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I love siege weapons!
The only constructive criticism I have with you're quaint mangonel catapult is in the use of the rubber band that is responsible for storing the elastic potential energy as it is stretched, thus liberating the associated kinetic energy upon release.
Perhaps a spring loaded tensioner Incorporated onto the axle of the throwing arm hidden from view!
By the way...The angle at which the throwing arm is pulled back too, will dictate both the distance the projectile will travel & also the height that it reaches while in the air.
Also... Flaming projectiles!
That would be spectacular.