tutorial-1 : bouncing ball

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NOTE: I wrote this tutorial in 2000, and intended it for students learning traditional, hand-drawn animation. Nevertheless, the principles can be adapted to Flash or 3D animation. The main tutorial page is here (there’s a walk cycle tuturial, and I’ll be adding Flash lessons soon).

This exercise will teach you the most important priciples of animation, namely:



Squash and Stretch.


This is the first lesson taught to any animation student. It may seem boring, but by following it you will grasp most of the principals used in animation. Study the bouncing ball scene above: Look at it again with all the frames superimposed.

Now some of the techniques used become easier to see.

1. Arcs. The ball falls in an elliptical arc through space. Most things move in an arc of some kind. If the ball were to move in a straight line between the high and low points of the bounce, then the action would look very unnatural.

2. Timing. (or Spacing). As the ball falls it is accelerated by gravity, the gap between each frame growing all the time until the ball contacts the ground. As the ball bounces from the ground the opposite happens: as the ball hops up it moves very fast at first, then slows down by gravity into the high piont of its bounce. Note that at the high point of the bounce the ball is weightless…perfectly balanced between the force of gravity pulling it down, and its own momentum moving it forward.

3. Squash and Stretch. As the ball falls it stretches. When it impacts the ground it squashes. When it bounces off the ground it stretches again. Note how quickly the ball regains its circular shape. Too much squash and stretch can make an object look “mushy”.

4. Volume. The ball should remain the same mass as it squashes and stretches. If the ball were to squash too much it would seem to be growing physically bigger. This is very eye catching, and looks weird.

How to animate the ball. The process of animating the ball is straightforward. On a single sheet of paper, draw the arc path that the ball will follow.

figure 2: bouncing ball arcs

On this drawing, tick off the position of each ball on the arc path with an X. Be sure to number them. In feature and tv animation, frames are usually numbered 1,3,5,7,9 and so on. To simplify things here, let’s number them 1,2,3,4, etc. For an explanation of why odd numbers are used in animation, see the appendix at the bottom of the page. It’s really boring, and should be a really nice cure for insomnia.

figure 3: arcs with frame numbers

If you have a backlight, then switch it on. Put a clean sheet over the arc path drawing. Now you are ready to begin drawing the “Key” drawings of the animation: the points where the ball is at its most extreme. In this example, its highest and lowest points in the bounce.As you can see, frame 1 is the first and highest point in the sequence. It is therefore an extreme drawing. Frame 7 is the squash drawing where the ball hits the ground. It is also an extreme, as are drawings 12,17,21,25,28 and 31.

figure 4: arcs and extreme ball positions

On seperate sheets of paper, you should draw the different key frames as named above. If done correctly you should have a series of drawing numbered 1,7,12,17,21,25,28 and 31.Be sure that you write the frame numbers on the top right and bottom right of each drawing. If your drawing is a key frame (as these are) then put a circle around the number.

figure 5: drawing 1

Place them on the peg bar with the lower numbers on the bottom and the higher numbers on the top. Now you are ready to “roll” the drawings.

How to Roll the drawings:A lot of people working in animation seem to forget how tricky this is. It is a fairly easy skill, it just takes a little practice. Do it slowly at first, as you progress you’ll begin to do it instinctively. There are people working in the industry who aren’t smart enough to chew gum and fart at the same time, and they can do it. So don’t worry. It takes a little time, but you’ll get the hang of it.

rolling paper

Back to the ball: Now you must add the inbetween frames. These are the drawings that go between the keys in order to make the action look smooth. It’s common for these to be called “tweens”, thanks to digital animation programs – but traditional animators call them “inbetweens” (the correct term).

All frames are equal, but some frames are more equal than others. You must determine which is the most important frame to draw next. Which has the most important action?

figure 6: main stretch drawing

In this case, the most important is frame 6. It is the most stretched frame in the falling sequence. Therefore I would consider this almost as much a key frame as 1 and 7. If you have a backlight, switch it on. Put the arc path drawing on the pegs first. Then put down 1. Put down 7. Then put down a blank sheet. You should see something like this:

figure 7: first two keyframes

Now you are going to draw frame 6. Begin to sketch in the stretched ball. When stretching the ball, keep the volume consistent. The overall mass of the ball must be the same. Position it around the x drawn on the arc path. When you have finished, you will have to flip the paper to see if it moves right:

How to flip the drawings:

Flipping is similar to rolling, but whereas with rolling you move through the pages sequentially, here you move from the bottom drawing, to the top one, then to the middle one. “WHY?” you ask….because this way you can see the inbetween in motion and make subtle corrections as you work. Incredible as it seems, this method is far more accurate than a lighttable.

flipping paper

Watch the paper closely. Notice that both index and middle fingers are wedged between the top two layers. You begin flipping by holding up both top sheets of paper towards you. You are now looking at the lowest frame, frame 1. Then you drop the two sheets down to the board, revealing the topmost drawing, i.e. the inbetween frame. Then you lift up the top drawing to reveal the one in the middle, i.e the final keyframe. It takes time to get the hang of this. It will be well worth the effort if you do.

Now you will need to add the remaining inbetween drawings between 1 and 5. The easiestway to do this is with a timing chart. Lets look at what we’ve got so far:

figure 8: the spacing of the first 7 drawings

You could “eyeball” all the remaining frames, but the surest way to do them is by writing a timing chart. It will look something like this:

figure 9: the timing chart

The timing chart will go on frame 1, beneath the frame number on the top right of the drawing. This chart tells you that the next most important drawing is 5. That’s why it’s underlined. Note how the spacing on the timing chart relates to the spacing on the arc path above. The chart can determine the position of all the inbetween frames, and also their weight, mass, speed, etc.

Now you have keyframe 1 with a timing chart, and keyframe 6. Simply follow the chart, place the arc path on your drawing board, then 1, Then 6, and proceed to follow the timing chart. Draw 5.

figure 10: keep the ball shapes solid

Note: see how quickly the ball regained its shape…if you were to inbetween the shape as well as the position of the ball then the ball would feel very mushy…by drawing 5 as circular, the scene will be much snappier. Repeat inbetweening until the first arc of the bounce is complete. Repeat the process for all frames of the scene.

I have included all the original frames for this scene as digital files. They should print out onto regular A4 printer paper. You can print them out and peg them up onto strips of punched paper, allowing you to roll through the scene. You line them up with the crosshairs on the corners of the page. Simply paste up frame 1 as you like it, then put it on your drawing board. Then put down a strip of punched paper, and position frame 2 with its crosshairs lined up with frame 1.

IMPORTANT: all frames should be positioned against frame 1, otherwise the scene will “drift”.

drawing board

You can find the files here: Bouncing ball image files . You’ll need winrar to decompress them (most zip programs should work on them).

Appendix: Numbering drawings.

Most animation is still produced for film and tv. Film is projected at 24 frames per second (fps). Early cartoons were all drawn with 24 drawings for every second of film, i.e. onedrawing for every frame of film. Some clever chap finally realised that the animation looked just as good if only 12 drawings were drawn per second of film. Each drawing would be shot twice, to keep the overall timing the same. Nobody noticed the difference, and a lot of carpal tunnel doctors went out of business.

This discovery can be attributed entirely to prohibition. Animators of the twenties were notorious alcoholics. Not these days, glad to say. Today’s breed are wholesome family men, loyal to their wives, good fathers, upstanding members of society, clean living wackos.

The practice of animating 12 fps is called animating “on twos”, and the practice of animating 24 fps is called animating “on ones”. It was still occasionally necessary to animate scenes on ones if a fast action was required, or if the camera panned over the background, i.e. move from left to right to follow a character across the screen. Such shots would look jerky if shot on twos.

When working on twos the animators usually number their frames with odd numbers. 1,3,5 and so on. Frame one is shot twice, frame two is shot twice, ad nauseum. If a point in the scene demands a fast action such as a punch or a shake, then the scene can be switched to ones at thatpoint. The numbering can then include the even numbers that will make the action smoother.

If all this sounds like gibberish, don’t worry. It’s not relevant to anything in the next few lessons.

One last comment about timing: Today a lot of animation is made on computers, and can be projected at any frame rate desired. 10 fps looks fine. Most Japanese animation has been animated at 8 fps for years…a method known as animating “on threes”, as each drawing is shot 3 times, producing 8 frames per second.

That’s it for the ball…

Coming soon: Lesson 2: The Walk.

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31 Responses to tutorial-1 : bouncing ball

  1. Tim says:

    You my friend, are a legend. This is helping me out loads for Uni 🙂

  2. Dave Rosenberg says:

    Tim’s right!

  3. Carolina Elias says:

    thanks! I loved your blog

  4. ZYHQ says:


  5. Sagar says:

    Most enlightening! However the animation would be much more “lively” if the 6th frame was placed such that it touched the ground while squashing as said by richard williams.my animation turned out better when i used that “trick”

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  8. Chanelle says:

    Thanks for the animation lesson !!

  9. Pavlina Graikou says:

    Hallo from Thessaloniki,Greece,cross cultural high school

    I am the language/drama teacher in that remote place,

    creating drama/visual stories

    do you think students could make animations using your beautiful work here?we immerced in persian manuscripts and want to share

  10. Pedro Joésio Wilbert says:

    Sou um brasileiro apaixonado por animação. Suas aulas são muito importantes e muito esclarecedoras.

  11. DarthFanta says:

    cheers man, thats really helpful! 😀

  12. Graig says:

    Thanks man, really really helpful. The timing chart is kinda cool too. I’m gonna study on how to use it.

  13. Anna says:

    I’m a complete and utter art newb, and I have been desperately looking around for an article to explain the more technical bits to hand drawn animation, and you are literally the first article of dozens to explain things like numbering and the concept of ‘ones’ and ‘twos’. Thank you so much 😀

  14. Adnan says:

    The bouncing ball, the most crucial exercise on the animation learning journey…
    thank you so much for taking time to (teach and) shear all of this information with us.


  15. beni says:

    izin share ya… sorry im can’t speak english well… 🙂
    but i know what ur teach… i love this lesson…

  16. Céline Oberholzer says:

    I’m teaching myself to animate, and this was incredibly helpful! I love the detailed descriptions and visual aids. Thank you so much.

  17. Taro says:

    Awesome. Now I just have to animate the Great Dane dropping it from his mouth. Excellent tut, thank you 🙂

  18. I have been teaching myself animation, and even though I passed the bouncing ball phase a long time ago, this tutorial was extremely helpful.


  19. CGMaksik says:

    Great thanka for tutorial! Do you have tutorial for overlape?

  20. marty says:

    I am curious . Your sketch of the animation does not fit the forces on a bouncing ball
    I refer to the 1st animiaton in

    The ball’s parabolic motion is shown.
    The ball moves in a parabola, reaches its peak, gravity causes the ball to begin to fall. so far I agree OK .

    Why does the ball stretch? If the ball is super, super flexible, then the acceleration in falling from position_1 would indeed cause the force provided by gravity to distort its shape as shown in position_5; position_6 .

    An actual ball is NOT so very flexible: so the force exerted by its acceleration would NOT show a noticeable distortion.

    Does the example you have shown greatly exaggerates the change of shape for emphasis ?

  21. Quenten Tyler says:

    I really like this, it really helps because right now im using the Pencil 2D software

  22. Mike says:

    Amazing article! Helped me out a ton!

  23. Astrid says:

    Thnx! Ik keep returning to this page, also sending students here.
    Great work

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