<p>Given the fact that the ad hoc networks with flat architectures are not scalable, this study focuses on determining the conditions to guarantee the scalability in a hierarchical architecture based on the resources availability in the different layers of the network. A model based on the truncated geometric distribution that allows to characterize the available resources in an ad hoc network was proposed. Starting by this characterization, the concept of growth factor j was introduced as a constant value that represents the appropriate relationship among the available resources in two successive layers of the network to ensure scalability. Simulation scenarios were explored to develop the estimation process of the growth factor j in ad hoc networks of two and three-layer hierarchical architectures in the software ns-3. The results showed that the growth of resources between layers in an ad hoc network can be expressed through a linear model. Also, a relation was found between the estimated value of j and the golden ratio as a way to inspire the design of artificial system based on the attributes that can be found in nature. </p>