1. Upcoming Deadlines Fifth Homework (Video analysis of Path of Action): Due Friday, September 25 th (New Deadline); 15 points (10 points if late) Sixth Homework (Outline of First Term Paper) Due Wednesday, September 30 th Campus-wide Furlough Day Monday, October 19th (Art/Phys 123 will meet on Wed., Oct. 21 st ) For full schedule, visit course website: ArtPhysics123.pbworks.com

2. Homework Assignment #5 In this assignment you’ll again use Tracker software to analyze the motion of a moving object from video reference. First, shoot some reference of yourself doing a running jump. Position your camera so that you're in frame the entire time that you're in the air. Stage the jump to be in profile. Shoot at least 5 takes, even if they are more or less the same.

3. Homework Assignment #5 Import your video reference into the Tracker software (as in previous homework). Track the center of your waistline or beltline, which is approximately the location of your center of gravity. Marking your position from the time you leave the ground until you’ve landed. After tracking your motion, upload the screen image from Tracker to your blog into a post called "Video analysis of path of action".

4. Homework Assignment #5 Parabolic Path of Action Straight Line Parabolic Curve

5. Homework Assignment #5 Finally, rewind your video to the first frame of your jump and from the "File" menu select "Record -> Quicktime Movie". Hit the play button and allow the clip to play until the end of your jump. Next, in the "Capturing Quicktime MOV" window click "Save As" to save the recording. Check that your saved Quicktime movie has the track showing the path of action then upload both clips (original and with tracking) to the blog post.

6. Homework Assignment #5 Play Original ReferenceTracked Reference This assignment is due by 8am on Friday, September 25 th (This Friday). 15 points

7. Extra Credit Opportunity Exhibition runs through Jan. 10. Give me your ticket receipt for ten points extra credit. Hours: Tuesday – Sunday, 11am - 5pm Admission: $4.00 for students Location: 655 Mission Street San Francisco, California 94105 Near Moscone Convention Center Visit the Cartoon Art Museum in San Francisco to see “Once Upon a Dream: The Art of Sleeping Beauty.”

8. Activating your Clicker * Turn on your clicker. * Enter the number or letter that I give you for joining this class. Hit Enter/Send key. * Clicker should read PHY123SCI2 * Type in your student ID; hit Enter/Send. Clicker is now ready to use. Hit any key to wake the clicker from sleep mode.

9. Paths of Action

10. Path of Action Brick drop exercise illustrates the path of action for falling. Play The path of action is the trajectory or track of a moving object. By Danielle Domurat

11. Line of Action vs. Path of Action The path of action indicates the trajectory for a sequence of drawings in an animation. Individual drawings have a line of action, which indicates the visual flow of action in that single drawing.

12. Secondary Paths of Action The path of action is usually associated with the primary action but we can also consider paths of action for secondary actions, such as the motion of a character’s hand, arm, foot, etc. Primary (Jump) Secondary (Arm swing)

13. Parabolic Arcs Paths of action of the falling brick and of a bouncing ball are parabolic arcs When gravity is the only force, the path of action is a parabolic arc. Water stream

14. Characters in Motion Thomas Eakins Living beings obey the laws of physics, we’re just a little more complex than a bouncing ball. Play By Danielle Domurat

15. Moving & Falling Ball rolling off of a table combines horizontal and vertical motion. Falling starts with key #4, with vertical distances increasing as 1:3:5:7:… Horizontal distances equally spaced as with uniform motion. Arc is the combination of uniform horizontal motion and accelerating vertical motion.

16. Rolling off a Table, Tracked Play Video reference confirms that the horizontal motion stays uniform as the vertical motion slows out.

17. Class Demo: Fall and Fire 1 5 3 1 2 3 4 4 2 3 1 FALL FIRE One ball is released and falls straight down. Other ball is fired horizontally. At all times the balls are at the same height. Hit the ground at the same time.

18. “Shoot the Monkey” Monkey lets go of the branch the moment he hears the gun fire. Rifle is aimed at monkey’s nose. Bullet hits the monkey: A)Above the nose B)On the nose C)Below the nose Play B) The bullet and monkey are always at the same height.

19. 1 2 Falling Brick 5 3 1 3 4 5 6 The path of action for the falling brick is: Uniform motion in the horizontal (constant velocity). Accelerating motion in the vertical (slowing out as in the ball drop). The center of the brick has a smooth and consistent parabolic path of action Play

20. Full Parabolic Arcs Horizontal spacings are uniform. The rising and falling motion are the same. Vertical spacings slow in and out following the “Odd Rule.”

21. Common Errors in Arcs Wrong Right Most common error in arcs is making them straight. This example is exaggerated to make the error obvious.

22. Nacho Libre A scene in Nacho Libre has one of the worst paths of action in cinematic history. Play

23. Common Errors in Arcs (cont.) What’s Wrong? The arc is skewed; apex is closer to the left than right. This error also tends to make both legs of the arc too straight. What’s Wrong? Vertical spacings are uniform. Horizontal spacings are not.

24. Wile E. Coyote’s Path of Action Play In reality, Wile E Coyote would fall straight back down instead of curving in an arc. True or False? “Beep Beep” (1952) In this scene Wile E. Coyote (on rocket skates) is launched straight up the side of a vertical cliff.

25. Wile E. Coyote’s Path of Action (2) Play In reality, he would fall in a downward arc similar to his upward path of action. True or False? “Beep Beep” (1952) Wile E. Coyote travels in a roughly parabolic arc up to the apex, then stops and falls straight downward.

26. Staging Staging is one of the principles of animation. Motion that is usually more interesting when staged to occur in perspective. “Spend half your time planning your scene and the other half animating.” Ollie Johnston Play (by Ken Calvert)

27. Arcs in Perspective Parabolic arcs look different in perspective but the spacings follow all the same rules as for arcs in profile.

28. Half Arc in Perspective VP HL 1 3 Use the “Fourth Down at Half Time” rule to help locate points Falling towards foreground Perspective tends to straighten this arc

29. Half Arc in Perspective VP HL 1 3 Use the “Fourth Down at Half Time” rule to help locate points Falling towards background Perspective tends to increase curvature for this arc

30. Parabolic Arc in Perspective VP HL Ball starts and ends on the ground. Maximum height (ball at midpoint)

31. Parabolic Arc in Perspective (cont.) VP HL 1 3 Add points to the curve by using “Fourth Down at Half Time” rule.

32. Apex in Perspective Apex needs to be above the half- way point between take-off and landing, which is harder to judge with perspective.

33. Apex of a Jump Play Correct Apex

34. Hancock Parabolic arcs seen in perspective are interesting because the timing has texture as the object goes from the foreground to the background. Play But the timing in this scene from Hancock is wrong. Can you tell why?

35. Timing a Scene It’s easy to time a scene with a fall or a jump since we know how to time a straight drop.

36. Time in the Air When air resistance is negligible (which it is for a falling brick or jumping human), the rate at which an object falls due to gravity is given by this table. The distances listed here are the vertical distance fallen; horizontal distance is arbitrary. Time (seconds) FramesDistance fallen from apex 1 / 24 1 1 / 3 inch 1 / 12 21 1 / 3 inches 1/81/8 33 inches 1/61/6 45 1 / 3 inches ¼61 foot 1/31/3 81 ¾ feet ½124 feet 2/32/3 167 feet ¾189 feet 12416 feet 24864 feet

37. Timing Example This jump looks to be about one foot in the air, which takes a total of 12 frames (6 from take- off to apex and 6 from apex to landing). #1 #2 #3 #4 #5 FrameKey 1#1 2/ 3/ 4#2 5/ 6/ 7#3 8/ X X X X X X = Center of Gravity

38. Timing the Jump Frame 78 Frame 82 Frame 87 This jump has about 4 frames from take-off to apex and about 5 frames from apex to landing. This means that the height of the jump, given the time in the air, should be 6-8 inches. How high is this jump? About 12 inches high? More? Less? Given what the height looks to be, would you say the timing is OK? Play

39. Throwing at an Angle With no gravity, a thrown object would follow a straight line. Due to gravity, the object falls beneath this line, just as if released from rest. No Gravity With Gravity 12 Frames 4 feet 16 feet 36 feet 24 Frames 36 Frames

40. Speed (1994) In Speed, a city bus jumps across an unfinished freeway bridge in Los Angeles. Is this jump unrealistic? Play

41. Speed (1994) The bus should be in the air for about one second (although in the movie it’s over seven seconds). Missing section is about two bus lengths, which is 80-90 feet. At 65 m.p.h. you travel about 95 feet per second.

42. Speed (1994) Since the bus is in the air for about a second it drops 16 feet so the angle of the bridge would have to be about 10 degrees for the bus to land correctly on the other side. 90 feet 16 feet Popping a wheelie does not help!

43. Speed (1994) The film makers did not jump a bus over a gap in a bridge. In fact the gap in this bridge is fake; it was painted in digitally. However they forgot to paint out the shadow on the ground.

44. Maximum Range Maximum range is at a launch angle of 45 degrees (when air resistance is negligible). Range Height

45. 45 Ballista The ballista is a stone throwing war machine used in ancient Greece and Rome. The ballista resembles a giant crossbow but each arm is actually a separate torsion spring made of ropes. Typical range in battle was a few hundred yards, just out of range of enemy archers. Rope bundles provide tension Notice 45º angle of tilt

46. Onager (Catapult) The onager (wild donkey), was a torsion engine similar to the ballista but only one arm. Stone thrown from spoon or sling. This catapult was the largest weapon used by the Romans Rope bundles provide tension Stone ejected at 45º angle

47. Trebuchet Siege of Jerusalem The trebuchet was the ultimate mechanical siege engine. Developed in the Far East and brought west in the 10 th century by the Mongol and Muslim armies. European armies adopted the trebuchet during the Crusades of the 12 th century. Counterweight lifted by human powered “hamster wheels”

48. Mangonel The mangonel is a simplified trebuchet using a fixed counter-weight.

49. Releasing the Projectile The release mechanism is designed to throw the rock at a 45 degree angle. 45º Release

50. Kingdom of Heaven (2005) Several full-size trebuchets were built for the film “Kingdom of Heaven.” Many more were inserted into the movie by digital effects. Play

51. Next Lecture Arcs in Animation By Friday of this week: Complete the 5 th homework (Video analysis of Path of Action) Please return the clickers!

52. Coefficient of Restitution Roughly, each bounce is lower by the same fractional amount. 25% Lower

53. Bouncing Range Decreasing distance covered with each bounce since time in the air decreases. 9 frames in the air 8 frames in the air 7 frames in the air

54. Motion Graphs (cont.) The motion graph for uniform motion at a constant speed is a straight line. Position Frame

55. Projectile Motion & Air Resistance Range can be reduced by air resistance and the path of action changes shape. Shape of the arc is changed. Object lands at steeper angle.