Image caption The researchers hope their work will improve toilet hygiene and bring harmony to family bathrooms

US physicists have studied the fluid dynamics of urine "splashback" - and found tips to help men and women with their accuracy and hygiene.

Using high-speed cameras, the team filmed jets of liquid striking toilet walls and studied the resulting spray.

Splashback was low when the jets were used close up with a narrow "angle of attack", said the Brigham Young University team.

They will present their research at an American Physical Society meeting.

"In response to harsh and repeated criticisms from our mothers and several failed relationships with women, we present the splash dynamics of a simulated human male urine stream," reads their conference abstract.

Techniques to reduce splashes Getting as close as possible - a smooth unbroken stream is better than droplets

Angling the stream - aiming sideways or downwards instead of straight at the toilet water/wall

Placing toilet tissue in the bowl to soften impact

Hydrophobic coatings for toilets

Being a "sitzpinkler" - sitting down instead of standing

But there is a more serious side to the research.

The work is led by Prof Tadd Truscott and Randy Hurd of the "Splash Lab" at Brigham Young in Provo, Utah, who jokingly refer to themselves as "wizz kids".

"People ask me, are you serious? I tell them yes, this may involve 12-year-old humour, but it's also a real problem," Prof Truscott told BBC News.

"We've all been in disgusting toilets with puddles on the floor - these places are a breeding ground for bacteria."

For example, the detergents used to clean hospital toilets could actually increase the spray of disease-causing bacteria, by reducing the surface tension of water, according to a recent study.

Media playback is unsupported on your device Media caption Slow-motion video reveals the splashback when "urine" strikes toilet water

One might think the physics of aiming urination had already been summarised by the formula: "get it all in the bowl". But micturation is still a messier business than it needs to be, according to the research.

Taking measurements live "in the field" did not appeal to the scientists, so the duo built a urination simulator. The "Water Angle Navigation Guide" is a five-gallon bucket with hoses connected to two types of synthetic urethra.

Chaotic spray

The team fired coloured water at various target "toilets" at the velocity and pressure of average human urination.

Then, using a high-speed camera, they captured the moment of impact in remarkable visual detail.

Image caption The apparatus was carefully designed to simulate male urination

Splashback was heightened by a phenomenon known as Plateau-Rayleigh instability, where a falling stream of liquid breaks up into droplets.

"The male urine stream breaks up about 6-7 inches outside the urethra exit," Mr Hurd explained.

"So by the time it hits the urinal, it's already in droplet form. And these droplets are the perpetrators of the splash formation on your khaki pants."

His advice? "The closer you are, the better. If you can get stream impact with the porcelain, it's a lot less chaotic."

Of course, in a domestic bathroom, distance from the toilet is governed chiefly by one variable: "to stand or sit".

"People are always arguing over which is better. Because when you sit close, you're also closer to getting wet," said Prof Truscott.

"In Germany there is a derogatory term 'sitzpinkler' for a man who sits down to pee. It means he's kind of a wuss.

It seems that sitting down is the best surefire way to avoid unwanted splashing in a traditional toilet Randy Hurd, BYU Splash Lab

"So we wanted to look at whether sitting down is really effective. What are the splash differences?"

To compare the two positions, the scientists gave rulers to their friends and sent them into the toilet.

"It turns out you are five times as far away when you stand up - and that's a pretty significant difference in impact velocity for those droplets of urine," said Mr Hurd.

Impact with the toilet water is captured in a video by the team.

"You can see the droplets create a large cavity in the water, which then collapses, causing even greater splashback. The amount of splash is considerable," Mr Hurd explained.

"It seems that sitting down is the best sure-fire way to avoid unwanted splashing in a traditional toilet."

Angle of attack

Above all, he says, "the biggest thing you can do" to reduce splashback - sitting or standing - is to alter the "angle of attack".

Aiming directly at a vertical urinal wall - a 90 degree angle - causes a nasty kickback, as does aiming directly at the toilet water.

"Narrowing the angle really helps," said Mr Hurd. For a typical urinal, "best practice" means standing slightly to one side, and aiming downwards at a low angle of impact.

Image caption The angle of impact and smoothness of the stream dictate the level of spray

"This way you take advantage of both splash-reduction techniques," Hurd explains.

Prof Truscott encourages men and women to "be artistic" with their aim and find an angle to suit the particular facility they are faced with.

The designs of public toilets and home bathrooms does not always help us achieve 100% efficiency, he said.

"Most surfaces you pee into, such as porcelain, are hydrophilic, which is a disadvantage. The water spreads across them, creating a puddle to splash into," said Mr Hurd.

He believes that hydrophobic coatings will ultimately make toilets more hygienic, with important benefits for hospitals, schools, and workplaces.

The Brigham-Young team has been "inundated" with commercial products to reduce spray - such as fabric inserts, urinals with triangular fins, and toilet bowls with unusually sloping angles.

"Some work fantastically - others really don't work at all. It's almost worse than nothing," says Truscott.

"My favourite is painting a fly on the wall to indicate where you should aim. Unfortunately, some companies put that fly in the wrong place."

Sega has even developed a "Toylet" urinal game, installed in Tokyo Metro stations to award men points for accuracy.

But Prof Truscott says one of the most effective tricks is also the simplest - drop a few pieces of tissue into a toilet bowl to soften the blow.

The Splash Lab team plans to investigate further toilet designs and find "the optimal approach for urinal usage", removing some of the obstacles between men, women and bathroom harmony.