Is the object angling into the relative wind to maintain a strait path to a given point or is it following a curve as it is deflected by the side force? If the object is maintaining a straight path then an increase in drag will be relative to whatever deflection of the object is needed maintain that path. If the object is following a curve as it's trajectory is deflected by a side force it's drag shouldn't change because the object isn't deflecting from it's path of least resistance. Unfortunately I don't have the math to describe this. I would suggest a chat with your graduate advisor or thesis advisor. That is what they get paid for. Just be sure to cite every source of info when you write the thesis.