Random thoughts on the Air

Tahiti, 15th August 1992, 7 a.m.  Finally got to bed about 4.30 a.m. after an all-night flight from Los Angeles. Delayed out of LAX due to monumental stuff-up by Ground Movement Control which caused us to come face-to-face with an Aerolinias Argentinas jumbo on the same taxi-track that we were using. Just hope that that particular controller is never let loose on aeroplanes in flight, it could ruin the whole day! And now some blithering cockerel is practising his mating call right outside my room. Tonight I’ll make a point of having chicken for dinner and, Buster, I hope that you’re it! All of which leaves me wide awake and thinking idle thoughts about how to fill up a page or two of Dragnet to keep the troops amused. Maybe we’ll skip electronics this month and air some thoughts on air; the stuff you breathe, that is. Most of us take it very much for granted, yet it can be both friend and foe. We cannot live without it but at times it can kill us – witness the destructive force of a cyclone and you know what I mean. So here are some random ravings which might both amuse and amaze.

Have you ever considered just how heavy air is? The assembly area of Allawah Scout Hall is (to a rough guess) about 14 X 11 X 3.5 metres, or some 539 cubic metres in volume. Since one cubic metre of air at sea level weighs 1.2255 kilograms, then the weight of that amount of air is about 660 kg or about 1456 lb. Get that little lot going at a hundred miles per hour or more and you have a force to reckon with Everyone knows that “standard” sea-level pressure is 14.7 lb/sq.in. or 1013.2 hectopascals (which used to be called millibars until some committee or other decided to totally baffle us). This means that every square inch of surface at sea-level is exposed to the weight of a column of air of that area extending from sea-level up to the limit of the atmosphere, the weight being due to the force of gravity pulling the air molecules downward. (Weight  equals mass x gravity).

Consider the desk that I am writing on. It’s about 3 feet by 6 feet or 18 square feet in area. Each square foot has 12 x 12 square inches, so the total area is 18 x 144 = 2592 sq.ins. Each square inch supports (has) 14.7 pounds of air above it, so the total weight of air acting on the table-top is 2592 x 14.7 = 38,102 lb. Divide by 2240 (pounds to the ton) and we have around 17 tons of air. If you disbelieve this, then ponder this: standard atmospheric pressure is equal in weight to a column of water some 33 feet or 10 metres high. It also equals the weight of a column of mercury 29.92 inches high. A volume of water some 6 x 3 x 33 feet has 594 cu. ft. Each cubic foot of water weighs 64 lb, so the column weighs 594 x 64 = 38,016 lb., which, allowing for the approximations that I’m working to, does indeed confirm the weight of air above the table. The table doesn’t collapse because the (static) pressure acts equally in all directions on the surfaces of the table just as it would if, say, the table were immersed in water. But what if you had a vacuum beneath the table?

Have you ever considered the air forces at play inside the fuselage of a jet transport. Air forces, not Air Forces, that is! At cruise altitudes the pressure differential in a jumbo is about 8.6 lb/sq in., orabout 0.6 kg/sq cm. At 35,000 feet the atmospheric pressure is around 4 lb/sq in., so the actual or absolute pressure within the hull is 12.6 lb/sq in., giving a cabin altitude of 4,200 feet. A cabin window is some 9 x 15 inches with 8.6 lb pushing on each square inch. That’s a total of 1,161 lb or just over half a ton of pressure. In the unlikely event of the window failing whilst you were sitting next to it, chances are that you would lose rather more than your hat!

The forces acting on a main entrance door are even more interesting. Eight such doors are fitted to the main deck of a jumbo plus two on the upper deck. The door measures approximately 72 inches high by 50 inches wide, giving a total of 3,600 sq ins. Multiply this by 8.6 and you have 30,960 lb of pressure (14,043 kg) trying to open the door for you. Fortunately the door is made rather like an over-grown bath plug and the harder you push the tighter it fits. Cargo doors are of a different design however, and if one does let go – as happened to an aircraft departing from Honolulu a few years ago – you can appreciate the destructive forces involved. Going by sea next time? You might care to ponder upon the stresses placed on a ship’s hull by swell and wave motion!

We all know that a wing generates lift by moving through the air, which causes a pressure reduction on the top of the wing plus a small increase in the pressure under the wing, but what sort of pressure changes are involved? Much smaller than you might think. Once again, let’s consider a heavy jet transport aircraft. A jumbo carries a maximum of about 160 tonnes of fuel but must maintain a minimum reserve of 5 tonnes in the tanks on completion of the landing roll-out. An empty aircraft weighs around 171 tonnes and the maximum zero-fuel weight is about 240 tonnes, giving a possible pay-load of 69 tonnes. These figures vary depending on the mark of jumbo involved, but are representative. An average in-flight weight of 270 tonnes is also representative, so we’ll use this figure.

We’ll revert to Imperial measurements, because the 747 is American and Boeing use this system. Both the fuselage and tail contribute to the total lift, and we’ll assume that the total lifting area to be 10,000 sq ft. For illustration purposes, a ton and a tonne are near enough the same, so 270 tons equals 604,800 lb supported by 10,000 sq ft. Each square foot supports 60.48 lb, and each square inch supports 144th of this, or 0.42 lb. (.0295 kg/sq cm). Recall that atmospheric pressure at sea-level is 14.7 lb/sq in., so the required pressure differential above and below the wing of 0.42 lb/sq in. is not such a tall order, being a pressure reduction of only around 3%. As we go higher and the air becomes less dense, this same pressure differential represents a greater percentage change necessitating flight at a higher true speed to achieve the necessary lift.

A glider or ultra-light aircraft will have a “wing- loading” of only 2 to 4 lb/ sq ft which translates to quite minuscule changes in air pressure across the wing, and explains why these machines can fly so slowly.

How much power is absorbed by air-drag when you drive your motor car? Depends on how fast you drive, of course! However, you can make some pretty reasonable estimates. Suppose that the frontal area of your car is 25 sq ft.(say 5.5 feet wide by 4.5 feet high, approx), and suppose that the “co-efficient of drag” is 0.36. That is, the air drag of the car is the same as a flat plate of 0.36 x 25 sq ft., or 9 sq ft. The formula to calculate drag is

Drag(lb) = Cd_x_rho_x_velocity_sqd_x_area  where rho = air density in slugs per cubic foot.

Stay with it, you’ll soon see how it works out! A slug is a unit of mass, air having 0.002378 slugs/cu ft. Suppose we cruise at 80 mph or 128.7 kmph, which equals 117 ft per second.

Then,

Air drag = .36_x_.002378_x_117_x_117_x_25  = 146 lb.
2
Now one old-fashioned horse-power equals 550 ft.lb/sec. so the horse-power needed to overcome the drag is,

146lb_x_117ft/sec = 31 HP or about 23.1 kilowatts.       550

Bear in mind that this is just the power needed to push through the air and takes no account of rolling friction or losses in the transmission, etc. If you travel at a more leisurely 50 mph the HP required drops to a mere 7.6, thus emphasising the economy that can be achieved by driving at a more moderate speed.

Although air can be accelerated smoothly to supersonic speeds, the reverse does not apply. As air decelerates from super to sub-sonic speeds it forms a sudden pressure rise or  discontinuity known as a shock-wave. Depending upon the size, speed, and altitude of the object creating the shock-wave, this pressure discontinuity or wave-front may be several pounds per square inch above the ambient pressure, and therefore be potentially destructive. Back in the 1950s there was a serious proposal to fly supersonic aircraft at very low level along the lines of troop concentrations. The intense pressure rise due to the shock-wave generated by the passage of the aircraft would literally blow apart the lungs and other internal organs of the troops, thus greatly saving on the cost of ammunition!

Industrial aerodynamics are a rich source for discussion. Why are things the shapes that they are? Chimneys, for instance. Why does a wire “sing” in the wind? Why do birds fly in Vee-formations, with constant lead changes? Whereabouts in the world is there a low-level jet-stream where winds blow at 100 mph at less than 3,000 feet yet the surface wind is calm? What makes sound waves propagate and why does the speed of sound depend only on temperature? All food for thought, and perhaps discussion on the air – radiowise, that is!

Cheers for now, and having got that lot off my chest maybe I can catch up on those lost ZZZs.

Clive VK6CSW – September 1995.

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