In this blog post, we’ll explore the principles behind stable flight and the conditions for a paper airplane to fly well, based on concepts from physics.
Anyone who has tried all kinds of origami since childhood will surely agree with the proposition: “All paper airplanes are equal. But some paper airplanes are more equal than others.” Some paper airplanes fly so well that even the word “amazing” falls short, while others plummet tragically, like Icarus who crashed while flying toward the sun. The competition among children to learn how to fold paper airplanes that fly better often leads to a fierce battle of wits between those peeking over shoulders to steal folding techniques and those desperately trying to keep their methods secret; sometimes, small cliques form around the child who knows how to fold a paper airplane that flies exceptionally well. So, how can we make a “more equal” paper airplane that flies well? Let’s uncover the secret that could make a child a hero among their peers.
Most flying objects have wings. Wings generate lift, the force that keeps an object aloft. Since explanations of how wings create lift are readily available in various sources, let’s focus here on other conditions necessary for flight. Just having wings doesn’t automatically mean an object can fly. A paper airplane with only wings may seem to lift off briefly, but it simply plummets lifelessly like a falling leaf.
On the other hand, even if a standard folded paper airplane doesn’t demonstrate outstanding performance, it at least flies much more like an actual airplane than one made with just wings. If wings are so important for flight, you’d think that the larger the wings, the better it would fly, but in reality, paper airplanes with smaller wings fly much more stably. This fact alone shows that wings are not the only factor determining flight performance.
What causes this difference? If you observe how the two paper airplanes fly, you’ll discover something interesting. The paper airplane with only wings moves forward a little before quickly pitching upward, whereas a standard paper airplane maintains a steady attitude and moves forward without significant wobbling. In other words, how stably a paper airplane maintains its attitude is a key factor in determining its performance. This property is called stability. Let’s examine why stability is important for paper airplanes and the principles behind it, using various everyday objects as examples.
Physicists often use this method when exploring nature. They compare new phenomena to those they already understand well to identify commonalities, thereby gaining a deeper understanding of nature.
When throwing a frisbee or a boomerang, almost no one throws it upright so that it is perpendicular to the direction of flight. This is because they know from experience that throwing it that way results in significant air resistance, causing it to crash immediately. A similar phenomenon occurs with paper airplanes. An unstable paper airplane, no matter how well it is thrown, will quickly pitch up sharply and eventually crash due to strong air resistance, just like a disc thrown upright. In contrast, a stable paper airplane, even if it pitches up slightly, does so at a shallow angle, so it does not encounter significant resistance and continues to move forward. Ultimately, it is important to maintain a stable attitude without pitching up excessively.
In technical terms, this phenomenon is called a “stall.” When a stall occurs, an aircraft cannot generate sufficient lift, greatly increasing the risk of a crash. Generally, stalls are more likely to occur when the flight speed is too slow or the nose is raised excessively. In actual aircraft accidents, the risk associated with stalls can be relatively higher during low-speed flight phases, such as during takeoff and landing.
What is the secret behind the “More Balanced Paper Airplane” maintaining a stable attitude? To understand this principle, let’s first think of a pendulum. A pendulum is a device consisting of a heavy object (a bob) suspended from a string, with the other end fixed so that it can swing freely. As we often see in everyday life, a pendulum swings back and forth around its lowest position. A paper airplane that flies stably maintains its attitude based on a similar principle. In this case, the center of mass corresponds to the pendulum’s axis, and the center of pressure corresponds to the bob. In a pendulum, gravity acts on the bob, causing it to maintain a constant position relative to the axis. In the case of a paper airplane, the force generated by air pressure plays a role similar to gravity, helping the airplane maintain its original attitude.
Here, the term “center” does not simply refer to the middle of an object. In physics, the center denotes a single point that represents the whole. The center of mass is the point that represents the total mass of the object, and the center of pressure is the point that represents the total air pressure acting on the object. Since air pressure is distributed and acts across the entire surface of the object, calculating it directly is very complex. Therefore, using the concept of the center of pressure—which assumes that all pressure acts on a single point—makes analysis much easier.
The reason the center of mass acts as an axis can be found in the law of inertia. The law of inertia states that, unless an external force acts on it, an object tends to maintain its original state of motion. Since the center of mass represents the total mass of the object, it is the point that best reflects the effects of this law. Consequently, if you observe a freely flying object while moving alongside it at the same speed, the object appears to rotate around its center of mass. In other words, for a freely flying object, the center of mass serves as the reference point for rotation.
So why do unstable paper airplanes crash so easily? To put it simply, it is because the location of their center of pressure is not optimal. While the position of the center of pressure can vary depending on the direction and strength of the wind, as well as the object’s shape, it generally tends to be located in the bulging part where the air exerts the most force. The reason a badminton shuttlecock always flies stably with its head leading is that its center of mass is located in the heavy head section, while the feathers spread out widely, placing the center of pressure toward the rear. In a typical paper airplane, the center of mass is located toward the front due to the multiple folds in the nose section, while the center of pressure is located toward the rear because of the relatively wide, spread-out wings. In contrast, a simple paper airplane consisting only of wings has no particularly thick sections or significantly bulging parts, so the center of mass and the center of pressure end up in nearly the same position. This is the key factor that determines the difference in flight performance.
It is easier to understand this reason by observing the process by which an unstable paper airplane crashes. Once it begins flight, even the slightest disturbance in its attitude causes air resistance to start lifting the nose. As the nose rises, air resistance increases further, and as resistance increases, the nose rises even higher. Eventually, the paper airplane reaches an attitude nearly vertical, experiences extremely high air resistance, loses speed, and crashes. During this process, the center of pressure also continues to shift in response to changes in attitude.
Conversely, in a stable paper airplane, if the nose lifts slightly, air resistance works to pull it back down; conversely, if the nose drops too much, air resistance works to lift it back up. As this restoring force repeats, the paper airplane can glide stably without significant changes in attitude.
As we examined paper airplanes in an effort to become role models for children, we confirmed that even something as seemingly trivial as a paper airplane requires the harmonious interplay of various laws of physics to fly properly. While reading this article alone won’t enable you to fold a perfect paper airplane right away, it’s safe to say that you’ve taken the first step toward understanding how to make a paper airplane that flies better. Furthermore, it would not be an exaggeration to say that we’ve thrown our hat into the ring to become role models for children.
Meanwhile, we explored the principles behind paper airplanes through objects completely different from them—such as frisbees, shuttlecocks, and pendulums. It’s fascinating that, although they appear to be entirely different objects at first glance, they can all be explained by the same laws of physics. Physicists strive to discover common principles within such diverse phenomena and explain them through a single theory. I hope this article has provided you with at least a glimpse into the way physicists view nature. Furthermore, if you come to realize that physics is not merely a difficult and complex discipline, but an intriguing field that allows us to discover beautiful principles even in the ordinary phenomena around us, there could be no greater reward.
