22 Some Basics about Wind

Air has two types of energy, potential and kinetic. The potential energy associated with air comes from its pressure, which at sea level is about 14.7 pounds per square inch or 1013.3 millibars. At sea level, the air is squashed down by all the weight of the air that lies above it, sort of like the guy at the bottom of a football pile-up. Like a compressed spring, compressed air stores energy that can be released later.

The kinetic energy associated with air comes from its motion. When air is still, it has no kinetic energy. When it is in motion, it has kinetic energy that is proportional to its mass and the square of its velocity. When the velocity of air is doubled, the kinetic energy is quadrupled. This is why an 80-mph wind packs four times the punch of a 40-mph wind.

The relationship between the potential and kinetic energies of air was first formalized by Daniel Bernoulli, in what is now called Bernoulli's equation. In essence, Bernoulli's equation states that because the total amount of energy remains the same, when air speeds up and increases its kinetic energy, it does so at the expense of its potential energy. Thus, when air moves, its pressure decreases. The faster it moves, the lower its pressure becomes. Likewise, when air slows down, its pressure increases. When it is dead still, its pressure is greatest.

The equation developed by Daniel Bernoulli that describes this "sloshing" of energy between kinetic and potential when air is flowing more or less horizontally is given in Equation (i), which follows.

total energy = potential + kinetic

where Patmos = local pressure of air when still, p = density of air, about 0.076 lbf/ft3, P = pressure of air in motion, v = velocity of air in motion, and gc = gravitational constant for units conversion, 32.17 ft/(lbf-sec2).

It should be noted that Equation (i), assumes that gas compressibility effects are negligible, which considerably simplifies the mathematics. For wind speeds associated with storms near the surface of the earth and where wind streamlines wind streamlines

Figure 2.1 Side view of wind going over house.

air pressure changes are relatively small, the incompressibility assumption implicit in Equation (i) is reasonable and introduces no significant error.

Wading through the algebra and the English engineering units conversions, it is seen that a 30-mph wind has a kinetic energy of 30 lbf-ft. Since the total potential energy of still air at 14.7 lbf/in2 is 27,852 lbf-ft, then the reduction in air pressure when air has a velocity of 30 mph is 0.0158 lbf/in2 or 2.27 lbf/ft2. Similarly at 60 mph, the reduction in air pressure is 0.0635 lbf/in2 or 9.15 lbf/ft2.

What these figures mean becomes more clear when a simplified situation is considered. Figure 2.1, shows the side view of a house with wind blowing over it. As the wind approaches the house, several things occur.

First, some of the wind impinges directly against the vertical side wall of the house and comes more or less to a stop. The change in momentum associated with air coming to a complete stop against a vertical wall results in a pressure being exerted on the wall. The basic flow momentum equation that describes this situation is given below.

where P = average pressure on vertical wall, k = units conversion factor, p = mass density of air, about 0.0023 slugs/ft3, and v = velocity of air in motion.

Working through the English engineering units, Equation (ii) reduces to the following.

where P = pressure in lbf/square feet, v = wind velocity in ft/sec.

Table 2.1 Perpendicular Wind Speed Versus Average Pressure on Surface

Wind Speed ft/sec

Resulting Pressure lbf/sq it

10 20 30 40 50 60 70 80 90 100 120 150

52.4

By solving Equation (iii) for a number of wind speeds, Table 2.1 is generated. The table shows the relationship between a wind impinging perpendicularly on a flat surface and coming to a complete stop, and the resulting average pressure on that surface.

In practice, the pressure numbers generated by Equation (iii) and listed in Table 2.1 are higher than that actually encountered. This is because the wind does not fully impact the wall and then bounce off at a negligible speed, as was assumed. What actually occurs is that a portion of the wind "parts" or diverts from the flow and smoothly flows over and away from the wall without actually slamming into it, as is depicted in Figure 2.1. Therefore, to be more accurate, Equation (ii) can be modified as follows.

where P = average pressure on vertical wall, k = units conversion factor, p = density of air, about 0.0023 slugs/ft3, v1 = average velocity of air flow as it approaches wall, v2 = average velocity of air flow as it departs wall, and C = overall factor which accounts for the velocity of the departing flow and the fraction of the flow that diverts.

In general, the actual average pressure on a vertical wall when the wind is steady is about 60-70% of that generated by Equation (iii) or listed in Table 2.1. However, in consideration of the momentary pressure increases caused by gusting and other factors, using the figures generated by Equation (iii) is conservative and similar to those used in actual design.

This is because most codes introduce a multiplier factor in the wall pressure calculations to account for pressure increases due to gusting, build

ing geometry, and aerodynamic drag. Often, the end result of using this multiplier is a vertical wall design pressure criteria similar, if not the same, as that generated by Equation (iii). In a sense, the very simplified model equation ends up producing nearly the same results as that of the complicated model equation, with all the individual components factored in. This is, perhaps, an example of the fuzzy central limit theorem of statistics at work.

Getting back to the second thing that wind does when it approaches a house, some of the wind flows up and over the house and gains speed as it becomes constricted between the rising roof and the air flowing straight over the house along an undiverted streamline. Again, assuming that the air is relatively incompressible in this range, as the cross-sectional area through which the air flows decrease, the air speed must increase proportionally in order to keep the mass flow rate the same, as per Equation (v).

where Am/At = mass flow rate per unit time, A = area perpendicular to flow through which the air is moving (an imaginary "window," if you please), p = average density of air, and v = velocity of air.

Constriction of air flow over the house is often greatest at the roof ridge. Because of the increase in flow speed as the wind goes over the top of the roof, the air pressure drops in accordance with Bernoulli's equation, Equation (i). Where the air speed is greatest, the pressure drop is greatest.

Thirdly, air also flows around the house, in a fashion similar to the way the air flows over the house.

Lastly, on the leeward side of the house, there is a stagnant air pocket next to the house where there is no significant air flow at all. Sometimes this is called the wind shadow. A low pressure zone occurs next to this leeward air pocket because of the Bernoulli effect of the moving air going over and around the house.

A similar effect occurs when a person is smoking in a closed car, and then opens the window just a crack. The air inside the car is not moving much, so it is at high pressure. However, the fast moving air flowing across the slightly opened window is at a lower pressure. This difference in relative pressures causes air to flow from the higher pressure area inside the car to the low pressure area outside the car. The result is that smoke from the cigarette flows toward and exits the slightly opened window.

If a wind is blowing at 30 mph and impinges against the vertical side wall of a house like that shown in Figure 2.1, from the simplified momentum flow considerations noted in Equation (iii), an average pressure of 4.5 lbf/ft2 will be exerted on the windward side vertical wall.

If the same 30-mph wind increases in speed to 40 mph as it goes over the roof, which is typical, the air pressure is reduced by 4.0 lbf/ft2. Because the air under the roof deck and even under the shingles is not moving, the air pressure under those items is the same as that of still air, 14.7 lbf/in2 or 2116.8 lbf/ft2. The air pressure under the roof and under the shingles then pushes upward against the slightly lower air pressure of the moving air going over the roof. This pressure difference causes the same kind of lift that occurs in an airplane wing. This lifting force tries to lift up the roof itself, and also the individual shingles.

While 4.0 lbf/ft2 of lift may not seem like much, averaged over a roof area of perhaps 25 x 50 ft, this amounts to a total force of 5000 lbf trying to lift the roof. At a wind speed of 80 mph, the usual threshold for code compliance in the Midwest, the pressure difference is 16 lbf/ft2 and the total lifting force for the same roof is 20,000 lbf.

If the roof in question does not weigh at least 20,000 lbf, or is not held down such that the combined total weight and holding force exceed 20,000 lbf in upward resistance, the roof will lift. This is why in Florida, where the code threshold is 90 mph, extra hurricane brackets are required to hold down the roof. The usual weight of the roof along with typical nailed connections is not usually enough to withstand the lift generated by 90 mph winds.

It is notable that the total force trying to push the side wall inward, as in our example, is usually less than the total lift force on the roof and the shingles. This is a consequence of the fact that the area of the roof is usually significantly larger than the area of the windward side wall (total force = ave. pressure x area). Additionally, a side wall will usually offer more structural resistance to inward pressure than a roof will provide against lift. For these reasons, it is typical that in high winds a roof will lift off a house before a side wall will cave in.

Lift is also the reason why shingles on a house usually come off before any structural wind damages occur. Individual asphalt shingles, for example, are much easier to pull up than roof decking nailed to trusses. Shingles tend to lift first at roof corners, ridges, valleys, and edges. This is because wind speeds are higher in locations where there is a sharp change in slope. Even if the workmanship related to shingle installation is consistent, shingles will lift in some places but not in others due to the variations in wind speed over them.

Most good quality windows will not break until a pressure difference of about 0.5 lbf/sq in, or 72 lbf/sq ft occurs. However, poorly fitted, single pane glass may break at pressures as low as 0.1 lbf/sq in, or about 14 lbf/sq ft. This means that loosely fitted single pane glass will not normally break out until wind gusts are at least over 53 mph, and most glass windows will not break out until the minimum wind design speed is exceeded.

Assuming the wind approaches the house from the side, as depicted in Figure 2.1, as the wind goes around the house, the wind will speed up at the corners. Because of the sharpness of the corners with respect to the wind flow, the prevalent 30-mph wind may speed up to 40 mph or perhaps even 50 mph at the corners, and then slow down as it flows away from the corners and toward the middle of the wall. It may then speed up again in the same manner as it approaches the rear corner of the house.

Because of this effect, where wind blows parallel across the vertical side walls of a house, the pressure just behind the lead corner will decrease. As the wind flows from this corner across the wall, the pressure will increase again as the distance from the corner increases. However, the pressure will then drop again as the wind approaches the next corner and speeds up. This speed-up-slow-down-speed-up effect due to house geometry causes a variation in pressure, both on the roof and on the side walls.

These effects can actually be seen when there is small-sized snow in the air when a strong wind is blowing. The snow will be driven more or less horizontal in the areas where wind speed is high, but will roil, swirl, and appear cloud-like in the areas where the wind speed significantly slows down. Snow will generally drift and pile up in the zones around the house where the air speed significantly slows down, that is, the stagnation areas. The air speed in those areas is not sufficient to keep the snow flakes suspended. During a blizzard when there is not much else to do anyway, a person can at least entertain himself by watching snow blow around a neighbor's house and mapping out the high and low air flow speed areas.

Plate 2.3 Roof over boat docks loaded with ice and snow, collapsed in moderate wind.

Because a blowing wind is not steady, the distribution of low pressure and high pressure areas on the roof and side walls can shift position and vary from moment to moment. As a consequence of this, a house will typically shake and vibrate in a high wind. The effect is similar to that observed when a flag flaps in the wind, or the flutter that occurs in airplane wings. It is the flutter or vibration caused by unsteady wind that usually causes poorly fitted windows to break out.

Because of all the foregoing reasons, when wind damages a residential or light commercial structure, the order of damage is usually as follows:

1. lifting of shingles.

2. damage to single pane, loose-fitting glass windows.

3. lifting of awnings and roof deck.

4. damage to side walls.

Depending upon the installation quality of the contractor, of course, sometimes items 1 and 2 will reverse.

Unless there are special circumstances, the wind does not cause structural damage to a house without first having caused extensive damage to the shingles, windows, or roof. In other words, the small stuff gets damaged before the stronger stuff gets damaged. There is an order in the way wind causes damage to a structure. When damages are claimed that appear to not follow such a logical order, it is well worth investigating why.

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

Get My Free Ebook


Post a comment