5.7 V-n Diagram

5.7 V-n Diagram

To introduce the V-n diagram, the relationship between load factor, n, and lift coefficient, CL, must be understood. Pitch-plane maneuvers result in the full spectrum of angles of attack at all speeds within the prescribed boundaries of limit loads. Depending on the direction of pitch-control input, at any given aircraft speed, positive or negative angles of attack may result. The control input would reach either the CLmax or the maximum load factor n, whichever is the lower of the two. The higher the speed, the greater is the load factor, n. Compressibility has an effect on the V-n diagram. In principle, it may be necessary to construct several V-n diagrams representing different altitudes. This chapter explains only the role of the V-n diagram in aircraft design.

Figure 5.2 represents a typical V-n diagram showing varying speeds within the specified structural load limits. The figure illustrates the variation in load factor with airspeed for maneuvers. Some points in a V-n diagram are of minor interest to configuration studies – for example, at the point V = 0 and n = 0 (e.g., at the top of the vertical ascent just before the tail slide can occur). The points of interest are explained in the remainder of this section.

Inadvertent situations may take aircraft from within the limit-load boundaries to conditions of ultimate-load boundaries (see Figure 5.2).

5.7.1 Low-Speed Limit

At low speeds, the maximum load factor is constrained by the aircraft maximum CL. The low-speed limit in a V-n diagram is established at the velocity at which the aircraft stalls in an acceleration flight load of n until it reaches the limit-load factor. At higher speeds, the maneuver-load factor may be restricted to the limitload factor, as specified by the regulatory agencies.

Let VS1 be the stalling speed at 1 g. Then:

Let VSn be the stalling speed at ng, where n is a number. Then:

nW = 0.5ρ Vsn2 S CLmax

VA is the speed at which the positive-stall and maximum-load factor limits are simultaneously satisfied (i.e., VA = VS1√nlimit).

The negative side of the boundary can be estimated similarly.