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(RcUmb) + cruise distance(Remise)
+ landing distance( Rdescent)
where Rciimb = £Asciimb and Rdescent = £Asdescent are computed from the altitude increments.
mission fuel = climb fuel (Fuelciimb) + cruise fuel(Fuelcruise)
+ descent fuel(Fueldescent)
where Fuelclimb = £Afuelclimb and Fueldescent = £Afueldescent 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
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
Table 13.18. Bizjet range
* 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 (p = 0.00048 slug/ft3) is used. The methods to compute Rciimb 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 (p = 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 x 0.75 x 0.7 x 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 x 0.00046 x 677.72 x 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 x (0.5 x 0.00046 x 677.72 x 323) =
0. 033 x 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
Figure 13.18. Bizjet payload-range capability
speed and altitude is 0.73 lb/hr/ lb. The fuel flow per engine = 0.73 x 563 = 411 lb/hr; for two engines, it is 822 lb/hr.
From the initial and final cruise weight, the fuel burned during cruise is 3,460 lb. This results in a cruise time of 3,460/(2 x 411) = 4.21 hr (252.5 min) of cruise time in which the distance covered is 4.21 x 0.68182 (the conversion factor from feet to miles) x 677.7 = 4.21 x 462 = 1,945 miles = 1,688 nm.
This mission range just satisfies the requirement of 2,000 nm. The block time for the mission is 5.38 hours and the block fuel consumed is 4,923 lb (2,233 kg). On landing, the return taxi-in fuel of 20 lb is taken from the reserve fuel of 600 lb. The total onboard fuel carried is therefore 4,923 + 600 = 5,523 lb.
The payload-range graph is shown in Figure 13.18. A summarized discussion of the Bizjet design is in Section 13.7.
The fuel tank has a larger capacity than what is required for the design payload range. The payload can be traded to increase the range until the tanks fill up. Further reductions of payload make the aircraft lighter, thereby increasing the range.