Solving Air Drag Problem with Wind: A Closer Look

[haki]

Hi,

I have second doubts on air drag problem.

Let's say an object is moving with speed v_obj = 15 m/s and that the air is moving with speed v_wind = -2 m/s. What is the the force of air drag? If There would be no wind. The force would be 1/2*drag coeff.*density of air*area*v_obj^2. But with the wind blowing, should I say that there are 2 forces acting, force of wind which is 1/2*drag coeff.*density of air*area*v_wind^2 + force due to movement of the object in the air 1/2*drag coeff.*density of air*area*v_obj^2. Soo the solution is 1/2*drag coeff.*density of air*area*(v_obj+v_wind)^2. Soo the speed we use is actually 15 m/s - 2m/s. Which will give the same resoult as we would be moving trough still air with speed of 13 m/s? That doesn't seem logical to me.

 

[Astronuc]

Drag on an object is dependent on the relative fluid velocity with respect to the object, so if a plane is moving at 15 m/s (wrt to coordinate system - e.g. ground) and the air is moving at -2 m/s (wrt same coordinate system as plane) then the relative velocity is 17 m/s, and this would be the same as plane at 17 m/s in still air.

The coordinate reference is key.

 

[quicknote]

Hello,

I can understand your doubts about the air drag problem and the effect of wind on it. However, your proposed solution is not entirely accurate. The force of air drag is indeed affected by the wind, but it is not simply the sum of the two forces you mentioned. It is a more complex interaction between the object's movement and the wind velocity.

To accurately calculate the force of air drag with wind, we need to consider the relative velocities of the object and the wind. This is known as the relative wind velocity. In your example, the relative wind velocity would be 15 m/s - (-2 m/s) = 17 m/s. This is the speed at which the air is moving relative to the object, taking into account the wind velocity.

The correct formula for calculating the force of air drag with wind would be 1/2 * drag coeff. * density of air * area * (v_obj - v_wind)^2. This takes into account the relative wind velocity and gives a more accurate result.

In conclusion, while the wind does affect the force of air drag, it is not as simple as adding the two forces you mentioned. It is important to consider the relative wind velocity in order to accurately calculate the force of air drag. I hope this clarifies any confusion you may have had. Please let me know if you have any further questions.