Designing autonomous drone swarms is hampered by a vast design space spanning platform, algorithmic, and numerical‑strength choices. We perform large‑scale agent‑based simulations in three canonical scenarios: swarm‑on‑swarm battle, cooperative area search with attrition, and pursuit of scattering targets. We demonstrate how dimensional‑analysis and data‑scaling can be leveraged to collapse performance data onto scaling functions that are mathematically simple, yet counterintuitive and therefore difficult to predict a priori. These scaling laws reveal success-failure boundaries, including sharp break points which we show can be framed as an "effective swarm size." Additionally, we show how this technique can be used to quantify trade‑offs between agent count and platform parameters such as velocity, sensing or weapon range, and attrition rate. Furthermore, we show the benefits of embedding an optimal path planning loop within this framework, which can qualitatively improve the scaling laws that govern the outcome. The methods we demonstrate are highly flexible and would enable rapid, budget‑aware sizing and algorithm selection for large autonomous swarms.