Physics of Timing and Spacing www Animation Physics

Physics of Timing and Spacing www. Animation. Physics. com © 2009 Alejandro L. Garcia Creative Commons United States License Attribution-Noncommercial-Share Alike 3. 0

It’s all in the timing… An essential element of animation is the timing and spacing between drawings “It’s not important what goes on each frame of film; it’s the spaces between the frames that are important. “ Norman Mc. Laren Oscar winning animator of Neighbors

Ball Drop Animation Exercise Typically the first animation exercise you do is a falling ball. In this exercise, the drawing couldn’t be simpler. It’s just the same round ball in every drawing. Nevertheless, animating the ball so that it moves realistically can still be a challenge. But the challenge is not in how you draw the ball but where it is drawn on each frame.

Principles of Timing and Spacing The principles of timing and spacing used to create a believable ball drop apply to your other animation work, even character animation such as a jumping cat or effects animation such as a stream of water.

Timing: Frames, Keys, & Clocks We use three different ways of measuring time: • Frames (intervals of 1/24 th of a second) • Keys (given number of frames between poses) • Clocks (actual seconds as measured by a clock) For example, you may “slug out” a scene using a stop watch, then convert that into a number of key poses, which appear as frames on your dope sheet (also called an exposure sheet or X sheet).

Frames between Keys Here are the key poses in a jump with the drawings “shot on threes”, that is, three frames per drawing. #2 #1 #3 Dope Sheet #4 #5 Frame Key 1 #1 2 | 3 | 4 #2 5 | 6 | 7 #3 8 | IMPORTANT: For simplicity, in all our examples the key poses will always have an equal number of frames between each key.

Uniform Motion The simplest type of motion is uniform motion; a heavy ball rolling on a table is a good example. In uniform motion, the velocity is constant so the spacing from frame to frame is constant. Larger the spacing, the faster the ball is moving.

Uniform Motion & Speed The timing and spacing determine the speed. This bowling ball is 12 inches in diameter with two frames per drawing (shooting on twos). What is the speed of the bowling ball? 10 miles per hour 7 inches per frame 20 miles per hour 15 inches per frame 30 miles per hour 22 inches per frame 40 miles per hour 29 inches per frame 50 miles per hour 37 inches per frame 60 miles per hour 44 inches per frame 90 miles per hour 66 inches per frame The ball rolls about 20 inches per drawing so 10 inches per frame so about 15 m. p. h.

Uniform Motion in Perspective Uniform motion may not appear uniform due to distortion of scale when shown in perspective. Vanishing Point Horizon Line Ball rolling from foreground to background yl l a ve u q ti e e pec r a rs s ce n pe n a , i t s Di aced sp

Slowing In (or Easing In) If an object’s motion is not uniform, the object is either speeding up, slowing down, or changing direction. If the speed is decreasing then the spacing between drawings decreases, which in animation is called “slowing in” (or “easing in”). Slowing In A sled slowing by friction is a simple example of slowing in.

Slowing Out (or Easing Out) Slowing Out A ball rolling down an incline is an example of slowing out. Slowing Out If the speed is increasing then the spacing between drawings increases, which in animation is called “slowing out” (or “easing out”). A ball falling downward is another example of slowing out.

Distance Fallen from an Apex Distance fallen from the drawing at the highest point (called the apex) is given by this table. Time (seconds) Frames Distance fallen from apex 1/ 24 1 1/ 1/ 12 2 1 1/3 inches 1/ 8 3 3 inches 1/ 6 4 5 1/3 inches 6 1 foot 8 1 ¾ feet 12 4 feet 16 7 feet ¾ 18 9 feet 1 24 16 feet ¼ 1/ The formula to compute this table is: (Distance in inches) = (Number of Frames) x (1/3 inch) 3 ½ 2/ 3 3 inch

Distance Fallen and Weight The distance that an object falls does not depend on its weight so long as the force of air resistance is minimal. A softball and a bowling ball fall together when released from the same apex.

Home Demo: Catch a Buck Take a one dollar bill and have a friend put their thumb and index fingers near Washington’s head. At random, let go of the dollar. Can your friend react fast enough to catch the money? Half length of dollar bill is 3 inch so it takes about 1/8 of a second (0. 125 seconds) to fall this distance. Typical reaction time is 0. 20 to 0. 25 seconds so most people cannot catch the dollar.

Measuring Reaction Time Distance (inches) 1 2 3 4 5 6 7 8 10 12 14 16 18 Time (sec. ) 0. 07 0. 10 0. 12 0. 14 0. 16 0. 17 0. 19 0. 20 0. 23 0. 25 0. 27 0. 29 0. 30 Release Catch

Slugging and Reaction Time In planning a scene, you may use a stopwatch to time it as acted out in live action (called “slugging” a scene). Your reaction time is about a 1/ second delay so should you 4 subtract that much from your stopwatch reading? No, because there’s a reaction time delay in hitting START but also in hitting STOP.

Planning a Scene (1) You want to animate a softball falling straight down from a height of four feet. Diameter of a baseball is four inches. How many total frames will we need to animate? The table says it takes 12 frames (½ a second) for the ball to fall four feet. So there will be 13 frames, including the first frame, which is the release. ?

Planning a Scene (2) Let’s say we’ll “shoot on twos” and only draw every other frame. With key #1 being the release, how many drawings do you need? Seven drawings for the 13 frames Frame Key 1 #1 2 / 3 #2 4 / 5 #3 6 / 7 #4 8 / 9 #5 10 / 11 #6 12 / 13 #7 ?

Planning a Scene (3) The first key is when the ball is released and the second key is two frames later (since we’re “shooting on twos”). About where will the ball be on the second key? The table tells us that after two frames the ball to falls 1 1/3 inches (a third of its diameter).

The “Odd” Rule For a falling object, the distance between drawings follows a simple pattern, which we’ll call “The Odd Rule” because it uses the odd numbers, 1, 3, 5, 7, etc. Distance between keys increases in the ratios 1: 3: 5: 7: 9… starting from the apex drawing (key #1).

Total Distance & The Odd Rule If you’ve had a physics class then you probably learned the following formula for the distance that an object falls from an apex: (Total Distance) = ½ x g x (Time)2 Total distance from point of release (key #1) increases in the ratios 1: 4: 9: 16: 25: … or 12: 22: 32: 42: 52… The Odd Rule applies to the distance between drawings, not the total distance from the apex.

Rolling Downhill Key #1 is point of release Rolling downhill is also accelerating motion Very similar to falling except distances are smaller and depend on the slope of the incline. But the distances always go as 1: 3: 5: 7: 9: etc.

Class Demo: Galileo’s Ramps Roll wheels down notched, inclined ramps and listen for the clicks. 8 8 8 8 Click-----Click---Click-Click Downhill Start Click--Click--Click—Click--Click 1 3 5 7 9 11 13 15

Planning a Scene (4) We know that key #2 is a third of the ball’s diameter below key #1 (point of release / apex). About where do we draw the ball on key #3? The ball is accelerating (slowing out) so by the Odd Rule the spacing between keys #2 and #3 is three times the distance from #1 to #2. So key #3 is one diameter lower than key #2.

Planning a Scene (5) What if you’re uncertain about that last part. Is there a way to check key #3 using the table? Sure. Key #3 is four frames after release (because we’re shooting on twos). The table says that after 4 frames the ball falls a total of 5 1/3 inches

From the back row… Dude, I’m going to use a ruler and make my ball drop perfect! No! You need to draw free hand since future work relies on that skill.

Odd Rule (Increment Version) Here’s another way of thinking about the Odd Rule: Starting from the apex, the distance between keys increases in the ratios 1: 3: 5: 7: 9… Notice that: 3=1+2 5=3+2 7=5+2 9=7+2 etc. In other words, after the first increment, all the others are longer by the same amount.

Odd Rule Increment Each spacing after the first drawing below the apex is longer by the same increment and this increment is: 2/ 3 inch (if Shooting on Ones) 2 2/3 inches (if Shooting on Twos) 6 inches (if Shooting on Threes) Example: Shooting on twos the spacings increase 2 2/3 inches with each drawing, which is 2/3 of the softball’s diameter.

A Fourth Down at Half Time In time, Key #3 is half way between #1 and #5. In space, Key #3 is a fourth of the way down between #1 and #5. 3 frames per key (close-up) 6 frames per key (medium shot) This rule always applies for any key half-way in time from the point of release.

Planning a Scene (6) All the keys have now been drawn. What’s a simple way to check that the spacing is reasonable? Verify using the “Fourth Down at Half Time” check. Key #4 is the half-time key (half way between #1 and #7). The distance from #4 to #7 should be 3 times that from #1 to #4.

Drawing In-betweens Drawing in-betweens refers to adding extra drawings in frames in between the key pose drawings. To draw in-betweens of accelerating motion, divide the first spacing by FOUR, then keep the same ratios of 1: 3: 5: 7.

Drawing In-betweens (cont. ) Notice that the first in-between drawing is positioned rather close to the apex drawing. The other in-between drawings, although not exactly in the middle, are close to being halfway between the keys.

Falling a la Chai a e d c An approximation to real falling that’s easy to use for pose-to-pose animation b Recipe for “Falling a la Chai”: a) Draw interval from first & last keys. b) Divide interval in half. Mark a key. c) Divide top part in half. Mark a key. d) Divide top part in half. e) Divide top part in half. Mark a key. a Physical Falling a la Chai Prof. Dave Chai Animator Key #4 is a bit too high but who’ll notice?

Up and Down Coming Down Going up For a ball moving upward the timing and spacing as it slows into the apex is the same as when it falls downward and slows out of the apex.

Deceleration by Friction Spacings when decelerating by friction also follow the Odd Rule, slowing into the final key (coming to a stop). #1 #2 #3 #4

Acceleration “Stretch” Objects visually stretch as they gain speed due to motion blur. Objects do not physically stretch as they fall (not even raindrops). Actual Shape Human eye Motion blur does not depend on the object’s material, however, it will look more natural for rigid objects to stretch less than elastic objects.

Bounce “Squash” Most solid objects do not physically squash except under extremely large forces of impact. Though not physically correct, squash is used in animation to indicate impact on a bounce because it avoids a visually jarring halt in the motion.

Falling Speed With this table you can find the speed of an object from the distance it’s fallen. Distance fallen from apex Speed (inches per (miles per frame) hour) 1 foot 4 5 4 feet 8 10 However, this table is accurate only as long as the object’s weight is much larger than the force of air resistance. 9 feet 12 15 16 feet 16 20 25 feet 20 25 36 feet 24 30 49 feet 28 35 100 feet 40 50 400 feet 80 100

Falling Speed Example About how fast is Alice falling? (Shooting on twos). Distance between keys is about two feet; shot on twos that’s 12 inches per frame. Either she’s only fallen from just off -screen (above) or her dress is slowing her fall. Distance fallen from apex Speed (inches per frame) Speed (miles per hour) 1 foot 4 5 4 feet 8 10 9 feet 12 15 16 feet 16 20 25 feet 20 25 36 feet 24 30 49 feet 28 35 100 feet 40 50 400 feet 80 100

Motion Graphs Position In computer animation the timing and spacing of motion is often viewed using motion graphs. Frame Timing and spacing are determined by the motion graph, which can be manipulated in a graph editor.

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

Position Motion Graphs (cont. ) Frame The motion graph for constant acceleration is a parabolic arc.

Falling in Perspective When falling is viewed from directly above the perspective affects the timing and spacing. 1/24 second intervals

Falling in Perspective (cont. ) The Odd Rule is used to find the spacings, which determine the object’s size as it moves away from the viewer.

Advanced Bouncing This lecture covered the essentials of slowing in and out, focusing on the ball drop animation test. Specifically, we considered a ball falling straight up and down, focusing on the timing of a ball slowing out from (or back into) the apex. A more advanced test would have the ball travelling in an arc, possibly in perspective, and have it lose height with each successive bounce. This type of motion (and more) are discussed in the next lecture, Physics of Paths of Action.

Image Credits & Acknowledgements Illustrations not listed below are by Charlene Fleming; photos not listed are by Alejandro Garcia. Cat Jumping, Gail S. , cat-chitchat. pictures-ofcats. org/2008_03_29_archive. html Water Fountain, upload. wikimedia. org/wikipedia/commons/b/bb/Balboa_1_bg_020903. jpg Bowler bowling, commons. wikimedia. org/wiki/Image: Bowlerbowling. JPG Softball vs. Bowling Ball, Rebbaz Royee David Chai, www. houseofchai. net/ Basketball Players, sportscenteraustin. blogs. com/photos/uncategorized/ sports_center_basketball_injuries. jpg Golf ball squash, perfectgolfswingreview. net/TI-impact. jpg Empire State Building, Wallace Gobetz (wallyg), Flickr. Motion Graphs, Corey Tom Bouncing Ball, commons. wikimedia. org/wiki/Image: Bouncing_ball_strobe_edit. jpg Special thanks to Alice Carter, David Chai, John Clapp, Courtney Granner, Lizz Greer, Rex Grignon, Martin Mc. Namara, and the Shrunkenheadman Club at San Jose State. Physics of Animation is a project supported, in part, by the National Science Foundation’s Course, Curriculum, and Laboratory Improvement (CCLI) program