Help with physics of flight paths?

In summary: 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 :sRight, 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
  • #1
pr1ncesspeach
3
0
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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  • #2
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?
 
  • #3
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.
 
  • #4
Are you familiar with 2-dimensional vectors? That is the way you would approach the math for this setup.
 
  • #5
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
 
  • #6
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?
 

1. How do you calculate the trajectory of a flight path?

The trajectory of a flight path can be calculated using the equations of motion, which take into account the initial velocity, acceleration, and time. These equations can be solved using algebra or calculus, depending on the complexity of the flight path.

2. What factors affect the flight path of an object?

The flight path of an object is affected by several factors, including the initial velocity, air resistance, gravity, and the shape of the object. Other factors such as wind speed and direction can also have an impact on the flight path.

3. How does the shape of an object affect its flight path?

The shape of an object can greatly impact its flight path. Objects with a streamlined shape, such as airplanes, experience less air resistance and can travel further and faster compared to objects with irregular shapes. The shape can also affect the lift and drag forces acting on the object, which can alter its flight path.

4. What is the difference between a parabolic and elliptical flight path?

A parabolic flight path is a curved path that follows the shape of a parabola, while an elliptical flight path is a curved path that follows the shape of an ellipse. Parabolic flight paths are often seen in objects with a constant acceleration, while elliptical flight paths are seen in objects under the influence of gravity or orbital forces.

5. How can you manipulate the flight path of an object?

The flight path of an object can be manipulated by changing its initial velocity, direction, or shape. Other factors such as air resistance and gravity can also be altered to affect the flight path. In some cases, external forces such as propulsion or aerodynamic controls can also be used to manipulate the flight path of an object.

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