2023-12-07 11:00:43
Photography: Zoi Koraki (CC).
Who doesn’t remember that vague description of a place in La Mancha and that man on a horse who would later charge into a windmill, mistaking it for a giant. Gustave Doré helped perpetuate the image of the ingenious gentleman turned by a mill thanks to his popular engraving, reproduced ad nauseam. As a child I was plagued with doubt: could the blade hit you that hard when it was working? Because looking at the illustration, the impact left Alonso Quijano and Rocinante in foreshortening only within the reach of Spider-Man. Todd McFarlane: He only needed to dress them as a bullfighter. If you see a windmill at full capacity up close, it does seem like you can earn a good hit, but how hard?
The wind is air in movement
As the character would say Breaking Bad Jesse Pinkman: “science, bitch!” And that moving air can be used from a mechanical point of view. If we consider an imaginary cylinder of ten meters in diameter containing air moving at 25 km/h, the wind power it has is, in round numbers, about 20 horsepower (CV) or 15,800 watts (W); That is, similar to that of a Seat 600 from the late fifties or about forty 40 W light bulbs. If the wind from that same cylinder were blowing at 80 km/h we would already be talking about about 700 HP or 520,000 watts, the power of a Lamborghini Murcielago-type supercar or around thirteen thousand 40-watt light bulbs. This important difference is due to the fact that wind power depends on the cubed wind speed, so it varies rapidly. But all that power is not usable: for that to happen, the speed of the air after passing through the windmill blades would have to be zero; That is, all the kinetic energy of the wind would have been transformed into turning the blades. And you know what Homer Simpson said: “In this house we obey the laws of thermodynamics.” As demonstrated by the physicist Albert Betz, only a maximum of around 59% of the wind power can be used (what is called the Betz limit), which theoretically occurs when the blades are capable of reducing the leeward wind speed to a third of the incident speed. . Now that we know how powerful the wind is, there is only the small detail of taking advantage of it.
The La Mancha windmill
Intuitively we all know how a windmill works. In effect, the blades rotate with respect to their axis of rotation, a piece of wood about 60 or 70 cm in diameter called the “mill axis”, due to the aerodynamic forces that are generated when they are in a moving fluid (air). The iconic image of the La Mancha windmills has four blades… and why four? The most common wind turbines have been designed with three blades, the configuration considered the most efficient which has been arrived at after in-depth technical but also economic analysis: based on certain dimensions (some are more than 70 meters in length), build a blade extra is much more expensive both economically and in terms of implementation and maintenance. The four-bladed design of the La Mancha mills responds to several practical questions resulting from experience (we are talking about more than four hundred years ago, forget about computer simulations). On the one hand, the blades were joined two by two with a type of ring fixed to the shaft. Joining the four blades (or even three) into a single ring concentrated their weight too much and put the strength of both the shaft and the ring itself at risk. And on the other hand, placing an odd number of blades complicated the execution and balance of the assembly, which was not manufactured with the current exhaustive controls. Furthermore, if another pair of blades were provided to raise the total number to six, the section of the cantilever mill shaft would be longer (it would support three two-blade “rings”), implying more stress on the shaft that would make operation more difficult ( more diameter of the axle wood, more friction, more weight).
The axis of the windmill usually forms about 15º with the horizontal both for reasons of aerodynamic efficiency (the wind at low altitude is not completely parallel to the ground due to its roughness) and construction (this way the weight of the blades can be better balanced). Propelled by the wind, the blades made of wood and slats and covered with canvas begin to rotate, losing part of the energy due to the friction of the shaft with the supporting stone, the “bollega stone”, which is greased. From the support on the stone, the axis is already inside the building. The catalina wheel is embedded in the axis of the mill, which, as its name suggests, acts in a similar way to the chainring of a bicycle, engaging (without a chain, of course) to the lantern, another wheel located on a vertical axis. The relationship between one and the other multiplies the turns by five. Or put another way, for every turn of the blades, the flashlight makes five: a tough development for climb the Tourmalet. The shaft of the lantern is also attached to one of the proverbial “mill wheels”, large stone discs measuring six feet in diameter and weighing about 1,200 kilos (like for communion, come on), and that is where, between a wheel mobile and another fixed, the miracle of transforming the grain into flour is worked.
The iconic image of a La Mancha mill is made up of a large cylinder of whitewashed stone crowned by a wooden cover from which emerge both the blades and another piece of wood, called the government, which is anchored to the ground and serves to orient the mill towards the sea. wind. The conical cover, called the hood, is designed in such a way that it can rotate on the stone structure. Pulling on the steering wheel, the hood, which weighs more than five tons (which is why the walls of the mill are about a meter and a half thick), is slowly moved until the blades are facing the wind. Once placed in position, the steering is anchored to some fixed milestones on the ground already prepared, since the prevailing winds at the location of each mill are known in advance. The cylindrical shape of the main body of the building is thus, therefore, to facilitate the orientation of the cap and minimize the flight of the mill axis. Furthermore, the sprocket wheel remains engaged with the flashlight in any position of the cap. Everything is thought out.
These gears, turning points and elements of wood, stone and canvas executed in an artisanal way meant that, according to various studies, under a wind of about 25 km/h, the windmills gave a power of about 20 HP (remember, like a 600 ), while its blades, almost 8 meters long, will complete about twelve revolutions per minute. These studies conclude that around 30-35% of wind power is used. To establish a comparison, the latest generation wind turbines raise this figure to 46%, halfway between a La Mancha windmill and the Betz limit.
Windmill blade hit, clever gentleman dance
Now that we know approximately the speed at which the blades rotate (if they rotate twelve times per minute and measure about eight meters, the end moves at about 36 km/h), we only have the context. If we continue within fiction, for example in Knights of the Zodiac, the bronze knights were capable of delivering smacks at the speed of sound (about 1,224 km/h), while the golden knights had you looking at the constellation of Sagittarius delivering smack at the speed of light (about 300,000 km /s). Poor Don Quixote if Pegasus’ knight happens to get a meteor. These are figures very far from the windmill blades. Let’s get to something more real: boxers. If a live from the best Mike Tyson If it reached your face, it would do so at about 10 m/s; What would happen next will not surprise you. Curiously, 10 m/s is approximately 36 km/h, the same as our blade end, which helps us get situated quite well. It is estimated that the punches of professional boxers, trained to transmit maximum force in the punch, are equivalent to five times their own weight. If we take into account that the male of the blade weighs around a ton and a half, without going into in-depth physical analysis, the blow could be compared to that of a Tyson who weighed fifteen times more than the ear-biter. In short, you would eat a hostion like a castle.
In Don Quixote it is related that “taking a spear to the blade, the wind turned it with such fury that it broke the spear into pieces, taking the horse and the knight with it, who rolled very badly battered across the field.” Come on, there was no direct impact as such. If the wood hits him, Cervantes should have finished the story in said chapter VIII, either because Alonso Quijano folded the napkin or because the tremendous blow restored his lucidity.
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