How does a fan work?

Everywhere I turn, all the talk is about the coronavirus, and it’s exhausting because I already deal with news of the coronavirus as part of my day-job. It’s impossible to catch people having conversations about anything else at all. I don’t blame them, of course, but it’s frustrating nonetheless.

I must admit I relished the opportunity to discuss some electrical engineering and power-plant management when Prime Minister Narendra Modi announced the nine-minute power shutdown event on April 5. So now, to take a break from public health and epidemiology, as well as to remember that a world beyond the coronavirus – and climate change and all the other Other Problems out there – exists, I’ve decided to make sense of how a fan works.

Yes, a household fan, of the kind commonly found in houses in the tropics that have electricity supply and whose members have been able to afford the few thousand rupees for the device. The fan’s ubiquity is a testament to how well we have understood two distinct parts of nature: electromagnetic interactions and fluid flow.

When you flick the switch, a fan comes on, turning about faster and faster until it has reached the speed you’ve set on the regulator, and a few seconds later, you feel cooler. This simple description reveals four distinct parts: the motor inside the fan, the regulator, the blades and the air. Let’s take them one at a time.

The motor inside the fan is an induction motor. It has two major components: the rotor, which is the part that rotates, and the stator, which is the part that remains stationary. All induction motors use alternating current to power themselves, but the rotor and stator are better understood using a direct-current (DC) motor simply because these motors are simpler, so you can understand a lot about their underlying principles simply by looking at them.

Consider an AA battery with a wire connecting its cathode to its anode. A small current will flow through the wire due to the voltage provided by the battery. Now, make a small break in this wire and attach another piece of wire there, bent in the shape of a rectangle, like so:

Next, place the rectangular loop in a magnetic field, such as by placing a magnet’s north pole to one side and a south pole to another:

When a current flows through the loop, it develops a magnetic field around itself. The idea that ‘like charges repel’ applies to magnetic charges as well (borne out through Lenz’s law; we’ll come to that in a bit), so if you orient the external magnetic field right, the loop’s magnetic field could repel it and exert a force on the wire to flip over. And once it has flipped over, the repelling force goes away and the loop doesn’t have to flip anymore.

But we can’t have that. We want the loop to keep flipping over, since that’s how we get rotational motion. We also don’t want the loop to lose contact with the circuit as it flips. To fix both these issues, we add a component called a split-ring commutator at the junction between the circuit and the rectangular loop.


The commutator consists of two separate pieces of copper attached to the loop. Each piece brushes against a block of graphite connected to the circuit. When the loop has flipped over once, the commutator ensures that it’s still connected to the circuit. However, the difference is that the loop’s endpoints now carry current in the opposite direction, producing a magnetic field oriented the other way. But because the loop has flipped over, the new field is still opposed to the external field, and the loop is forced to flip once more. This way, the loop keeps rotating.

Our DC motor is now complete. The stator is the external magnetic field, because it does not move; the rotor is the rectangular loop, because it rotates.

A DC electric motor with a split-ring commutator (light blue). The green arrows depict the direction of force exerted by the magnetic field on the current carrying loop. Credit: Lookang/Wikimedia Commons, CC BY-SA 3.0

In an induction motor, like in a DC motor, the stator is a magnet. When a direct current is passed through it, the stator generates a steady magnetic field around itself. When an alternating current is passed through it, however, the magnetic field itself rotates because the current is constantly changing direction.

Alternating current has three phases. The stator of an induction motor is really a ring of electromagnets, divided into three groups, each subtending an angle of 120º around the stator. When the three-phase current is passed through the stator, each phase magnetises one group of magnets in sequence. So as the phases alternate, one set of magnets is magnetised at a time, going round and round. This gives rise to the rotating magnetic field. (In a DC motor, the direction of the direct current is mechanically flipped – i.e. reoriented through space by 180º degrees – so the flip is also of 180º at a time.)

A stator of ringed electromagnets produces a rotating magnetic field as a sum of magnetic vectors from three phase coils. Caption and credit: Mtodorov_69/Wikimedia Commons, CC BY-SA 3.0

The rotor in an induction motor consists of electrical wire coiled around a ring of steel. As the stator’s magnetic field comes alive and begins to rotate, the field ‘cuts’ across the coiled wire and induces a current in them. This current in turn produces a magnetic field coiled around the wires, called the rotor’s magnetic field.

In 1834, a Russian physicist named Heinrich Emil Lenz found that magnetic fields also have their own version of Newton’s third law. Called Lenz’s law, it states that if a magnetic field ‘M’ induces a current in a wire, and the current creates a secondary magnetic field ‘F’, M and F will oppose each other.

Similarly, the stator’s magnetic field will repel the rotor’s magnetic field, causing the former to push on the latter. This force in turn causes the rotor to rotate.

We’ve got the fan started, but the induction motor has more to offer.

The alternating current passing through the stator will constantly push the rotor to rotate faster. However, we often need the fan to spin at a specific speed. To balance the two, we use a regulator. The simplest regulator is a length of wire of suitably high resistance that reduces the voltage between the source and the stator, reducing the amount of power reaching the stator. However, if the fan needs to spin very slowly, such a regulator will have to have very high resistance, and in turn will produce a lot of heat. To overcome this problem, modern regulators are capacitors, not resistors. And since resistance doesn’t vary smoothly while capacitance does, capacitor regulators also allow for smooth speed control.

There is another downside to the speed. At no point can the rotor develop so much momentum that the stator’s magnetic field no longer induces a useful current in the rotor’s coils. (This is what happens in a generator: the rotor becomes the ‘pusher’, imparting energy to the stator that then feeds power into the grid.) That is, in an induction motor, the rotor must rotate slower than the stator.

Finally, the rotor itself – made of steel – cannot become magnetised from scratch. That is, if the steel is not at all magnetised when the stator’s magnetic field comes on, the rotor’s coils will first need to generate enough of a magnetic field to penetrate the steel. Only then can the steel rotor begin to move. This requirement gives rise to the biggest downside of induction motors: each motor consumes a fifth of the alternating current to magnetise the rotor.

Thus, we come to the third part. You’ve probably noticed that your fan’s blades accumulate dust more along one edge than the other. This is because the blades are slightly and symmetrically curved down in a shape that aerodynamics engineers call aerofoils or airfoils. When air flows onto a surface, like the side of a building, some of the air ‘bounces’ off, and the surface experiences an equal and opposite reaction that literally pushes on the surface. The rest of the air drags on the surface, akin to friction.

Airfoils are surfaces specifically designed to be ‘attacked’ by air such that they maximise lift and minimise drag. The most obvious example is an airplane wing. An engine attached to the wing provides thrust, motoring the vehicle forward. As the wing cuts through the air, the air flows over the wing’s underside, generating both lift and drag. But the wing’s shape is optimised to extract as much lift as possible, to push the airplane up into the air.

Examples of airfoils. ULM stands for ultralight motorised aircraft. Credit: Oliver Cleynen/Wikimedia Commons

Engineers derive this shape using two equations. The first – the continuity equation – states that if a fluid passes through a wider cross-section at some speed, it will subsequently move faster through a narrower cross section. The second – known as Bernoulli’s principle – stipulates that all times, the sum of a fluid’s kinetic energy (speed), potential energy (pressure) and internal energy (the energy of the random motion of the fluid’s constituent molecules) must be constant. So if a fluid speeds up, it will compensate by, say, exerting lower pressure.

So if an airfoil’s leading edge, the part that sweeps into the air, is broader than its trailing edge, the part from which the air leaves off, the air will leave off faster while exerting more lift. A fan’s blades, of course, can’t lift so to conserve momentum the air will exit with greater velocity.

When you flick a switch, you effectively set this ingenious combination of electromagnetic and aerodynamic engineering in motion, whipping the air about in your room. However, the fan doesn’t cool the air. The reason you feel cooler is because the fan circulates the air through your room, motivating more and more air particles to come in contact with your warm skin and carry away a little bit of heat. That is, you just lose heat by convection.

All of this takes only 10 seconds – but it took humankind over a century of research, numerous advancements in engineering, millions of dollars in capital and operational expenses, an efficient, productive and equitable research culture, and price regulation by the state as well as market forces to make it happen. Such is the price of ubiquity and convenience.

The new and large fly the farthest

British Airways and Air France mutually retired the Concorde supersonic jet in 2003. Both companies cited rising maintenance costs as being the reason, which in turn were compounded by falling demand after the Paris crash in 2000 and a general downturn in civil aviation after 9/11. Now, American and French scientists have found that Concorde was in fact an allometric outlier that stood out design-wise at the cost of its feasibility and, presumably, its maintenance. Perhaps it grounded itself.

One thing Adrian Bejan (Duke University), J.D. Charles (Boeing) and Sylvie Lorente (Toulouse University) seem to be in awe of throughout their analysis is that the evolution of commercial airplane allometry seems deterministic (allometry is the study of the relationship between a body’s physical dimensions and its properties and functions). This is awesome because it implies that the laws of physics used to design airplanes are passively guiding the designers toward very specific solutions in spite of creative drift, and that successive models are converging toward a sort of ‘unified model’. This paradigm sounds familiar because it could be said of any engineering design enterprise, but what sets it apart is that the evolution of airplane designs appears to be mimicking the evolution of flying animals despite significant anatomical and physiological differences.

One way to look at their analysis is in terms of the parameters the scientists claim have been guiding airplane design over the years:

  1. Wingspan
  2. Fuselage length
  3. Fuel load
  4. Body size

Among them, fuel load and body size are correlated along the lines of Tsiolkovsky’s rocket equation. It says that, for rockets, if two of the following three parameters are set, the third becomes immovably fixed in a proportional way: energy expenditure against gravity, potential energy in the propellant, and the fraction of the rocket’s mass made up by the propellant. According to Bejan et al, there is a corresponding ‘airplane equation’ that shows a similar correlation between engine size, amount of fuel, and mass of the whole vehicle. The NASA explainer finds this association tyrannical because, as Paul Gilster writes,

A … rocket has to carry more and more propellant to carry the propellant it needs to carry more propellant, and so on, up the dizzying sequence of the equation

Next, there is also a correlation between wingspan and fuselage length corresponding to an economy of scale such as what exists in nature. Bejan et al find that despite dissimilarities, airplanes and birds have evolved similar allometric rules on the road to greater efficiency, and that like bigger birds, bigger airplanes are “more efficient vehicles of mass”. Based on how different airplane components have evolved over the years, the scientists were able to distill a scaling relation.

S/L ~ M1/6 g1/2 ρ1/3 σ1/4aV2Cl)-3/4 21/4 Cf7/6

Be not afraid. S/L is the ratio of the wingspan to the fuselage length. It is most strongly influenced by ρa, the density; σ, the allowable stress level in the wing; g, the acceleration due to gravity; and Cf, the fixed skin-friction coefficient. More interestingly, the mass of the entire vehicle has a negligible effect on S/L, which pans out as a fixed S/L value across a range of airplane sizes.

Citation: J. Appl. Phys. 116, 044901 (2014);
Citation: J. Appl. Phys. 116, 044901 (2014);

Similarly, the size of a plane’s engine has also increased proportional to a plane’s mass. This would be common sense if not for there being a fixed, empirically determined correlation here as well: Me = 0.13M0.83, where Me and M are the masses of the engine and airplane, respectively, in tons.

During the evolution of airplanes, the engine sizes have increased almost proportionally with the airplane sizes (the data refer only to jet engine airplanes). J. Appl. Phys. 116, 044901 (2014);
During the evolution of airplanes, the engine sizes have increased almost proportionally with the airplane sizes (the data refer only to jet engine airplanes). J. Appl. Phys. 116, 044901 (2014);

In terms of these findings, the Concorde’s revolutionary design appears to have been a blip on the broader stream of traditional yet successful ones. In the words of the authors,

In chasing an “off the charts” speed rating the Concorde deviated from the evolutionary path traced by successful airplanes that preceded it. It was small, had limited passenger capacity, long fuselage, short wingspan, massive engines, and poor fuel economy relative to the airplanes that preceded it.

That the Concorde failed and that the creative drift it embodied couldn’t achieve what the uninspired rules that preceded it did isn’t to relegate the design of commercial airplanes to algorithms. It only stresses that whatever engineers have toyed with, some parameters have remained constant because they’ve had a big influence on performance. In fact, it is essentially creativity that will disrupt Bejan et al‘s meta-analysis by inventing less dense, stronger, smoother materials to build airplanes and their components with. By the analysts’ own admission, this is a materials era.

Bigger airplanes fly farther and are more efficient, and to maximize fuel efficiency, are becoming the vehicles of choice for airborne travel. And that there is a framework of allometric rules to passively maximize their inherent agency is a tribute to design’s unifying potential. In this regard, the similarity to birds persists (see chart below) as if to say there is only a fixed number of ways in which to fly better.

The characteristic speeds of all the bodies that fly, run, and swim (insects, birds, and mammals). J. Appl. Phys. 116, 044901 (2014);
The characteristic speeds of all the bodies that fly, run, and swim (insects, birds, and mammals). J. Appl. Phys. 116, 044901 (2014);

From the paper:

Equally important is the observation that over time the cloud of fliers has been expanding to the right . In the beginning were the insects, later the birds and the insects, and even later the airplanes, the birds, and the insects. The animal mass that sweeps the globe today is a weave of few large and many small. The new are the few and large. The old are the many and small.


The evolution of airplanes, J. Appl. Phys. 116, 044901 (2014); DOI: 10.1063/1.4886855

Brazuca over Jabulani for better football, say physicists

Say hello to Brazuca, the official football of the 2014 FIFA World Cup. Brazuca is a ball designed and produced by sportswear manufacturer Adidas, which also produced the Jabulani used in the 2010 World Cup. Both balls are part of a legacy where designers are reducing the number of panels they are constituted by. Until the late 2000s, the conventional football had 32 panels of hexagonal and pentagonal shapes. Jabulani has eight panels and Brazuca, six.

However, that didn’t do much good for Jabulani, which faced a lot of flak during the 2010 FIFA World Cup, for which it was made, because of its wobbly movement through the air. And according to a study in Scientific Reports published May 29, scientists have figured out why and found the problem fixed in Brazuca.

Sungchan Hong and Takeshi Asai, both from the University of Tsukuba’s Institute of Health and Sports Science, used a wind-tunnel and a robot to kick balls toward goal-posts 25 m away, to study the spheres’ non-spin aerodynamics. Their results show that Brazuca displayed very little of the irregular fluctuations that Jabulani did, and other improvements besides, because of the shape of its panels and their rough surface.

Photograph of the wind tunnel test setup. Image: doi:10.1038/srep05068

Photograph of the wind tunnel test setup. Image: doi:10.1038/srep05068
Photograph of the wind tunnel test setup. Image: doi:10.1038/srep05068

When a smooth, spherical ball with seams is kicked up, streams of air moving near the seams exert a different amount of force on the ball than air flowing around elsewhere. This asymmetry gives rise to a wobbly movement of the ball, which Jabulani was especially susceptible to. At the time, it was considered to be one of the reasons the tournament’s first leg had as few goals as it did. Rabindra Mehta, Chief Aerospace Engineer at NASA Ames Research Centre, told Discovery, “You want to see more consistent, rounder balls that are totally water-proof. That’s all good stuff, but perhaps the aerodynamics was not looked at as carefully as [Adidas] should have.”

Jabulani also fell behind because, according to Hong and Asai, the asymmetry of forces was influenced by how the ball was oriented, too. Specifically, “the amplitude of the unsteady aerodynamic forces acting on soccer balls changes according to the number of panels as well as the directions they are facing,” they write in their paper. This means Jabulani moved differently depending on how it was facing when kicked.

Amplitude with respect to unsteady aerodynamic forces (blue line: side force, red line: lift force) of soccer balls derived using fast Fourier transform at flow speed of 30 m·s−1.
Amplitude with respect to unsteady aerodynamic forces (blue line: side force, red line: lift force) of soccer balls derived using fast Fourier transform at flow speed of 30 m·s−1. (a, b) Brazuca, (c, d) Cafusa, (e, f) Jabulani, (g, h) Teamgeist 2, and (i, j) conventional ball. From: doi:10.1038/srep05068

Hong and Asai also observed that there was a marked difference in the asymmetry of forces on Jabulani and Brazuca at higher speeds, such as during a freekick (30 m/s), with Jabulani consistently out-wobbling the others.

Brazuca overcomes these issues by boasting a rough, nubby surface. It reduces the asymmetry of air-flow and makes the ball’s motion smoother through the air. Second, the arrangement of Brazuca’s six curvaceous panels ensure the ball moves the same way no matter how it is kicked. With respect to the other balls, Hong and Asai write, “Brazuca and the conventional ball exhibited relatively stable and regular flight trajectories compared to Cafusa, Teamgeist 2, and Jabulani, whose panel shapes varied significantly with the orientation and were characterized by relatively irregular flight trajectories.”

However, this stamp of approval doesn’t count for much because conditions on a football field in Brazil are going to be very different from a controlled environment in a lab in Japan. There’s going to be wind, more or less humidity, different temperatures, the ball’s attitude during rains, etc. – not to mention players’ level of comfort. These are the real deciders, and only time will tell if Brazuca is in every way better than Jabulani.

But as far as the physics is concerned, Brazuca should make for better football.

Featured image: Adidas Brazuca, ИЛЬЯ ХОХЛОВ/Wikimedia Commons