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Swimmer about to dive from the pool side into the water

The science of swimming

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by Chris Woodford. Last updated: February 8, 2017.

Humans evolved from sea creatures but—looking at our bodies—you'd never know it. We couldn't be less well suited to moving through water if we tried. We don't float too well, can't breathe for long beneath the surface, and rapidly tire as we thrash through the waves trying to move ourselves along; in a straight race with a dolphin or a shark, you'll always come last! But there's one big advantage we humans do have: we know about science. We understand how forces work and how to use them to our advantage. If you've never thought about swimming as a science, now's the time to start. Apply some scientific thinking and you'll find you can swim much more effectively. If you're a nervous nonswimmer, thinking about the solid science that keeps people afloat can give you enough confidence to break through your fear. So what are we waiting for? Let's take the plunge—with a closer look at the science of swimming!

Photo: Swimming takes humans back from the land to the ocean—or the pool! You have to apply forces to move yourself through the water and other forces slow you down. Understand those forces and you can swim much more effectively. Photo by R. Jason Brunson courtesy of US Navy.

What is swimming?

That sounds like a trivial question, but it helps to be clear. Swimming is moving your body through water (a moderately viscous fluid) that's either still (as in a swimming pool), turbulent (as in the ocean), or somewhere in between. If you're swimming completely under the surface (for example, scuba diving), you're moving through relatively still water; other times, you're going to be moving along at the more turbulent interface between air and water, with your legs, arms, head, and body moving from one element to the other and back again, speeding up or slowing down as they cross the border.

Photo of a swimmer breathing to the side.

Photo: Even the best swimmers have to move along the choppy interface between air and water. It's the most inefficient place to swim, but the only place you can do it if you need to breathe air! Photo by Jennifer A. Villalovos courtesy of US Navy.

Water versus air

Before we can understand the science of swimming, it helps to remember that air (a gas) is very different from water (a liquid). The biggest difference is that water is much more dense (the same volume of it weighs much more) and viscous (in other words, thicker—in the same way that treacle is more viscous than water).

The difference between air and water makes a huge difference to how we can move on air and land. When you walk on land, the main thing your body has to do is work against gravity (lifting your legs, swinging your arms, and keeping you from toppling over through constant adjustments of your balance) and a little bit of friction where your shoes meet the ground. If you move more quickly (say, on a bicycle), air resistance becomes a more important force than gravity; unless you're walking into a really strong wind, you barely notice the air while you're walking. When you're in the water, gravity is much less important because your buoyancy (tendency to float) largely cancels it out. The main force you have to think about as a swimmer is drag—water resistance. We'll come to that in a moment.

Other differences between water and air are important if you swim outdoors, particularly in the winter months: because water is much more dense than air, it removes heat from your body about 25–40 times faster than air at the same temperature. (That's why surfers and "wild" outdoor swimmers tend to wear wetsuits to avoid hypothermia, the very dangerous cooling of the body's core that can kill you.) Because water is so dense, it takes a long time to warm up. That's why the ocean temperature typically lags behind the land temperature by 2–3 months in countries such as the East Coast of the United States and the UK (where the ocean is often warmest in September).

Newton's laws of swimming

If you love science but swimming scares you, you'll find it very helpful—as I did when I was learning to swim—to think about Newton's three laws of motion. Among the most fundamental rules of physics, these three basic principles are enough to explain completely the movement of almost every single object you're ever likely to come across.

The first law outlines the concept of inertia. It says that things stay still or move steadily (at the same speed) unless something pushes or pulls them (unless some kind of a force is applied). The second and third laws are of more interest. The second law explains the connection between force and acceleration: if you push or pull something, it starts moving (if it was still to begin with) or goes faster (if it was moving already); the bigger the force you apply, the more acceleration you get; the longer you apply the force, the bigger the change in momentum you can achieve.

Swimmer underwater pulling water back to go forward.

Photo: Isaac Newton tells us we have to pull water backward to go forward, as this swimmer is doing by using his outstretched hand and forearm as a paddle. Photo by Alan D. Monyelle courtesy of US Navy.

Where swimming is concerned, the third law is perhaps the most important. It says that when you apply a force to an object, the object returns the favor and applies an equal force to you—in the opposite direction. This law is often called action and reaction and it's the simplest way for a scientific non-swimmer to make sense of the water. You probably know already that if you kick backward against the wall of a swimming pool, you shoot forward through the water. The same applies to actual swimming strokes. Simply speaking, if you want to swim forward through water, you have to pull water backward with your hands. If you want your body to stay up, floating on the surface, you need to kick down with your legs. If you're swimming along and you want to stop suddenly and stand up, you can pull your hands down in front of you (in a kind of circular motion—a bit like bowing down) and your legs will swing down behind you, so you land in an upright position on your feet. Master these basic moves—simple applications of Newton's third law—and you'll find you'll be able to swim easily and stop confidently whenever you need to.

Minimizing your drag

Photo of a speed cyclist wearing a helmet.

Photo: Speed cyclists realize they have to minimize drag because they can feel the air pushing hard against them. Even though water is "thicker" and swimmers feel the drag of the water much more, they don't always realize the importance of minimizing drag.

Lots of other scientific factors make a big difference to how well you can move through the water. Once you've mastered the basic science of swimming, minimizing your drag in the water is the next step: that will help you swim faster and for longer. Many beginners don't really understand this, but it's exactly the same as cycling: in the same way that cyclists have to minimize the surface area they present to the wind (crouch forward, put their arms in, and generally streamline themselves), so swimmers have to create as little resistance to the water as they possibly can. In practice, this means making your body completely horizontal, so (in the case of front crawl) your head is well down in the water rather than poking up with your body sloping down behind it. (That's why you have to learn how to breathe in at the side and breathe out underwater.) You can also minimize drag by slicing your hand in and out of the water to make your strokes and, in front crawl, you can learn to swivel your body as you swim from side to side.

It's worth noting that sea-water is harder to swim in than pool water, for several reasons. First, except on beautifully calm summer days, the ocean is almost always more turbulent, so your body doesn't slice through the water like a dolphin. Sea-water is also more dense than freshwater because of the salt it contains, and that makes it slightly more viscous too. And cold water (in the ocean) is more viscous than hot water (in a heated pool); the viscosity of water at 10°C (50°F) is twice that of water at 40°C (~100°F). All these things make a cold ocean swim a tougher proposition than a swim in the heated pool, but the upshot is that your body is working harder and getting more exercise.

Unlike with cycling or sprinting through air, it's hard to built up any momentum when you're swimming: the water resistance is constantly trying to bring you to a halt. What we have here is the first law of motion in action. If water were as light as air but you could still float and swim through it, you could stroke for a while and then rest, allowing your momentum to keep you moving forward (much as you can stop pedaling on a bicycle every so often). But the force of the water pushing against you brings you rapidly to a rest. You'll also experience inertia when you try to change direction: since velocity is speed in a particular direction, changing direction means changing velocity—and it requires you to use a force, even if you swim at constant speed. If you're doing front crawl and you decide you want to turn around in a semi-circle and go back the way you came, it's actually quite hard to change the direction of your motion without stopping and reversing or doing a somersault.

Swimming efficiently

Swimming is superb aerobic exercise (vigorous exercise that really pumps your heart and lungs) and very tiring; the two things are, of course, connected. You can swim further for longer by swimming more efficiently, which means using as little energy as possible for each stroke by getting as much forward propulsion as possible.

With front crawl, the object is to extend your hand as much as you can and bring it back as far as possible, dragging as much water back (with a cupped hand and a bent forearm) as you possibly can. If you make a long, complete stroke with a proper follow-through, you're applying your pulling force for longer and each stroke will count for more. You can see this from Newton's second law of motion, which is often written:

force = mass × acceleration
F = m a

Since acceleration is velocity divided by time, it's also true that force is equal to the rate of change of momentum:

F = mv / t

and that:

force × time = mass × velocity
F t = m v

To put it another way, if you want to produce the biggest possible change of momentum, you need to apply your force (pulling back on the water) for as long as possible—with as long a stroke as possible and a good, complete follow-through. It's also worth remembering that the human body is a machine (in the strict scientific sense of that word): our limbs work like levers, pivoted at our joints (which are effectively fulcrums), multiplying force or speed. When you're doing front crawl, it's important to reach forward and pull your arm backward as much as you possibly can. You get more leverage on the water that way and the force you create pulling backward will give you more force to go forward. A good follow-through also decelerates your limbs more slowly, and reducing the acceleration reduces the force they feel, reducing the likelihood of pulled muscles and other injuries.

Swimmer reaching arm forward as far as possible during front crawl.

Photo: It's important to reach forward and extend your arm as much as possible. Photo by Joseph M. Clark courtesy of US Navy.

The conservation of momentum tells us that the momentum you give your body, going forward, is the same as the momentum you give the water, pulling backward. That implies that you need to pull as much water backward as you possibly can with each stroke. Cupping your hand helps; so does using your forearm as a kind of paddle, so you pull back an entire arm's worth of water rather than a mere handful. You'll find this is much harder and more tiring to begin with, which is a good sign: it shows you're creating much more force.

Energy and power

It takes energy to push your body through the water—and your body loses the same amount of energy in the process. The rate at which something uses energy is called power. According to an interesting blog post in Wired by physicist Rhett Allain, champion swimmers can briefly achieve a power of 1200 watts (the maximum power of a clothes washing machine or a very powerful vacuum cleaner), which is about three times what a champion cyclist achieves. It's not surprising that a swimmer uses more energy than a cyclist given that all four of a swimmer's limbs are moving all the time (compared with just a cyclist's legs), and in a more dense fluid. But it is surprising to me that the difference is so great: there's no obvious reason why a human body working at full tilt should be able to produce so much more power in one fluid (water) than another (air). In his book The Human Machine, British zoology professor R. McNeill Alexander quotes power figures for swimming that are in the hundreds of watts. Consistent with what cyclists produce, that seems more likely to me. (It's also similar to the figure in the calculation in the box at the end of this article.)

Bar chart comparing the power consumption of swimming in watts to other everyday types of power use.

Chart: Top swimmers (and cyclists) can produce several hundred watts of power, which is about twice as much as the rest of us. This chart shows how that amount of power compares to some familiar everyday appliances. In theory, a swimmer could power three LCD TVs, four old-fashioned lamps, or 20 energy-efficient lamps.

Floating and buoyancy

Things float because when we place them in water, the pressure of the water underneath them pushes up and supports them; in other words, water pressure pushing upward balances weight (the force of gravity) pulling downward. That's one of the reasons why we swim in a horizontal position: spreading the body flat makes it work more like a raft, so there's more upthrust from the water below. You probably know that it's much easier to float on your back than standing straight upward, when you need to "tread water" (kick and push your arms downward to create an upward force that stops you sinking).

Photo of a swimmer practicing the dead man's float survival technique.

Photo: Our bodies are surprisingly buoyant, but we float better in some positions than others. This swimmer is practicing a survival technique called the prone or "dead man's float," which helps you float in water for longer and conserve energy. Photo by William R. Goodwin courtesy of US Navy.

A non-swimmer's biggest fear is sinking under the water and drowning, but it's much harder to sink when you're swimming than you might suppose. (Unlike when you accidentally fall into a river, where you're more likely to sink and drown because your clothes get wet and stop you swimming properly; factors such as the coldness of the water also play a part.) Depending on your body type (how big you are, how much you weigh, how big your lungs are, how fat you are, and so on), you may be surprisingly buoyant: you might find it quite hard to sink even if you want to. It's fairly well known that fatter people are more buoyant than skinnier ones, and that's because fat is less dense (more buoyant) than muscle. Wearing a wetsuit (made from a synthetic rubber called neoprene, which traps air bubbles inside it) makes you even more buoyant, which is why scuba divers typically have to wear weights to make them sink.

Is it better to float or to sink? If you're a boat, it's certainly better to do one or the other! Unfortunately, most boats do a bit of both: they crash and drag straight through the waves—in the very turbulent interface between the air and the water. The fastest boats are hydrofoils and hovercraft (which aim to lift themselves clear of the waves) and submarines (which sink beneath them). If you're a swimmer, neither of these is really an option. We can't choose whether to sink or float: we have to drag through the water. Even so, understanding the science of swimming and mastering how we apply it can help us poor land creatures to move as efficiently through the water as possible!

Question: Does swimming warm the pool?

James Prescott Joule's famous experiment to calculate the mechanical equivalent of heat using a falling weight and a paddle wheel inside a container of water.

If you're a fan of science, you probably know about one of the greatest physics experiments of all time, which was carried out by James Prescott Joule in 1840. He was proving what's now called the law of conservation of energy—the basic idea that we can't create or destroy energy, but only convert it from one form to another. He did it using this apparatus, in which a weight (1) running over a pulley (2) pulls on a rope (3) and spins a paddle wheel so it agitates water inside a closed container (4), heating it up by a small amount. After repeating the experiment quite a few times to get a measurable temperature rise, Joule calculated that the potential energy lost by the falling weight was exactly the same as the heat energy gained by the water in the container.

Recently someone emailed me asking whether swimmers warm the water they're standing or moving in, which is a more complex question than you might think for all sorts of reasons. But it set me thinking about Joule's experiment and whether a pool full of people, swimming furiously, would warm the water by a noticeable amount. This is the kind of "back-of-envelope" calculation that all physicists love!

Let's assume some things to make life easy:

  1. As people swim, all the energy their bodies produce in the process ends up as heat in the water.
  2. The only thing warming the water is the physical agitation caused by the swimming. I'm going to completely ignore the ordinary heat lost from the swimmer's bodies to the cooler water (mostly by conduction).
  3. All the energy that goes into the water stays there. None goes into the air above or the material surrounding the pool.
  4. The swimmers can happily keep swimming away at a constant rate indefinitely, no matter how hot the water gets (if indeed it does). There's no reason why the swimmers couldn't be replaced by other people and, if necessary, we could put them in heatproof suits!
  5. The specific heat capacity of water (the amount of energy it takes to raise 1g of water by 1°C) stays the same as the temperature changes.
  6. And so on. I'm just interested in a "guesstimate," not an exact calculation.

Let's assume that there are 50 swimmers in an Olympic size pool and they swim so fast that each of them consumes 1500 kJ of energy per hour and puts that much heat into the water. (That's a figure I've pulled from p26 of Richard Muller's excellent book Physics for Future Presidents, but it seems to be confirmed elsewhere. It's the equivalent of a few hundred calories.)

If 50 swimmers swim for one hour, we get a total heat energy input of 7.5 x 107J.

How much does that warm the water? An Olympic-sized pool has a (fairly gigantic) volume of 2.5 million liters, and a liter weighs about a kilogram, so we have a mass of water of 2.5 x 106kg.

The specific heat capacity of water is about 4.2 joules per gram per °C (in other words, it takes 4.2 joules to raise the temperature of 1 gram of water by 1°C).

So an energy input of 7.5 x 107J raises the pool temperature by 7.5 x 107 / (4.2 × 1000 to convert kilograms to grams × 2.5 x 106) = 0.007°C!

If the water is 20°C to start with, how long would it take the swimmers to make it boil?

We'd need a temperature rise of 80°C and we know it takes an hour to give us 0.007°C, so we'd need our swimmers to keep going for 11,200 hours = 466 days = about a year and three months.

Answer

Does swimming warm the pool? 1. Yes—the energy swimmers generate has to go somewhere. 2. No—the heat they produce by swimming is so minute that it makes no difference whatsoever, and the heat lost from the water would more than make up for it.

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Woodford, Chris. (2012/2016) Science of swimming. Retrieved from http://www.explainthatstuff.com/swimming-science.html. [Accessed (Insert date here)]

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