By how much will I miss the target?

  • Context: High School 
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Discussion Overview

The discussion revolves around the relationship between the distance from a target and the accuracy of shots fired from an air gun. Participants explore how errors in aiming at different distances may not scale linearly and consider various factors that could affect projectile trajectory, including physical forces and equipment alignment.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether a 2 cm miss at 5 meters would result in a 4 cm miss at 10 meters, suggesting that this might not be the case due to various factors.
  • Another participant agrees that the relationship could hold under certain conditions, but emphasizes that other sources of error, such as barrel alignment and pellet symmetry, can influence accuracy.
  • A third participant introduces the Coriolis effect as a potential factor affecting aim, citing historical context from the Falklands War where soldiers had to adjust their aim based on geographical location.
  • One participant counters the idea of linear error scaling, explaining that the projectile loses speed over distance, which affects its drop due to gravity, indicating that the relationship between distance and error is not straightforward.
  • It is noted that there exists a range where projectile speed remains relatively constant, within which the initial claim might hold true.

Areas of Agreement / Disagreement

Participants express differing views on whether the error scales linearly with distance. While some acknowledge that certain conditions could allow for this, others argue that various factors complicate this relationship, leading to an unresolved discussion.

Contextual Notes

Participants mention several factors that could affect accuracy, including barrel alignment, pellet characteristics, air resistance, and gravitational effects, but do not reach a consensus on how these factors interact with distance and error.

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I just started shooting with an air gun that I got. What I wonder is this; if I from 5 meters miss the bullseye with let's say 2 cm (0,02 m), does that automatically mean that I'll miss it by 4 cm from 10 meters? I thought I would miss it by much more in the latter case, but that's what I found playing around with the law of sines, cosines etc. Can that be right...?
 
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It depends.

If you miss because your barrel is not perfectly straight and aligned with the sight, because your pellet is not symmetrical, etc., then yes, 2 cm error from 5 meters means 4 cm error from 10 meters.

There are other possible sources of error. Earth's gravity makes the pellet drift downwards. As the pellet flies through the air, it slows down because of air resistance and, the slower it goes, the more it is susceptible to crosswinds.
 
In addition to the error sources mentioned by hamster, the Coriolis force can have a subtle effect.

This was experienced by British soldiers in the Falklands War; they had been trained to aim slightly off-target in order to compensate for the Coriolis effect, but going to the southern hemisphere, they had to re-adjust by aiming off-target to the OTHER side from which they were used to.
 
hamster143 said:
It depends.

If you miss because your barrel is not perfectly straight and aligned with the sight, because your pellet is not symmetrical, etc., then yes, 2 cm error from 5 meters means 4 cm error from 10 meters.

No, that's not necessarily true. The projectile (pellet, BB, etc.) loses speed as it continues to fly through the air, therefore, the farther you are from the target, the more speed the projectile loses and the farther it will drop from the point you are aiming at. Since the projectile's speed is not constant, and the effect of gravity is constant, the ratio of error to distance is not linear. That being said, there is a distance within which the projectile's speed remains fairly constant (which depends on the projectile, itself as well as the barrel design and means of acceleration); within that range, you can expect the results you quoted.
 
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