MAXIMUM ENDURANCE

Endurance refers to the time that elapses in remaining aloft. Here one is concerned with the time spent in the air, not the distance covered. A pilot in a holding pattern awaiting clearance for an instrument landing is concerned with endurance. The maximum endurance will be obtained at theairspeed that requires the minimum fuel flow rate. In the case of a turbojet on turbofan engine, the product of TSFC and the drag is minimized. v—^

ii Assuming a constant TSFC for the jet airplane leads to Equations 7.36 and 7.37, which relate to the maximum range for a propeller-driven airplane. Thus, for a given weight of fuel, Wf, the maximum endurance, te, of a turbojet will be

1 ЖГ7гМТ/2

‘ 2(TSFC) W/ L(//S)J C7 41)

Notice that the endurance is independent of altitude. This follows from

the fact that the minimum drag does not vary with altitude. To obtain this endurance, the airplane is flown at the airspeed given by Equation 7.37.

Assuming a constant SFC, a propeller-driven aircraft will have its maxi­mum endurance when flown at the airspeed for minimum required power. This speed has been given previously as Equation 7.22. At the minimum power, the induced power is three times the parasite power. Hence,

Pmin — 2pfV3

= _2_ r4(W/b)2~l3/4 fm Vcr L 3ne J Po1’2

The endurance time for a propeller-driven airplane then becomes

t = ^a Г 37ГЄ Г Po n A1

te 2(SFC) |4(w/b)2J 1th (7 43)

(SFC) in this equation has units consistent with the other terms; that is, weight per power second where the weight is in newtons or pounds with the power in newton meters per second or foot-pounds per second. For example, if

BSFC = 0.5 lb/bhp-hr

then

SFC = 2.53 x КГ7 lb/(ft-lb/sec)/sec

Actually SFC used in this basic manner has the units of 1/length. In the Engli^system this becomes ft-1 and in the SI system it is m-‘.

Notice that the endurance of a propeller-driven airplane decreases with altitude. This follows from the fact that the minimum power increases with altitude.

Some of the foregoing equations for range and endurance contain the weight which, of course, varies with time as fuel is burned. Usually, for determining the optimum airspeed or the endurance time, it is sufficiently accurate to assume an average weight equal to the initial weight minus half of the fuel weight. Otherwise, numerical and graphical procedures must be used to determine range and endurance.

DESCENT

^ The relationships previously developed for a steady climb apply as well to descent. If the available thrust is less than the drag, Equation 7.15 results in a negative R/C. In magnitude this equals the rate of descent, R/D. The angle of descent, in radians, во, is given by,

(7.44)

Civil aircraft rarely descend at angles greater than 10°. The glide slope for an ILS (instrument landing system) approach is only 3°. Steeper slopes for noise abatement purposes are being considered, but only up to 6°.

The minimum eD value in the event of an engine failure is of interest. From Equation 7.44 we see that this angle is given by

0Dmin = emin rad (7.45)

Thus, the best glide angle is obtained at the CL giving the lowest drag-to-lift ratio. This angle is independent of gross weight. However, the greater the weight, the higher the optimum airspeed will be. The minimum e and corresponding airspeed have been given previously as Equations 7.36 and 7.37. Of course, in the event of an engine failure, one must account for the increase in / caused by the stopped or windmilling propeller, or by the stopped turbojet.

LANDING

The landing phase of an airplane’s operation consists of three segments; the approach, the flare, and the ground roll. FAR Part 25 specifies the total landing distance to include that required to clear a 50-ft (15.2-m) obstacle. A sketch of the landing flight path for this type of approach is shown in Figure

7.20. The ground roll is not shown, since it is simply a continuous deceleration along the runway. FAR Part 25 specifies the following, taken verbatim.

Figure 7.20 Landing approach and flare.

§ 25.125 Landing.

(a) The horizontal distance necessary to land and to come to a complete stop (or to a speed of approximately 3 knots for water landings) from a point 50 feet above the landing surface must be determined (for standard temperatures, at each weight, altitude, and wind within the operational limits established by the applicant for the airplane) as follows:

(1) The airplane must be in the landing configuration.

(2) A steady gliding approach, with a calibrated airspeed of not less than 1.3 Vs, must be maintained down to the 50 foot height.

(3) Changes in configuration, power or thrust, and speed, must be made in accordance with the established procedures for service operation.

4 (4) The landing must be made without excessive vertical acceleration,

tendency to bounce nose over, ground loop, porpoise, or water loop. (5) The landings may not require exceptional piloting skill or alertness.

(b) For landplanes and amphibians, the landing distance on land must be determined on a level, smooth, dry, hard-surfaced runway. In addition—

(1) The pressures on the wheel braking systems may not exceed those specified by the brake manufacturer;

(2) The brakes may not be used so as to cause excessive wear of brakes or tires; and

(3) Means other than wheel brakes may be used if that means—

(i) Is safe and reliable;

(ii) Is used so that consistent results can be expected in service; and /(iii) Is such that exceptional skill is not required to control the

airplane.

(c) For seaplanes and amphibians, the landing distance on water must be determined on smooth water.

(d) For skiplanes, the landing distance on snow must be determined on smooth, dry, snow.

(e) The landing distance data must include correction factors for not more than 50 percent of the nominal wind components along the landing path opposite to the direction of landing, and not less than 150 percent of the nominal wind components along the landing path in the direction of landing.

(f) If any device is used that depends on the operation of any engine, and if the landing distance would be noticeably increased when a landing is made with that engine inoperative, the landing distance must be determined with

that engine inoperative unless the use of compensating means will result in a landing distance not more than that with each engine operating.

The total distance thus calculated must be increased by a factor of 1.667.

FAR Part 23 is somewhat simpler in defining the landing for airplanes certified in the normal, utility, or acrobatic categories. It states the following,

§ 23.75 Landing.

(a) For airplanes of more than 6,000 pounds maximum weight (except skiplanes for which landplane landing data have been determined under this paragraph and furnished in the Airplane Flight Manual), the horizon­tal distance required to land and come to a complete stop (or to a speed of approximately three miles per hour for seaplanes and amphibians) from a point 50 feet above the landing surface must be determined as follows:

(1) A steady gliding approach with a calibrated airspeed of at least 1.5 VSt must be maintained down to the 50 foot height.

(2) The landing may not require exceptional piloting skill or exceptionally favorable conditions.

(3) The landing must be made without excessive vertical acceleration or tendency to bounce, nose over, ground loop, porpoise, or water loop.

(b) Airplanes of 6,000 pounds or less maximum weight must be able to be landed safely and come to a stop without exceptional piloting skill and without excessive vertical acceleration or tendency to bounce, nose over, ground loop, porpoise, or water loop.