An Empirical Approach towards the Rapid Derivation of Vehicle Scaling Laws in Conceptual Design

In the design of any aircraft, a good set of scaling laws can play a pivotal role in accelerating the design process without negatively impacting the quality of the results. When dealing with concepts for which a signi cant amount of comparable prior-art exists, the corresponding historical data can be used to evaluate these scaling laws. Alternatively, when very small adjustments are required photographic, scaling can be used. A number of challenges arise when a vehicle is being designed around an unconventional or disruptive technology. First of all, historical-data based regressions become implicitly unreliable by virtue of the fact that the technology is unconventional and may thus bring with it diametrically opposed weight and volume requirements. Second, it was shown that simpler approaches such as photographic scaling can result in highly suboptimal concepts even for very small scaling factors. Yet good scaling information is critical to the success of any conceptual design process. Balaba proposed the Con guration Space Exploration and Scaling Methodology (CESM) as a means of rst of all designing baseline geometries around these technologies and second of all, deriving custom scaling laws. This paper focuses on the scaling law derivation process. (It is assumed that a subsystem layout has been identi ed for the unconventional technology and that a baseline geometry has been de ned around it.) In the CESM methodology, it is also assumed that the new technology has matured enough to permit the prediction of the scaling behavior of the various subsystems in response to requirement changes. Updated subsystem geometry data is generated by applying the new requirement settings to the a ected subsystems. All collisions are then eliminated using the NSGA-II genetic algorithm. This is done while minimizing the adverse impact on the vehicle packing density by making this metric part of the objective function. Once all collisions are eliminated, the vehicle geometry is reconstructed and system level data such as fuselage volume can be harvested. This process is repeated for all requirement settings. Dimensional analysis and regression can be carried out using the resultant data and all other pertinent metrics in the manner described by Mendez and Segel.The dominant parameters for each response show up in dimensionally consistent groups that form the independent variables. More importantly the impact of changes in any of these variables on system level dependent variables can be easily and rapidly evaluated. In this way, the conceptual design process can be accelerated without sacri cing analysis accuracy. Scaling laws for take-o gross weight and fuselage volume as functions of fuel cell speci c power and power density for a notional fully electric General Aviation vehicle are derived for the proof of concept. Scaling laws generated from custom data for each concept are less susceptible design noise than say, regression based approaches. Through these laws, key physics-based characteristics of vehicle subsystems such as energy density can be mapped onto key system level metrics such as fuselage volume or take-o gross weight. These laws can then substitute some historical-data based analyses thereby improving the delity of the analyses and reducing design time.