Help with physics of flight paths?

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Discussion Overview

The discussion revolves around the physics of flight paths, specifically how to express a plane's angular velocity and position on a circular flight path as a function of time, considering constant airspeed and known wind conditions. The scope includes mathematical reasoning and technical explanation related to flight dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks to understand how to express angular velocity and position on a circular path, given constant airspeed and wind conditions.
  • Another participant suggests using 2-dimensional vectors to approach the mathematical setup of the problem.
  • A participant mentions having expressed ground speed and position vectors as functions of angle but struggles to convert these into a time-dependent function.
  • It is proposed that the vector sum of the plane's airspeed and wind speed should be used to determine ground speed, and that the plane must be angled to maintain a tangential path around the circle.
  • Integration is suggested as a method to determine the time required to reach specific positions on the circular path.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the method to express the plane's angular position as a function of time, and multiple approaches are being discussed without resolution.

Contextual Notes

There are unresolved aspects regarding the integration process and the specific mathematical relationships needed to convert angular measures into time-dependent functions.

pr1ncesspeach
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Hi all,
If anything here is incorrect or confusing or seems trivially simple, I apologize: I'm not a physicist and created an account specifically to get help on this from some people who are!
My question is this:
Assume a plane has a constant airspeed and you wish to fly a circular pattern (with a specific, constant turn radius). Wind speed and direction are also known and constant. (So bank angle would need to be continuously changing in order to maintain the circular path.) How would you go about expressing the plane's angular velocity/position on the circle as a function of time?
I've tried a couple of things but I'm fairly sure there's something I'm missing or misunderstanding.
Thanks in advance for your help!
 
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pr1ncesspeach said:
Hi all,
If anything here is incorrect or confusing or seems trivially simple, I apologize: I'm not a physicist and created an account specifically to get help on this from some people who are!
My question is this:
Assume a plane has a constant airspeed and you wish to fly a circular pattern (with a specific, constant turn radius). Wind speed and direction are also known and constant. (So bank angle would need to be continuously changing in order to maintain the circular path.) How would you go about expressing the plane's angular velocity/position on the circle as a function of time?
I've tried a couple of things but I'm fairly sure there's something I'm missing or misunderstanding.
Thanks in advance for your help!

Welcome to the PF.

What is the context of your question? Is it for schoolwork?
 
berkeman said:
Welcome to the PF.

What is the context of your question? Is it for schoolwork?

No, not for school work. It's just one part of a larger problem I'm working on.
 
Are you familiar with 2-dimensional vectors? That is the way you would approach the math for this setup.
 
Yes, I am. I've been able express ground speed vectors, position vectors, etc, as functions of theta/course; I'm just not sure how to convert what I have into something that is a function of time. So for every position on the circle I know what the plane's course, heading, and ground speed will be - but I have no idea how long it will take to get to that position :s
 
pr1ncesspeach said:
Yes, I am. I've been able express ground speed vectors, position vectors, etc, as functions of theta/course; I'm just not sure how to convert what I have into something that is a function of time. So for every position on the circle I know what the plane's course, heading, and ground speed will be - but I have no idea how long it will take to get to that position :s

Right, you would use the vector sum of the plane's airspeed and the wind speed vector to get the ground speed. Then you need to angle the plane so that it travels tangentially around the circle above the ground. To figure out times, I believe you will need to do an integration. Are you familiar with calculus?
 

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