RANGE PAYLOAD

Specifications of military aircraft and many larger civil aircraft indue range-payload curves. This is a graph, that for a particular mission profit presents the effect of trading off payload for fuel on the range of an airplam In determining such a curve, one must consider the operational phases th; have been treated thus far in this chapter. .

As an example in calculating a range-payload curve, consider the Cessn Citation I. Figure 7.21 presents a side-wiew sketch of this airplane. Table 7. presents a general description and some of its specifications. The rang calculation will include: [3]

The reserve fuel is calculated on the basis of holding at 25,000 ft (7620 m).

Using methods similar to those just presented and given engine per­formance curves (including installation losses), one can calculate, for a number of fixed airplane weights, information similar to that presented in Tables 7.2 to 7.5.

The maximum ramp weight for Citation I is 12,000 lb (53.4 kN). During taxi, 150 lb of fuel is assumed to be burned, so that the maximum allowable takeoff weight is 11,8501b (52.7 kN). The maximum fuel capacity at this takeoff weight allowing for the 1501b expended during taxi is 36301b (16.3 kN). This is the fuel available to fly the cruise profile. This maximum fuel together with the empty weight of 6470 lb (28.7 kN) and an oil weight of 341b leaves 17161b for payload. Thus, if 10 persons are on board (including the cre(w) at 200 lb per person, 284 lb of fuel must be removed resulting in a direct reduction in the range.

The total fuel for the range profile can be expressed as

(7.51)

where CLB, CR, HLD, and DES refer to climb, cruise, hold, and descent.

Figures 7.22 and 7.23 present in graphical form data from Tables 7.2, 7.3, and 7.5 necessary to determine the range-payload curve. In determining the range, in a manner of speaking, we begin at the ends and work toward the middle. During the hold, the average airplane weight will equal

(7.52)

In Equation 7.52 Wfms is the fuel required to descend from the holding altitude of 25,000 ft. Consider first takeoff at maximum allowable takeoff weight with full fuel. Thus,

WTO= 11,8501b Wf = 3630 lb W, DES = 83 (Table 7.4) lb

Table 7.2 Climb Performance. Maximum Rate Climb; 175 KIAS at Sea Level; Time, Distance and Fuel;® Standard Day TO Wt. 1000 Lb 11.85 11.50 10.50 9.50 11.85 11.50 10.50 9.50 Pressure Altitude 5,000 ft 10,000 ft Min 2 2 2 2 4 4 4 3 Nmi 6 5 5 4 12 12 10 8 Lb 65 63 56 50 129 124 111 99 Pressure Altitude 15,000 ft 21,000 ft Min 6 6 6 5 10 9 8 7 Nmi 20 19 16 13 13 29 25 21 Lb 194 186 165 147 272 261 231 204 Pressure Altitude 25,000 ft 29,000 ft Min 12 12 10 9 15 15 13 11 Nmi 40 38 32 26 52 48 40 33 Lb 327 313 276 243 387 369 323 284 Pressure Altitude 31,000 ft 33,000 ft Min 17 16 14 12 19 18 16 14 Nmi 59 55 45 38 68 63 52 42 Lb 419 399 349 305 455 433 376 328 Pressure Altitude 35,000 ft 37,000 ft Min 22 21 18 15 26 24 20 17 Nmi 79 73 59 48 94 86 69 55 Lb 497 470 406 351 549 517 440 378 Pressure Altitude 39,000 ft 41,000 ft Min 32 29 24 20 53 42 29 23 Nmi 121 108 83 65 214 165 107 79 Lb 631 585 485 411 886 741 555 454 "Time in “min” (minutes), distance in “nmi” (nautical miles), fuel in “lb” (pounds used).

The average weight for holding thus becomes

W = 8303 + ^“-°

Referring to Figure 7.23, guess at a W of 85001b. This leads to a fuel flow rate of 540 lb/hr or, for 45 min, a-holding fuel of 405 lb. From Equation 7.53, W is then calculated to be 8708, .which is higher than the guessed value. Iterating in this manner, the holding fuel is found to equal 415 lb.

The fuel to climb to 41,000 ft from Figure 7.22 equals 8861b. To descend from 41,000 ft to sea level requires 1341b – Thus, the fuel left for cruising equals: f

W7c„ = Wf – W/HLD – VV/DES – 4V/CIB = 2195 lb

The average weight during the cruise will be

W = WTO- WfcLB-^

= 9867 lb

From Figure 7.23, the cruising speed at this weight equals 328 kt. The fuel

Table 7.4 Descent Performance. Low-Power Descent, 3000ft/min; Fuel Flow at 3000 Ib/hr/Engine; Gear and Flaps Up; Speed Brakes Retracted; Zero Wind Pressure Altitude (1000 ft) Time (min)8 Fuel Used (lb)8 Distance (nmi)8 41b 13.7 134 69 39b 13.0 129 65 37b 12.3 124 61 35 11.7 117 57 33 11.0 110 53 31 10.3 103 48 29 9.7 97 44 27 9.0 90 41 25 8.3 83 37 23 7.7 77 33 21 7.0 70 30 19 6.3 63 26 17 5.7 57 23 15 5.0 50 20 10 3.3 33 13 5 1.7 17 6 “Time, fuel used, and distance are for a descent from in­dicated altitude to sea level, standard day. bUse high-speed descent between 41,000 and 35,000 ft.

(lb)	(KIAS)	S. L.	5	10	15	20	25	30
10,500	165	955	870	792	728	691	673	661
9,500	155	886	810	738	673	625	607	590
8,500	145	807	745	682	622	569	536	522
7,500	135	705	678	625	570	520	479	460

Table 7.5 Holding Fuel; Two-Engine Fuel Consumption, Ib/hr

Aircraft Pressure Altitude (1000 ft)

Weight Speed

Source.

Figure 7.22 Fuel required and distance traveled. by Citation I in climbing to 41,000 ft.

Airplane weight, lb Figure 7.23 Holding fuel flow and cruising airspeed for Citation I.

flow rate for maximum cruising thrust is found from Table 7.3 to equal 688 lb/hr. The total cruising fuel, fuel flow, and speed give a distance covered during the cruise of 1046 nmi. To get the range, we add to this the distance covered during the climb and descent. These are – obtained from Figure 7.22 and Table 7.4, respectively. These two distances total 283 nmi. giving a total range of 1329 nmi.

This range and payload represent one point on the range-payload curve. A break in the slope of the range-payload curve will occur at this point because

of the following. For lighter payloads, the gross weight will decrease, resulting in increased ranges for the same total fuel. For heavier payloads, less fuel must be put aboard, resulting in a direct loss of range. At a cruising airspeed of around 328 kt and a fuel flow of 688 lb/hr, one can see immediately that the range will decrease by approximately 48 nmi/100 lb of additional payload over 17161b.

Consider two additional points on the range-payload curve: a payload of 2000 lb corresponding to a crew of two and eight passengers at 200 lb per person, and a minimum payload of 400 lb corresponding to the crew alone.

For the 2000-lb payload, the takeoff weight will remain the same, but the fuel weight is reduced by 2841b to 33461b after taxi. The average holding weight now becomes

W = 8587 +

By iteration, W/HLD = 421 lb

The fuel to climb remains unchanged, so that

WfcR = 1905 lb

The average weight during cruise equals 10,012 lb. From Figure 7.23, the cruising speed at this average weight will be 325 kt. This speed and a fuel rate of 688 lb/hr result in a distance of 900 nmi. The distances gained during climb and descent remain unchanged, so the total range for the 20001b payload becomes 1183 nmi.

For a minimum payload of 4001b, the takeoff gross will be reduced to 10,534 lb.

The equation for the average holding weight now reads

W = 6987 +

so VF/hid = 3441b. The fuel weight to climb to 41,000 ft at this reduced gross weight equals 5571b and the distance travelled during the climb is 110 nmi. The descent fuel and distance are assumed to remain the same. Thus the fuel for cruising equals 2595 lb. The average cruising weight becomes 8680 lb. At this weight, the cruising speed equals 339 kt with the fuel consumption rate unchanged. Therefore the cruising distance equals 1279 nmi. Added to the distances covered during climb and descent, this figure results in a total range of 1458 nmi.

The preceding three points define the range-payload curve for the Cita­tion I as presented in Figure 7.24. The calculated points are shown on the curve. Again, the break in this curve corresponds to maximum allowable takeoff weight with a full fuel load.