Science for Model Flyers
Part V: Evolution and Visual Acuity
Although by no means is it a prerequisite, you may want to read the preceding parts of this series before reading this final instalment. — Ed.
Our bodies are wonderful machines. The story of how they evolved over time is a fascinating one. The drive in nature to breed selectively those random ‘favourable variations’ that improve survival to reproduction age have resulted in very ingenious but sometimes imperfect devices, a good example being our eyes. Jim Smith wrote an excellent article in a the December 1994 edition of the RC Soaring Digest, which I have inset below. Don’t forget that there are great articles in the legacy RC Soaring Digest archive dating back to 1984 (see Resources). But before I get to Jim’s article here is an explanation of how our eyes work.
People with all kinds of disabilities can enjoy our hobby. There is one that rules it out and that is poor eyesight. Fortunately science now enables us to correct or cure many minor faults. If I take on a trainee one of the first things we talk about is vision. It pays therefore to know about the eye. As you will see, even if you have excellent eyesight there are still traps you can fall into.
So far in this series of articles we have talked about reflection and diffraction. For understanding our eyesight we now need a new term, refraction.
Refraction
In a vacuum light always travels at about 300 million metres per second (m/s). In other transparent media such as air, plastic, diamond, water and glass it goes more slowly depending on density. Its frequency can’t change or else its colour would. The only thing in the equation c = f λ that can change is the last term lambda λ, which as you now know is wavelength. So when light slows down its wavelength drops, called refraction.
Why does refraction matter to us as flyers? Because it is how we see our models clearly and how we take sharp pictures and videos of them.
A new type of diagram was devised by Christiaan Huygens in 1678. He drew lines representing the peaks of a series of waves that he called wavefronts. You might have watched similar waves in a ripple tank in a science lesson at school. Wavefront diagrams allow us to see waves in two dimensions.
In Picture 1 you see the wavefront peaks hitting the surface at an angle between the air (above) and glass (below). They slow down and simple geometry shows us that the reduction in wavelength gaps between the peaks from A to B causes the waves to change direction. The greater the angle at which the incident rays hit the surface the greater the change in angle.
Refraction is how lenses work and diamonds sparkle. It is also why a prism produces a spectrum of colours, as different colours with different wavelengths change angles differently. Incidentally take a look at the the sleeve of the Pink Floyd album Dark Side of the Moon. One day, out of the blue my boss asked me to stay after work to help a photographer take a picture of optics in my lab. Turned out that’s what it was for.
Let us look at the shape of a lens in Picture 2. As you see, a parallel beam of light hits a curved lens surface at different angles in different places. At the lens centre it does not change direction at all. At the extreme position it has maximum deflection — the line labelled normal is at right angles to the surface at that point. The curved surface will cause the straight wavefronts to become curved. A parallel beam will come to a single point called a focus if the surfaces are curved accurately. Faults in a lens’ curvature are called spherical aberration. The ability of a lens to change the direction of light is called its optical power, usually measured in dioptres. You take the dioptre number, say four, and divide one metre by it. That gives the distance from the lens centre to the point at which the lens can focus a parallel beam of light. In the case the focal point will be 250mm away.
As I mentioned above different densities of media cause differing deflections. That is why equally powerful lenses will have differing thicknesses depending on the the type of plastic or glass they are made from. And of course the best, ‘high refractive index’ ones cost a lot more don’t they? When I lived in London I used to visit the Design Centre to see the latest clever designs. They were expensive. I wondered then why good looking objects had to cost more. After all they were all mass produced using similar techniques and materials. So naive!
Christiaan Huygens (1629–1695)
Huygens was born on 14 April 1629 in The Hague in the Netherlands, into a rich and influential Dutch family. Christiaan was educated at home until the age of sixteen, and from a young age liked to play with miniatures of mills and other machines. From his father Constantijn he received a liberal education including languages, music, history, geography, logic and rhetoric, alongside dancing, fencing, and horse riding. He corresponded with intellectuals across Europe; his friends included Galileo and Descartes.
He was a mathematician, physicist, engineer, astronomer and inventor, and regarded as one of the most important figures in the scientific revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, a breakthrough in timekeeping, remaining the most accurate timekeeper for almost 300 years. An exceptionally talented mathematician and physicist, he was amongst the first to use mathematical methods to explain phenomena. As a result, he has been called the first theoretical physicist.
Huygens is especially remembered in optics for his wave theory of light, which he first communicated in 1678 to the Académie des Sciences in Paris. Huygens’ theory was published in 1690 under the title Treatise on Light. It posits light as radiating wavefronts, at right angles to the actual light rays. Propagation of the wavefronts is then explained as the result of spherical waves being emitted at every point along the wave front (known today as the Huygens–Fresnel principle). This was the basis for the advancement of physical optics, explaining all aspects of light propagation until Maxwell’s electromagnetic theory that resulted in quantum mechanics and the discovery of the photon.
Two Other New Words Are Object and Image
In Picture 3 we see three ‘rays’ of light going from the top of the object being viewed through various parts of the lens. This changes their directions and brings them together to form an image that might be different in size depending on the ‘power’ of the lens. This image might be on the retina or the sensor in a camera. Notice the light from each part of the object goes through every part of the lens. As you cover part of the lens it just reduces the brightness not the image size or sharpness.
Total Internal Reflection
This is important to you for two reasons. First it explains how you receive this magazine, through fibre optics, all or part of the way from the data centre. Secondly it can cause strange optical effects when there are warm and cold air layers that might conceal a model or make it appear to be in the wrong place, and it can cause mirages.
In Picture 4 you see three different situations. In the one on the left light is leaving glass or plastic into air at a small angle to the right angle normal line. If the angle increases the refracted ray’s angle does too. Eventually, as in the middle case, the light moves along the interface and does not leave the heavier medium at all. Angle C is called the critical angle and depends on density and other things. Increase the angle further as shown on the right and the light reflects back at the same angle as it hits. This is called total internal reflection. The value for C is around 45° for most materials but for diamond it is 24°. This means that light will bounce around inside a diamond a great deal before it is able to leave it at less than 24°. That is why a diamond sparkles and why the angles at which the many faces are cut are important.
Fibre Optic Cable
In Picture 5 you see light being internally reflected along a transparent fibre. The fourth reflection is at quite a steep angle but not quite enough for the light to break out of the cable. Fibre cables should not given very sharp bends.
Faults and Their Correction
What faults do we flyers and trainers have to watch out for? Some can be fixed but not all. Here are the fixable faults:
- Lenses become stiffened with age and don’t change shape so well, causing blurring that needs corrective glasses.
- The muscles that stretch the lens become weaker, also needing corrective glasses, though some say exercise can help.
- Have you noticed how a long day looking into the distance when flying can counteract the effect of aching eyes due to lots of close work?
- Lenses can become cloudy, also called cataract, which is usually due to exposure to ultraviolet from the sun. Always get your glasses and sunglasses treated with a UV coating. The operation for cataract is almost miraculous according to friends I know who have had it. The lens is then fixed in shape so you have to choose between needing glasses for reading or for distant vision.
- Laser treatment is available to reshape the eye lens permanently to correct faults.
These two faults are currently not easily curable:
- The high resolution part around the fovea called the macular, degenerates.
- The retina becomes detached and blindness results. There have been attempts to refix it with a laser.
For a modest fee (£10 in the UK) opticians (optometrists) will now do a 3D scan of your eyes to check for problems with the macula, which is the high resolution part around the fovea, and with the retina in general. I was amazed at how useful and clear it was when I had the first one a few months ago.
Our Eyes
Picture 6 illustrates how light is focussed by the lens onto the sensitive layer at the back of the eye called the retina.
The iris surrounding the pupil opens and closes to let varying amounts of light in. When the surroundings are bright it is small and uses only the almost parallel-sided centre of the lens. This gives the fewest distortions so gives the sharpest image and focusses on the greatest range of distances. It’s one reason why squinting can sometimes sharpen your sight. It’s a sort of second iris. If you use a proper single lens reflex camera you will know that focus and depth of focus become better at smaller iris settings, such as f/16. It’s a good way to blur backgrounds too. Use a small f-setting, for example f/2.8 that produces a large iris, and a short exposure. Phone cameras are great but you still can’t beat a large diameter lens SLR for flexibility.
The eye lens is made thicker or thinner by the ciliary muscles to focus distant or close objects sharply on the retina. As mentioned above, lenses stiffen and muscles weaken with age so you might need glasses (spectacles) to help. Picture 7 of a cross-section of the retina shows us that it contains cells that detect brightness and colour. The small, brightness ones called rods are more tightly packed and give better resolution while the three types of colour cells called cones are less sensitive to light and are larger. The three detect red, green or blue light. Their low sensitivity is why in low light you only see grey through the rods. You must bear in mind that your vision will be poorer in low light levels. If we didn’t have colour vision our eyesight would be very much sharper.
Picture 7 of the retina also shows you what I meant above about bits of our bodies being rarely perfect. The ability to see is a key to survival and reproduction so it evolved vigorously, though not always optimally. Our eyes work well but one part is poor. The light has to go through two layers of retinal tissue before it reaches the rods and cones, so loses energy. The evolution of different types of sight in various animals is a fascinating story. Wallace and Darwin didn’t tackle vision, being forced by lack of technology to study larger scale evidence. My favourite Darwin joke is a spoof quote of his, “Finches? Seen one seen ’em all.” To find out why it is funny read the next verbal thumbnail and the Wikipedia link in Resources. Even some plants are sensitive to light and turn to follow the sun or close up at dusk. It is after all why the Spanish for sunflower is girasol — sun turner.
Charles Darwin (1809–1882)
Darwin came from a wealthy and religious family and had the illustrious grandfathers Erasmus Darwin and Josiah Wedgwood. His intelligence and curiosity led him to become a natural scientist. Key to that was joining a round-the-world voyage of exploration on the Beagle starting in 1831. Evidence piled up in the form of geology, fossils and living specimens, with the key work being in the Pacific Galapagos Islands. Here he studied how related species changed to adapt to the environment on the different islands, particularly finches, hence the joke. He was very slow to publish his findings, partly due to the fact that they clashed with his religious ideas. He anticipated a backlash from the churches and got it. Contact with Wallace convinced him of the need to publish and their relationship was remarkably amicable and co-operative, unlike some bitter scientific disputes over priority. His book, On The Origin Of Species published in 1859, gave the central role to what he called natural selection.
Alfred Russell Wallace (1823–1913)
Wallace was born in Wales in a large but gradually less well-off family. They claimed the Scots revolutionary William Wallace as a predecessor. He conceived the notion of evolution through natural selection independently of, and in parallel with, Darwin. He was also a social reform campaigner, particularly against the malign effect of the rich and powerful on working people. Like Darwin he was a traveller and collector. Unlike Darwin he was keen to publish. His book The Malay Archipelago (1869) was widely acclaimed and earned him much needed money.
Don’t get me wrong. Despite its faults, the human body is an amazing thing. After all it took over four thousand million years to get to it. As Mike Skinner wrote in 2008 in his song On the Edge of a Cliff for his group The Streets:
For billions of years since the outset of time
Every single one of your ancestors survived
Every single person on your mum and dad’s side
Successfully looked after and passed onto you life
What are the chances of that, like?
That sums it all up, or should I say ‘raps’ it up? I imagine it will be available on streaming sites. We need to bear in mind the limitations of our sight when flying. By the way, Mike’s hero was not on the cliff to do some soaring.
▶️ Experiment
Here is an experiment that you can try. Note from Picture 6 that the eye has a blind spot where the optic nerve goes through the retina. Get a piece of paper and write a 10mm high letter L on the right and a similar R on the left about 100mm away. Close your right eye and look at the L. Move your head backward and forward about 300mm away and at the correct distance the R will disappear. Do the same for the left eye looking at R this time. Normally one eye fills in the blind spot from the other. The lesson is don’t close one eye when trying to spot your model, and of course it could cause a problem for someone with only one working eye.
There is a further complication. Science has now discovered that our brains don’t create pictures based only on the signals from our eyes. The image processing involved is so onerous that, to save effort and time, our brains make up parts of the picture based on assumptions and past experience. That’s why few people see the gorilla in the background of the classic video The Invisible Gorilla (see Resources) that tests our perception and why we quite often miss things or see them differently from reality. So as well as Jim Smith’s very sound ideas (below) we have to add that as a further warning. Remember that you now know that the gorilla will be there ‘cos I told you so. But you could try it on someone else who hasn’t seen it before.
20/20? or Where Did That Airplane Go?
Jim Smith’s article as it originally appeared in the legacy RC Soaring Digest. A link to a clean, easy-to-read version of this article is linked in Resources, below.
It’s not just me then. The above shows why, if you take your eyes off a completely visible model, you can’t pick it up again when you look back. So bring your model close before you look around.
Afterthought
The British Broadcasting Corporation is very good over its coverage of science. On the BBC World Service there are three excellent programmes: Science In Action, Crowd Science and The Science Hour. All are available anywhere in the world as podcasts unless of course your government blocks such things. Crowd Science invites people to send in questions and then spends time investigating and reporting. It could be you.
Thanks for reading!
©2023 Peter Scott
Resources
- On The Shoulders of Giants — The Wikipedia links for those historical figures mentioned in this article and on which the short, italicised bios are based: Christiaan Huygens, Charles Darwin and Alfred Russell Wallace
- 20/20? or Where Did That Airplane Go? — A link to an OCR’d, cleaned up version of this great article by Jim Smith, provided in PDF format.
- The RC Soaring Digest Legacy Index — A link to PDFs of every issue of the legacy RC Soaring Digest from January of 1984 through December of 2018.
- Popular Science on the BBC — Here’s where you can find the shows mentioned in the article: Science In Action, Crowd Science and The Science Hour.
- On the Edge of a Cliff by The Streets on Apple Music.
- The Invisible Gorilla — “At some point, a gorilla strolls into the middle of the action, faces the camera and thumps its chest, and then leaves, spending nine seconds on screen. Would you see the gorilla?”
Erratum: In my previous article Part IV: Aerials I made a mistake over the first picture that I am sure you noticed. I replaced the original with one that showed one and half waves rather than the two in the text but didn’t change the words. Well spotted all of you. — PS
All images are by the author unless otherwise credited. Read the next article in this issue, return to the previous article in this issue or go to the table of contents. A PDF version of this article, or the entire issue, is available upon request.
