The Physics of Butterflies

Marilyn Trent (the founder of Rochester Pollinators, left), my wife Shirley (center), and me (right).

While my wife and I like birds and bees, we love the butterflies. We’re both part of a group called Rochester Pollinators, whose mission is 

to provide education and resources to preserve the Monarch butterfly and pollinator population. We believe every citizen can help our local pollinators flourish by reintroducing Michigan native plants into local landscapes, including home gardens, businesses, and municipal landscapes. We aim to reach as many people as we can with this message!

Hooray for butterflies! Not only are they fun to see, but they illustrate a lot of physics. So now, in this last installment of my series on The Physics of Native Gardening, we turn to the physics of butterflies.

Flight

Birds, bees, and butterflies each have their own unique way of flying. Christoffer Johansson and Per Henningsson have analyzed butterfly flight. Below is the abstract of their article (Journal of the Royal Society Interface, Volume 18, Article Number 20200854, 2021).

Butterflies look like no other flying animal, with unusually short, broad and large wings relative to their body size. Previous studies have suggested butterflies use several unsteady aerodynamic mechanisms to boost force production with upstroke wing clap being a prominent feature. When the wings clap together at the end of upstroke the air between the wings is pressed out, creating a jet, pushing the animal in the opposite direction. Although viewed, for the last 50 years, as a crucial mechanism in insect flight, quantitative aerodynamic measurements of the clap in freely flying animals are lacking. Using quantitative flow measurements behind freely flying butterflies during take-off and a mechanical clapper, we provide aerodynamic performance estimates for the wing clap. We show that flexible butterfly wings, forming a cupped shape during the upstroke and clap, thrust the butterfly forwards, while the downstroke is used for weight support. We further show that flexible wings dramatically increase the useful impulse (+22%) and efficiency (+28%) of the clap compared to rigid wings. Combined, our results suggest butterflies evolved a highly effective clap, which provides a mechanistic hypothesis for their unique wing morphology. Furthermore, our findings could aid the design of man-made flapping drones, boosting propulsive performance.

Compound Eye

The Feynman Lectures on Physics, by Richard Feynman.

Butterflies, like most insects, have a compound eye. Richard Feynman, in his famous Lectures on Physics, discusses the visual acuity of these eyes.

A compound eye… is made of a large number of special cells called ommatidia, which are arranged conically on the surface of a sphere (roughly) on the outside of the… head…

How well can such an eye see? The angle subtended by the ommatidia depends on its width on the sphere surface. The closer the ommatidia are packed, the finer the visual acuity. However, light also undergoes diffraction. When the size of the ommatidia is similar to the wavelength of the light, diffraction smears the light out, destroying your resolution. Feynman writes

If we make the [width] too small, then each ommatidium does not look in only one direction, because of diffraction! If we make them too big, each one sees in a definite direction, but there are not enough of them to get a good view of the scene. So [evolution] adjusts the [width] in order to make minimal the total effect of these two.

So the structure of the butterfly’s eye is a trade off between having a lot of small ommatidia and having fewer that are not corrupted by diffraction. I find it interesting how physics often constrains and guides evolution.

Polarization Vision

Feynman also describes another fascinating ability of butterflies and other insects: they can sense polarized light. Recall that light is an electromagnetic wave. The electric field is directed perpendicular to the direction that the wave propagates. But if the wave propagates in the z direction, then there are two possibilities for the direction of the electric field: x or y. These two, or some combination, is what we mean when we talk about the polarization of the light. Feynman writes about bees, but the same thing applies to butterflies.

Another interesting aspect of the vision of the bee is that bees can apparently tell the direction of the sun by looking at a patch of blue sky, without seeing the sun itself. We cannot easily do this. If we look out the window at the sky and see that it is blue, in which direction is the sun? The bee can tell, because the bee is quite sensitive to the polarization of light, and the scattered light of the sky is polarized.

We sometimes get Monarch butterflies visiting our gardens. We plant various types of milkweed specifically to attract them. Monarchs may use polarization to help them migrate from here in Michigan down to Mexico to spend the winter.

Wing Color

From Photon to Neuron, by Philip Nelson.

 The color of butterfly wings is a fascinating example of optics at work. For an explanation, I quote from Philip Nelson’s book From Photon to Neuron: Light, Imaging, Vision.

Some animals display vivid colors, for purposes such as identifying potential mates. Many of these colors involve pigment molecules that selectively absorb light. But some colors, for example, those on certain butterfly wings, beetle wing cases, and bird plumage, have a very different character…

The wings of Morpho butterflies are covered with scales made mainly of a transparent substance (called cuticle)… The scales [contain] a complex structure with alternating layers of cuticle and air…

The color arises from constructive and destructive interference. Reflections off of each layer interfere constructively if the difference in path length is equal to one, two, or more integral number of wavelengths of the light. In that case, the reflected light appears bright. If the difference in path length is a half, or one and a half, etc. wavelengths, the light undergoes destructive interference and appears dark. The wavelength depends on the color of the light, so some colors will be bright and some dark. Moreover, the condition for interference depends on the angle that the light hits the wing, so the color will change with the viewing angle: iridescence.

Unfortunately, I’ve never seen a Morpho butterfly in Michigan. We have mostly monarchs and swallowtails, and a lot of those little cabbage whites. We hope this year we’ll have many more.

Before I end, I want to share with you a beautiful poster of a butterfly garden, painted by Thomas W. Ford. We purchased it at the Four Seasons Nursery in Traverse City, Michigan. Enjoy!

Butterfly Garden, by Thomas W. Ford.

This concludes my four-part series on the physics of native gardening. It’s cold now, but spring is just a few weeks away. I can’t wait to be back at it! 

 Why Native Plants

https://www.youtube.com/watch?v=trJKZDEfvrc&t=25s