Unveiling a Few Secrets of Nature and Engineering (Part 2 of 2)

Birds flying near branches of trees

This blog is the second part of our previous discussion on the same topic. Here, we explore more examples of geometric shapes in nature.

Trees and Leaves

Different leaf shapes are adaptations to various environments, featuring large surface areas for maximum light absorption, pointed tips to channel water off the leaf, and smaller, narrower shapes to minimize water loss in dry climates. But there’s more to a leaf’s shape, it is also influenced by wind and water loads.

• Trees, their branches, leaves, flowers, and fruits all exhibit cantilevered structures, meaning they are anchored at one end only. This design allows them to bend in response to wind and rain forces. For example, the trunk of a coconut tree bends during a storm, just as branches and leaves flex under external forces. This bending creates a moment proportional to the length of the tree or leaf—longer structures experience greater bending. As a result, significant sheer forces occur at the base, which is why the roots, stems, and branches of trees are thicker at the base and gradually taper towards the tip, where the sheer load decreases to nearly zero.

• Leaf tips typically curve upward toward the sun, helping to channel rainwater. Rainwater exerts force on the leaf’s surface, much like wind. Gravity then directs the water along the central vein toward the ground, preventing damage to the leaf while nourishing the tree’s roots. The veins of the leaf act as cantilevered support, ensuring structural stability. Thus, every leaf functions as a natural gardener, efficiently distributing excess water to the roots.

  
  

Leaves and stems are attached to the tree at a single point. Photo Credit: unsplash.com/Mack

Birds

When a bird takes flight, four key forces come into play: lift, thrust, drag, and gravity. These forces interact to help the bird overcome its weight and achieve flight. The shape of a bird’s wing, known as an airfoil, is crucial for generating lift. As the wing moves through the air, its curved upper surface causes air to travel faster above the wing than below it. This speed difference creates a pressure difference—lower pressure above and higher pressure below—resulting in an upward force called lift, which counteracts gravity.

·      Thrust propels the bird forward, generated as the bird flaps its wings and pushes air downward and backward. According to Newton’s third law of motion, every action has an equal and opposite reaction, meaning the downward force exerted by the wings results in forward motion. Drag, the force resisting movement, comes from air friction and resistance. Once airborne, the bird balances lift and drag against gravity by continuously flapping its wings. When landing, it reduces lift and thrust, allowing gravity to bring it back to the ground.

Flight of birds involves four forces. Photo Credit: Pixabay.com

Today, airplanes undergo rigorous aerodynamic testing in sophisticated wind tunnels, with computational models estimating drag forces across different speeds. However, nature had already perfected these principles—birds and fish possess highly optimized shapes for effortless movement through air and water, long before humans developed aerodynamic tools.

In fact, humans first learned to design airplanes by closely studying birds in flight for centuries!

Did You Know?

·      A cantilever is a long projecting beam or girder fixed at only one end. It is typically used in bridge construction.

·      A sheer force is unaligned force acting on one part of a body in a specific direction, and another part of the body in the opposite direction.

·      When a force acts perpendicular or "normal" to the surface of an object, it exerts a normal stress. When a force acts parallel to the surface of an object, it exerts a sheer stress.

#nature #geometryinnature #birds #trees