Longitudinal Stability Criteria for a Propeller-Driven Aircraft

Gil Iosilevskii

doi:10.1155/2010/762329

Abstract

The Routh criterion is used to assess longitudinal dynamic stability of a propeller-driven aircraft. Under a few plausible assumptions on possible ranges of the pertinent stability derivatives, it reduces to a pair of simple conditions imposing a traditional aft limit (the forward of the maneuver and the neutral-speed-stability points) on the center-of-gravity position and an upper limit on the longitudinal moment of inertia. It is demonstrated that most aircraft have sufficiently small inertia to remain stable as long as their center-of-gravity is properly placed. At the same time, sailplane-like aircraft (as, e.g., long endurance UAVs), with an engine installed at the rear extremity of the aircraft, may have sufficiently high inertia to become unstable regardless of their center-of-gravity placement.

Highlights

Linear analysis of the longitudinal dynamics of a rigid aircraft can be found practically in any textbook on flight mechanics
With at = 5, St/Sw = 6, and the data of our model aircraft, R1 equals, approximately, 0.4(xn−xt)— almost half the distance between the tail and the center-ofgravity (it is implied here that). This result marks out a single configuration which may be at risk of becoming unstable because of the excessive inertia
The key element underlying the preceding derivations is that, under assumptions (10) and (17), the coefficients a, . . . , e of the characteristic polynomial can be approximated by a few dominant terms only

Summary

Introduction

Linear analysis of the longitudinal dynamics of a rigid aircraft can be found practically in any textbook on flight mechanics. Stability of a system (the aircraft, in this case) can be assessed without solving its characteristic equation—by the Routh criterion, the number of roots of (4) which are in the right-half-plane equals the number of sign alternations in the five-member sequence S = {a, b, f , g, e}, where f = c − ad/b and g = d − be/ f [3, pages 253–255] This approach is hardly ever used with (4)—the unwieldiness of the expressions for the members of S renders it rather unattractive as compared with the instant numerical solution of the generalized eigenvalue problem leading to (4).

Approximate Stability Criterion

An Example

Maximal Moment of Inertia

Concluding Remarks

Coefficients of the Characteristic Polynomial

Parameter P