Figure 13.14. Specific range of a Bizjet

performances of fuel consumed, distance covered, and time taken to climb at the desired altitude.

13.5.5 Initial High-Speed Cruise (Bizjet)

An aircraft at the initial HSC is at Mach 0.74 (i.e., 716.4 ft/s) at a 41,000-ft altitude (ρ = 0.00055 slug/ft3). The fuel burned to climb is computed (but not shown) as 700 lb. The aircraft weight at initial cruise is 20,000 lb. At Mach 0.74, the aircraft lift coefficient CL = MTOM/qSW = 20,000/(0.5 × 0.00055 × 716.42 × 323) = 20,000/45,627 = 0.438.

The clean aircraft drag coefficient from Figure 9.2 at CL = 0.438 gives CDclean = 0.0324. The clean aircraft drag, D = 0.0324 × (0.5 × 0.00055 × 716.42 × 323) = 0.0324 × 45,627 = 1,478 lb.

The available all-engines-installed thrust at maximum cruise rating at the speed and altitude from Figure 13.3 at Mach 0.74 is T = 2 × 790 = 1,580 lb (adequate). The capability satisfies the market requirement of Mach 0.74 at HSC.

13.5.6 Specific Range (Bizjet)

Specific range is a convenient way to present cruise performance. Using Equation 13.27, the Sp.Rn is computed. The details of the specific range are not a direct

substantiation requirement; it is needed to compute the cruise-segment performances (i.e., fuel burned, distance covered, and time taken). Figure 13.14 shows the specific range for the Bizjet (i.e., the worked-out example). When readers redo the specific-range computations, there may be minor differences in the results. From the Sp. Rn values, the fuel burned and distance covered is worked out, which in turn gives the time taken for the distance.

13.5.7 Descent Performance (Bizjet)

It is also explained in Section 13.1 that only results of the integrated descent performance in graphical form are provided, as shown in Figures 13.16 through 13.18. It is convenient to establish first the descent velocity schedule (Figure 13.16) and the point performances of the rate of descent (Figure 13.17) down to sea level (this is valid for all weights; the difference between the weights is ignored). When readers redo the calculations, there may be minor differences in the results.

The related governing equations are explained in Section 13.4.3, which also mentions that the descent rate is restricted by the rate of the cabin-pressurization schedule to ensure passenger comfort. Two difficulties in computing the descent performance are the partial-throttle engine performance and the ECS pressurization capabilities, which dictate the rate of descent that, in turn, stipulates the descent velocity schedule (these are not provided in this book). Instructors may assist in establishing these two graphs, which – in the absence of any information – may be used. The following simplifications are useful.

The first simplification is in obtaining the partial-throttle engine performance, as follows:

1.The zero thrust at idle rpm is at about 40% of the maximum rated power/ thrust.

2.The maximum cruise rating is taken at 85% of the maximum rated power/ thrust.

3.The descent is carried out from 40 to 60% of the maximum cruise rating.

The second simplification is provision of the descent velocity schedule for the ECS capability.

In the industry, the exact installed-engine performance at each partial-throttle condition is computed from the engine deck supplied by the manufacturer. Also, the ECS manufacturer supplies the cabin-pressurization capability, from which aircraft designers work out the velocity schedule.

The inside cabin pressurization is restricted to the equivalent rate of 300 ft/min at sea level to ensure passenger comfort. An aircraft’s rate of descent is then limited to the pneumatic capability of the ECS. A Bizjet is restricted to a maximum of 1,800 ft/min at any time (for a higher performance at lower altitudes, it can be increased to 2,500 ft/min). The descent speed schedule continues at Mach 0.6 from the cruise altitude until it reaches the approach height, when it then changes to a constant VEAS = 250 knots until the end (for a higher performance, it can be increased to Mach 0.7 and VEAS = 300 knots). The longest ranges can be achieved at the minimum rate of descent; this requires a throttle-dependent descent to stay within the various limits.

Figure 13.15. Descent point performance

It is convenient to establish first the point performances of the velocity schedule (Figure 13.15a) and the rate of descent (Figure 13.15b is for all weights; the variation is minor). The descent is performed within the limits of the passenger comfort level. However, in an emergency, a rapid descent is necessary to compensate for the loss of pressure and for oxygen recovery.

An integrated descent performance is computed in the same way as the climb performance; that is, it is computed in steps of approximate 5,000-ft altitudes (or as convenient) in which the variables are kept invariant. (Computation work is not shown herein.)

Figure 13.16 plots fuel consumed, time taken, and distance covered during the descent from the ceiling altitude to sea level. When readers redo the integrated descent performances, there may be minor differences in the results.

13.5.8 Payload Range Capability

A typical transport aircraft mission profile is shown in Figure 13.17. Equations 13.14 through 13.18 give the mission range and fuel consumption expressions as follows:

mission range = climb distance(Rclimb) + cruise distance(Rcruise)

+ landing distance(Rdescent )

where Rclimb = sclimb and Rdescent = sdescent are computed from the altitude increments.

mission fuel = climb fuel (Fuelclimb) + cruise fuel(Fuelcruise)

+ descent fuel(Fueldescent )

where Fuelclimb = fuelclimb and Fueldescent = fueldescent are computed from the altitude increments.

The minimum reserve fuel is computed for an aircraft maintaining a 5,000-ft altitude from Mach 0.35 to Mach 0.4 at about 60% of the maximum rating for

Figure 13.16. Integrated descent performance for a Bizjet

45 minutes or a 100 nm diversion cruising at Mach 0.5 and at a 25,000-ft altitude plus 20 minutes. The amount of reserve fuel must be decided by the operator and be suitable for the region of operation. The worked-out example uses the first option.

Fuel is consumed during taxiing, takeoff, and landing without any range contribution; this fuel is added to the mission fuel and the total is known as block fuel. The time taken from the start and stop of the engine at the beginning and the end of the mission is known as block time, in which a small part of time is not contributing to the gain in range. The additional fuel burn and time consumed without contributing

Figure 13.17. Transport-aircraft mission profile

From operational statistics.

to range are shown in Table 13.17, taken from operational statistics. The descent fuel is estimated at 300 lb and the end cruise weight is computed as Wend cruise = 12,760 + 2,420 + 650 + 300 = 16,280 lb. This is then iterated to correct the descent fuel in the final form, as shown in Table 13.17.

The cruise altitude of a Bizjet starts at 43,000 ft and ends at 45,000 ft (the design range is long in order to make an incremental cruise). The average value of cruising at 44,000 ft (ρ = 0.00048 slug/ft3) is used. The methods to compute Rclimb and Rdescent are discussed in Section 13.4.3. Using Figures 13.11 through 13.13, the required values are given as Rclimb = 162 nm, Fuelclimb = 800 lb, and Timeclimb = 25 min, and Rdescent = 150 nm, Fueldescent = 340 lbs, and Timedescent = 30 min (in a partial-throttle, gliding descent). Table 13.18 displays the aircraft weight at each segment of the mission profile. The aircraft is at the LRC schedule operating at Mach 0.7 (OEW = 12,760 lb and payload = 2,420 lb).

For reserve fuel, at a 5,000-ft altitude (ρ = 0.00204 lb/ft3) and Mach 0.35 (384 ft/s) gives CL = 0.323, resulting in CD = 0.025 (see Figure 9.2). Equating thrust to drag, T/engine = 610 lb with sfc = 0.7 lb/hr/lb. For 45 minutes of holding, fuel consumed = 2 × 0.75 × 0.7 × 610 = 640 lbs. For safety, 800 lbs is used (operators can opt for higher reserves than the minimum requirement).

An aircraft must carry a reserve fuel for 45 minutes of holding and/or diversion around a landing airfield, which amounts to 600 lb. The range performance can be improved with a gradual climb from 43,000 to 47,000 ft as the aircraft becomes lighter with fuel consumed. From Table 13.18, the midcruise weight is (19,700 + 16,240)/2 = 17,970 lbs.

The LRC is at Mach 0.7 (677.7 ft/s). The engine-power setting is below the maximum cruise rating. The aircraft lift coefficient, CL = 17,970/(0.5 × 0.00046 × 677.72 × 323) = 17,970/34,120 = 0.527. From Figure 9.2, the clean aircraft drag coefficient, CD = 0.033. The aircraft drag, D = 0.033 × (0.5 × 0.00046 × 677.72 × 323) = 0.033 × 34,120 = 1,126 lb.

Therefore, the thrust required per engine is 1,126/2 = 563 lbs. Figure 13.3 shows the available thrust of 620 lb per engine at the maximum cruise rating meant for HSC; that is, it allows throttling back for the LRC speed. The sfc is not much affected by the throttling back to the cruise rating. From Figure 10.6, the sfc at the