SCIENCE BEHIND A GAME OF DARTS
Researchers in the United States have published the secret behind the perfect throw and why shoelaces come undone. While sceptics deem such findings insignificant, scientists may be on to something that may yet make history, reports Robert Matthews
Researchers turn to the real matters in life – such as the best way to tie shoelaces,
Scientists have a reputation for being somewhat unworldly types working on out-of-this-world problems. But while their breakthroughs may be cosmic, these rarely make a difference to our lives.
Sure, it’s nice to know the universe is expanding or that Higgs particles really exist, but it’s not going to affect the kind of day we have.
Fortunately, a growing number of scientists are turning their attention to less esoteric conundrums and coming up with insights we can all benefit from.
And it often turns out that many of these supposedly trivial problems have causes that are anything but.
For example, this month, researchers in the US revealed the source of one of those little irritations in life: shoelaces that keep coming undone.
The obvious cause is failing to tie the knot tight enough. However, by actually measuring what happens to knotted laces when we move, the team at University of California, Berkeley, made a surprising discovery.
Our feet strike the ground with huge acceleration – up to seven times the force of gravity – leading the knot to stretch and slightly loosen.
The swinging action of our legs then applies another force akin to tugging on the ends, and begins to pull the knot apart.
In effect, the forces generated by walking mimic the effect of some invisible gremlin sitting on our shoes and messing with our laces.
So what’s the solution? Again, the obvious answer is to use a better knot but, again, there’s a twist – quite literally.
Most people tie their laces by wrapping one over and then under the other, then forming a bow, and finally wrapping the laces over and under once more. But according to the researchers, that’s where we go wrong. By using the same wrapping motion each time, we end up with a relatively weak knot.
Instead, once we’ve formed the bow, we should wrap the laces in the opposite direction we used first time: under and then over. The result is a far stronger knot.
Exactly why is unclear – and is currently the subject of further research by the team, whose results appear in the current issue of the Proceedings of the Royal Society, the world’s oldest scientific academy.
The society – whose founders include Sir Isaac Newton – has now published a study of another everyday puzzle, and one that would surely have intrigued the genius behind the laws of motion: how to throw accurately.
From professional darts players to office workers lobbing paper into bins, everyone knows it’s tricky to hit distant targets. Practice makes perfect, of course, but what rules are we unconsciously learning as we get better?
Researchers at Yale and Harvard have now cast light on the secrets of the perfect throw.
According to professors Madhusudhan Venkadesan and Lakshminarayanan Mahadevan, the key factors are the speed of throw and the height of the target. A high-speed throw follows an almost straight-line trajectory, which amplifies any inaccuracies. In contrast, slower throws are far more forgiving – but run the risk of falling short. So the first top tip for wannabe office crack-shots is to focus on judging distance accurately.
As for throwing technique, the team recommends under-arm if the bin is less than three arm-lengths away and below shoulder height. If farther away or higher, go over-arm.
Published in the current issue of the Royal Society journal Open Science, these top tips might sound simple but the theory behind them is dauntingly complex.
Even so, the researchers found that sports players have mastered it all through practice.
Studies of darts players show that they typically launch the dart at about 22 kilometres an hour, just before their arm is perfectly vertical and just as optimal throwing theory predicts.
It’s unlikely that the contestants at this year’s World Series of Darts tournament, being held next month in Dubai, have much to learn from wading through all the equations.
But those of us just content to hit the board can benefit from scientific research into the best place to aim.
As ever, the answer to this one might seem obvious: emulate the professionals and aim for the highest-scoring part of the board – the triple 20. But there’s a big problem. Unless you’re deadly accurate, you’re likely to end up scoring just 5 or 1, which lie to either side of the 20.
Fortunately, a team led by statistician Dr Ryan Tibshirani, at Stanford University, California has some much better strategies for amateurs. Novices should actually avoid trying for the triple 20. That’s because a dart thrown completely at random at the board will score about 12 – higher than many achieve by aiming at the 20.
For those with a bit more talent, Dr Tibshirani and his colleagues recommend aiming slightly to the left of the bullseye, near the point where the 8 and 16 meet.
Even a poor player can average about 37 from three darts by aiming there.
It may not be a coincidence that interest in such trivial problems is growing just as disenchantment sets in about attempts to solve serious questions about the nature of life, the universe and everything. But whatever its origins, the trend is helping to solve some age-old annoyances. Want to stop your bathroom mirror steaming up? Then rub a soapy hand over it and then wipe clean. The molecule-thin layer of soap that remains cuts the surface tension of the moisture droplets, so they flatten out and leave your reflection undistorted.
Fed up with your headphones – or any type of flex, string or cable – tangling up? Just gather together the free ends and clip them together, forming a loop. The mathematics of self- avoiding random walks shows this drastically reduces the risk of tangles.
Not everyone thinks scientists should be spending their time on such things. Yet the history of science is littered with examples of trivial problems that have led to serious advances.
Even Sir Isaac himself was happy to claim inspiration for his work on gravity from watching an apple fall to the ground. Who knows what cosmic insights may yet emerge from understanding the flight of a dart through the air.
The key factors behind the perfect throw are speed and height of target