How Wings and Sails Work

I recently visited The Australian Museum in Sydney and saw this sign in the bird exhibit.

I had seen it before and complained without a response and it drives me nuts every time I see it. Why? Because it is wrong in almost every aspect of how a bird stays in the air.

Even on Facebook when I railed against this, expert yachtsmen, bird lovers and pilots alike still misunderstand how this all works.

So let us sort this out once and for all.

Square Rig Sails and Spinnakers (Running Downwind)

This is the simplest form of sail from a physics perspective.

The square sails get pushed by the wind.

In physics, F=ma=mdv/dt=d(mv)/dt

In other words, the force (F) generated is equal to the change of momentum (mv) that creates it. The momentum of the air is the mass of the air captured by the sail multiplied by the velocity of the air (relative to the ship).

So, for a square rig running downwind, the fastest you can ever go is the speed of the wind because, when you are travelling the same speed of the wind, the relative velocity of the air to the ship is zero. In reality, the water resistance will slow the ship down making it sail slower than the wind.

Spinnakers (the big bloated sail on the front of a yacht) work the same way.

Now, in fact, a square rig can run with the wind in front (well, off to the side and in front, at least) but to tackle the physics of this we will look at a fore and aft rig.

Fore and Aft Rigs

These are the sails we think of these days and they do not catch the wind at all, which is why they can sail very close to wind i.e. into it and can sail faster than the wind.

Often the explanation for how these work talk about Bernoulli’s Principle, which is valid, just not very intuitive. I prefer to think in terms of the Coanda Effect, which is a different way of thinking about the same thing.

The Coanda Effect describes the phenomena that flowing air likes to stick to the surface it is running along.

So in terms of our fore and aft sail, the wind runs along the leading edge and then tends to bend around with the curve of the sail.

So how does this move the boat?

Remember before that the force generated is due to the change in momentum? Well momentum is what is called a ‘vector quantity’ so as well as an amount, it also has a direction. So, even if moving along the sail does not diminish the speed of the air, via the Coanda Effect, the direction does change and this has an equal and opposite effect on the sail, effectively pulling it.

In this case, the force generated is trickier to calculate because it involves vector maths and trigonometry. For those with an interest in such things, here is a great link.

Laminar flow and turbulent flow often get mentioned in the explanation of how sails work. Again, it is easier to think about this in terms of the Coanda Effect. A laminar flow means the air travels nicely along the sail and pops out the other side, redirected. Turbulent flow happens when the viscosity of the air is insufficient to keep it running along the sail and it goes any which direction. Therefore less air makes it to the end of the sail and we are redirecting less air and generating less force.

In short though, as long as the sail can be set so the wind runs along the edge and make the boat move forward, the limit to the amount of force that can be generated is not limited by the wind’s speed, but by the momentum of the air whose direction we are changing (its mass multiplied by its speed). If we have a big sail which can redirect a lot of air, we get a lot of force. That force then accelerates the ship (Force = ship mass * acceleration) until the force of the water against the hull matches it and we reach our top speed.

A lightweight ship with a square rig running downwind can still only go as fast as the wind. A lightweight ship using a fore and aft sail can literally fly.

Plane and Bird Wings

So which is the mechanism for plane and bird wings? Plane wings are often not curved and can fly upside down. Even birds can fly upside down.

The fact is, planes and birds fly by pushing the air down (flapping in the case of birds and the air hitting the underside of the wing and flaps, redirecting it downwards in the case of planes). Even a gliding bird is flying by pushing air down off the bottom of the wing.

If you doubt this, look at a bat’s wing and try and work out how a nice laminar flow could happen across it.

In terms of our sails, planes and birds work like a square rig running downwind. Only, in this case, the plane’s engine generates the relative movement of the air and the plane, rather than relying on wind. In the case of a bird, as well as pushing down, they are pushing forward for the same effect in a very complex motion (which makes it very hard for us to replicate with machines).

It is true that high performance aircraft make use of a curved wing to optimise the efficiency of the plane, but the lift is primarily pushing the air downwards and having this change of momentum impart a force on the plane, lifting it up, not from the finer details of the curve on the wing.

When you think about it in these terms, extending the flaps to land makes sense (a larger wing, means you can push a greater mass air downwards, changing more momentum and this means you can fly slower and generate the same lift).

It also explains a plane stalling because if the lift generated off the wings and flaps does not counter gravity, the plane will sink like a stone. This is why a pilot will fly into the stall to increase velocity and try and generate the lift to pull out.

Conclusions

Boats are very clever and use a combination of being pushed by the wind and being pulled by the wind, depending on the sail used and the direction they are going. Planes and birds, however, use straight redirection of the air to generate lift.

And THAT is SCIENCE ;)

How to think about dimensions

OK, so I've finally resolved how to understand dimensions (it's only taken me about 15 years ;)). The key is asking "How do I make two points equivalent?".

So if we start with a line (1 dimension), we can define a point on the line by a single number. To make two points appear at the same place, we need to bend the line and make it cross itself (travel through a second dimension).

Similarly, if we have a 2-D plane of co-ordinates, to make two co-ordinates the same we need to bend the plane through a third dimension.

Here is the fun one. Let's say we have a 3-D space of points (x,y,z). To make two points equivalent we now need to bend through a fourth dimension. Generally we refer to this as time but then it is not measuring a distance like the others. What we really need is 'ct', time multiplied by the speed of light. This is equivalent to saying 'time stops when you travel at the speed of light'. In other words, if you want two points in space to be at the same place, travel between them at the speed of light. We could conceive of a 4-D wormhole which carries us from one point to another at the speed fo light.

So let us now say we have a 4-D space (x,y,z,ct) which defines a point in space at a point in time. To travel in time and space (like the TARDIS) and make two points equivalent, we need to fold 4-D space through a fifth dimension. We now need a 5-D wormhole which connects two points in space and time. This is pretty much where our brains stop because of a lack of everyday experience of such things.

The two ultimate inventions of science

While some would say the green revolution or the harnessing of electricity are the greatest achievements of modern science, I look to the inventions which are elegant applications of scientific principles and whose impact has been ubiquitous. Two come to mind:

Polarised Sunglasses

Not only do they filter light, they do it selectively by filtering out only light reflected from flat surfaces. You stare at a body of water. The sun's reflection disappears but the light from the objects under the water comes through loud and clear.

You're staring through your windscreen while driving. The sun's light reflected off the dirt on the screen if filtered out while the light everything else outside comes through.

Not only do they do this but they require no batteries! Let's say we didn't have polarised materials. How many billions would the military send trying to develop such fantastic devices which we can buy for a few bucks from any discount store?

Thermos Flasks (Dewar Flasks)

They keep hot things hot and cold things cold all using the principles of thermodynamics. No CFCs, no greenhouse-generating power, just a chamber surrounded by a vacuum (or at least a chamber with lower pressure). 

How much of modern science owes a thank you to the humble thermos? All those cool experiments you see on tv with liquid nitrogen. How do they store it? In a termos flask. How many picnics and family outings are made so much better by a hot cup of (slightly weird tasting) tea or a cool drink protected from the elements by a thin wall of nothing.

Simple devices, leveraging science and making the world a better place.

Why projectiles are so 19th century

I was so infuriated by a YouTube video:

http://blogs.techrepublic.com.com/geekend/?p=1661

I had to set the record straight.

Don't get me wrong, there is nothing wrong with the guy's physics (for the most part), it's his application of the physics that is lacking.

There are a number of flaws in the arguments presented. 

Firstly, the author posits a high-frequency beam would be superior to a low-frequency beam. While it is true that the energy of the beam is higher for higher frequencies, this says nothing about the beam intensity. The more power my beam has, the more energy it delivers per second. Physics defines power as energy delivered per second. So a high intensity, low frequency beam can deliver much more of a blow than a low intensity, high frequency beam. This is why we can look at a purple light but not at a powerful red laser. If I have technology that produces high intensity beams, I don't really care what the frequency is.

Where it makes sense that different 'races' would use different light frequencies is in protecting their own ships. Just as the skin of a stealth bomber is designed to absorb radio frequencies to make them difficult to detect by radar, spaceships could design their skins to reflect the frequencies of their own weapons to avoid loss from 'friendly fire'. 

The reason microwave ovens are so effective, despite using a longer wavelength than the infrared radiation of a typical oven, is that water absorbs microwave energy really well. If I'm using microwave beams, I want to be hitting ships that absorb like water.

The author also suggests red light is 'slower' than violet light. In a vacuum, all light moves at the same speed, namely the speed of light (c). Even in the air they move at practically the same speed and the difference in velocity certainly has no impact on their performance as a weapon.

The author then moves on to kinetic energy weapons, referring to weapons which make a mass move rapidly and cause damage by coming to a rapid stop, delivering their energy to the target. He says they are the basis for virtually all our killing devices for the last 5,000 years. 

The fact is most modern day weapons do not fall into this category, other than conventional bullets. Rockets and missiles do not do their damage because of their speed, but because of the explosive charge in them. It is the rapid release of chemical energy on impact that does the damage. Also, the ultimate weapon of mankind, the nuke, doesn't even hit their targets physically. Nuclear devices are detonated in the atmosphere above their targets and it is the release of energy which either irradiates its target or blasts it with the shock wave. Nuclear bombs are an energy weapon and they are much more powerful than a practical kinetic equivalent. The Hiroshima bomb contained just 64kg of uranium of which just 0.6g was converted into energy. 0.6 grams (0.02 ounces) destroyed an entire city. It is easier to destroy stuff by converting mass into energy and rapidly releasing that energy than throwing the same amount of mass at something.

The exception to this rule is referred to in the video. If I'm bombarding a planet, all I have to do is nudge a large mass towards the planet and gravity will do the rest. The thing is while this is good if I'm sitting on the moon and have a large supply of big rocks, this is completely impractical for a spacecraft. 

However, let us say I am towing a collection of boulders behind me while exploring the less civilised regions of the galaxy and I want to accelerate them. I still need a good supply of energy to do this. Let's say I now throw this boulder at a particularly aggressive alien some distance away (this is space after all). What happens if the alien moves? We need to pump in a bunch more energy to make the mass change its course. Or I could simply put the same energy into my energy weapon, rapidly change its direction and knock out the interstellar blackguard. 

In short, if I'm attacking a planet, the planet's gravity will do the heavy lifting, if I'm a spaceship I have to do it all myself. Velocity may be easy but nuclear fusion is much easier than accelerating a decent sized object to near-light speeds without the help of gravity and beam weapons are a lot more manageable than fast moving rocks.

The other disadvantage is accelerating masses in space introduces a finite resource. Whether we use an energy weapon or rocks, we need a significant source of energy but if we are using rocks, and we run out of rocks, we are a sitting duck.

Finally, the video suggests the kinetic energy of a mass travelling as fast as physics allows is (1/2)mc^2. When masses move at near light speed the 'easy physics' no longer applies and a new physics called Special Relativity kicks in. The fact is masses moving at near light speeds store energy far in excess of (1/2)mv^2, but the fact is you have to pump the energy in for the mass to release it on your enemy so why not use it in the form of an energy weapon?

In conclusion, all conventional weapons rely on delivering a large amount of energy in a short amount of time to a target. Kinetic weapons do this by being thrown. Explosive weapons generally do this through chemical reactions and nuclear weapons do this by converting mass into large amounts of energy. In all cases we need a source of energy and generally the denser the better.

The reason to choose one form of weapon over another are reasons of practicality and efficiency. It is practical and efficient to drop rocks on a planet. It is practical to nuke cities rather than try to accelerate the same, tiny mass to inflict the same damage. It is not practical for a spaceship to carry rocks around, accelerate them and throw them at enemies if they have the ability to deliver the energy directly in the form of an intense beam of radiation.

Also, a visible beam weapon is not ruled out by considerations of frequency employed but more by the ability to efficiently generate an intense beam of energy. There is no doubt that sparkly weapons used in movies are there for the audience first and consider physics, if at all, a distant second but physics does not rule out the possibility as suggested.