Induced drag relation with speed

Hi everyone. I was wondering if you guys could explain me why I saw people say that:
Induced drag changes for a factor of 1/V2
Induced drag coefficient for a factor of 1/V4

If I don't make any mistakes, Drag = 1/2 rho * S * V² * Cd.

Manipulating the formula I find, 1/Cd = 1/2 rho * S * V² * Drag so here we can see that Cd inversely proportional to V², not V⁴.
And I still find that Drag is proportional to V² so why it's different with Induced Drag and Cdi ?

The drag coefficient doesn't change with speed. It includes everything that influences drag EXCEPT density, some predefined reference area, and speed.

Yes, maybe I misspoke, I know that drag is influenced by the design of the airfoil ect but let's pretend that we study an airfoil, I learnt that the drag formula was the same that the lift formula. So I don't understand why Induced drag change for a factor of 1/V² and why Cdi for a factor of 1/V⁴

Owells said:

... so why it's different with Induced Drag and Cdi ...

There are two different forms of drag mechanism.

The profile drag is due to airflow passing the wing, that also generates lift.

The induced drag is due to airflow around the wingtip, the end of the wing. That unwanted flow is normally from below the wing, to above the wing.

I understand better now.

The induced drag ##F_{di}## is ##\frac{1}{2} \rho C_{di}A_i v^2##. We already said ##C_{di}## includes everything that influences the drag force but ##\rho A_i## and speed. The lift force influences the induced drag force. No lift force, no induced drag force. Double the lift, you will [approximately] double the induced drag force. If this is what we observed then ##C_{di}## is proportional to the lift force ##\frac{1}{2}\rho C_L A_L v^2## or:
$$F_{di} = \frac{1}{2} \rho \left(C_{di*} \frac{1}{2}\rho C_L A_L v^2\right) A_i v^2$$
$$F_{di} = \frac{1}{4} \rho^2 C_{di*} C_L A_L A_iv^4$$
Where ##C_{di*}## is a coefficient including everything that is affecting the induced drag force excluding the lift coefficient, reference areas, density, and speed.

jack action said:

The drag coefficient doesn't change with speed.

In general it does, but there are problems where we neglect this.