One of the many activities you can participate in the SCA is Archery. There are two different classes: Combat Archery and Target Archery.
Combat archery is used in conjunction with field combat in battle situations. This requires restrictions on power or poundage of the recurve bow, and arrows of a safe design to hit men in armor. Trebuchets and catapults are included in this class.
For more, go to http://www.sca.org/officers/marshal/combat/archery/index.html.
Target archery is used for battle points in many of the "wars", as well as for fun by the participants. Archery shoots can be as simple as lining up and shooting at a target with the highest score being the winner, to various novelty shoots. A very short list of novelties includes storming the castle, defending the castle, tower shoots, War of the Roses, duck-goose!, friend-foe, berserker, York, modified York. The archery link below can bring you to links with these and other shoots listed in greater detail.
On archery in the Midrealm, go to http://www.midrealm.org/marshal/archery.