Our heavyweight helicopter equal in the world does not have
In Rostov started production of the most load-lifting rotary-wing car The Russian holding «Helicopt[...]
APPROXIMATE EQUATIONS FOR THE LONGITUDINAL MODES
It is frequently useful and desirable to have approximate analytical expressions for the periods and dampings of the characteristic modes. These are convenient for assessing the influence of the main flight and vehicle parameters that affect the modes, and are especially useful when conventional methods of servomechanism analysis are applied to automatic control systems (ref. 9.4). There are two approaches generally used to arrive at these approximations. One is to write out a literal expression for the characteristic equation and, by studying the order of magnitude of the terms in it, to arrive at approximate linear or quadratic factors. For example, if the characteristic equation
•S’4 + %S’3 -(- c2s2 + crs c0 = 0
is known to have a “small” real root, an approximation to it may be obtained by neglecting all the higher powers of s, i. e.
Cis + c0 = 0
Or if there is a “large” complex root, it may be approximated by keeping only the first three terms, i. e.
s2 + C3s + c2 = О
This method is frequently useful, and sometimes the only reasonable way to get an approximation.
The second method, which has the advantage of providing more physical insight, proceeds from a foreknowledge of the modal characteristics to arrive at approximate system equations of lower order than the exact ones. For the longitudinal modes we use the second method (see below), and for the lateral modes (see Sec. 9.6,1) both methods are needed.
It should be noted that no simple analytical approximations can be relied on to give accurate results under all circumstances. Machine solutions of the exact matrix is the only certain way. The value of the approximations is indicated by examples in the following.
To proceed now to the phugoid and short-period modes, we saw in Fig. 9.2 that some state variables are negligibly small in each of the two modes. This fact suggests certain approximations to them based on reduced sets of equations of motion. These approximations, which are quite useful, are developed below.
