Large Language Models (LLMs) have transformed software engineering, but their application to physical engineering domains remains underexplored. This paper evaluates LLMs' capabilities in high-powered rocketry design through RocketBench, a benchmark connecting LLMs to high-fidelity rocket simulations. We test models on two increasingly complex design tasks: target altitude optimization and precision landing challenges. Our findings reveal that while state-of-the-art LLMs demonstrate strong baseline engineering knowledge, they struggle to iterate on their designs when given simulation results and ultimately plateau below human performance levels. However, when enhanced with reinforcement learning (RL), we show that a 7B parameter model outperforms both SoTA foundation models and human experts. This research demonstrates that RL-trained LLMs can serve as effective tools for complex engineering optimization, potentially transforming engineering domains beyond software development.