Scientists have only recently discovered the answer to a very modern dilemma: why does coffee spill when you walk? Dr Karl spills the beans on the very serious science of sloshing liquids.

Earlier this year, two engineers systematically explored why coffee spills when we walk (Source: iStockphoto)

Coffee is probably the world’s most popular legal drug. And so, in our busy day, at some stage we will usually walk from here to there carrying a cup of coffee. And every now and then, the coffee will spill. Now this might be a surprise to you, but it took till 2012 before two engineers systematically explored this very familiar phenomenon.

The engineers were H C Mayer and R Krechetnikov from the University of California. The problem of spilling coffee is very complex, and involves two separate fields biomechanics and the engineering of sloshing liquids.

Let’s deal with sloshing liquids first. This field is, surprisingly, very important. Liquids that are out-of-control and sloshing can sink a tanker ship, starve a car engine of fuel, and make a liquid-fuelled rocket fail.

Now for biomechanics, which lead to the coffee cup going through some very complicated motions.

As you walk, your centre of mass follows a rather strange pathway. Your gait depends on many factors such as your gender, age, state of health and so on. After all, walking has been described as “a series of controlled falls”. Your centre of mass is continually speeding up and slowing down in your direction of travel, as well as rising and falling and oscillating from side to side to boot. When you are walking, you typically rock from side to side at about 1.25 hertz, while you oscillate back and forth at around 2.5 hertz. But that’s just the motion of your centre of mass.

Your cup of coffee is joined to your centre of mass via your hand, and your wrist, elbow and shoulder joints. Each of these can move in a motion that is very different from what your centre of mass is doing. Your cup of coffee can tilt to the left or right, it can pitch down or up in your direction of travel, or it can even swivel to the left or right.

The engineers drew the appropriate diagrams of a walking person and of a cup, and then labelled all the relevant positions, velocities and accelerations. What they called “a frictionless, vorticity-free, and incompressible liquid”, you and I would call “coffee”. And we would know “an upright cylindrical container” as a “cup”.

And then they began to work out the natural resonant frequency of the coffee oscillating in the cup.

But what is a ‘natural resonant frequency’?

Suppose you half fill a bathtub with water. Get something with a decent surface area (such as a breadboard) and gently pat it onto the surface of the water at one end of the bathtub – and then remove the breadboard. You’ll see a wave head to the other end of the bathtub. It will then bounce off and head back to your end. And it will continue back and forth, bouncing off the ends of your bathtub every few seconds. So for water, your bathtub has a natural resonant frequency of a few seconds.

Your coffee cup is much smaller, so it has a higher natural resonant frequency. Depending on whether you have your coffee as an exquisite espresso or a cavernous cappuccino, the frequency might range between 4.3 and 2.6 hertz.

Typically, you pick up your cup of coffee while you are stopped, and then you accelerate. This acceleration generates the initial slosh of coffee. You continue to accelerate for a few more steps until you reach cruising speed. Typically, the initial slosh will continue to amplify until get your first coffee spill around the sixth step.

The engineers suggest a few solutions.

First, if you make the walls of the coffee cup flexible, they will absorb the energy of the incoming wave and dampen down the initial slosh. Second, you could install (inside the top of the cup) a series of concentric rings (like egg rings). These would break down the large mass of a single slosh into a bunch of smaller sloshes, which would be much easier to control. A third solution would be to perforate or to drill holes in these rings. Not only would this make the rings lighter, but it would further dampen down the sloshing.

Of course, you’ll always try the low-tech approach of “the targeted suppression of resonance frequencies”, otherwise known as “watching your step”.

Tags: engineering, physics

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Published 29 May 2012

2012 Karl S. Kruszelnicki Pty Ltd

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29 May 2012 6:14:12pm

When carrying a number of cups on a tray, place spoons in each cup. This will dampen the sloshing.

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30 May 2012 10:14:38am

I have noticed coffee spills more in cylinder shaped cups, but there seems less in cone shaped cups… the extra volume higher up may absorbs the wave?

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04 Jun 2012 9:52:32pm

The circle has a higher frequency because it follows the pattern of a ripple, and doubles up on itself, whereas the cone breaks itself up much as the rings mentioned would.

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30 May 2012 10:18:13am

…or, as well as watching your step, you could just use a lid on the cup, which is what most take-away coffee places do for precisely the reasons described above!

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30 May 2012 2:22:26pm

If you are carrying the cup or mug with a handle the orientation of the handle in the hand, I’ve found by trial and error, makes quite a difference. If you are carring the cup so the handle is in line with your arm try turning it 90 degrees inwards (more control and less stiff).

Good to know someone else is working on this stuff!

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30 May 2012 2:40:00pm

If you do not look at the cup, but instead focus your eyes in front of you it won’t spill – every server knows this.

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30 May 2012 3:17:03pm

I generally find I have better luck at not spilling it if I look at where I’m going and ignore the cup. Otherwise watch it, watch it, watch it, slosh – self fulfilling prophecy maybe….

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30 May 2012 10:27:10pm

It really depends if you are a clumsy person or not & whether the cup is almost brim full.I never spill coffee when I carry it. & it’s always 1/4 in below the rim of the cup.Only clumsy people will spill coffee.

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31 May 2012 7:06:50am

Well if you can, always carry coffee in one hand and not with both. If you have takeaways, use the lid to rest the second one so that are all using one hand. Your brain will use your other arm that is free to absorb the sway and steady the cup. If that doesn’t work for you, then learn to roller skate as then your steps wont be an issue. 🙂


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31 May 2012 9:44:46am

Wow – I have always thought that I was just incredibly clumsy carrying my coffee – I am happy that this is not the case!

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31 May 2012 9:51:46am

Work went into this? We wait-staff seem to get by just fine by simply picking it up and walking with it. I fail to understand why that’s a special ‘professional’ skill. I will admit though, sometimes the bottom of a paper cup flexes and pops up – that can’t be controlled but thankfully is also rare

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31 May 2012 10:12:51am

Ever heard of a lid.

Sorry, that should be a solid state, static friction dynamic liquid escape suppressor!

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31 May 2012 10:56:51am

I just put a lid on my cup.

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31 May 2012 10:58:53am

Just put a lid on the cup

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31 May 2012 11:58:24am

Or alternatively you could buy a re-usable coffee cup with a lid that actually seals, preventing any spills and also better for the planet.

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31 May 2012 11:34:29pm

Someone who truly appreciates coffee will not have this problem as they will not get it take-away

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01 Jun 2012 12:54:36pm

Or….you could just not fill the cup so much.

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01 Jun 2012 5:44:19pm

What about tea?

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03 Jun 2012 3:53:43pm

I remember at school in the 60s we studied simple harmonic motion and in cadets we always broke step when crossing a bridge. I just automatically break step carrying glasses or cups of liquid. Never spill a drop!

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06 Jun 2012 6:20:14pm

And how much did this essential research cost the taxpayers?

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21 Jun 2012 2:25:41pm

Nothing for the taxpayers in this country, the work was done at UCal.

Personally, I pay taxes… and would RATHER have a couple of engineers paid to study biomechanics and hydrodynamics (who take a day or two to engage the broader community with an inane example of their research outcomes) THAN a couple of athletes paid to win some golden vicarious olympic glory.

But hey, that’s just me apparently, so I’ll be taking my PhD to California.

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06 Jun 2012 7:38:41pm

Wow, have they made tests on spilling water or tea yet?

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21 Jun 2012 4:46:52pm

Well, they were going to try milk, but they were worried their testers would cry too much over it…

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21 Jun 2012 11:30:06am

There is no cup.

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21 Jun 2012 3:16:01pm

Or the other low tech method of buying coffee with a lid…

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22 Jun 2012 9:50:04pm

… of course there’s always this …

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24 Jun 2012 7:41:36pm

Many years ago when I was a student I wondered about this problem. I had done a course on wave motion and also another course on mathematical methods. I decided to do a fourier analysis of the sloshing modes of a simple container. I took a punt that if the perturbing function was a constant acceleration then there would be no stimulation of the resonant frequencies. This turned out to be correct. Next cuppa I experimented. The solution? When you walk with a cuppa accelerate uniformly slowly getting faster and faster, then slow down going slower and slower. Repeat this cycle until you get to your destination. Do NOT maintain a constant speed. And bingo, should be OK.

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