I'm building a boomerang for a project, but I've made it a goal for myself to have a boomerang which can fly at lest 200 feet, so how would I increase the flight path. Angular momentum increases in the direction of the torque, but why? Is there a way I can increase the angular momentum through a longer path? please help, thank you for your time.
A full exposition of the equations of motion of a boomerang can be found at this link - it is really quite hard work to read through. Let me try to summarize the main points:
- A boomerang derives "lift" from the winged shape and its rotation
- The boomerang returns because the lift is asymmetrical: when you add the velocity of linear motion to the velocity due to rotation, you can see that the leg that is moving forward is experiencing greater lift than the leg moving backwards
- The differential lift results in torque on the boomerang, and will cause it to start tilting; this results in an approximately circular path
- If you throw the boomerang so it has a vertical component of velocity, it will lose linear speed as it "climbs" - this makes the flight path less circular
So what do we learn for getting the boomerang to go far? First - we need to slow down the rate at which it turns in its path: this means that the linear velocity needs to be small compared to the wing velocity (less differential lift), so we need fast rotation and a wing with small angle of attack. Second, we need a large moment of inertia so the boomerang maintains rotation during flight - @CuriousOne's suggestion of a tungsten tipped blade is certainly interesting (consider a 3 legged boomerang to give a more favorable construction). Finally - throw it hard.
But I think that keeping the lift small and the rotation fast are the keys. Do google "equations of motion of boomerang" - you will find quite a treasure of papers with more detailed analysis. Probably the most accessible are http://plus.maths.org/content/unspinning-boomerang and http://large.stanford.edu/courses/2007/ph210/moon2/