I've peiced together a list that covers most of the different areas that I would like to exlpore in my physical training. Each contributes to the development of the physical and mental attributes that a 'real world' superhero would need to have. Over the next few weeks, I'll be posting articles about each, to provide readers with a basic idea of what that sport or activity is all about and how it might contribute to the project.
General Fitness - See the article "Starting Out - Fighting Fit", posted here earlier.
Martial Arts - This will include both Asian and non-Asian arts, covering kicking and striking, grappling, joint manipulation, throwing, armed and unarmed combat, and more.
Parkour - One of the fastest growing sports world-wide, traceurs (Parkour participants) move in ways that you'll normally only see in comic books. It's an amazing sport, and one perfectly suited to Project Superhero.
Weight Training - Builds strength and muscle mass.
Pilates/Yoga/etc. - Develops flexibility, muscle control, breathing, mental focus and more.
Aerobic Kickboxing (or similar) - Increases endurance, improves aerobic conditioning and ties in perfectly with martial arts training.
Swimming - Aside from improving a necessary skill, swimming provides a full body workout, improves lung capacity, aerobic conditioning, coordination, etc.
Rock Climbing/Bouldering/Etc. - Builds strength and toughness of both mind and body. Also, will certainly come in handy when dealing with rooftops and buildings.
Spelunking - Provides many of the benefits of climbing, but has the added bonus of heightening the senses through stimulus deprivation.
Sky Diving/BASE Jumping/Bunjee Jumping - Falling at a fast rate acclimates the body to high speed and high adrenaline circumstances.
Hang Gliding - Hey, a superhero has to fly somehow, right?
SCUBA diving - A handy Batman/James bond type skill.
Urban Exploration - Though it brushes the edges of legality, this is essentially recreational tresspassing. Aside from the skills it would develop and the familiarity with the lesser seen side of any city, it still makes sense. What, you think Spiderman gets permission to be on people's rooftops?

