Aircraft trajectory prediction

I have an aircraft that is controlled by player and i need to predict it’s position at needed time. It’s not a problem if the plane is just moving straight but most of the time aircraft is maneuring. So i came up with an aproximation that aircraft movement can be described as a helix.

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So i have a point A and linear velocity V_1 that aircraft had at a time of t_1. Point B and linear velocity V_2 that aircraft had at a time of t_2. In that approximation we may assume that |V_1| equals |V_2| so it will be a perfect helix. And i need to find a point C in that aircraft will be at a time of t_3.