Exploring Buoyancy & Wind Effects on a Weather Balloon

[Jonsson]

Hello there,

A weather balloon is released, and its acceleration in the z-x-plane, a is governed by a buoyancy force, B, which is constant in the k-direction. gravitational acceleration, 9.81 m/s^2, in the k-direction, and F_D, which is is like this:

$$F_D = -D|\vec{v}|\vec{v}$$

where D is some constant. Furthermore, the balloon is experiencing some wind in the i-direction:

$$\vec{w} = w\vec{i}$$

Then:

1. Does the following look reasonable:

$$F_D = D(|\vec{w}|\vec{w} - |\vec{v}|\vec{v})$$

And if the above is correct, 2., I fail to see how this can be a coupled motion:

$$\vec{a} = {D \over m}(|\vec{w}|\,\vec{w} - |\vec{v}|\,\vec{v}) + ({F_B \over m} - g)\vec{k}$$

Will you kindly explain how it is coupled?

Thank you for your time.

Kind regards,
Marius

 

[LightHero]

Yes, the equation you wrote looks reasonable. The equation you wrote describes a coupled motion because it shows how the acceleration of the balloon is affected by both the force due to the wind and the buoyancy force. The equation states that the acceleration of the balloon is equal to the sum of the force due to the wind, the buoyancy force, and the gravitational force. Thus, this equation describes the coupled motion of the balloon in the z-x-plane.