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You will wonder why and how an animator cares about physics? But the truth is as a character animator a basic understanding of mechanics and bio-mechanics is helpful. In Chuck Amuck, Chuck Jones writes, “Comparative anatomy is a vital tool of the complete animator or director.”
The purpose of this article “6 Principles of Physics for Amazing Animation” is to make physics another tool in your animator’s toolbox. The focus of this article is character animation, though many of the concepts are also useful for character effects, such as hair and clothing.
Apart from the “12 Principles of Animation” as described by Ollie Johnston and Frank Thomas, physics plays an important role in depicting the overall behaviour of characters in animation. For example, the animation principle of follow-through is based on the Law of Inertia.
More specifically, the following are the 6 principles of animation physics:
1. Timing, Spacing, and Scale
The first concept that animators practice is usually the bouncing ball. This concept is about how to adjust the timing and spacing so that it slows into and out of the apex in a believable way.
Timing and spacing indicate speed and when spacings change there’s acceleration. Because the acceleration of gravity is constant the ball’s spacings follow a simple pattern. Such a pattern follows the “Odd Rule” because the spacings from the apex go like 1, 3, 5, 7, 9, and so on. The process of Slowing-Out and Slowing-In also follows the Off Rule. Mathematically, the Odd Rule is expressed as x = 1/2 at2.
2. Law of Inertia
The Law of Inertia, also known as Newton’s First Law of Motion, says that a character will move with constant velocity unless acted on by an external force.
Let’s understand this by an example of a character standing on a bus (as shown in the figure). When the bus suddenly stops the character goes flying forward. Before the bus hit the brakes he was moving and by the Law of Inertia, he’ll continue moving until a force acts to stop him (such as when he hits the floor).
Now, let’s see the second aspect of the Law of Inertia is that a character at rest will remain at rest until acted on by an external force. If the bus suddenly accelerates forward then our standing character falls on his back (as shown in the figure). A stationary observer standing outside the bus would realize as if there’s a force pulling everything backward but that’s because we’re moving with the bus.
The same law explains this process also – as the characters turn their bodies their hair and clothing drag behind due to the Law of Inertia.
3. Momentum and Force
Any moving character has momentum, which depends on the character’s speed and its weight. A character that weighs 10 kg can have as much momentum as a 30 kg character if the small character runs three times faster than the big guy. Momentum also depends on the direction of the motion so deflecting a moving object is considered a change of momentum.
To change a character’s momentum you need an external force; the bigger the force, the quicker the momentum changes. This change in momentum could be slowing or increasing a character’s speed or it could be a change in direction (such as making a turn). In physics, this is known as Newton’s Second Law of Motion.
The figure shows two examples of a ball hitting the ground. The momentum change could be about the same in the two cases but in the real impact that change occurs quickly, implying a large force at impact. Using “squash and stretch” the cartoony version softens the impact by having the change in momentum spread over a few frames. In brief, crisp timing means large forces and vice versa.
4. Centre of Gravity
The centre of gravity is the average location of an object’s weight. This is the geometric (visual) center for most objects but for non-uniform objects (e.g., a hammer with a wooden handle and an iron head) it’s located closer to the heavier side. A person’s center of gravity is roughly located in the center of the torso, at about the height of the belly button, but it can shift depending on the pose.
The centre of gravity is important for various reasons. First, a character is in a balanced stationary pose only if the centre of gravity is positioned over the character’s feet. More precisely, the centre of gravity has to be over the “base of support”, which is the area around the feet
Second, when a character changes pose the centre of gravity shifts, causing a weight shift from one leg to another. Simply shifting the centre of gravity by a few inches is enough to cause a significant weight shift. Weight shifts from foot to the foot are reflected in the pose, typically raising the hip and lowering the shoulder on the weight-bearing side (an effect known as “contrapposto”). When animated well it should be clear whether a character is standing or sitting even if the shot only shows the character’s upper body.
Finally, when we consider the path of action of a moving character the point that we’re most interested in tracking is the center of gravity. For example, when flying through the air it is the center of gravity that follows a parabolic arc, independent of any rotation in the body or twisting of the limbs (as shown in the figure).
5. Weight Gain and Loss
Under normal circumstances character’s weight remains constant but when the character accelerates its weight effectively varies. For example, if the character is:
- Moving upward and gaining speed: Gain weight
- Moving upward and losing speed: Lose weight
- Moving downward and gaining speed: Lose weight
- Moving downward and losing speed: Gain weight
In brief, if you’re going against gravity (rising but speeding up or falling but slowing down) then you gain weight but if you’re going with gravity (rising & slowing down or falling & speeding up) then you lose weight. An extreme case is when a character is in free-fall and becomes weightless.
As a character moves (walks, runs, jumps, etc.) the changes in weight create many overlapping actions in the movement of hair, clothing, and flesh. Gaining weight pulls these downward while losing weight causes them to almost float.
Poorly animated characters sometimes look “floaty” as they walk because their actions lack this variation in weight.
The principle of action-reaction, also known as Newton’s Third Law, tells us that when a character interacts with an object (or with another character) both are affected. Paul Hewitt poetically describes this as, “You cannot touch without being touched.”
A formal statement of the principle is, For every “action” force there’s an instantaneous “reaction” force that’s equal in magnitude and opposite in direction.
Let’s consider each part of this statement.
First, the action and the reaction are a pair of matched forces. For example, suppose Mr. A punches Mr. B. The action is the force of Mr. A’s fist hitting Mr. B’s face so the reaction is the force of Mr. B’s face pushing back on Mr. A’s fist.
Second, these two forces are instantaneous so if Mr. B punches back that’s not the reaction, that’s a new action.
Furthermore, if Mr. A punches with 100 Newtons of force towards the left then there’s an equal force of 100 Newtons on his fist towards the right. Since forces change momentum the action force causes Mr. B’s head to start moving towards the left while the reaction force changes the momentum of Mr. A’s fist, possibly bringing it to a stop.
To animate this scene successfully it’s essential to match the action and reaction. A common mistake is to focus on animating Mr. B’s motion while neglecting the reaction that must simultaneously be occurring on Mr. A.
Judging the effect of action-reaction is complicated by the fact that there are usually several action forces to be considered.
Take the simple case of a man pushing a rock. The man exerts a force on the rock so the rock exerts a force back on him. If he was on roller skates he’d move backward and the rock would move forward. But he’s barefoot so there’s another set of action-reaction forces: he also pushes back on the ground and the ground pushes him forward. For him to push the rock forward the force exerted by his legs cannot be less than the force exerted by his arms. These actions and reactions have to appear to match to animate this scene believably.