AIRPLANE PERFORMANCE

When a customer buys an airplane, whether it be a private individual, a corporation, an airline, or the military, the buyer wants to know what the airplane will do. How fast will it fly, how high, and how far? How long a runway is required from which the airplane will operate? How expensive will it be to operate, and what are the operating limitations? How fast will it climb? Will it take a half hour to get up to cruising altitude or only 5 min? This chapter provides methods for answering these questions and others related to the general subject of airplane performance. The groundwork for doing so has been presented in the preceding chapters. With the use of this material, one can calculate lift, drag, and thrust. Aside from weight, these are the principle forces acting on an airplane that determine its performance. We will begin, as every flight begins, by first considering the problem of calculating the distance required to take off safely over a prescribed obstacle height.

TAKEOFF

The takeoff of an airplane certified in the transport category is illustrated in Figure 7.1. Starting from a resting position at the far left, the airplane accelerates under takeoff power. At some point the velocity exceeds the stalling speed, Vs. Beyond this point, the airplane is capable of flying. However, the airplane continues to accelerate on the ground until the mini­mum control speed, Vmc is reached. At this speed, if a critical engine fails, the manufacturer has demonstrated that the airplane is able to maintain straight flight at that speed with zero yaw or with a bank angle of less than 5°. Under these conditions at this speed, the required rudder force may not exceed ‘ 1801b. Continuing to accelerate on the ground, the airplane reaches a cali­brated airspeed of Vlt the critical engine failure speed. This speed may not be less than Umc and represents the speed at which the average pilot could safely continue with the takeoff in the event of a critical engine failure. At a speed that can equal Vj but that must be 5% higher than Vmc, the pilot rotates the airplane. This speed, VR, is called takeoff rotation speed.

Because of tail interference with the ground, the angle of attack at VR may not be sufficient to lift the airplane. The pilot therefore continues to

0 К vm v-, Kmu vL0F v2

Figure 7.1 FAR Part 25 takeoff.

accelerate up to a speed of Vmu, the minimum unstick speed. At this speed, the pilot could lift the airplane off of the runway and continue the takeoff, even with one engine inoperative, without any hazardous characteristics. However, to provide an additional margin of safety, the airplane continues to accelerate to the lift-off speed, Vlof, at which point the airplane becomes airborne. Vlof must be at least 10% higher than Vmu, with all engines operating or 5% higher than Vmu with one engine inoperative. After lift-off, the airplane continues to accelerate up to the takeoff climb speed, V2. V2 is the speed attained at a height of 35 ft (10.7 m) above the ground. V2 must be greater than 1.2 V",, in the takeoff configuration and 1.1 Vmc.

This description, applicable to the takeoff of a turbojet or turbofan transport, is in accordance with the definition of these various speeds as presented in the Federal Air Regulations (FAR) Part 25. These regulations govern the airworthiness standards for airplanes in the transport category. Similar regulations for other categories of nonmilitary airplanes can be found in FAR Part 23. The Cherokee 180, which has been used as an example in the preceding chapters, is certified under FAR Part 23. The total horizontal distance, ground roll and airborne, which is required to reach the altitude of 35 ft, starting from rest, is referred to as the FAR takeoff distance.

FAR Part 23 is simpler in specifying the takeoff procedure. For airplanes over 6000 lb (26,700 N), maximum weight in the normal, utility, and acrobatic categories, it is stated simply that the airplane must attain a speed at least 30% greater than the stalling speed with one engine out, Vs,. For an airplane weighing less than 6000 lb, the regulations state simply that the takeoff should not require any exceptional piloting skill. In addition, the elevator power must be sufficient to lift the tail (fctr a “tail dragger”) at 0.8 Vs, or to raise the nose for a nose-wheel configuration at 0.85 VS|.