Category: Kinetics

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Bullets vs. Water: The Physics of Drag Force in Action

Ever wondered what happens when you shoot a bullet in water?
The deeper the water, the faster the bullet slows down. Water’s higher density causes much more resistance than air, rapidly draining the bullet’s kinetic energy. In just a few meters, the bullet can come to a complete stop!
Why? Water creates a drag force that decelerates the bullet. The formula behind this?
Drag Force (Fₑ) = ½ * Cₔ * ρ * A * v²
Where:
Cₔ​ = Drag coefficient (depends on the bullet shape)
ρ = Water’s density (about 1000 kg/m³)
A = Bullet’s cross-sectional area
v = Bullet’s velocity

As the bullet travels, drag slows it down and uses up its energy quickly. In just a few meters, the bullet is stopped dead in its tracks!

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Perception in Motion: Illusion, Confusion, and Zen Insight

Many perceive the two 3D cross-like shapes as moving significantly, though they remain stationary!

The interplay of color shades (light/dark) on the edges and body of the cross-like wire frames creates the illusion of motion. The alternating shadings simulate “motion blur,” leading some researchers to attribute these illusory movements to delays in luminance processing, producing a signal that deceives the motion system and induces “kinetopsia” (motion perception)..

This brings to mind an anecdote: Two Zen monks debated a flag moved by the wind. One claimed, ‘The flag is moving…’ while the other countered, ‘The wind is moving!’ The monastery’s prior intervened, stating, ‘Not the wind, not the flag; the mind is moving…’

This short anecdote serves to explain that the concept and perception of motion is sometimes ambiguous.

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Autokinetic Illusion

Immerse yourself in the mesmerizing experience as blue droplets seemingly sway gracefully, creating an illusion of gentle motion. The yellow horizontal lines contribute to a wave-like dance, enhancing the visual allure.

“Hold On Tight” by Gianni A. Sarcone, crafted in 1997.

This op art piece embodies a peripheral drift illusion (PDI), wherein a sawtooth luminance grating in the visual periphery induces the illusion of movement.

Fascinatingly, studies by vision researchers reveal that the illusory motion activates brain regions akin to those triggered by actual movement.

Noteworthy accolades include a feature on Google Science Fair (@googlescifair):

Explore and acquire “Hold On Tight” as prints and posters through our online gallery.

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Throwing a Curve

When the plate turns, the umbrella moves through a vertical plane. What shape does the umbrella make in the plane? Surprisingly, it’s a hyperbola (with the umbrella handle included).

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Fibonacci Zoetropes

The Fibonacci Zoetropes are sculptures by John Edmark. The spirals in the sculptures follow the Fibonacci sequence. When filmed at 24 frames per second and spun at 550 revolutions per minute, each frame represents a 137.5 degree rotation, which is equivalent to the Golden Angle.

© John Edmark
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A Neat Geometrical Illusion: The Scintillating Starburst

As you maybe know, I am an expert in optical illusions… So, I would like to show you one of my oldest illusions I created in the 90s. In the picture you may see ghost-like dark radial beams. This illusion is a variant of the Herman’s scintillating grid illusion. I designed this illusion just by turning 45 degrees the Herman grid and then by applying a polar transformation.

Scintillating starbust illusion
From my book “Eye Tricks“, 2001-2007.

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