In my post about Silexica ( Silexica: Mastering Multicore ) I said that I like to use planes as an analogy for cores in a multi-core system. As I said there: They haven't got appreciably faster but you can have lots of them. If you want to transport 10,000 people from London to New York, that works great. Getting a single very important person from London to New York in 10 minutes, forget it. The Boeing 707 had a top speed of 607 mph in 1958, the Boeing 787 (Dreamliner) has a top speed of 593mph (the huge Airbus 380 is a little faster at 634mph...I did say a little). But why? Why haven't aircraft got faster? Haven't we learned how to build more powerful engines? Carbon fiber wings? Computer-optimized engine control? Well, it's the day before a break and time for another of my off-topic posts. Not totally off-topic, there is a lot of semiconductor content in a plane. But today we are going to look at aerodynamics, not electronics. Bernoulli If you remember high-school physics, you probably got taught that planes fly because of Bernoulli's principle, something to do with the pressure decreasing as the velocity of a fluid increases. With the wing shaped like it is, curved on top, less curved on the bottom, the air on top has to go further, so there is lower pressure, so there is lift. This is not incorrect. It just doesn't generate nearly enough lift. Sorry, but your high-school physics teacher was not telling you the truth. In fact, shaping a wing like an "aerofoil" serves mainly to decrease the stall speed, at which the wing stops generating lift when the airflow separate completely. Here is the TL;DR picture that shows that the Bernoulli aerofoil stuff is not how a plane flies: Here's a photograph of a plane that I took in the Smithsonian Air and Space Museum. The Wright Flyer's surfaces were a little curved but not much. Like all planes (and propellers, which are just spinning wings) most of the lift comes from angling the wings to the airflow. A wing generates lift the same way your hand does if you stick it out of the window of a fast-moving car and angle it. It is actually Newton's 3rd Law of Motion, the one about equal and opposite reactions. The lift is equal to the downward impulse given to the air displaced by the sloped wing (or hand). Once the angle of attack of the wing (or hand) reaches about 15º the the airflow over the top gets messed up, the drag increases a lot. In a plane, it drops out of the sky, with your hand it gets pushed back hard towards the rear of the car, and if you are not careful it gets slammed against the car door. It is this angle that generates the lift. Propellers, which are just spinning wings, generate pretty much all their force this way. Airplane propellers usually do have an aerofoil cross-section for a little extra oomph, but if you have a fan at home, I bet its blades are just made out of flat steel, wood, or plastic. A Little Mathematics If you are allergic to math then you can skip this section, and skip to the amazing Great Flight Diagram that shows, on one diagram, how everything from flies and butterflies at the low end, up to the Boeing 747 and Airbus 380 at the high end, all follow the same rule, with birds and Spitfires in between. So, to make the idea of sticking your hand out of the car window more precise, we have that the lift is the rate of change of the momentum of the airflow past the wing, times the change in speed (directing the air downwards since we want to generate lift upwards). That flow of mass past the wing is ρVA kg/s where ρ (rho) is the air density, V is the air velocity, and A is the area of the wing (or hand). For a Boeing 747-400 cruising at 39,000 feet, the mass flow around the wings computes as 42 tons of air per second. The downward motion imparted to the air is proportional to the airspeed V and the angle of attack of the wing α. Putting that together, we get the lift L = αρV 2 A kg m/s 2 or Newtons (N). In level flight, the weight of the plane equals the lift (or else the plane would be going up or down). For a normal plane in cruise then, we have that the lift/weight is proportional to the density of the air, the square of the velocity, and the area of the wing. In fact W = 0.3 ρ V 2 A, where the 0.3, the constant of proportionality, is the right value for long-distance flight where the angle of attack will be about 6º. Let's go back to that Boeing 747-200 which has a wing area A = 511 square meters and flies at V = 560 mph (900 kph, 250 m/s) at 7 miles (12 kilometers) altitude where air density is 1/4 of its sea-level value. So ρ is 0.3 kg/m 3 and that tells us that the weight/lift will be 300,000 kg or 30 tons. Which, ta da, is the weight of a 747-200 at the midpoint of a long intercontinental flight. The Universal Link Between Wings and Weight Near the ground, air density is 1.25 kg/m 3 and so we can take our weight equation W = 0.3 ρV 2 A and fill in a fixed value for ρ and then divide by A to get the wing loading equation W/A = 0.38V 2 . So, if you are a bird, you can vary your wing loading and your speed. The greater the wing loading, the faster you have to fly. In fact, near sea-level (which birds are, but planes are not) the cruising speed depends only on the wing loading. As a general rule, if you make a flying machine/bird bigger, the weight goes up as the cube, but the wing area as the square, and so the wing loading will increase. So larger birds/planes have to fly faster. There is a reason that a 747 flies a lot faster than a sparrow. But there is a square in there. If the weight increases by 100, the wing loading W/A increases by a factor of 5 and so the airspeed increases by a bit more than 2. This is also why planes have not got faster, since they would need to be a lot heavier. That would be fine once they were in the air, but it would mean longer runways at any airport they needed to operate, since they need to get up to speed (not cruising speed, you don't have to get a 777 up to 500 mph to get off the ground, but it is still related to weight). Also, faster planes would be desirable for business reasons but it is questionable whether larger ones are. Airbus is struggling to sell enough 380s (it is not good when Forbes titles its article The Death Watch Begins ), and it looks like Boeing's bet to invest in the 787, which is a much smaller extended range aircraft, was the better bet. It already has orders for about 4 times the order book for the 380, although with planes what counts as an order seems to be extremely sketchy. The 787 can go point to point on long flights like San Francisco to Tel Aviv where the number of passengers wouldn't justify a much larger aircraft. I, for one, prefer to fly to Tel Aviv on a Boeing 787, rather than an Airbus 380 to Frankfurt and then an Airbus 320 (or something similar) to Tel Aviv. On the topic of long flights, the current longest scheduled flight in the world is Auckland (New Zealand) to Doha (Qatar) taking 18 hours 10 minutes (flying a 777). And the answer to an even more trivial question is Westray to Papa Westray in the Orkney Islands off the north coast of Scotland. That is the shortest scheduled flight in the world, scheduled for one and a half minutes, although it is less than a minute in the air. Logan Air has been flying the route since 1967, so for 50 years. You can also waste a lot of fuel and go faster, even supersonic. But apart from sonic boom issues, it takes over 3 times as much fuel to fly supersonically, due to the huge increase in drag (remember, drag is proportional to the square of the speed). British Airways and Air France were quite happy to see the end of Concorde since its fuel economy was so terrible it was impossible for them not to lose a lot of money on every flight. So finally, pulling it all togther, it is time for... The Great Flight Diagram This is truly an extraordinary diagram, like one of those Moore's Laws plots that goes from chips with 64 transistors to chips with 6 billion transistors without much deviation from the (logarithmic) straight line. In the bottom left are insects (with exoskeletons). You don't even see a kink in the curve when it goes to tiny birds (with endoskeletons), or when large birds change to planes. There are some weird ones with things like the human powered Gossamer Condor, which has to cope with being underpowered by having very large wings for its weight. The Boeing 737 is the other way around: for its weight, it should have larger wings and fly slower, but instead it is designed to fly at the same speed as its larger brethren so that it can stay in place in the same flight lanes. The Simple Science of Flight All this comes from Henk Tennekes marvelous book The Simple Science of Flight: From Insects to Jumbo Jets . This is a "revised and expanded" edition, which presumably has some more material in since the edition I have from the mid-1990s. Poking around to find a picture of the cover, I discovered that MIT has a PDF version of the first chapter , which derives all these basic equations to get to the Great Flight Diagram. I'll give Henk the closing paragraph, on just how efficient flying is: A 747 with 350 people [out of 400] on board consumes 0.016 gallon per passenger-mile, no more than a car with two people in it...Nine times as fast as an automobile, at comparable fuel costs: no other vehicle can top that kind of performance. But birds perform comparable feats. The British house martin migrates to South Africa each autumn, the American chimney swift winters in Peru, and the Arctic tern flies from pole to pole twice a year. Birds can afford to cover these enormous distances because flying is a relatively economical way to travel far. Happy Holidays Happy Holidays to you all. Cadence is shutdown for the next two weeks, until January 2nd. But Breakfast Bytes will restart on January 1st, since it is the 200th anniversary of something. You'll have to wait for that post to find out what. Sign up for Sunday Brunch, the weekly Breakfast Bytes email.![]()
↧