Unveiling the Hidden Physics of Stone Skipping: The Art and Science of Skipping Stones

Published in

Modern Physics

6 min readMay 31, 2023

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In this article, we embark on a fascinating journey into the world of stone skipping, where the interplay of various physical forces and principles converge to create the remarkable phenomenon we all enjoy. From the choice of stone to the technique employed, every aspect of stone skipping is governed by the laws of physics, providing a deeper understanding of the art and science behind this timeless activity.

Introduction

When walking along a serene lake or a gently flowing river, one might find themselves irresistibly drawn to the age-old pastime of stone skipping. There is an undeniable thrill in watching a smooth stone gracefully dance across the water’s surface, defying gravity and creating mesmerizing ripples.

But have you ever wondered about the intricate physics behind this seemingly simple act? Does a successful stone skip depend on the rock’s velocity, shape or rotation? Or may be it’s all about the water, since some people say that specific lakes are “better for stone skipping”, like Norwegian lakes?

Join us as we delve into the secrets behind achieving the perfect skip, exploring concepts such as angular momentum, surface tension, and fluid dynamics. Discover how the shape, weight distribution, and velocity of a stone determine its trajectory and the number of skips it can achieve. Uncover the factors that affect the impact angle, including the angle of release, stone spin, and even the water’s surface properties.

So grab a stone, find a peaceful spot by the water’s edge, and prepare to be amazed by the intricate physics of stone skipping.

Basic concepts

Let’s start with defining a physical model. We describe our process as a two-dimensional interaction of the rock with water.

Two primary forces come into play during the stone skipping process: gravity force and lift force. The lift force is closely related to air friction. To illustrate this, consider throwing a piece of paper and a rock of the same size. You’ll notice a significant difference in their trajectories, and this is due to the influence of the air friction. Objects with larger volume, higher velocity, or lower mass experience a greater impact from this force. In the case of stone skipping, the lift force helps propel the stone upwards, leading to a successful skip. But what other factors determine the skip?

Firstly, the angle of release plays a crucial role. For an optimal skip, the stone should be launched at a low angle to the water’s surface. This angle allows the stone to utilize the surface tension of the water to create lift, similar to an airplane wing. By maintaining a shallow angle, the stone can stay in contact with the water for a longer duration, increasing the chances of multiple skips.

Secondly, the spin or rotation of the stone is essential. A clockwise or counterclockwise spin, imparted by the thrower’s hand, creates gyroscopic stability. This stability helps the stone maintain its orientation during the skip, reducing the chances of it flipping over and prematurely losing contact with the water.

The shape and weight distribution of the stone also affect its skipping ability. Flat, smooth stones with a uniform weight distribution tend to perform better. The flat shape increases the stone’s contact area with the water, allowing it to generate more lift. Additionally, a balanced weight distribution helps to maintain stability and minimizes wobbling during the skip.

Finally, properties of the water have an impact too. If water is dense, it makes lift force bigger, and as a result we have a higher probability of successful skip. Also, if water is more smooth and less wavy, it provides less resistance and allows the stone to glide more easily across the water, enabling longer and smoother skips.

An idealized collision model for our stone.

So, let’s make a conclusion. What makes a successful skip?

A flat, weight-balanced rock. If the rock is too light, it makes air friction bigger, and stone will fly for smaller distance and lose its velocity. If the rock is too heavy, the lift force may be not big enough, and stone will drown.
A good throw. The bigger velocity the rock has, the better. Apart from that, you should throw it at around 20-degrees angle. And if you give it a good spin, it’s less likely to flip over and drown.
A nice lake. This factor is the least important, but it still makes a change. Your lake should look for a dense water (for example, when it’s cold, water has a higher density) that has no waves.

Practical use

You may not know this, but the idea of stone skipping is actually used in a lot of technologies! Here are the most interesting ones.

Firstly, the concept of stone skipping has been utilized in the design of an aircraft that “skips” through specific layers of air, much like a stone skips across water. This innovative approach takes inspiration from the principles of stone skipping to create a unique flying mechanism. By carefully selecting layers of air with varying properties and utilizing the lift generated through these transitions, researchers have developed a novel aircraft design that can efficiently navigate through the atmosphere. This concept aims to optimize flight efficiency, reduce fuel consumption, and potentially revolutionize air transportation in the future.

Hypersoar — plane that bounces from air. Source.

Another intriguing technology involves the development of a bomb that exhibits bouncing behavior when it comes into contact with water. Taking inspiration from the principles of stone skipping, this innovative bomb design aims to enhance its effectiveness and minimize collateral damage. By incorporating specialized materials and engineering techniques, the bomb is engineered to skip across the water’s surface upon impact, increasing its chances of reaching its intended target while reducing the risk of prematurely detonating or sinking into the water. This bouncing bomb technology holds promise in various applications, including military operations and underwater demolitions, where precise targeting and minimizing unintended consequences are of utmost importance. Ongoing research and development in this field continue to explore the potential of this unique bouncing bomb concept.

A bouncing bomb. Source. Another source.

Lastly, the concept of stone skipping has found application in spacecraft landing techniques. Traditionally, spacecraft descend in a direct trajectory, subjecting them to high levels of heat and atmospheric friction during re-entry. However, by implementing a stone skipping-inspired approach, spacecraft can utilize the Earth’s atmosphere to “bounce” off it multiple times, gradually reducing their speed and dissipating the heat generated. This method, known as aerobraking, not only increases safety during re-entry, but also conserves valuable fuel by utilizing atmospheric drag to slow down the spacecraft. By incorporating stone skipping principles into spacecraft landing strategies, scientists and engineers aim to enhance mission success, improve landing precision, and advance the exploration of other celestial bodies within our solar system.

Unveiling the Hidden Physics of Stone Skipping: The Art and Science of Skipping Stones

Introduction

Basic concepts

Practical use

Let’s connect!

References

Written by Artem Shelamanov