Chapter 4       Air and water as they act on a yacht

 

Yachtsmen sail their boats relative to the surface of the water and the air moving over the water is the source of motive power. Both are in their natural state and we should really have some idea what this is.

 

Water

Everyone is familiar with water in the sense that we know what it looks like, what it tastes like, and we have had plenty of opportunity to observe the way in which it moves. However we need to know more than this.

 

We commonly see water in the gravitational field of the Earth. If we look at the water in a lake on a windless day we see a smooth flat surface and little else. Others have experimented to find out more about water when it is at rest. They have found out what is going on inside it, how the pressure changes with depth, and how it is that an object can float in this water. We need some of this information.

 

The structure of water when it is at rest

Most people will accept that the everyday substances that surround us are made up of molecules and probably that these molecules are made up of smaller pieces called atoms. Atoms of elements combine chemically to produce molecules and water is made up of two hydrogen atoms and one oxygen atom combined in a way that is very difficult to disrupt. We need to have some idea of the effective size of these molecules that are too tiny for us simply to imagine. We can become convinced that molecules are unimaginably small by thinking about insects. We are totally familiar with insects and are aware that some insects are very small yet these insects walk on articulated legs. The legs have joints and the joints are made of molecules that must be thousands of times smaller than the joints so the molecules must be very small indeed. But we are still a long way from the size of molecules. At ordinary temperatures molecules of water form clusters of two, three, four, five or six molecules but it seems that a cluster lasts less than a trillionth of a second before it is broken up to recombine in some new cluster. So short a time is beyond comprehension but it suggests than any attempt to envisage the size of molecules will fail because they are so small. It is important to keep this in mind when talking about, say, the surface finish on a yacht. Any imperfection is gigantic on a molecular scale.

 

We have seen film of the behaviour of water in conditions of weightlessness when it floats about in globules of ever changing shape. The movement of the weightless water indicates the presence of a stretchy film on the water keeping the water in one mass. We call this surface tension and we get plenty of opportunity to see its effects on Earth. In a lake the effect of gravity is dominant and the water settles with a level surface to fill the hollow containing it with the film attributable to surface tension on the top. When waves or wavelets form on a lake their shape is in part determined by surface tension and so is the wave pattern formed by a moving boat.

 

The motion of water near to the surface resulting from a wind blowing over it.

The most important effect acting on a lake is the wind. Most people see the surface ripples or waves without thought of what is going on in the lake. In some way the air acts on the water to cause ripples or wavelets or waves according to the speed of the wind. Any tiny object on the surface will follow a more or less circular path as a wave passes. This means that the water also makes circular movement. But this movement cannot be confined to the surface and must extend downwards. The effect of the wavelets peters out at a depth of a couple of wavelengths but, in between, the water moves as if smaller waves of the same wavelength are passing. At these depths the water moves in ellipses. Inside all this complicated motion the molecules are unaffected and carry on forming their clusters as before.

 

As our yachts must move in this complicated motion one might expect the interaction between the yacht and the waves to change as the height of the waves changes.

 

Pressure variation in water at rest

As the molecules of water are close enough for weak bonding to determine the molecular behaviour it would be surprising if the application of a pressure to a liquid produced any significant reduction in the distance between the molecules. Indeed for most practical purposes it is quite good enough to imagine that water cannot be compressed. Then the number of molecules in a given volume is fixed and so therefore is the weight of this volume. Water weighs 62.4 pounds/cubic foot (or 1 kilogramme per litre).

 

Everyone knows that pressure in water increases with depth. The pressure is given by:- pressure = 62.4.d pounds per square foot if d is the depth in feet. (At one foot the pressure is 0.433 pounds per square inch and atmospheric pressure of 14.7 psi occurs at a depth of 33.9 feet ie 11 metres). The pressure at any point in a liquid is the same in every direction.

 

We must decide how to think about how the pressure in the water varies with depth when the surface in not flat as in the case of surface waves. The answer depends on what application we are thinking about. Normal surface waves do not affect a super-tanker but waves of only a few inches are important for a model yacht. Then we think of the pressure as increasing with depth from the free surface just as if it were stationary.

 

Air

We rely on the existence of wind to make our boats go. Everyone now recognises that wind is a flow of air and that winds can exert very large forces. We need to know more than this and our first need is to know something about air as a gas.

 

Air as a gas

Strictly speaking air is a mixture of gases. It is about 70% nitrogen and 27% oxygen with the rest carbon dioxide and trace gases. At ordinary atmospheric conditions these two gases do not change to liquids if compressed. They are very ordinary in behaviour and for most purposes of science the mixture can be treated as if it were a single gas.

 

The structure of a gas

We said that a liquid is made up of many molecules all attracting each other and existing in a closely packed arrangement with all the molecules behaving in an agitated way. It is known that intensity of this motion increases if the temperature of the liquid increases. We might ask what happens when the motion becomes very great. The answer is that the simple closely packed structure breaks down and molecules escape to fly freely. This is evaporation. The ultimate result is that all the liquid changes to a gas in which all the molecules fly freely. The gases that go to make up air are at temperatures which are much higher than that at which evaporation occurs and they are said to be permanent, that is they do not liquefy under pressure alone. Of course there is still a high concentration of molecules in air, so many in fact that a molecule collides with other molecules many thousands of times every second.

 

Despite the fact that the molecules of a gas are close together by any ordinary standards, on a molecular scale they are relatively free to move. This means that, if a quantity of gas is enclosed in a container, the volume of the container can be reduced to compress the gas into a smaller space. A gas is compressible where a liquid is not. The compression of a gas is associated with a rise in pressure and, if the gas is not cooled, with a rise in temperature.

 

Air has weight just as water does. The air that our yachts might meet weighs about 0.0076 pounds/cubic foot. We do not need to know how air pressure varies with depth.

 

The air in the atmosphere always shares its space with water vapour. This vapour may be invisible or visible as mist or cloud. The water vapour is a small fraction of the total weight of the atmosphere but it does produce important effects on the air. The heat from the sun is transferred to the air by several processes but the dominantly radiant heating of the ground and the sea is distorted by clouds and by variations in the texture of the cover of the land. The resultant variations in the temperature in the air means that the air is very, very seldom still. Instead, in “natural” air there are large-scale motions both vertically and horizontally taking place on the scale of meteorology. Model yachts are sailed in these winds.

 

It is important to have an idea of the behaviour of a “normal” wind if we are to attempt to design sails or to understand the flow over them. Obviously part of the problem (and the fun) of sailing on most ponds is responding, by adjusting the sailing rig, to changes in wind direction. These changes are often caused by obstructions in the surroundings of the lake. But just what does the wind do in the relatively thin layer that we sail in when there are no obstructions? Anyone can find out by going to a very large open space and using a lightweight windsock on an old telescopic aerial. For much of the time the wind veers through about 10° either side of the mean direction in a random way and then, much less frequently, changes in direction of 45°occur[1]. Over a grassy surface the wind speed is fairly constant above about a foot and seems to fall off just a little near to the ground.[2]

 

The air we sail has a flow pattern which is usually the product of the interaction of the large scale movements and ground based obstructions like trees and buildings and, as air is invisible in the normal course of events, we have to guess what the wind might look like if we could see it. Sometimes smoke or fog will show the nature of the motion but not often or predictably. It is worth looking at any visible flow to try to relate it to the topography with which it is associated. A useful idea of what happens can be gleaned from the study of the flow in a small river (say 10 feet wide).

 

A river is a natural watercourse and the water flows in a channel that is uneven in shape and modified by weed growth so that the flow of water is forever changing speed and direction. Observation of such a flow in a more or less straight length of the river shows that there are many little eddies moving along with the stream. No two eddies seem to behave in exactly the same way yet, over a sufficiently long period of observation, it becomes clear that the size of the eddies does not change much, the ones passing a particular point go in the same direction and one comes to know what to expect the flow to look like. This means that despite the evident randomness there is some element of repeatability in the flow. The water has the same old flow with minor variations.

 

When we look at the river we see only the surface and the eddies that seem to have their axes more or less vertical. Yet the obstructions causing the disturbance must be acting in three dimensions. There must be rolling going on under the surface. We have to remember that surface tension is acting to prevent us from seeing the real nature of the motion by smoothing out the smaller disturbances. There is no reason to suppose that air behaves in any different way so we must expect eddies and swirls on a larger scale to be present in the flow of air in which we sail model yachts. The more testing that I do in the open space the more certain I am that the flow of water in a river is a good mental picture for the flow of air near to the ground or to the surface of a lake.

 

The action of wind on a lake

When a wind blows over a lake the obvious result is the disturbance of the surface to form ripples or wavelets or even waves. Our yachts have to work in this disturbed surface and waves can easily have a height that severely impairs the performance of a yacht. It would be convenient if the wind speed and the wave height were to be linked in some obvious way but this is not the case. When a steady wind blows over a large lake with an unobstructed approach the waves gradually increase in height from nothing at the windward end to become sizeable or even high enough to have white tops at the windward end. At one end conditions for model yacht racing may be ideal and at the other impossible. Clearly the wave size and the wind are not linked.

 

There is a further complication that is important in model yachting and that is the effect of the surroundings of the lake. For example let us look at a small lake that has a line of trees forming a windbreak across one end. When the wind blows from the trees the lake will be largely sheltered and the air flowing over the lake will have swirls and eddies which do not lead to the growth of waves. When it blows towards the windbreak the waves will build up in the ordinary way until the flow of air slows down as it prepares to lift up over the trees and the build up of waves stops. This is evident from the wave pattern on the lake.



[1] If this is what happens in the air flowing over an open space there is little point to designing a sailing rig which is sensitive to the angle at which the wind approaches.

[2] I did make an attempt using a Dwyer anemometer to measure this variation in wind over a grassy down in winter when the grass was short. The low speed range of this instrument is 2 - 10 mph and I made tests when the mean wind speed was about 6 mph. From 1 foot to 7 feet above the ground there was a small change in speed but the most noticeable change was in the fluctuation in speed. The speed was steadier at the higher levels. My impression was of mixing in eddying flow going on near the ground rather than a velocity gradient. Over the tarmac in a small car park at the site the flow was not so unsteady near to the ground.