Scale Modeling for Landing of a Lunar Probe

In this paper, a scaling law on the landing behavior of a lunar probe is discussed. In order to derive an effective scaling law, all of possible non-dimensional numbers, called pi-numbers, were examined at first based on the principle equations of physics related to the phenomena. One strict relationship was then derived in terms of the size between a real model and a corresponding scale model. The relationship suggests that the scale models should have the size of one sixth of the real ones when studying the motion behavior of mechanical systems on the Moon. The fact has been well known in the space community. However, such a strict law is not always practical in laboratory experiments on the ground. Therefore, possibilities to relax the law were investigated; hence two candidate relationships were obtained. Experiments in a vacuum chamber using simulated lunar soil were carried out to validate these relaxed laws, and concluded was that inertia forces and soil-cohesion forces dominate over gravity forces for the landing dynamics. Elimination of the gravity forces from the primary consideration in the scale model experiments will make the verification process of the lunar landing systems easy and more practical.