1. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 1 Chapter 2 Coordinate Frames

2. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 2 Reference Frames In guidance and control of aircraft, reference frames used a lot Describe relative position and orientation of objects –Aircraft relative to direction of wind –Camera relative to aircraft –Aircraft relative to inertial frame Some things most easily calculated or described in certain reference frames –Newton’s law –Aircraft attitude –Aerodynamic forces/torques –Accelerometers, rate gyros –GPS –Mission requirements Must know how to transform between different reference frames

3. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 3 Rotation of Reference Frame

4. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 4 Rotation of Reference Frame

5. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 5 Rotation of a Vector

6. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 6 Inertial Frame and Vehicle Frame

7. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 7 Euler Angles Need way to describe attitude of aircraft Common approach: Euler angles Pro: Intuitive Con: Mathematical singularity –Quaternions are alternative for overcoming singularity

8. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 8 Vehicle-1 Frame

9. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 9 Vehicle-2 Frame

10. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 10 Body Frame

11. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 11 Inertial Frame to Body Frame Transformation

12. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 12 Stability Frame Stability frame helps us rigorously define angle of attack and is useful for analyzing stability of aircraft

13. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 13 Wind Frame

14. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 14 Wind Frame (continued) Wind frame helps us rigorously define side-slip angle Side-slip angle is nominally zero for tailed aircraft

15. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 15 ground track Airspeed, Wind Speed, Ground Speed a/c wrt to inertial frame expressed in body frame wind wrt to inertial frame expressed in body frame a/c wrt to surrounding air expressed in body frame

16. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 16 Airspeed, Angle of Attack, Sideslip Angle

17. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 17 Flight path projected onto ground horizontal component of groundspeed vector Course and Flight Path Angles

18. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 18 ground track north Wind Triangle

19. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 19 Wind Triangle

20. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 20 When wind speed and sideslip are zero…

21. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 21 Differentiation of a Vector

22. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 22 2 1 3 4 5 6 7 8 10 9 11 14 13 16 15 12 Project Aircraft

23. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 23 wing_l fuse_l3 fuse_l2 fuse_l1 tailwing_l tail_h fuse_h Project Aircraft

24. Beard & McLain, “Small Unmanned Aircraft,” Princeton University Press, 2012, Chapter 2: Slide 24 fuse_l1 fuse_l2 fuse_l3 tailwing_l wing_l wing_w tailwing_w fuse_w Project Aircraft