Help with physics of flight paths?

[pr1ncesspeach]

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!

 

[berkeman]

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?

 

[pr1ncesspeach]

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.

 

[berkeman]

Are you familiar with 2-dimensional vectors? That is the way you would approach the math for this setup.

 

[pr1ncesspeach]

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

 

[berkeman]

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?