HALAMAN 30with the help of Eq. (1-1

HALAMAN 30
with the help of Eq. (1-11). The above equation can be written in terms of the thrust specific fuel consumption as.


Using Eqs. (1-17) and (1-19), we can write the following for TSFC


Example 1-1. An advanced fighter engine operating at mach 0.8 and 10 km altitude has the following uninstalled performance data and uses a fuel with hpr 42.800 kJ/kg:
F = 50 kN mo = 45 kg/sec and mr = 2.65 kg/sec
Determine the specific thrust, thrust specific fuel consumption, exit velocity , thermal efficiency , propulsive efficiency, and overall efficiency (assume exit pressure equal to ambient pressure).
Solution.















HALAMAN 31
Specific thrust versus fuel consumption
for a jet engine with a single inlet and single exhaust and exit pressure equal to ambient pressure, when the mass flow rate of the fuel is much less than that of air and the installation losses are very small, the specific thrust F/mo can written as
F/M_0 =(V_(e- ) V_0)/g_o (1-21)
then the propulsive efficiency of Eq.(1-16) can be rewritten as
η_p
substituting Eq. (1-22) into Eq. (1-20) and noting that TSFC = S, we obtain the following very enlightening expression :


aircraft manufacturers desire engines having low thrust specific fuel consumption S and high specific thrust F/mo . low engine fuel consumption can be directly translated into longer range, increased payload, and/or reduced aircraft size. High specific thrust reduces the cross-sectional area of the engine and has a direct influence on engine weight and installation losses. This desired trend is plotted in fig. 1-18. Equation (1-23) is also plotted in fig. 1-18 and shows that fuel consumption and specific thrust are directly propotional. Thus the aircraft manufacturers have to make tradeoff. The line of Eq. ( 1-23) shifts in the desired direction when there is an increase in the level of technology (increased thermal efficiency) or an increase in the fuel heating value.
Another very useful measure of merit for the aircraft gaas turbine engine is the thrust/weight ratio F/W . for a given engine thrust F, increasing the thrust/weight ratio reduces the weight of the engine. Aircraft manufacturers can use this reduction in engine weight to increase the capabilites of an aircraft (increased payload, Increased fuel, or both) or decrease the size (weight) and cost of a new aircraft under development.








HALAMAN 33
Engine companies expend considerable research and development effort on increasing the thrust/weight ratio of aircraft gas turbine engines. This ratio is equal to the specific thrust F/m0. For a given engine type, the engine weight per unit mass flow is related to efficiency of the engine structure, and the specific thrust is related to the engine thermodynamics. The weights per unit mass flow of some existing gas turbine engine are plotted versus specific thrust in fig. 1-19. Also plotted are lines of constant engine thrust/weight ratio F/W .
Currently, the engine companies, in conjuction with the department of defense and NASA, are involed in a large research and development effort to increase the engine thrust/weight ratio F/W and decrease the fuel consumption while maintaining engine durability, maintainability, etc. this program is called the integrated high performance turbine engine technology (IHPTET) initiative ( see refs 5 and 6)
1-5 AIRCRAFT PERFORMANCE
This section on aircraft performance is included so that the reader may get a better understanding of the propulsion requirements of the aircraft (ref.7). the converage is limited to a few significant concepts that directly relate to aircraft engines. It is not intended as a substitute for the many excellent references on this subject.
Performance Equation
Relationships for the performance of an aircraft can be obtained from energy considerations (see ref . 12). By treating the aircraft (fig.1-20) as a moving mass and assuming that the installed provulsive thrust T, aerodynamic drag D , and other resistive forces R atc in the same direction as the velocity V , it follows that



Note that the total resistive force D+R is the sum of the drag of the clean aircraft D and any additional drags R associated with such protuberances as landing gear , external stores , or drag chutes.
By defining the energy height ze as the sun of the potential and kinetic






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Lift and drag
We use the classical aircraft lift relationship
L= Nw = CLqSw (1-29)
Where n is the load factor or number of g’s perpendicular to v (n=1 for straight and level flight ), CL is the coefficient of lift , SW is the wing planfrom area , and q is the dynamic pressure. The dynamic pressure. The dynamic pressure can be expressed in terms of the density p and velocity v or the pressure p and mach number m as
q = 1/2 p V^2/g_c =1/2 σp_ref V^2/g_c (1-30a)
q = y/2 PM_0^2=y/2 δP_ref M_0^2 (1-30b)
or
Where δ and σ are the dimensionless pressure and density ratios defined by eqs. (1-2) and (1-4) , respectively , and γ is the ratio of specific heats ( y=1.4 for air). The reference density Pref and reference pressure Pref of air are their sea level values on a standard day and are listed in App. A .
We also use the classical aircraft darg relationship
D=CDqSw (1-31)
Figure 1-21 is a plot of lift coefficient CL versus dra coefficient CD, commonly called the lift drag polar, for a typical subsonic passenger aircraft. The drag coefficient curve can be approximated by a second-order equation in CL written as
CD=K1C2L+K2CL+CD0 (1-32)

























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Where the coefficients K1, K2, and CD0 are typically functions of flight mach number and wing configuration (flap position, etc ).
The CD0 term in Eq.(1-32) is the zero lift drag coefficient which accounts for both frictional and pressure drag in subsonic flight and wave drag in supersonic flight. The K1 and K2 terms account for the drag due to lift normally K2 is very small and approximately equal to zero for most fighter aircraft.

Example 1-2. For all the examples given in this section on aircraft performance, two types of aircraft will be considered.

An advanced fighter aircraft is approximalety modeled after the YF22 advance tactical fighter shown in fig.1-22. For convenience, we will designate our hypothetical fighter aircraft as the HF-1, having the following characteristic :
Maximum gross takeoff weight Wro = 40,000 lbf (177,920N)
Empety weight = 24.000 lbf (106,752N)
Maximum fuel plus payload weight = 16,000 lbf (71,168N)
Permanent payload = 1600 lbf (7117N, crew plus return armament)
Expended payload = 2000 lbf (8896 N, missiles plus ammunition )
Maximum fuel capacity = 12,400 lbf (55,155 N)
Wing area Sw = 720ft2 (66.9m2 )

































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Table 1-4
Drag coefficients for fighter aircraft (HF-1)
M0 K1 K2 CD0
0.0 0.20 0.0 0.0120
0.8 0.20 0.0 0.0120
1.2 0.20 0.0 0.02267
1.4 0.25 0.0 0.0280
2.0 0.40 0.0 0.0270

Engine : low-bypass-ratio, mixed-flow turbofan with afterburner
Maximum lift coefficient CLmax = 1.8
Drag coefficients given in the table 1-4



An advanced 253-passeger commercial aircraft approximately modeled after the boeing 767 is shown in fig.1-23. For convencience. We will designate our hypothetical passenger aircraft as the HP-1, having the following characteristic:

Maximum gross takeoff weight Wro = 1,645.760 N (370.000 lbf )
Empty weight = 822.880 N (185.500 lbf )
































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TABLE 1-5
Drag coefficients for hypothetical passenger aircraft
(HP-1)
M0 K1 K2 CD0
0.00 0.056 -0.004 0.0140
0.40 0.056 -0.004 0.0140
0.75 0.056 -0.008 0.0140
0.83 0.056 -0.008 0.0150

Maximum landing weight = 1,356,640 N (305,000 lbf)
Maximum payload = 420,780 N (94,600 lbf, 253 passengers plus 196.000 N of cargo)
Wing area Sw = 282.5 m2(3040 ft2 )
Engine : high-bypass-ratio-turbofan
Maximum lift coefficients CLmax = 2.0
Drag coefficients given in table 1-5






































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Example 1-3. Determine the drag polar and variation for the HF-1 aircraft at 90 percent of maximum gross takeoff weight and the HP-1 aircraft at 95 percent of maximum gross takeoff weight.

The variation in CD0 and K1 with mach number for the HF-1 are the plotted in fig.1-24 from the date of table 1-4. Figure 1-25 shows the drag polar at different mach numbers for the HF-1 aircraft. Using these drag data and the above equations gives the variation in aircraft drag with subsonic mach number and altitude for level flight (n=1), as shown in fig. 1-26a. note that the minimum drag is constant for mach numbers 0 to 0.8 and than increases. This is the same variation as CD0. The variation of drag with load factor n is shown in fig. 1-26b at two altitudes. The drag increases with increasing load factor, and there is a flight mach number that gives minimum drag for a given altitude and load factor.
The variation in CD0 and K2 with mach number for the HP-1 is plotted in fig.1-27 from the data of table 1-5. Figure 1-28 shows the drag polar at different mach numbers for the HP-1 aircraft. Using these drag data and the above equations gives the variation in aircraft drag with subsonic mach number and altitude for level flight (n=1), as shown in fig.1-29. Note that the minimum drag constant for mach numbers 0 to 0.75 and than increases. This is the same variation as CD0.