A program of research has addressed a methodology of scaling of flight tests of unmanned air vehicles (UAVs) intended primarily for military use in observing and/or attacking targets on the ground. The main goal of this research is to make it possible to design a model UAV that is suitable for evaluating the performance of a given real UAV or family of UAVs. This research also demonstrates the use of results of computational simulations and ground hardware experiments on models of vehicles other than UAVs to predict performances of UAVs prior to conducting flight tests.

In the development of UAVs, as in many other engineering endeavors, testing of models offers obvious advantages of economy and safety over testing of fullsize systems, provided that, for a given UAV or other system, it is possible to establish the necessary mathematical relationships for scaling of dimensions and other physical quantities. The mathematical basis for scaling in the present methodology is the Buckingham pi theorem, which was introduced by E. Buckingham in 1914 and is a key theorem in dimensional analysis. For a given physical system, the Buckingham pi theorem provides a means of computing groups of dimensionless parameters (usually represented by symbols that include the eponymous Greek letter pi) from the given physical variables, even if the form of the dynamical equation of the system is unknown. For the purpose of the theorem, two systems (e.g., a model and the system being modelled) for which the dimensionless parameters coincide are said to be similar; they are equivalent for the purpose of the equation.

In order for a model of a UAV to be suitable for evaluating the performance of the real UAV, the two versions of the UAV must have dynamic similarity in the sense that there is a match between the groups of dimensionless variables ("pi groups") of the two versions. Dynamic similarity is shown by using the Buckingham pi theorem to replace the dimensional physical parameters with dimensionless products and ratios. Heretofore, often it has been seen that once a scale model is developed, either (1) it is necessary to modify the fullsize vehicle to match the pi groups of the scale model, or (2) the pi groups of the scale model are such as to afford similarity to only a certain subset of UAVs. The concern in the present research is to overcome these limitations, enabling development of a model that can afford the full range of dynamic similarities for a general UAV.

Thus far, the research has included investigations of the scaling of flight and sensor dynamics between two surrogate vehicles and a basic UAV that could be used to search wide areas. One surrogate vehicle was a 1/20-scale model of a mammoth dump truck; the other was a Chinese-built jet airplane used for training pilots (see figure). The Buckingham pi theorem was applied to the governing equations of the UAV/sensor system under simplifying assumptions (ignoring wind, friction, and aerodynamic loads) flying over a rectangular ground area. The vehicle dynamics and sensor behavior were studied to develop seven pi groups. Computational simulations of the three vehicles were performed and the results of the simulations were compared to study the possibilities and effects of scaling.

*This work was done by Jeevani I. Abeygoonewardene of the Air Force Institute of Technology for the Air Force Research Laboratory. For more information, download the Technical Support Package (free white paper) at www.defensetechbriefs.com/tsp under the Physical Sciences category. AFRL-0036*

##### This Brief includes a Technical Support Package (TSP).

###### Scaling of Flight Tests of Unmanned Air Vehicles

(reference AFRL-0036) is currently available for download from the TSP library.

Don't have an account? Sign up here.

##### Defense Tech Briefs Magazine

This article first appeared in the August, 2007 issue of *Defense Tech Briefs* Magazine.

Read more articles from the archives here.