What is the optimal barrel length for maximum distance in a blow-gun?

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Discussion Overview

The discussion centers on determining the optimal barrel length for maximizing the distance a projectile can travel when fired from a blow-gun. Participants explore the relationship between barrel length, air pressure, and projectile velocity, with a focus on both theoretical calculations and practical experimentation.

Discussion Character

  • Exploratory, Technical explanation, Experimental/applied

Main Points Raised

  • One participant notes that different barrel lengths affect firing ranges and seeks a method to calculate the optimal length.
  • Another participant suggests that the optimal barrel length depends on the air source volume and pressure, indicating that the barrel volume should allow the internal pressure to equal atmospheric pressure as the projectile exits.
  • It is proposed that a barrel that is too short wastes air, while one that is too long may cause the projectile to decelerate due to friction and air resistance.
  • A later reply mentions the possibility of using calculus to express velocity as a function of barrel area or length to maximize escape velocity, though uncertainty about the complexity of this approach is expressed.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific method for calculating optimal barrel length, and multiple approaches are suggested, indicating that the discussion remains unresolved.

Contextual Notes

The discussion highlights the dependence on various factors such as air pressure, barrel volume, and friction, which may not be fully defined or quantified in the contributions.

funkyreuben
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I recently made a few mini-marshmallow blow-guns out of PVC and I noticed that different barrel lengths provided different firing ranges. Does anyone know how I can calculate the optimal barrel length for maximum distance? I haven't done anything physics related since college (2002) and I'm drawing a blank as to calculating this. Any help would be greatly appreciated.

Chris
 
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Welcome to PF, Funkyreuben.
I'm not exactly sure how you would go about this. It depends upon the air source volume and pressure. Ideally, the barrel volume (area x length) should be such that the internal propulsive pressure reaches atmospheric just as the projectile is leaving the muzzle. If the barrel is too short, a lot of your air will be wasted; if it's too long, the marshmallow will begin to decelerate due to friction and air resistance before it can get out.
Trial and error might be the easiest approach.
 
Thanks! I plan on doing some real world testing but I was hoping for a way to calculate it as well.

Chris
 
if you were to write velocity as a function of either area or length you could use calculus to maximize the escape velocity... I don't know how hard that would be though
 

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