I have a radius, R, for an aircraft traveling at velocity, V. If we start at point, (X,Y,Z), what is the position of the point at time, t in terms of coordinates(X1,Y1,Z1)?
For example: The aircraft is at point (0,0,0) and traveling at 250 knots and initiates a turn with a bank angle, phi, of 5 degrees. Assume that the aircraft can instantaneously rotate to the five degree bank. The equation for the turn radius, R where g is the acceleration due to gravity (9.81) is: R=V2gtanϕ
For this example, R = 10.4 nautical miles. Where is the aircraft at t = 2 if the aircraft is traveling at a heading of 90 degrees (straight along the y axis)in three dimensional space
Elaboration of the above question: I would like to elaborate the question a bit more. Suppose an aircraft is moving at a certain fixed altitude above the ground. It follows a path defined by latitude and longitude. Now if we want to define the position of an aircraft at any point in the air, three variable are required for example X for latitude, Y for longitude and Z for the altitude. Suppose an aircraft flies and reach a certain fixed altitude Z, it then follows a route defined by X and Y. Now suppose that at any stage during the flight the aircraft decides to take a turn. As long as Z remains constant to predict any future position of the aircraft during the turn, the answer you gave in " Given a radius and velocity calculate position of an aircraft banking to make a turn " works fine. But if the turn of the aircraft is on a sphere rather than a circle then in the case the new Z position also needs to be calculated. In other words if the aircraft does a maneuvre in such a way that it turns either to the left or right and increases or decreases it's altitude in the same time then a new equation for the Z needs to be found. Assuming knowing the speed and the current three Dimensional position of the aircraft, how can the future position of the aircraft after a known time t can be predicted? Also assume that other aircraft related constant parameters are also known like phi etc