Could we make a bow with better range and power than a gun?

Question

Assuming there was a human who could draw it, do we have the materials to make a bow that could fire arrows or bolts or whatever that has better range and or stopping power than a gun? (assuming the human is the size of an average human today) and if so, what would it have to be made of, what kind of draw weight and all that good stuff?

Update:

Also, can someone tell me the correct category for this? It automatically put it in hunting but that wasn't right, I figured engineering might work, but doesn't feel quite right.

LG · Accepted Answer

IMO, more power probably wouldn't be too much of a problem.  But then we do have to qualify the word "gun".  Does gun mean like a rifle shouldered by a person?  Or could it mean something like the main armament of a battleship?  In the former case, sure.  In the latter, I'm no so sure.
The main thing with range, given the size of the projectile is big enough to provide a good ballistic coefficient, is velocity.  And I think there would be several issues with making a bow shoot something at supersonic speeds.  There's a "speed of sound" in the bow string that says how fast energy can be transferred from the bow to the string to the projectile.  The higher the tension and the lighter the string, the faster this speed will be.  But then getting enough force on the projectile to propel it to supersonic speeds may require a string that's so strong it cannot be made light.  A bullet in a gun undergoes thousands of G's of acceleration.  
In addition to this, a lot of power might be lost trying to move the bowstring at several times the speed of sound through the air.  Sure, that rifle crack and flash represents energy that's lost in the process.  It's just a question of how much.  But the faster we try to go, the more of a factor it becomes.
And finally, I think the physical size of the contraption may be as much a reason as any it's not typically done.  Even if all the problems with supersonic speeds are surmounted, the contraption required to propel an arrow at supersonic speeds may be much larger and heavier than a comparable gun.

Tim · Answer

There's no way guns can shoot over 2 miles it's impossible unless you used a magnetically charged metal arrow but that's pretty much a rail gun

Philomel · Answer

No unless you can make a bow to fire a 180 Gr arrow at 3000ft/s and can hit a target the size of a man at 1.5 miles.

? · Answer

NO !

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Could we make a bow with better range and power than a gun?

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