Different Types of Balls: Mass, Elasticity, and Friction

Not all balls are equal. Mass and elasticity affect how high the ball will bounce, and how far it will travel. So does the friction of the surface on which the ball lands. This lesson compares the bouncing of a bocce ball, a tennis ball, and a golf ball.

Even a hard rubber ball won’t bounce, if you drop it onto the dry part of a sandy beach. In this lesson, we assume that the balls are bouncing on a hard, uniform surface such as smooth concrete or a hardwood floor. An uneven surface can cause unexpected motion: That is the subject of the lesson that follows.

The friction of air (air resistance or “drag”) can affect a ball’s motion as well. Usually this is a subtle effect. On the other hand, even a lightweight, highly elastic ball such as a golf ball eventually loses momentum and comes to a stop. So unlike the indefinitely bouncing basketball in the previous lesson, the balls in this lesson bounce for a limited time only, and with decreasing energy.

Bouncing a Bocce Ball

We’ll start with a heavy ball that doesn’t have much bounce to it, at all. Bocce balls weigh from 31 ounces to 42 ounces (900 to 1200 grams): on the average, a bit over 2 pounds (about 1 kilogram).

Here is the graph of a bocce ball dropped onto a hard, smooth floor from a height of just over 25 feet (7.6 meters):

As the graph shows, the ball bounces only twice, and does not have much forward momentum, either.

NoteThis chart, as well as the charts for the tennis and golf balls, is based on real-world values. It was created by videotaping the actual bounce of the ball, and then rotoscoping the height and forward distances.

Open the starting scene:

• On the Quick Access toolbar, click (Open File), navigate to the \scenes\animation\auto_key folder, and open compare_bocce_start.max.
NoteIf a dialog asks whether you want to use the scene’s Gamma And LUT settings, accept the scene Gamma settings, and click OK. If a dialog asks whether to use the scene’s units, accept the scene units, and click OK.

The scene contains a bocce ball and a plane that will act as the floor. It isn't animated yet.

Keyframe the bounces and adjust the keys:

1. Turn on (Auto Key), and then in the Front viewport, move the ball to create the following keyframes:
• Frame 12: Down to floor level, and forward about 20 units.

Don’t sink the ball through the floor as you did with the basketball: Bocce balls are typically metal or wood, so squash and stretch is not an issue in this exercise!

TipAfter you key the first contact with the floor, you can click (Zoom Extents Selected) to get a better view of the ball and its trajectory.
• Frame 19: In the air again, to a height of about 60 units, and forward about 20 units.
• Frame 26: Back to floor level, and forward about another 20 units.
• Frame 28: In the air again, to a height of about 10 units and forward about 10 units.
• Frame 30: Back to the floor, and forward about 10 units.
• Frame 60: At floor level, forward about 100 units. At this point, the ball is just rolling, so you all you need to do is move it to the right along its X-axis.
2. Turn off (Auto Key).

The bounce is now blocked out.

As with the basketball, the keys where the ball strikes the floor are not crisp enough, yet.

3. Right-click the bocce ball, and choose Curve Editor from the quad menu.
TipIf the tracks and curves don’t appear when the Curve Editor opens, pan in the controller window at the left until you see the position tracks, then click and Ctrl+click to highlight them.
4. In the Curve Editor, click the Z Position track to highlight it. Then click and Ctrl+click the three keys where the ball strikes the floor.

The three Z Position floor keys selected

5. On the Curve Editor toolbar, click (Set Tangents To Fast).

The Z Position bounce keys corrected

6. Click to highlight the X Position track. In the curve window, drag a box to select all the keys along the X Position curve, and then click (Set Tangents To Linear).

X Position rolling keys corrected

NoteThe ball is actually rolling as well as bouncing, but because (unlike the basketball) it has a uniform texture, we don’t need to worry about rotating it: In viewports, it would look just the same.

Trajectory of the bocce ball after adjusting the keys

7. Play the animation.

The keys you created give a convincing animation of a heavy, solid ball.

• Save the scene as my_bouncing_bocce_ball_completed.max.

Bouncing a Tennis Ball

As you might expect, a tennis ball bounces more often than a bocce ball, and travels farther while it does so.

A tennis ball is hollow rubber, coated with felt. The standard weight of a tennis ball is 22 ounces (624 grams).

In this section, we won’t make you enter keyframes by hand again. Instead, we demonstrate a shortcut way to model the diminishing energy and magnitute of bounces: This is a technique that you could apply to an out-of-range, repetitious bounce such as you created for the basketball in the previous lessons.

Open the starting scene:

• On the Quick Access toolbar, click (Open File), navigate to the \scenes\animation\auto_key folder, and open compare_tennis_start.max.

The scene contains a tennis ball and a plane that will act as the floor. The ball is animated, but it keeps bouncing back to approximately the same height: the scene doesn’t yet model a normal loss of energy. (As the ball travels, its bounces do grow closer together: The spacing of the keyframes is based on the real-world chart shown above, but the height of the bounces isn’t adjusted, yet.)

Adjust the Z Position curve by using a multiplier curve:

1. In any viewport, select the tennis ball, right-click it, and choose Curve Editor from the quad menu.
TipIf the tracks and curves don’t appear when the Curve Editor opens, pan in the controller window at the left until you see them, then click to highlight the position tracks.
2. In the Curve Editor controller window, click the Z Position track to display this curve in the curve window.

3. From the Curve Editor menu bar, choose Curves Apply - Multiplier Curve.

3ds Max adds a multiplier curve to the Z Position track. It also changes the curve window display so all curves are visible.

4. Click (the plus-sign icon that now appears next to the Z Position entry in the controller window). Then click the Multiplier Curve track to highlight it.

As you can see, the default value of the multiplier curve is completely flat.

5. Ctrl+click the Z Position track so you can see both the Z Position track and its multiplier.

6. Click to highlight the key at the right of the multiplier curve.

This key is close to the final key for the tennis ball itself, but is slightly above it, overlapping.

7. A transform curve is extremely sensitive to changes in the multiplier curve you apply to it. Because of this, adjusting the multiplier by dragging in the curve window is not the best method: You can get wild results. Instead, type in the value.

The Key Stats toolbar is the status bar at the lower left of the Curve Editor. The first field shows the current frame number, and the second field is the key value. In this field, initially set to 1.000, enter –0.01.

Now the multiplier curve “damps” the bounce of the tennis ball, simulating the loss of energy as it travels and strikes the floor.

Are the new values realistic? Comparing the results obtained from the multiplier curve with the chart for an actual tennis ball, it appears that in real life, the tennis ball loses energy, and bounce height, even more quickly than our simulation. If realism is a concern, consider keyframing each bounce, as you did for the bocce ball. But if your main concern is creating a general impression, then the multiplier curve is a useful shortcut.

• Save the scene as my_bouncing_tennis_ball_completed.max.

Comparing the Golf Ball

In this section, you simply compare the path of a bouncing golf ball to the other two balls in this example.

A golf ball typically weighs 1.62 ounces (45 grams), and is made of rubber (or a comparably elastic plastic) wound around a core, then encased in a plastic shell. Its extreme elasticity means that it bounces a lot: So much so, that to animate it requires more than the default 100 frames of a 3ds Max scene.

Open the scene with all three balls:

• On the Quick Access toolbar, click (Open File), navigate to the \scenes\animation\auto_key folder, and open compare_completed.max.

The scene contains the bocce ball, the tennis ball, and the golf ball. They are animated already. All are dropped from the same height at the same time.

Compare the balls and how they bounce:

• Play the animation.

The balls bounce according to their mass and elasticity.

Incidentally, the golf ball hits the floor slightly before the tennis ball, which precedes the bocce ball: So our real-world measurements account for air resistance, as well as mass and elasticity.

Click (Stop) when you are done observing the animation.

You can also play the movie compare.avi to see a rendered version of this animation.