I have a question about the drag coefficient in the drag equation.
Let's say I have a rectangular prism oriented such that, looking down on it, the long side is parallel to the y-axis. Moving forward in a fluid at high velocity (Re > 100000), based on what I've read, the front surface area would experience drag with a coefficient of ~1.28. The drag coefficient on the side is equivalent because they are both rectangles, however, it would experience no drag because there is no relative velocity in that direction. Now assume the rectangle rotates, but it is still moving in the direction of the same face, as if it were a boat for example. See the image below:
I'm thinking of it as a vector, so in the first image it moves vertically some velocity, and horizontally at no velocity. In the second, it moves both vertically and horizontally. The magnitude of the velocities should each be the same; let's say each is moving at the object's terminal velocity.
The drag coefficient MUST change (if expressed as a vector like I'm saying) because if it didn't, the object would never be able to reach it's terminal velocity moving at an angle like in the second picture. Obviously the area increases, so the if the drag coefficient was constant, the drag would increase, so the velocity would decrease. So is there a known drag coefficient for a flat plate at an angle of attack $\theta$? Any help in understanding what's happening here would be greatly appreciated!