Fully autonomous aerial systems (FAAS) fly complex missions guided wholly by software. If users choose software, compute hardware and aircraft well, FAAS can complete missions faster and safer than unmanned aerial systems piloted by humans. On the other hand, poorly managed edge resources slow down missions, waste energy and inflate costs. This paper presents a model-driven approach to manage FAAS. We fly real FAAS missions, profile compute and aircraft resource usage and model expected demands. Naive profiling approaches use traces from previous flights to infer resource usage. However, edge resources can affect where FAAS fly and which data they sense. Usage profiles can diverge greatly across edge management policies. Instead of using traces, we characterize whole flight areas to accurately model resource usage for any flight path. We combine expected resource demands to model mission throughput, i.e., missions completed per fully charged battery. We validated our model by creating FAAS, measuring mission throughput across many system settings. Our FAAS benchmarks, released through our open source FAAS suite SoftwarePilot, execute realistic missions: autonomous photography, search and rescue, and agricultural scouting using well-known software. Our model predicted throughput with 4% error across mission, software and hardware settings. Competing approaches yielded 10-24% error. We used our SoftwarePilot benchmarks to study (1) GPU acceleration, scale up, and scale out, (2) onboard, edge and cloud computing, (3) energy and monetary budgets, and (4) software driven GPU management. We found that model-driven management can boost mission throughput by 10X and reduce costs by 87%.