System and method for calculating the orientation of a device

A method for determining a diameter of a curved structure over which a vehicle travels comprising the steps of:

• determining geometric data of the vehicle;
• determining an orientation of the vehicle relative to the curved structure;
• and
• measuring an angle of rotation about a hinge joint that is part of the vehicle to determine the diameter of the curved structure.

A system for determining orientation of a vehicle relative to a surface having defined geometric data that represents a curvature of the surface comprising:

• a drivable vehicle including:
• a hinge joint connecting a first part of the vehicle to a second part of the vehicle such that the first and second parts are capable of movement with respect to one another as the vehicle is driven across the surface, the movement of the first and second parts being translated into rotation of the hinge joint;
• a sensor configured to measure an angle of rotation about the hinge joint;
• and
• a processor configured to determine an orientation of the vehicle relative to the surface based on defined vehicle geometric data, the defined geometric data of the surface, and a measured angle of rotation about the hinge joint and wherein the processor is configured to control operation of the vehicle in view of a determined orientation.