How far away is a plane in the sky?

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SUMMARY

To determine the distance of a plane in the sky, one can apply the rule of similar triangles, especially for aircraft like a Boeing 747, which is approximately 70 meters long and typically flies at altitudes between 30,000 and 40,000 feet. However, practical measurement methods, such as using a ruler held 80 cm from the eye, introduce significant errors, potentially making the calculated distance an order of magnitude inaccurate. Thus, while similar triangles provide a theoretical framework, practical applications may yield unreliable results.

PREREQUISITES
  • Understanding of similar triangles and their properties
  • Basic knowledge of aircraft dimensions and altitudes
  • Familiarity with practical measurement techniques
  • Concept of perspective in visual measurements
NEXT STEPS
  • Research the mathematical principles behind similar triangles
  • Explore the typical cruising altitudes of commercial aircraft
  • Learn about practical measurement techniques in physics
  • Investigate common errors in visual estimation and measurement
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Aerospace enthusiasts, physics students, and anyone interested in understanding the principles of distance estimation and measurement in aviation contexts.

Johndigger
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Ok, my brother & I were trying to work this out.

Without directly knowing the angles is it possible to work out how far away a plane is in the sky?

For example, a boeing 747 is about 70m long. It appeared to be about 0.001m holding out a ruler about 80cm from my eye.


I look forward to reading your replies.

Thank you.
 
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Welcome to PF.

Airliners at cruise are flying at an altitude between 30,000 feet and 40,000 feet 90% of the time.
 
Apply the rule of similar triangles.
 
As a purely practical thing, the mesurement method used makes any answer he's going to get from similar triangles meaningless. The error is likely to be an order of magnitude out. (at least)

But yeah, in a textbook case, similar triangles is the method.
 

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