For commonwealth games, I could not find any special scientific principles used adopted by CGF.
Sports Science principles are applied in general at games of that level. These are related to giving proper nutrition to athletes, study of movement of athletes using biomechanics, use of technology to do performance analysis, and physiological principles to help athletes to recover from fatigue. Most important point is related to anti-doping measures.
The following are some of the principles of the Commonwealth that are related to science. I am mentioning the keywords as points for simplicity.
1. Protecting the environment. Protection and Conservation of natural ecosystem, Sustainable management of the natural environment, To address Adaptation & mitigation challenges of climate changing, Development, diffusion and deployment of Affordable environmentally friendly technologies and renewable energy Prevention of illicit dumping of toxic and hazardous waste, Prevention and mitigation of erosion and desertification.
2. Access to Health, Education, Food Clean drinking water, Sanitation, Promotion of health, Combating communicable and non-communicable diseases, Recognition of the right to safe, sufficient and nutritious food.
3. Recognition of the Needs of Small States Assisting in small states in tackling their energy, climate change challenges.
science - principles
Projectile motion principle are used in javelin throw, shot put ball throws, discuss throw, extreme sports like cycle jumping with cycles in air, with skate board in air, motor cycle jumping, jumping in to air on ice skates:
A body is projected by an external force and it continues in motion by its own inertia. There is an external force influencing its flight in air. The projectile motion equations for maximum range or height are used to find out the optimum method for the sport.
Biomechanics tells us mechanics of our body. We can use it for better performance.