In this blog post, we’ll examine the principles of lift and thrust in airplanes, as well as control surfaces and three-axis motion, using the flying sequences of Toothless from the animated film ‘How to Train Your Dragon’.
The DreamWorks animated film ‘How to Train Your Dragon’ depicts the adventures of the Viking Hiccup and the dragon Toothless. In a land where battles between brave Vikings and ferocious dragons are constant, Hiccup and Toothless become inseparable friends through their many adventures. Then one day, Toothless’s tail fin tears, and he can no longer fly as freely as before. Why is it that flying becomes impossible just because a small tail fin is damaged, even though his large wings are perfectly intact?
With its streamlined body, large wings attached to the center, and a tail fin at the end of its body, the dragon Toothless bears a striking resemblance to an airplane. Toothless flies by moving its wings up and down, while airplanes use thrust generated by engines to take to the sky. Additionally, airplanes are made of metals and composite materials, making them quite heavy. The principle that allows such a heavy object to fly lies in lift, and Bernoulli’s principle plays a crucial role in explaining how lift is generated. Bernoulli’s principle describes the relationship between the velocity and pressure of a fluid; under constant conditions, it states that as the fluid’s velocity increases, static pressure decreases, and conversely, as velocity decreases, static pressure increases.
Looking at the cross-section of an airplane wing, a typical wing has different shapes on its upper and lower surfaces, and the airflow and pressure distribution around the wing vary depending on the wing’s angle of attack and the airflow velocity. When an airplane moves at high speed and air strikes the wing, the airflow splits and flows over and under the wing. At this point, the airspeed around the wing changes, and differences in the pressure distribution occur. A common explanation states that the air flowing over the upper surface of the wing moves faster than that on the lower surface, causing the pressure on the upper surface to decrease; the pressure difference between the upper and lower surfaces then generates an upward force on the wing. Lift results from the combined effect of this pressure difference and airflow across the entire wing. However, lift is not simply generated because the air on the upper surface of the wing travels a greater distance; the pressure distribution and airflow around the wing must be considered together. NASA also explains that, rather than simplifying lift to Bernoulli’s principle alone, one must consider the process by which the wing deflects the airflow downward and the resulting reaction force.
The lift generated in this way is the force that counteracts the weight of the aircraft and keeps it aloft. Lift varies depending on the aircraft’s motion and airflow, and is influenced by air density, flight speed, wing area and shape, and the wing’s angle of attack. The basic lift equation can be expressed using the lift coefficient, air density, the square of the flight speed, and the wing area. In particular, as flight speed increases—all other conditions being equal—lift increases in proportion to the square of the speed.
Airplanes move forward using both lift and the thrust generated by their engines. Jet engines expel air rapidly backward, and as a result of this reaction, the airplane moves forward. Thus, flight involves not only lift and thrust but also weight due to gravity and drag caused by air resistance. Ultimately, an airplane flies through the sky by balancing the relationships between lift, thrust, weight, and drag.
However, airplanes do not simply rise and move forward; they perform various maneuvers, such as turning, moving the front of the aircraft up and down, and changing direction from side to side. This is referred to as the three-axis motion of an airplane. The three-axis motion of a typical airplane is categorized as roll, pitch, and yaw. Roll is the movement of the aircraft tilting left or right around its vertical axis; pitch is the movement of the nose moving up or down around the horizontal axis; and yaw is the movement of the nose moving left or right around the vertical axis.
If you look at an airplane’s main wings, you’ll see control surfaces attached to the rear of the wings that can be moved to control the aircraft. Among these, the ailerons—one on each wing—move in opposite directions. The paper airplanes we often folded as children serve as a good example for understanding this principle of rotation. If you fold a paper airplane, trim the tips of both wings slightly, raise one wing and lower the other, and then throw it, you’ll see the paper airplane spin in a circle. Similarly, when one aileron moves up and the other moves down, the lift and drag generated by each wing differ, causing the aircraft to tilt to one side and rotate. In actual aircraft, ailerons control roll movement, and the left and right ailerons move in opposite directions.
Airplanes also have a horizontal stabilizer, which features a control surface called the elevator. Depending on the movement of the elevator, the aerodynamic forces acting on the tail change, causing the nose of the airplane to move up or down. In a typical airplane, when the elevator is lowered, an upward force on the tail increases, causing the nose to dip downward and the airplane to descend. Conversely, when the elevator is raised, the nose tilts upward, allowing the aircraft to climb. In this way, the elevator controls the aircraft’s pitch movement.
Dragon Toothless found himself in a situation similar to an airplane with a broken tail wing. Flapping his wings to rise into the sky was only a temporary solution; with his balance off, his body inevitably tilted to one side, causing him to plummet to the ground almost immediately. At this point, Hiccup, his Viking friend, attaches a handmade wing made of iron and cloth to replace Toothless’s broken wing. Riding on Toothless’s back, Hiccup spreads the artificial wing wide or moves it up and down in sync with the movement of the remaining tail fin, allowing the two to fly perfectly just as they did before. Combining the lift generated by Toothless’s main wings with the force created by his flapping wings, along with Hiccup’s piloting skills, they formed a fantastic duo capable of soaring through the skies. Mechanical and aerospace engineering—which humans, unable to fly, have developed to realize that dream—has evolved through the process of understanding the principles of flight found in nature and applying them to the design of actual machines and aircraft.
