFC with flight velocity and altitude 4.2.12 Loss of propeller efficiency at high speeds 4.3 Gas turbine engines 4.3.1 Propulsive efficiency 4.3.2 Why turboprop, turbo fan and turbojet engines? 4.2.10 Procedure for obtaining THP for given h, V, BHP and N For calculating the performance of the airplane, the thrust horse power (THP) is needed at different values of engine RPM(N), break horse power (BHP), flight speed (V) and flight altitude (h). In this context the following may be noted. (a) The engine output (BHP) depends on the altitude, the RPM (N) and the manifold air pressure (MAP). (b) The propeller absorbs the engine power and delivers THP; p THP = ? BHP ? (c) The propeller efficiency depends, in general, on BHP, V, N and ß. (d) The three quantities viz. d, V and n can be combined as advance ratio (J = V/nd). (e) Once p ? is known : THP = p ? x BHP and T = THP×1000/ V . The steps required to obtain p ? depend on the type of propeller viz. variable pitch propeller, constant speed propeller and fixed pitch propeller. The steps in the three cases are presented below. Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 2 I) Variable pitch propeller In this type of propeller the pitch of the propeller is changed during the flight so that the maximum value of p ? is obtained in various phases of flight. The steps are as follows. (a) Obtain the ambient density ? ? ? for the chosen altitude. Also obtain engine BHP at chosen V and N. (b) Obtain ? ? 35 P C = P/ ? n d ; P is BHP in watts (c) Obtain J = V/nd (d) Calculate 1/5 P S C = J/C (e) From the design chart for the chosen propeller (e.g. Fig 4.5c for a two bladed propeller), obtain ß which will give maximum efficiency. Obtain corresponding p ? . Consequently, THP = p ? x BHP and T = THP x 1000 / V ; note V ? 0 (f) To get the thrust (T) at V = 0, obtain BHP of the engine at V = 0 at the chosen altitude and RPM. Calculate P C . From P C vs J plot (e.g. Fig 4.5b for a two bladed propeller) obtain C T and ß at this value of P C and J = 0. Having known C T , the thrust(T) is given by : T = 2 T 4 ? n d C II) Constant speed propeller The variable pitch propellers were introduced in 1930’s. However, it was noticed that as the pilot changed the pitch of the propeller, the engine torque changed and consequently the engine RPM deviated from its optimum value. This rendered, the performance of the engine-propeller combination, somewhat suboptimal. To overcome this problem, the constant speed propeller was introduced. In this case, a governor mechanism alters the fuel flow rate so that the required THP is obtained even as rpm remains same. The value of ß is adjusted to give maximum possible p ? . The steps to obtain p ? are the same as mentioned in the previous case. Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 3 III) Fixed pitch propeller From Fig 4.5b it is observed that a fixed pitch propeller has a definite value of C P for a chosen value of advance ratio (J). Consequently, the propeller can absorb only a certain amount of power for a given value of J. Thus when the flight speed changes, the power absorbed by the propeller also changes. However, for the engine-propeller combination to be in equilibrium i.e. run at a constant r.p.m, the power absorbed by the propeller and that produced by the engine must be the same. This would render the problem of determining power output as a trial and error procedure. However, it is observed that the fixed pitch propellers are used in light airplanes which use piston engines. The torque of such an engine remains nearly constant over a wide range of r.p.m’s. Using this fact, the torque coefficient (C Q ) and torque speed coefficient (Q s ) are deduced in Ref. 3.7, chapter 16, from the data on C P & C T . Further a procedure is suggested therein to obtain p ? at different flight speeds. Herein, the procedure suggested in the Appendix of Ref 4.1 is presented. It is also illustrated with the help of example 4.5. It is assumed that the propeller is designed for a certain speed, altitude, rpm and power absorbed. Let, V 0 = design speed (m/s) N 0 = design rpm ; n 0 = N 0 / 60 BHP 0 = BHP of the engine under design condition (kW) d = diameter of propeller (m) J 0 = Advance ratios under design condition = V 0 / n 0 d 0 ß = design blade angle; this angle is fixed 0 ? = efficiency of propeller under design condition The steps, to obtain the THP at different flight speeds, are as follows. 1. Obtain from propeller charts, C T and C P corresponding to J 0 and 0 ß . These values are denoted by C TO and C PO . Page 4 Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 1 Chapter 4 Lecture 15 Engine characteristics – 3 Topics 4.2.10 Procedure for obtaining propeller efficiency for given h,V, BHP and N 4.2.11 Variations of THP and BSFC with flight velocity and altitude 4.2.12 Loss of propeller efficiency at high speeds 4.3 Gas turbine engines 4.3.1 Propulsive efficiency 4.3.2 Why turboprop, turbo fan and turbojet engines? 4.2.10 Procedure for obtaining THP for given h, V, BHP and N For calculating the performance of the airplane, the thrust horse power (THP) is needed at different values of engine RPM(N), break horse power (BHP), flight speed (V) and flight altitude (h). In this context the following may be noted. (a) The engine output (BHP) depends on the altitude, the RPM (N) and the manifold air pressure (MAP). (b) The propeller absorbs the engine power and delivers THP; p THP = ? BHP ? (c) The propeller efficiency depends, in general, on BHP, V, N and ß. (d) The three quantities viz. d, V and n can be combined as advance ratio (J = V/nd). (e) Once p ? is known : THP = p ? x BHP and T = THP×1000/ V . The steps required to obtain p ? depend on the type of propeller viz. variable pitch propeller, constant speed propeller and fixed pitch propeller. The steps in the three cases are presented below. Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 2 I) Variable pitch propeller In this type of propeller the pitch of the propeller is changed during the flight so that the maximum value of p ? is obtained in various phases of flight. The steps are as follows. (a) Obtain the ambient density ? ? ? for the chosen altitude. Also obtain engine BHP at chosen V and N. (b) Obtain ? ? 35 P C = P/ ? n d ; P is BHP in watts (c) Obtain J = V/nd (d) Calculate 1/5 P S C = J/C (e) From the design chart for the chosen propeller (e.g. Fig 4.5c for a two bladed propeller), obtain ß which will give maximum efficiency. Obtain corresponding p ? . Consequently, THP = p ? x BHP and T = THP x 1000 / V ; note V ? 0 (f) To get the thrust (T) at V = 0, obtain BHP of the engine at V = 0 at the chosen altitude and RPM. Calculate P C . From P C vs J plot (e.g. Fig 4.5b for a two bladed propeller) obtain C T and ß at this value of P C and J = 0. Having known C T , the thrust(T) is given by : T = 2 T 4 ? n d C II) Constant speed propeller The variable pitch propellers were introduced in 1930’s. However, it was noticed that as the pilot changed the pitch of the propeller, the engine torque changed and consequently the engine RPM deviated from its optimum value. This rendered, the performance of the engine-propeller combination, somewhat suboptimal. To overcome this problem, the constant speed propeller was introduced. In this case, a governor mechanism alters the fuel flow rate so that the required THP is obtained even as rpm remains same. The value of ß is adjusted to give maximum possible p ? . The steps to obtain p ? are the same as mentioned in the previous case. Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 3 III) Fixed pitch propeller From Fig 4.5b it is observed that a fixed pitch propeller has a definite value of C P for a chosen value of advance ratio (J). Consequently, the propeller can absorb only a certain amount of power for a given value of J. Thus when the flight speed changes, the power absorbed by the propeller also changes. However, for the engine-propeller combination to be in equilibrium i.e. run at a constant r.p.m, the power absorbed by the propeller and that produced by the engine must be the same. This would render the problem of determining power output as a trial and error procedure. However, it is observed that the fixed pitch propellers are used in light airplanes which use piston engines. The torque of such an engine remains nearly constant over a wide range of r.p.m’s. Using this fact, the torque coefficient (C Q ) and torque speed coefficient (Q s ) are deduced in Ref. 3.7, chapter 16, from the data on C P & C T . Further a procedure is suggested therein to obtain p ? at different flight speeds. Herein, the procedure suggested in the Appendix of Ref 4.1 is presented. It is also illustrated with the help of example 4.5. It is assumed that the propeller is designed for a certain speed, altitude, rpm and power absorbed. Let, V 0 = design speed (m/s) N 0 = design rpm ; n 0 = N 0 / 60 BHP 0 = BHP of the engine under design condition (kW) d = diameter of propeller (m) J 0 = Advance ratios under design condition = V 0 / n 0 d 0 ß = design blade angle; this angle is fixed 0 ? = efficiency of propeller under design condition The steps, to obtain the THP at different flight speeds, are as follows. 1. Obtain from propeller charts, C T and C P corresponding to J 0 and 0 ß . These values are denoted by C TO and C PO . Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 4 2. Choose values of J from 0 to a suitable value at regular intervals. Obtain from the relevant propeller charts, the values of C T and C P at these values of J’s and the constant value of 0 ß . 3. Calculate J/J 0 , C T /C P and C P0 /C P from values obtained in step 2. 4. Calculate: T 0 = 0 0 0 ? BHP ×1000/ V and (4.22) 0 0 PO TO K = T C /C (4.23) 5. The assumption of constant torque (Q 0 ) gives that N and P are related. Note: 0 0 0 Q = P / 2pn This yields: 3 (4.24) 0 00 JN V = V × × JN (4.25) and P0TT 00 T0 P P CCC T = T = K C C C (4.26) Consequently, THP = TV/1000 and BHP = THP/ p ? The procedure is illustrated with the help of example 4.5. Example 4.5 Obtain the thrust and the thrust horse power at sea level for V upto 60 m/s for the propeller engine combination of example 4.4 Solution: From example 4.4 it is noted that the propeller is designed to absorb 97.9 kW at 2500 rpm at V = 59 m/s.The propeller diameter is 1.88 m and ß = 20 o . Hence, V 0 = 59 m/s, N 0 = 2500, n 0 = 41.67, 0 ß = 20 o BHP 0 = 97.9 kW, 0 ? = 0.83 0 0 0 V 59 J = = = 0.753 n d 41.67×1.88 From Fig 4.5d, C TO = 0.046 From Fig 4.5b, C PO = 0.041 Hence, C TO /C PO = 0.046/0.041 = 1.122 Page 5 Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 1 Chapter 4 Lecture 15 Engine characteristics – 3 Topics 4.2.10 Procedure for obtaining propeller efficiency for given h,V, BHP and N 4.2.11 Variations of THP and BSFC with flight velocity and altitude 4.2.12 Loss of propeller efficiency at high speeds 4.3 Gas turbine engines 4.3.1 Propulsive efficiency 4.3.2 Why turboprop, turbo fan and turbojet engines? 4.2.10 Procedure for obtaining THP for given h, V, BHP and N For calculating the performance of the airplane, the thrust horse power (THP) is needed at different values of engine RPM(N), break horse power (BHP), flight speed (V) and flight altitude (h). In this context the following may be noted. (a) The engine output (BHP) depends on the altitude, the RPM (N) and the manifold air pressure (MAP). (b) The propeller absorbs the engine power and delivers THP; p THP = ? BHP ? (c) The propeller efficiency depends, in general, on BHP, V, N and ß. (d) The three quantities viz. d, V and n can be combined as advance ratio (J = V/nd). (e) Once p ? is known : THP = p ? x BHP and T = THP×1000/ V . The steps required to obtain p ? depend on the type of propeller viz. variable pitch propeller, constant speed propeller and fixed pitch propeller. The steps in the three cases are presented below. Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 2 I) Variable pitch propeller In this type of propeller the pitch of the propeller is changed during the flight so that the maximum value of p ? is obtained in various phases of flight. The steps are as follows. (a) Obtain the ambient density ? ? ? for the chosen altitude. Also obtain engine BHP at chosen V and N. (b) Obtain ? ? 35 P C = P/ ? n d ; P is BHP in watts (c) Obtain J = V/nd (d) Calculate 1/5 P S C = J/C (e) From the design chart for the chosen propeller (e.g. Fig 4.5c for a two bladed propeller), obtain ß which will give maximum efficiency. Obtain corresponding p ? . Consequently, THP = p ? x BHP and T = THP x 1000 / V ; note V ? 0 (f) To get the thrust (T) at V = 0, obtain BHP of the engine at V = 0 at the chosen altitude and RPM. Calculate P C . From P C vs J plot (e.g. Fig 4.5b for a two bladed propeller) obtain C T and ß at this value of P C and J = 0. Having known C T , the thrust(T) is given by : T = 2 T 4 ? n d C II) Constant speed propeller The variable pitch propellers were introduced in 1930’s. However, it was noticed that as the pilot changed the pitch of the propeller, the engine torque changed and consequently the engine RPM deviated from its optimum value. This rendered, the performance of the engine-propeller combination, somewhat suboptimal. To overcome this problem, the constant speed propeller was introduced. In this case, a governor mechanism alters the fuel flow rate so that the required THP is obtained even as rpm remains same. The value of ß is adjusted to give maximum possible p ? . The steps to obtain p ? are the same as mentioned in the previous case. Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 3 III) Fixed pitch propeller From Fig 4.5b it is observed that a fixed pitch propeller has a definite value of C P for a chosen value of advance ratio (J). Consequently, the propeller can absorb only a certain amount of power for a given value of J. Thus when the flight speed changes, the power absorbed by the propeller also changes. However, for the engine-propeller combination to be in equilibrium i.e. run at a constant r.p.m, the power absorbed by the propeller and that produced by the engine must be the same. This would render the problem of determining power output as a trial and error procedure. However, it is observed that the fixed pitch propellers are used in light airplanes which use piston engines. The torque of such an engine remains nearly constant over a wide range of r.p.m’s. Using this fact, the torque coefficient (C Q ) and torque speed coefficient (Q s ) are deduced in Ref. 3.7, chapter 16, from the data on C P & C T . Further a procedure is suggested therein to obtain p ? at different flight speeds. Herein, the procedure suggested in the Appendix of Ref 4.1 is presented. It is also illustrated with the help of example 4.5. It is assumed that the propeller is designed for a certain speed, altitude, rpm and power absorbed. Let, V 0 = design speed (m/s) N 0 = design rpm ; n 0 = N 0 / 60 BHP 0 = BHP of the engine under design condition (kW) d = diameter of propeller (m) J 0 = Advance ratios under design condition = V 0 / n 0 d 0 ß = design blade angle; this angle is fixed 0 ? = efficiency of propeller under design condition The steps, to obtain the THP at different flight speeds, are as follows. 1. Obtain from propeller charts, C T and C P corresponding to J 0 and 0 ß . These values are denoted by C TO and C PO . Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 4 2. Choose values of J from 0 to a suitable value at regular intervals. Obtain from the relevant propeller charts, the values of C T and C P at these values of J’s and the constant value of 0 ß . 3. Calculate J/J 0 , C T /C P and C P0 /C P from values obtained in step 2. 4. Calculate: T 0 = 0 0 0 ? BHP ×1000/ V and (4.22) 0 0 PO TO K = T C /C (4.23) 5. The assumption of constant torque (Q 0 ) gives that N and P are related. Note: 0 0 0 Q = P / 2pn This yields: 3 (4.24) 0 00 JN V = V × × JN (4.25) and P0TT 00 T0 P P CCC T = T = K C C C (4.26) Consequently, THP = TV/1000 and BHP = THP/ p ? The procedure is illustrated with the help of example 4.5. Example 4.5 Obtain the thrust and the thrust horse power at sea level for V upto 60 m/s for the propeller engine combination of example 4.4 Solution: From example 4.4 it is noted that the propeller is designed to absorb 97.9 kW at 2500 rpm at V = 59 m/s.The propeller diameter is 1.88 m and ß = 20 o . Hence, V 0 = 59 m/s, N 0 = 2500, n 0 = 41.67, 0 ß = 20 o BHP 0 = 97.9 kW, 0 ? = 0.83 0 0 0 V 59 J = = = 0.753 n d 41.67×1.88 From Fig 4.5d, C TO = 0.046 From Fig 4.5b, C PO = 0.041 Hence, C TO /C PO = 0.046/0.041 = 1.122 Flight dynamics-I Prof. E.G.Tulapurkara Chapter IV Indian Institute of Technology, Madras 5 0 97.9×1000×0.83 T = = 1377.24N 59 PO 0 TO C 0.041 K = T = 1377.24× = 1227.54 C 0.046 The remaining calculations are presented in Table E 4.5 J J/J 0 C T * P C $ T P C C C P0 /C P N/N 0 £ V € T (N) €€ N # p ? ** THP $$ BHP ££ 0 0 0.104 0.066 1.576 0.621 0.788 0 1927 1971 0 0 - 0.1 0.133 0.104 0.065 1.589 0.629 0.793 6.21 1951 1983 0.17 12.15 71.23 0.2 0.266 0.104 0.065 1.606 0.636 0.792 12.49 1971 1993 0.33 24.61 74.60 0.3 0.398 0.102 0.062 1.631 0.657 0.811 19.05 2002 2027 0.49 38.14 77.83 0.4 0.531 0.093 0.060 1.545 0.683 0.827 25.91 1897 2067 0.62 49.15 79.28 0.5 0.664 0.082 0.058 1.420 0.712 0.844 33.05 1743 2109 0.70 57.61 82.29 0.6 0.797 0.070 0.059 1.306 0.765 0.875 41.12 1603 2187 0.77 65.91 85.60 0.7 0.930 0.055 0.046 1.185 0.884 0.900 51.55 1455 2350 0.81 75.00 92.60 0.8 1.062 0.040 0.036 1.099 1.126 1.061 66.50 1349 2653 0.83 89.71 108.1 *From Fig 4.5d ; $ From Fig 4.5b; £ From Eq.(4.24); € From Eq (4.25); €€ From Eq.(4.26); # N = (N/N 0 )x N 0 ; ** From Fig 4.5a; $$ THP = TV/1000 ; ££ BHP = THP/ p ? Table E4.5 Thrust and power output of an engine-propeller combination with fixed pitch propellerRead More

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