Appendix A Aircraft moments of inertia
The aerodynamic characteristics of an aircraft can be estimated fairly accurately given sufficient geometric information using the ESDU Data Sheets or other information sources. The same is not true for the aircraft inertias for which there is very little easily available information. This appendix presents the results of an attempt to correlate the inertias with geometric parameters. It can be used to estimate the inertias at an early stage of a design or for the purpose of setting student exercises. There is also some information on inertia in pitch in reference (A.I). Data for this correlation have been taken from references (A.2), (A.3) and (A.4) and cover a mass range from 800 to 210 000 kg. The inertias quoted in reference (A.3) were estimated using a method given in reference (1.1) and the aircraft types are not
~ classified as low inertia
• classified as high inertia
span (m) Fig. A.1 Radius of gyration about the roll axis against wing span, b, in metres
Aircraft moments of inertia 281
identified; the other inertias have been obtained by calculation from the known masses of the components and the aircraft types are given. Reference (A.3) correlated the inertias obtained by plotting the corresponding radii of gyration against an appropriate geometrical parameter; the same process and parameters have been used here. In a few cases data were available on an aircraft at both the maximum mass and the minimum; this is indicated on the plots by joining the points by a vertical line. It should be noted that these values of the radii of gyration are unlikely to be either the maximum or the minimum that can occur. Figure A. 1 shows a plot of radius of gyration about the roll axis against wing span, b, in metres. Fairly obviously, if the engines are located well out on the span of the aircraft we would expect the inertia to be larger than for a comparable aircraft with engines in or near the fuselage. For the data with known aircraft type, multi-engine propeller aircraft were classified, as expected, to have relatively high inertia; single-engined aircraft and jet-engined aircraft with engines close to the fuselage were classified as of low inertia. It proved possible to draw lines of reasonable fit to the two sets of data. The data reference (A.3) were then added and can be seen to fall close to the other data. The slopes of the lines are 0.16 for the multi-engined propeller aircraft and 0.128 for the other types; reference (A.3) found no effect of number of engines and a slope of 0.157. Figure A.2 shows a plot of radius of gyration about the pitch axis against fuselage length, Is, in metres. Again the aircraft were classified into low and high inertia, with aircraft with engines near a spanwise line through the cg classified, as expected, to have lower inertia. In this case the classification did not separate the data and a single relation between the parameters was assumed. Linear regression gives the radius of gyration in pitch as ky = 0.1816Is 0.214 m, with a standard deviation of the fractional error of 0.134.
o classified as low inertia
• classified a s high inertia
IB(m) Fig. A.2 Radius of gyration about the pitch axis against fuselage length, I,, in metres
Aircraft moments of inertia
,II~ + I~ (rn)
Fig. A.3 Radius of gyration about the yaw axis against ~ l 2 + b 2
Figure A.3 shows a plot of radius of gyration about the yaw axis against ~l 2 + b2 In this case no simple classification of the aircraft by engine arrangement was considered likely to be useful. Linear regression was used to obtain the relation k,. = 0.1613 ~/l 2 + b 2 - 0.124 m, with a standard deviation of the fractional error of 0.136. .