Substantial disagreement among results based on correlating pilot ratings with shortperiod damping and natural frequency (ref. 12.16) has resulted
Fig. 12.12 Longitudinal shortperiod oscillation—pilot opinion contours (from ref. 12.15).

in a search for more meaningful parameters. One such was derived by noting that the pilot’s opinion of an aircraft’s longitudinal dynamics is very much influenced by the response of the vehicle to control inputs. This in turn depends on terms in both the numerator and denominator of the longitudinal transfer functions, whereas the shortperiod characteristics appear in the denominator only [see (10.2,11)]. An important transfer function is the approximate one relating pitch rate response to elevator angle input, given by (10.2,11c and b). (See also Figs. 10.6, 10.3.) If we neglect CLi, 0L(l, and Cm ■ in (10.2,126) and convert to dimensional form, we get the approximation
g = MsL* 1 + mVsjLx g
A5e mIyV (e2 + 2toons + con2) ‘ ’
where q is in rad/sec, and s corresponds to djdt, not djdt. mn (in rad/sec) and £ are, of course, the approximate shortperiod frequency and damping, respectively. The quantity (LJrnV) in the numerator is the lead time constant in this response and has been identified as an important parameter for longitudinal handling qualities (ref. 12.31). In ref. 12.16 it is argued that the appropriate correlation of pilot ratings is with the parameters shown in Fig. 12.13. It is stated that when the aircraft load :factor response to angle of
514 Dynamics of atmospheric flight na < 15.0

Fig. 12.13 Pilot ratings based on LalmVojn and nalcon (from ref. 12.16).

attack (nx = (dLjW)/da = LJW) is less than 15 g/rad, pilot opinion correlates well with
—^2— and
mVmn
The importance of LjmV can easily he inferred. Figure 10.6 shows that the early part of the response to elevator separates clearly into two phases— an initial pitchup to a nearly steady Да, and a subsequent flightpath curvature associated with the lift increment AL = La Да. The magnitude of the curvature is approximately ДLjmV = (LjmV) Да. The changeover in correlating parameter at about nx of 15 appears to be due to the pilot’s concern to control load factor at large na, whereas he concentrates on flight path at low na. Figure 12.13 shows isoopinion curves based од the use of these parameters.
An additional parameter has been developed based on the consideration of pilot comments and the physiology of the pilot (ref. 12.17). It is called the
“Control Anticipation Parameter” or GAP. The GAP is defined to be the ratio of the instantaneous angular acceleration in pitch to the steadystate change in load factor when the pilot applies a step input to the longitudinal control. Thus
CAP = ^
An,
This theory is based on the fact that in order to make precise adjustments to the flight path, the pilot must infer from the initial attitude response of the vehicle, the ultimate response of the flight path. It is found that the best cue for sensing attitude response is the initial angular acceleration in pitch (q0) which the pilot senses through his inner ear. For precision control tasks the pertinent steadystate parameter is taken to be the change in steadystate load factor (Дnss), which is related to flightpath curvature (see Sec. 6.10).
It is found that if an aircraft has a CAP which is too small, the pilot tends to overcontrol and rates the pitch response as sluggish. This comes about as follows.
When the flight path requires adjustment the pilot moves the controls and monitors the effect of this action by noting the size of the q0 generated. If the CAP is too small no q0 will be detected because it is below the threshold of the pilot’s inner ear. Consequently he will apply more control input until a q is finally sensed. The result is an extremely large Anss and the desired response is exceeded.
On the other hand, if the CAP is too large, the pilot tends to undershoot his desired flightpath corrections, and rates the response as fast, abrupt, and too sensitive. This occurs because any slight pitch control inputs from the pilot generate a large q0 which is interpreted as the prelude to a gross change in vehicle state and not the small desired change. As a result the pilot tends to reduce or reverse his pitch control input to avoid this, resulting in a steady – state response that is too small.
The CAP can easily be derived from relations previously given. q0 is simply the initial pitching moment divided by Iy, i. e.
. MsAd,
1f> = —~—
■*■41
The steadystate load factor is obtained from (10.2,9), in conjunction with the shortperiod approximation (10.2,11) (note that Gvs = 0 in this approximation). The aerodynamic transfer functions are replaced by stability derivatives, we let s = 0, and neglect CL and CL& to get the approximate
result for the static gains:
After conversion to dimensional form we get
The acceptable range in CAP extends upward from about 15 deg/sec2/g. The upper limit has not been determined, with good pilot ratings obtained from 2550 deg/sec2/gr. Figure 12.14 compares the pitch response of two different jet fighters. Under the conditions which prevailed for this test, the F105A with a CAP of 16 deg/sec2/g received an adverse rating while the F84F was rated as “good” with respect to formation flying.
SPEED STABILITY
In addition to the vehicle’s attitude response, the pilot also considers the speed stability of the aircraft when rating its handling qualities. This is especially true when performing such rectilinear maneuvers as the landing approach. In Sec. 11.5 it was shown that the aircraft response to a disturbance Д F0 in forward speed could be written as AV0etlT. The response is convergent for T negative. Although no clear criterion for speed stability exists it appears that if in all other respects the aircraft is rated as satisfactory, then the pilot will rate the speed response as satisfactory if it is convergent with a time to half amplitude less than 35 sec. However, it is found that under certain conditions a vehicle can be rated as acceptable even if the speed response is divergent, provided that the time to double amplitude is greater than 17 sec.