What Einstein Told His Barber: More Scientific Answers to Everyday Questions - Robert L. Wolke (2000)
Chapter 1. Movin’ and Shakin’
Everything is moving.
You may be sitting quietly in your armchair, but you are far from motionless. I don't mean merely that your heart is beating, your blood is coursing through your veins and you are panting at the prospect of learning so many fascinating things from this book. In short, I don't mean simply that you are physically and mentally alive.
I mean that while you are sitting there so peacefully, Earth beneath your feet is spinning you around at about 1,000 miles per hour (1,600 kilometers per hour). (The exact speed depends on where you live). Mother Earth is simultaneously hauling you around the sun at 66,600 miles per hour (107,000 kilometers per hour). Not to mention the fact that the solar system and all the stars and galaxies in the universe are racing madly away from one another in all directions at incredible speeds.
Okay, you knew all that. Except maybe for the exact speeds. But we're still not done.
You are made of molecules. (Yes, even you.) And all your molecules are vibrating and jiggling around to beat the band, assuming that your body temperature is somewhere above absolute zero. In motion also are many of the atoms of which your molecules are made, and the electrons of which the atoms are made, and the electrons, atoms and molecules of everything else in the universe. They were all set into motion about 12 billion years ago and have been quivering ever since.
So what is motion? In this chapter we'll see how every-thing from horses to speeding automobiles, sound waves, bullets, airplanes and orbiting satellites move from one place to another.
Horsing Around on the Highway
Why do they drive on the left in some countries and on the right in others?
It goes back to the fact that most humans are right-handed.
Long before we had modern weapons such as guns and automobiles, people had to do battle using swords and horses. Now if you are right-handed, you wear your sword on the left, so that you can draw it out rapidly with your right hand. But with that long, dangling scabbard encumbering your left side, the only way you can mount a horse is by throwing your free right leg over him. And unless you are in a Mel Brooks movie and want to wind up sitting backward on your steed, that means that the horse's head has to be pointing to your left. To this day we still train horses to be saddled and mounted from their left sides.
Now that you are mounted, you will want to stay on the left side as you start down the road, because anyone coming toward you will be on your right, and if that someone turns out to be an enemy, you can whip out your sword with your right hand and be in position to run the scoundrel through. Thus, prudent horsemen have always ridden on the left side of the road.
This left-side convention was also honored by horse-drawn carriages in order to avoid annoying collisions with horse-men. When horseless carriages made their appearance, some countries continued the habit, especially during the overlap period when both kinds of carriages were competing for road space.
So why do people drive on the right in the U.S. and many other countries?
When swords went the way of bows and arrows, the need for defending one's right flank disappeared and traffic rules were suddenly up for grabs. Younger or less tradition-bound countries migrated to the right, apparently because the right-handed majority feels more comfortable hugging the right side of the road. It quickly occurred to left-handed people that it was unhealthy to argue with them.
Some countries that I've been in must have large populations of ambidextrous people, because they seem to prefer the middle of the road.
Why do highway and freeway intersections have to be so complicated, with all those loops and ramps?
They enhance the traffic flow—from construction companies to politicians' campaign chests.
They allow us to make left turns without getting killed by oncoming traffic. It's a matter of simple geometry.
When freeways and superhighways began to be built, engineers had to figure out how to allow traffic to make turns from one highway to an intersecting one without stopping for red lights. Because we drive on the right-hand side of the road in the U.S., right turns are no problem; you just veer off onto an exit ramp. But a left turn involves crossing over the lanes of opposing traffic, and that can cause conflicts that are better imagined than expressed.
Enter the cloverleaf. It allows you to turn 90 degrees to the left by turning 270 degrees to the right.
Think about it. A full circle is 360 degrees; a 360-degree turn would take you right back to your original direction. If two highways intersect at right angles, a left turn means turning 90 degrees to the left. But you'd get the same result by making three right turns of 90 degrees each. It's the same as when you want to turn left in the city and encounter a “No Left Turn” sign. What do you do? You make three right turns around the next block. That's what the loop of a cloverleaf does; it takes you 270 degrees around three-quarters of a circle, guiding you either over or under the opposing lanes of traffic as necessary.
The highway interchange is a four-leaf clover, rather than a two- or three-, because there are four different directions of traffic—going, for example, north, east, south and west—and each of them needs a way to make a left turn.
For readers in Britain, Japan and other countries where they drive on the left, just interchange the words “left” and “right” in the preceding paragraphs, and everything will come out all right. That is, all left. You know what I mean.
Ready, Set … Jump!
If every person in China climbed to the top of a six-foot (two-meter) ladder and then all jumped off at the same time, could it nudge Earth into a different orbit?
No, but it sure would create a windfall for Chinese podiatrists.
I suppose that everybody picks on China when they ask this question because China is the most populous country on Earth, containing 2.5 billion potentially sore feet.
There are really two questions here, aside from the question of why people who ask this question don't have anything better to do. (Just kidding; it's fun to wonder about such things.) The first question is how strong the jump-thump would be, and the second question is whether any size thump at all could change Earth's orbit.
It's easy to calculate the amount of energy from a gravitational fall. (And don't tell me they're not falling because China is upside down.) Assuming a population of 1.2 billion Chinese weighing an average of 150 pounds (68 kilograms) each, their collective pounce would hit the ground with an energy of 1.6 trillion joules. (A joule is just a unit of energy; don't sweat it.) That's just about the amount of energy released in a medium-sized earthquake measuring 5.0 on the Richter scale. Such earthquakes have been occurring for millions of years, and there is no evidence that they have nudged Earth into different orbits.
But no amount of earthquake or footquake energy could change the orbit anyway, so both earthquakes and Chinese ladders are irrelevant. Planet Earth continues circling the sun because it has a certain amount of momentum, which means that it has a certain amount of mass and a certain velocity, because momentum is a combination of mass and velocity. Our planet carries along with it everything that is attached to it by gravity, including jumping Chinese and acrobats on trampolines. We're all one big package of mass, and no amount of jumping up and down can change Earth's total amount of mass. Nor can it change the planet's velocity, because all the Chinese are being carried along through space at the same speed as the rest of the planet; we're all in one big, interconnected spaceship. You can't change the speed of your car by pushing on the windshield, can you? Nor can you lift it by pushing on the inside of the roof.
We might put it in terms of Newton's Third Law of Motion, which you must have heard a million times (and will again, if I have anything to do with it): “For every action there is an equal and opposite reaction.” Push on a brick wall and the wall pushes back. If it didn't, your hand would go straight through. When the Chinese land, their feet hit the ground with a certain amount of force, but at the same time the ground hits their feet with an equal amount of force in the opposite direction. Thus, (a) there is no net (unbalanced) force that could affect our planet's motion and (b) their feet hurt.
Jump … Now!
If I'm in an elevator and it starts to fall to the bottom of the shaft, can I jump up at the last instant and cancel the impact?
Ho hum. I don't know how many times this question has flashed into the minds of worrywarts in elevators, or how many times it has been asked of every friendly neighborhood physicist. It is easy to answer in one word (No), but thinking about it does raise a whole bunch of fun questions.
First, here's the quick answer: Your objective is to arrive at the bottom of the shaft like a feather, without any appreciable downward speed, right? That means that you have to counteract the elevator's downward speed by jumping upward with an equal amount of speed. The elevator (and you) might be falling at, say, 50 miles per hour (80 kilometers per hour). Can you jump upward with anywhere near that speed? The best basketball players can jump at maybe 5 miles per hour (8 kilometers per hour). End of quick answer.
Let's consider the instant before your elevator's cable snaps. In the seventeenth century, long before elevators, Sir Isaac Newton (1642–1727) realized that when a body exerts a force on another body, the second body exerts an equal and opposite force on the first body. Today, that's known as Newton's Third Law of Motion. When you're standing on the elevator floor and gravity (force number one) is pulling you down against the floor, the floor is pushing you back up with an equal force (force number two). That's why gravity doesn't win out and make you fall down the shaft. It's the same with the elevator car itself; in this case it's the cable's upward pull that counteracts gravity's downward pull on the car. So neither you nor the elevator falls down the shaft. You both move upward or downward at a speed that is controlled by a motor's slow winding and unwinding of the cable from a big drum at the top of the shaft.
When the cable snaps, both the upward pull of the cable and the upward push of the floor are suddenly gone, so both you and the elevator are free to succumb to gravity's will and you both begin to fall. For an instant you are left floating—feeling “weightless” because the customary push of the floor on your feet is gone. But following that instant of blissful suspension, gravity has its way with you and you fall, along with the elevator.
About that moment of “weightlessness” when the elevator begins to fall: Obviously, you haven't really lost weight. Earth's gravity is still pulling on you as it always has, and the strength of that pull is what we call weight. What you've lost is apparent weight. Your weight just isn't apparent because you're not standing on a scale or a floor that feels your pressure and presses back upon your feet.
Of course, this whole question of falling elevators is hypothetical because elevator cables just don't snap. And even if they did, there are spring-loaded safety devices that would keep the car from falling more than a couple of feet. But, as roller coasters prove, some people seem to enjoy the contemplation of imminent disaster.
If you happen to be one of those roller coaster fans, that “floating” feeling you get as the car falls from one of its high spots is exactly the same thing you'd feel in a falling elevator. It's called free fall. Astronauts in orbiting spacecraft also feel it.
When my car's tire treads wear out, where has all the rubber gone?
It has been rubbed off—and no, that's not why they call it rubber—onto the road, whence it was scattered in the form of fine dust into that vast, complex everywhere that we call the environment. Some of it was then washed off the road and into sewers by rain, or else it was blown around by the wind and eventually fell or was rained out of the air onto any and all surfaces. Eventually, all the rubber joined the soil and the seas as part of the Earth from which it was born. Like everything else, a dead tread returns unto dust.
We tend to think of automobile tires as rolling smoothly along, without any scuffing against the road that might scrape away rubber. That could be true only if there were no resistance whatsoever between the tire's surfaces and the road's surface. And if there were no resistance, your tires couldn't get a grip and you'd go nowhere. You'd get a spectacular warranty on a set of tires like that, because they'd never wear out.
Between any two surfaces that are attempting to move past each other—even a tire and a road—there is always some resistance; it's called friction. Even rolling wheels experience friction against the road, although rolling friction is a lot less than sliding friction. When necessary, you can roll your car straight ahead by pushing, but just try to slide it sideways.
Friction gobbles up some of the energy of motion and spits it out as heat. If there were no diminishment of motion by the conversion of some of it to frictional heat, a machine could go on forever without slowing down: perpetual motion. Because there always must be some frictional heat loss, however small, every device that has ever been touted as a perpetual motion machine has to be a fake, however well-intentioned its inventor.
If you don't think that tire-against-road friction makes heat, just feel your tires before and after driving for an hour or so on the freeway. Much of the heat you'll feel comes from friction against the road, but some comes also from the continual flexing and unflexing of the rubber.
Regarding the disappearing tread on your tires: Wherever there is frictional resistance between two materials, one of them has to “give”—that is, have some of its molecules scraped off by the other. Between your soft tire and the hard highway, it's no contest; it's the rubber that gives and gets rubbed off gradually in tiny particles.
If all of our roads were made of a substance that is softer than rubber, the roads would wear out instead of the tires. Instead, our society has decided that it's less trouble for car owners to replace their tires than for governments to continually replace road surfaces. Then why, you may ask, do we continually have to dance the orange barrel polka to get through interminable road reconstruction zones? Unfortunately, I can answer only scientific questions, not political ones.
The squealing tires in movie car chases are the result of sliding friction: rubber scraping, rather than rolling, on the pavement. On a microscopic scale, we would see the tire alternately grabbing and slipping thousands of times per second, producing a series of chattering vibrations that fall in the frequency range of a screech. It's easy to see that with all of this frictional dragging of rubber against the road, a lot of rubber will be rubbed off. In fact, the friction makes enough heat to melt some of the rubber, which paints itself onto the road as a black skid mark.
You Didn't Ask, but …
Why are the tires on racing cars so smooth? You'd think they'd need all the traction they could get.
That's precisely why they're smooth. Regular tires waste a lot of their potential road-grabbing surface by having grooves, which act like gullies to channel out rain and mud. But racing cars usually compete in good weather, so the rain-and-mud grooves aren't necessary. They're just wasted space that can better be used to add more road-grabbing rubber for better handling in turns and better braking response. To get even more road-grabbing surface, the tires are made much wider than those on your family chariot. And they're made of a softer rubber that wears off like crazy onto the track. You think you don't get good tire mileage? Why do you think they're always stopping to change tires?
Ready, Aim, Scram!
In movie westerns, and even in many parts of the world today, people fire guns straight up into the air as warning shots or just to make noise during a celebration. But those bullets have to come down somewhere. How dangerous will they be if they hit somebody?
Quite dangerous. As we'll see, physics tells us that when it hits the ground the bullet will have the same velocity it had when it left the muzzle of the pistol, which can be 700 to 800 miles per hour (1,100 to 1,300 kilometers per hour). But that ignores air resistance. More realistically, the bullet's landing speed can be around 100 to 150 miles per hour (160 to 240 kilometers per hour). That's fast enough to penetrate human skin, and even if it doesn't penetrate it can still do a lot of damage. But just try to tell that to the idiots who like to shoot their guns “harmlessly” into the air.
There are two kinds of forces that affect the bullet's speed on the way up and on the way down: gravity and air resistance. Let's look first at the effects of gravity, neglecting air resistance entirely.
It will be easier to understand the bullet's flight if we consider it in reverse. That is, we'll start at the instant at which the bullet has reached the top of its flight and is just starting to fall downward. Then we'll consider its upward journey and compare the two.
Gravity is a force that operates on a falling object—and is indeed what makes it fall—by pulling on it, attracting it toward the center of the Earth, a direction that we call “down.” As long as the object is in the air, gravity keeps on tugging on it, urging it to fall faster and faster. The longer it falls, the more time gravity has to work on it, so the faster it falls. (Techspeak: It accelerates.)
The strength of Earth's gravitational field is such that for every second of pull—that is, for every second that an object is falling—the object speeds up by an additional 32 feet per second (9.8 meters per second) or about 22 miles per hour (35 kilometers per hour). It doesn't matter what the object is or how heavy it is, because the strength of the gravitational field is purely a characteristic of Earth itself. So for every second of downward fall, the bullet gains 22 miles per hour (35 kilometers per hour) of speed. If it falls for ten seconds, its speed will be 220 miles per hour (350 kilometers per hour), and so on.
But gravity was pulling on the bullet with the same force when it was on its way up. That's what slowed it down so much that it eventually reached zero speed at the top of its flight before starting to fall. For every second that it was on its way up, gravity's pull removed 22 miles per hour (35 kilometers per hour) of speed. The total amount of speed removed on the way up must be the same as the total amount of speed regained on the way down, because the gravitational effect was the same all the time. If that weren't true, the bullet would have to have acquired some speed or lost some speed because of some other outside force. And there was no other outside force (except air resistance, and we'll get to that).
So we see that what gravity taketh away on the way up, gravity giveth back on the way down. On the basis of gravitational effects alone, then, the bullet would have no more or less speed when it hits the ground than it had when it left the gun: its muzzle velocity, and that's how fast it will be going when it hits the ground.
… Or an innocent bystander.
Up to now, we've ignored the slowing-down effect of the air. As you can tell by sticking your hand out the window of a moving car, the faster you go the more the air tries to hold you back. So as our bullet falls faster and faster under the influence of gravity, air resistance tries to make it go slower and slower. Pretty soon, the two conflicting forces become equal and cancel each other out. After that, no matter how much farther the object falls it won't go any faster. It has reached what physicists like to call its terminal velocity, which is Techspeak for final speed.
(Because “terminal velocity” is such an impressive-sounding term, many an innocent physics student—I was one—gets the impression that it's some kind of fundamental limitation of Nature, like the speed of light. But there's absolutely nothing sacred or fixed about it. The final speed of a falling object simply depends on its size and shape, and on how it catches the air. If you fall out of an airplane, your terminal velocity will certainly be a lot less if you're wearing a parachute. Teams of sky divers adjust their air resistance by making their bodies more compact or more extended, so they can rendezvous at the same terminal velocity and frolic around together before pulling their rip cords.)
If a shooter is fairly close to a target, there isn't much opportunity for air resistance to slow the bullet down during its short flight. Even when fired into the air, a streamlined object like a bullet doesn't suffer much air resistance on the way up, because it is pointing straight ahead along its path. But during its fall it is probably tumbling, or even more likely falling base-first, because that's the most stable orientation for a bullet-shaped object. The air resistance on a tumbling or base-first bullet is quite a bit greater than on a straight flyer, so it may be slowed down substantially on the way down and end up quite a bit slower than its muzzle velocity. One expert estimates that a.22LR bullet with a muzzle velocity of 857 miles per hour (1,380 kilometers per hour) might fall to the ground with a velocity of 96 to 134 miles per hour (154 to 216 kilometers per hour), depending on how it tumbles. That's more than enough speed to do serious or lethal damage to a cranial landing site.
And by the way, the jerk who fires the bullet isn't very likely to be hit by it, no matter how carefully he aims straight up. In one experiment, out of five hundred.30-caliber machine-gun bullets fired straight upward, only four landed within 10 square feet (3 square meters) of the gun. Wind has a great effect, especially since.22- to.30-caliber bullets can reach altitudes of 4,000 to 8,000 feet (1,200 to 2,400 meters) before falling back down.
War Is … Swell
Why do guns put spin on their bullets?
A spinning bullet flies farther and truer than it would without the spin. And if your favorite sport is football rather than shooting, just about everything I'm going to say about spinning bullets also goes for spiraling passes.
The fact that a spinning bullet or football goes farther may sound strange, because you'd think that the range would depend only on the amount of energy it gets from the gunpowder charge or the quarterback's arm. But bullets and footballs have to fly through the air, and air drag plays an important part in any projectile's trajectory, whether it is fired from a handgun, rifle, machine gun, howitzer or arm.
First, let's see how a gun makes the bullet spin.
Running the length of the inside of the barrel are spiraling grooves, called rifling. As the bullet passes through the barrel, these grooves cut into it, making it rotate to conform to the spiral. Some guns have grooves that twist to the right and some have grooves that twist to the left; it doesn't matter. (And no, they don't twist one way in the northern hemisphere and the other way in the southern hemisphere.)
Early bullets were round balls of lead, like miniature cannonballs. Bullet-shaped (Techspeak: cylindroconoidal) bullets were developed around 1825, when it was found that they maintained their speed better in flight. That's because for a given weight of lead an elongated, tapered-nose shape meets with less air resistance than a round ball; it's streamlined.
But there's a problem with elongated bullets that spherical bullets don't have. When an elongated bullet is fired, any tiny irregularities on its surface can catch the air and push it slightly sideways, so that its nose is no longer pointing straight ahead. This slight misalignment increases the air resistance on the forward side, which turns the bullet even more. Pretty soon it is tumbling end-over-end, which causes even more air drag, seriously shortening its range and pushing it off-course. Thus, both distance and accuracy suffer.
That's where the rifling comes in. If the bullet is spinning properly around its long axis as it flies, it resists any change in its orientation or direction of flight. The reason for that is that a heavy, spinning object has a lot of momentum. Not only does it have momentum along its direction of travel (linear momentum), but because of its spin it also has rotational momentum, or what physicists call angular momentum. And momentum, whether linear or angular, is hard to upset. In fact, the momentum of an object will remain unchanged unless and until it is disturbed by some outside force. (Techspeak: Momentum is conserved.) The spinning bullet, therefore, will maintain its angular momentum by spinning with its axis in the same direction for as long as it is in the air, because there is no outside force to disturb it. Those tiny surface irregularities are now peanuts compared with the bullet's substantial amount of angular momentum.
With its nose pointed straight ahead, the projectile encounters less air resistance and thus flies farther and truer. When it ultimately hits an object, its momentum—both linear and angular—still won't disappear, but will be transferred to the unfortunate target—or in the case of a football, the fortunate receiver.
International law actually requires that bullets spin. Otherwise, a tumbling bullet might hit its victim sideways, doing more damage than if it had made a nice, clean, round hole. It's just one of those niceties of war: If you're going to kill somebody, please do it neatly.
The Geneva Convention spells out certain other niceties about how to kill people. For example, because lead is soft and deformable, it can go splat when it hits its target, again producing a very unsightly hole. So bullets have to be jacketed with a harder metal, such as copper. The world's military establishments gladly comply with that requirement, but it's not because of any humanitarian motives. It's because modern military assault weapons fire their bullets at such high speeds that if they weren't jacketed with high-melting copper the lead would melt from friction with the air, making them fly erratically and miss their targets. After all, a clean, round hole in an enemy is so much preferable to no hole at all.
You Didn't Ask, but …
Why does the Lone Ranger use silver bullets?
They serve mostly as a calling card, but they do have a very slight advantage over lead.
Ordinary bullets are made of lead because lead is so heavy, or dense. And it's cheap. We want a bullet to be as heavy as possible because we want it to have as much damage-causing energy as possible when it hits its target, and energy is a combination of mass and speed. (Techspeak: Kinetic energy is directly proportional to the mass and to the square of the velocity.) It's easier to gain energy by increasing the bullet's mass than by increasing its velocity, because increasing the velocity would require a longer barrel in order to give the explosion's gases more time to accelerate the bullet.
A silver bullet is about 7.5 percent lighter than a lead bullet of the same length and caliber. Since a given powder charge imparts the same amount of energy to any bullet, the lighter silver bullet must travel faster. It works out to be 4 percent faster than a lead bullet.
So the Lone Ranger's silver bullets get to their targets very slightly sooner than a lead bullet would. If the bullet's velocity is 1,000 feet per second (300 meters per second) and an outlaw fifty feet (fifteen meters) away is drawing his gun, the silver bullet gives our hero a two-millisecond advantage—not even long enough for Tonto to say, “Ugh!”
Also, because silver is a lot harder than lead, when the Lone Ranger shoots the gun out of a bad guy's hand—he never shoots the guy himself—it must really sting. And when it strikes, instead of the dull thud of lead, a silver bullet makes a great “ping” sound for the microphones that seem always to be nearby.
The Lone Ranger's silver bullets fly faster than lead bullets.
How to Stop an Airplane
When there's an airplane flying overhead, why is it that when I walk in the opposite direction it looks as if it's almost stationary? Certainly my walking speed is peanuts compared with the plane's speed, so how can it be having any effect?
Whether we realize it or not, we judge the motion of an airplane in the sky by its relation to common things on the ground, such as trees, telephone poles and houses. That's the only way motion can be detected: in relation to something else. There's no such thing as absolute motion; it's all relative to something else. So the faster the plane appears to be passing the trees and houses, the faster we judge the plane to be moving.
But when you yourself are moving in relation to the trees and houses, you upset this simple association because the trees and houses appear to be moving also. As you walk forward, they appear to be moving backward, don't they? Of course, you know that they're not really moving backward because your daddy told you so when you were two years old.
So as you walk forward (which, I trust, is your customary direction of locomotion), but in the opposite direction from the airplane's, the trees and houses also appear to be moving backward with respect to your direction; that is, they appear to move in the same direction as the plane. It appears, then, that the airplane and the houses are moving together; the plane doesn't seem to be overtaking them. And any airplane that can't even pass a house would seem to be one very slow airplane.
Want to do the passengers a favor and get them to their destination sooner? Just walk in the same direction as the plane. As the trees and houses “move backward” it'll look as if the plane is passing them even faster.
It's Truly Not Bernoulli
I just can't bring myself to believe that huge airplanes can fly, supported as they are on thin air. How do they do it?
Join the club. Even though I know something about how airplane flight works (and you will too, soon), it never ceases to amaze me. I remember landing after a transatlantic flight in a Boeing 747 and being directed by the crew to deplane directly onto the ground and into a waiting bus, instead of through one of those people tubes. I looked up in utter dis-belief at the four-hundred-ton monster that had just wafted me across the Atlantic Ocean at an altitude of more than five miles above Earth's surface.
My awe was magnified by the fact that back when I was “taught” what makes airplanes fly, I was misled. In spite of the fact that most flight training manuals attribute an airplane's lift to something called Bernoulli's Principle, that is not the main reason airplanes stay up. It just happens to be a quick, easy explanation, but like all simple answers it is misleading, bordering on downright wrong.1
First, let's put the Swiss mathematician Daniel Bernoulli (1700–1782) on the witness stand and see what he has to say for himself.
In 1738 Bernoulli discovered that as the speed of a moving fluid (gas or liquid) increases, its pressure on adjacent surfaces decreases. For example, air that is blowing by as a horizontal wind doesn't have the time or energy, so to speak, to press very hard upon the ground.
How does this affect airplanes?
The top surface of a conventional airplane wing is humped upward, while the bottom surface is relatively flat.
As the plane flies, air sweeps over these two surfaces. On its way to the back (trailing) edge of the wing, the air on the top surface has farther to go because of its curved path. The Bernoulli-Makes-Planes-Fly advocates claim that the top and bottom air must reach the wing's back edge at the same time—that's called the equal transit time assumption—and that inasmuch as the top air has farther to travel it must move faster. According to Mr. Bernoulli, then, the faster top air exerts less pressure on the wing than the slower bottom air does, so the wing is pushed upward by a net force called lift.
That's all very well except for one thing: The top air and the bottom air don't have to reach the trailing edge of the wing at the same time; the equal transit time assumption is just plain wrong, in spite of all the arm-waving that physics teachers and flight instructors do to try to justify it. You and I can both forget our embarrassment at never having understood that point in school. There is simply no good reason that the top air has to arrive at the trailing edge at the same time as the bottom air.
The Bernoulli effect does contribute some lift to an airplane wing, but acting by itself it would require a wing that is either shaped like a humpback whale or traveling at an extremely high speed.
Thank you, Mr. Bernoulli. You may step down now.
We now call Sir Isaac Newton to the stand.
Newton's three laws of motion are the ironclad foundation of our understanding of how things move. Newtonian mechanics (as distinguished from quantum mechanics and relativity) can explain the motions of all objects, as long as they are not too small (smaller than an atom) and are not traveling too fast (near the speed of light). Newton figured out his laws for the motions of solid objects, but they can be applied as well to the interactions between airplane wings and air. Let's see how.
Newton's Third Law of Motion (again) says that for every action there must be an equal and opposite reaction. So if the plane's wing is being pushed or lifted up, then by gosh something else is being pushed down. It is. The air. The wing must be whooshing a stream of air downward with a force equal to the lift it is getting. We'll call it downwash.
When a fluid such as water or air flows along a curved surface, it tends to cling to the surface more tightly than you might expect. This phenomenon is known as the Coanda Effect. (See the explanation, but instead of water flowing over a curved glass surface, think of air flowing over a curved airplane wing.) Because of this clinging, the air flowing over the surfaces of the wing is constrained to hug the shapes of the wing; the top-of-the-wing air clings to the top surface and the bottom-of-the-wing air clings to the bottom surface. The streams not only take different paths, but as a consequence of the wing's shape they wind up flowing in different directions at the back of the wing. It's not as if the wing were simply cutting through the air like a flat knife blade, with the airstream parting to let it through and then closing back to its original direction after the wing passes.
As the top-of-the-wing air meets the leading edge of the wing it flows first upward over the surface and then downward again as it leaves the trailing edge. But the shape of the wing leads it farther downward than where it began; it leaves the trailing edge of the wing in a net downward direction. In other words, the top-of-the-wing air is actually being thrust downward by the wing's shape. And according to Newton's Third Law, the wing is therefore thrust upward with an equal amount of force. Voilà! Lift!
Do you think this can be only a small amount of force, coming as it does from a push by “thin air”? Hah! Think again. Even a small plane like a Cessna 172 flying at 110 knots (204 kilometers per hour) is pumping three to five tons of air downward every second. Just think of the hundreds of thousands of tons of air that an 800,000-pound (360,000-kilogram) Boeing 747 is pumping downward every second to get off the ground and stay there.
We can give Isaac Newton still more credit for lifting airplanes, because the lift doesn't all come from downwash (with a slight assist by Mr. Bernoulli). Some of it comes from yet another application of Newton's Third Law. Airplane wings are not parallel to the ground; they are made to be tilted slightly upward in front—usually about 4 degrees when the plane is in level flight. That makes more pressure on the bottom surface than on the top, thereby pushing the wing upward and contributing to the lift. The pilot can tilt the plane even farther upward in front (Flyspeak: He can increase his angle of attack) to get even more lift from this effect. Sir Isaac's Third comes in because as the plane moves, the wing is pushing the air down in front of it, so the air responds by pushing the wings up.
We see, then, that two different wing actions create lift: the wings' shape—the “airfoil”—and their upward tilt, or angle of attack. Both must be used to maximum effect in order to grunt a heavy plane off the ground during takeoff. That's why you see planes taking off from the airport at such steep angles of climb; the pilots must increase their angle of attack to gain extra lift while the plane is so loaded down with fuel, not to mention that fat lady in the seat next to you.
And you thought the pilot was simply pointing the plane's nose in the direction he wants it to go in, as if it were a horse.
BONUS: Have you ever wondered why ski jumpers bend over so far forward when they're in the air that their noses practically touch the tips of their skis? Two reasons. First, if they stood straight up they'd encounter more air resistance, which would slow them down. But second, their arched backs simulate an airfoil. Their upper surfaces are curved like an airplane wing, and they actually gain some lift that keeps them in the air longer.
Flying with the Top Down
If an airplane's wings are shaped to give it lift, how can an airplane fly upside down?
It can be done to wow the crowd at an air show, but it wouldn't work for a commuter flight to Schenectady because, although it's theoretically possible, passenger planes aren't built to stand the stress. (Nor are the passengers.)
A conventional airplane's wings are curved or humped on top, and that produces lift for reasons that are far from simple. But if the wing were upside down, wouldn't that produce the opposite effect, turning the “lift” into “plunge”? Yes, if the pilot weren't partially offsetting that effect by changing the plane's angle of attack, the angle at which the wings hit the air.
Stick your hand out the window of a speeding car—not above the speed limit, of course. When you hold your hand flat, palm parallel to the ground, you feel the air's pressure on what pilots would call the leading edge of your hand—the thumb edge. But then if you tilt your hand slightly upward, so that your palm gets the brunt of the wind, your wing—uh, hand—is pushed upward. There's more push on the bottom than on the top, and that makes lift, no matter how your hand—or a wing—might happen to be shaped, as long as it's reasonably flat.
So when flying upside down, the stunt pilot points his nose (the plane's, that is) upward, so that the bottoms of the wings—which used to be the tops—are getting the brunt of the wind and are being forced upward. As a matter of fact, stunt planes don't even have wings that are more curved on top; the top and bottom surfaces are the same shape, so it doesn't matter which side is up—everything is accomplished by angle of attack.
As you saw from your hand-out-the-window experiment, increasing your angle of attack produces not only lift, but drag— more wind resistance trying to hold your hand back. Similarly, when the stunt pilot increases his angle of attack, the plane experiences more drag against which the engines have to labor. Stunt planes, therefore, have to have powerful engines, as well as crazy pilots. Well, crazy like a fox, perhaps, because it takes great strength and presence of mind to think in three dimensions while you're being subjected to forces that are eight or ten times as strong as gravity. And stunt pilots aren't protected by “g-suits,” those pressure suits that fighter pilots wear to keep the blood from leaving their heads and blacking them out during high-acceleration maneuvers.
All the same, I'll just watch from the ground.
How Astronauts Lose Weight
Does gravity peter out at a certain distance from Earth? Otherwise, how can orbiting astronauts be weightless?
Answer to the first question: No.
Answer to the second question: They're not weightless. There's a completely different reason why astronauts can do all those silly tricks for the cameras, such as performing somersaults in midair or sitting upside down on absolutely nothing, looking more witless than weightless.
Earth's gravitational attraction, like all gravitational attraction, reaches out indefinitely; it keeps getting weaker and weaker the farther away you go, but it never diminishes to zero. Every atom in the universe is gravitationally pulling on every other atom, no matter where. But of course, the bigger the agglomeration of atoms you have, such as a planet or a star, the stronger will be their cumulative pull.
That's all beside the point, however, because the paltry 250-mile (400-kilometer) altitude at which the space shuttle goes ’round and ’round is peanuts as far as gravitational weakening is concerned. After all, Earth holds on to the moon pretty well, doesn't it? And that's 239,000 miles (385,000 kilometers) away. (Okay, so the moon is much more massive than an artificial satellite and the strength of the attraction is proportional to the mass, but you get the point.)
If those floating folks aren't weightless, what do we mean by weight, anyway?
Weight is the strength of the gravitational pull that Earth exerts on an object. Because that strength diminishes the farther an object goes from the center of the Earth, its “weight” diminishes also. But never to zero.
Okay, then. If orbiting astronauts aren't exactly weightless, how come they can float around in the shuttle like that? The answer is that their still-considerable weight is counteracted by something else: a force that comes from their orbital speed. (Techspeak: centripetal force.)
Tie a string firmly to a rock and swing it around in a circle (outdoors!), holding your hand as stationary as possible. The rock is the shuttle and your hand is the Earth. Why doesn't the rock fly off? Because by means of the string you're pulling on the rock with exactly enough force—an imitation gravitational force—to counteract its tendency to fly away. Pull a little less hard (let some string slip out) and it flies outward, away from your hand. Pull tighter by pulling the string in (imitating a stronger gravitational attraction) and the rock “falls” inward toward where your hand used to be.
It's the same with the shuttle. The fact that the shuttle keeps going around in a stable circle rather than flying off into space means that its tendency to fly away from Earth is being exactly counterbalanced by Earth's gravitational pull, which holds it down. In other words, gravity is continually making the shuttle “fall” toward Earth, exactly enough to keep it from “rising” farther above Earth.
The same thing is happening to the astronauts inside. Their tendency to fly away from Earth is exactly balanced by Earth's pull, so they neither fly away nor fall to Earth; they stay suspended in midair, not knowing which way is up. Which is perfectly okay, because there is no “up.” “Up” has always meant “in the opposite direction from gravity's pull,” and gravity's pull is no longer discernible. That's why it's so much fun for them to pose for the camera with one guy upside down. Or is it downside up?
Incidentally, the fact that Earth's gravitational force is balanced by the orbiting astronauts' centripetal force doesn't entirely exempt them from the effects of gravity. It's only Earth's gravity that is balanced out. The moon, the planets, the shuttle and the astronauts themselves still attract one another because they all have mass. But because the moon and planets are so far away, and because the astronauts and their equipment don't have much mass, all these gravitational effects don't amount to much. They're still there, however, and that's why space scientists never talk about zero gravity; they say that the astronauts are operating in an environment of microgravity.
Up, Up … and Around!
How high does a rocket have to go before it can orbit around Earth?
It's not how high—it's how fast. There is a certain speed called the escape velocity that an object must achieve before it can keep circling Earth in a stable orbit and not fall down.
Let me take you out to the ball game.
Suppose that a center fielder tries to throw a runner out at home plate with a single mighty throw instead of relaying it via the second baseman. He throws the ball horizontally or slightly higher than horizontally, straight at the catcher. If there were no gravity (and no air resistance), the ball would continue in a straight line and go on forever. Or as Isaac Newton said in his First Law of Motion, “An object will continue moving in a straight line at a constant speed unless some other force screws it up.” (He may not have said it exactly that way.)
But in this case there is another force: gravity, which is pulling continuously down on the ball whether it is moving or not. The combination of horizontal motion from the throw and vertical motion from gravity results in the ball's following a curved path or trajectory. Unfortunately, few out-fielders can throw as fast and far as is necessary to pick off a runner at home plate, so the ball will hit the dirt well in front of the catcher.
Now let's ask Superman to throw a baseball horizontally out over the Pacific Ocean. (And again we'll ignore the air's resistance.) If he throws the ball at, say, 1,000 miles per hour (1,600 kilometers per hour), its curved path will be a lot longer and broader than in the case of the outfielder, but eventually, gravity will still be able to bring it down after perhaps a few miles.
Embarrassed by this pipsqueak performance, our hero then winds up and hurls another baseball out over the ocean at 25,000 miles per hour (40,000 kilometers per hour). This time the ball's trajectory is such a broad, shallow, flat curve that it matches the curvature of Earth's surface itself, so it just keeps going at a constant height above the surface and never falls down. It has gone into orbit.
So you see, putting a baseball or a satellite into orbit is purely a matter of throwing or shooting it fast enough that its trajectory will match the curvature of Earth. That speed, the escape velocity, is 6.96 miles per second (11.2 kilometers per second) or just about 25,000 miles per hour (40,000 kilometers per hour). Any slower than that and gravity will bring the object down before it has gone full circle around Earth. Any faster than that and it will still go into orbit, but it will reach a higher altitude above the surface before gravity wins out and bends its trajectory to the curvature of Earth.
In a very real sense, the orbiting baseball or satellite never does stop trying to fall to the surface; it's just that it is going fast enough “outward” to counteract gravity's inward pull.
That's why physicists and space scientists say that an orbiting satellite or space shuttle is in continuous free fall, falling freely toward the center of the Earth, just as if it had been dropped from a height. And that's why the astronauts inside an orbiting shuttle float freely in the air, just as they would if they were in a falling elevator whose cable had snapped.
You Didn't Ask, but …
If Earth is spinning, why doesn't the atmosphere go flying off into space?
In order to leave this planet, the air—just like anything else—would have to be moving at a speed equal to the escape velocity. That would amount to a humongous wind. While Earth's motion does affect the winds, the effect is nowhere big enough to get them to blow as fast as the escape velocity.
Individual air molecules may reach escape velocity, however, and some of the lightest atoms such as hydrogen and helium do indeed go into orbit at the top of the atmosphere.
Eavesdropping on the Lake
Sometimes when I'm in my summer cabin on the lakeshore at night, I can hear actual conversations of people on the opposite shore, even though it's half a mile or more away. How come?
It's as if the lake magnifies the sound somehow, isn't it? But it isn't actually magnifying the sound, as a microphone and amplifying system would do; it's just that more of the sound is being funneled toward your ears.
Sound consists of vibrations of the air. The guy on the other side of the lake makes sounds by forcing air from his lungs over his vocal cords, which makes them vibrate. They, in turn, make the air exiting his mouth vibrate. He shapes these vibrations into words with his lips and tongue, and the modified vibrations are transmitted through the air to you as air-pressure waves, similar to ripples moving across the surface of water.
As you can see by dropping a rock into a quiet pool of water, water waves spread out equally in all directions. It's the same with sound waves, but in three dimensions; they spread out through the air in all directions: up, down, north, east, south and west. Naturally, when you're at some distance from the speaker you will be able to hear—that is, your ears will intercept—only a small fraction of the spreading waves. The farther away you are, the smaller the fraction of the total sound energy your ears will be able to intercept, because most of it has gone in other directions and the farther away you are, the more “other directions” there are. At half a mile away, the fraction that reaches your ears is usually so small that you can't hear the guy at all if he's speaking at a normal conversational level.
The unusual effect that you're describing has to do with the fact that sound travels slightly faster in warm air than in cool air. That's because air molecules can transmit vibrations only by actually colliding with one another, and warmer molecules collide more frequently because they're moving faster. So we have to take a close look at the temperature of the air above the lake, to see what temperature effects there might be and how they might affect the sound.
During the day, the sun had been beating down on the air and water. But compared with air, water is very hard to heat up, so the water remained cooler than the air. (You may even have jumped into the lake to cool off, right?) The cool water cools the layer of air immediately above it, so that there is now a layer of cool air beneath the upper layers of warmer air. And if there is no wind to scramble up the air layers, they'll stay that way into the evening.
You, at the edge of the lake, are pretty much in the cool layer. The sound coming from bigmouth across the water travels mostly through the upper, warm layer, but when it gets to you it encounters cooler air and slows down. This sudden slowing down of the sound waves makes them bend downward; they are refracted, just as light waves are bent downward when they are slowed down while going from air into water. You can think of it as the faster, upper sound waves overtaking the slower, lower sound waves and tumbling over them, so that the sound spills downward. Thus, an unusual number of sound waves are aimed downward to your ears and you hear more than you have any “right” to hear, based solely upon your distance.
Of course, this works both ways. So when you're sitting on your cabin porch in the early evening hours on a calm, summer day, watch what you say—especially about that jerk on the other side of the lake.
If I could drive my car faster than the speed of sound, would I still be able to hear the radio?
As your question implies, this is purely an exercise in “What if?” Automobiles, of course, aren't built sleek enough or strong enough to exceed the speed of sound or to withstand the physical stresses of the sound barrier. But it's fun to think about.
The answer is simple: Yes.
Or, I could have posed a different question that would settle the issue: On the supersonic Concorde airliner, can the passengers converse? At those prices they'd better be able to. But how, if they are traveling faster than sound?
Even if you were driving faster than the speed of sound, you and the car and the radio and your terrified passengers would all be moving at exactly the same speed relative to the countryside. You're all in the same boat, so to speak. As far as sound is concerned, the important thing to realize is that you and the radio and the air in between aren't moving relative to one another. The radio has the same spatial relationship to you as if the car were standing still. It emits its sound waves through the car's air to your ears with the speed of sound as if nothing unusual were happening, because inside the car, nothing is. In fact, if the speedometer and windows were blacked out (God help you), you wouldn't even know you were moving except for the noise and vibration from the wind and the tires.
What if you were driving a supersonic convertible with no windshield and the radio speaker in the back? Could you still hear it? No. Not even considering the effects of the wind on your poor, battered ears and brain, you wouldn't be able to hear the radio. The sound waves from the speaker are being transmitted through the air toward you at the speed of sound, but the air itself—the transmission medium for the sound—is moving backward away from you even faster. So the sound will never reach you. The sound is like a rowboat rowing upstream more slowly than the water is flowing downstream.
By the way, the radio receives its signals by radio waves, not sound waves, and radio waves travel at the speed of light, which is a million times faster than the speed of sound. So any motion of your car is certainly not going to have any effect on the radio's ability to play.
Now what about the sounds that escape from your car? What would a roadside cow hear? (You're not doing this on city streets, I hope.)
Your car noises, whether from radio, tires, engine or screaming passengers, are being sent out in all directions at the speed of sound. But you are approaching the cow faster than that; you are actually outrunning your own sound. As your car approaches the cow, then, she can hear none of the car noises that are trailing behind you until shortly after you pass, when she will hear a sonic boom and all the car noise.
Note that if you are outrunning sound, you won't be able to hear any sounds coming from behind you, because they can't catch up with you. That's why you can see the flashing lights on that police car that's chasing you, but you can't hear the siren. I doubt, however, that the trooper will accept that as an excuse.
1 The following treatment of airplane flight is based upon David Anderson and Scott Eberhardt's article “How Airplanes Fly: A Physical Description of Lift” (Sport Aviation, February 1999), which was pointed out to me by Richard E. Eckels.