# Semi-empirical Equation Method (Statistical)

Semi-empirical relations are derived from theoretical formulation and then refined with statistical data to estimate aircraft component mass. It is an involved process to capture the myriad detailed parts. Mass estimation using semi-empirical relations can be inconsistent until a proper one is established. Several forms of semi-empirical weight-prediction formulae have been proposed by various analysts, all based on key drivers with refinements as perceived by the proponent. Although all of the propositions have similarity in the basic considerations, their results could differ by as much as 25%. In fact, in [5], Roskam describes three methods that yield different values, which is typical when using semi-empirical relations. One of the best ways is to have a known mass data in the aircraft class and then modify the semi-empirical relation for the match; that is, first fine-tune it and then use it for the new design. For a different aircraft class, different fine-tuning is required; the relations provided in this chapter are amenable to modifications (see [5] and [6]).

For coursework, the semi-empirical relations presented in this chapter are from [2] through [7]; some have been modified by the author and are satisfactory for con­ventional, all-metal (i. e., aluminum) aircraft. The accuracy depends on how closely aligned is the design. For nonmetal and/or exotic metal alloys, adjustments are made depending on the extent of usage.

To demonstrate the effect of the related drivers on mass, their influence is shown as mass increasing by (t) and decreasing by (^) as the magnitude of the driver is increased. For example, L(t) means that the component weight increases when the length is increased. This is followed by semi-empirical relations to fit statistical data as well as possible. Initially, the MTOM must be guesstimated from statistics as in Chapter 6. When the component masses are more accurately estimated, the MTOW is revised to the better accuracy.