1 MATLAB Digest
In this article, we will derive analytical models of the loads and bending moments on the wing of a small
passenger aircraft to determine whether the wing design meets strength requirements. We will derive
the models in the notebook interface in Symbolic Math Toolbox™. We will then use the data management
and analysis tools in MATLAB® to simulate the models for different scenarios to verify that anticipated
bending moments are within design limits.
While this example is specific to aircraft design, analytical models are useful in all engineering and
scientific disciplines –for example, they can be used to model drug interactions in biological systems, or to
model pumps, compressors, and other mechanical and electrical systems.
Deriving Analytical Model of Wing Loads
We will evaluate the three primary loads that act on the aircraft wing: aerodynamic lift, load due to wing
structure weight, and load due to the weight of the fuel contained in the wing. These loads act perpendicu-
lar to the wing surface, and their magnitude varies along the length of the wing (Figures 1a, 1b, and 1c).
By Dan Doherty
Analytical Modeling of Aircraft Wing Loads
Using MATLAB and Symbolic Math Toolbox
When modeling engineering systems, it can be difficult to identify the key parameters driving
system behavior because they are often buried deep within the model. Analytical models can
help because they describe systems using mathematical equations, showing exactly how differ-
ent parameters affect system behavior.
Figure 1a. Lift on the wing.
2 MATLAB Digest
We derive our analytical model of wing loads in the Symbolic Math Toolbox notebook interface,
which offers an environment for managing and documenting symbolic calculations. The notebook in-
terface provides direct support for the MuPAD language, which is optimized for handling and operating
on symbolic math expressions.
We derive equations for each load component separately and then