Myth Or Fact? - Wind drag on flaming arrows

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Myth Or Fact? -- Wind drag on flaming arrows

In a stable atmosphere would arrows that have their head on fire accelerate faster than a regular arrow?
 
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Why? A flaming arrow in flight cannot reduce the density of air in its flight path to any meaningful extent without inducing an equal amount of drag. This is a back door 'free energy' hypothesis.
 


This is a back door 'free energy' hypothesis.
Could you please elaborate.
 


My best guess (I've never really seen this myth before): You'd be applying the same amount of energy initially to the arrow (same pull back of the string.) But when it's about to land, it has more energy?
 


You'd be applying the same amount of energy initially to the arrow (same pull back of the string.) But when it's about to land, it has more energy?
I don't think that's the case. You are applying excessive energy in firing the bow.
So, that's the tricky part.
 


I was saying for a flaming arrow vs a nonflaming one. We're applying the same energy in firing.
 


Arrow travels too fast for effect of added heat on unstable atmosphere to catch on. Air has quite a bit of inertia of its own. Once the flaming arrow lands, it can create updraft over it. So maybe if you've set an entire field ablaze with flaming arrows, the arrows launched over it will carry a bit further (they still won't accelerate faster), but it'd be due to fire on ground, not fire on the arrow.