Image copyright Bridge to Moscow Image caption Katerina Pigusova leading a stopover tour of Moscow

As any frequent flyer can attest, there are few things more soul destroying than spending any number of hours sitting in an airport terminal waiting for a connecting flight.

There you are, sitting in the departure lounge watching the clock, or looking round the duty free shop for the eighth time.

Bored out of your mind, you might buy some overpriced, processed food just for something to do.

To add to your frustration, nearby, outside the airport is a foreign city you'd rather like to look around. It's full of great tourist attractions, restaurants and shops.

Yet you wouldn't dream of leaving the airport to go and take a look, because not knowing the local transport system, language or geography, you are terrified that you wouldn't get back in time, and therefore miss your flight.

Frenchman Emmanuel Rozenblum and his sister were on such a stopover at Warsaw's main airport three years ago. But, faced with having to wait eight hours for their connecting flight to Tel Aviv in Israel, they decided to risk venturing into the Polish capital.

Image copyright Getty Images Image caption There are better things to do than spend hours at an airport

Mr Rozenblum, who had flown into Warsaw from Paris, says: "We left the airport on our own, but we didn't know which bus to take, and we were really stressed about making it back in time."

Although the siblings did make their flight, the experience sparked the idea for a fast-growing business.

It dawned on Mr Rozenblum that with millions of air travellers each year having to make a stopover to change fights, there must be a huge untapped demand for short guided trips into the nearest city or countryside.

His idea was that a guide would pick up the travellers at the airport, whiz them around the sights and to a restaurant, and then guarantee to get them back to the airport well in time for their connecting flight.

So in March 2015, he and business partner Anna Veyrenc launched such a "stopover tours" business, calling it TripAside.

Initially based just in Paris, it was an immediate hit, and today has expanded to Frankfurt, London, Brussels, Rome and Madrid.

Meanwhile, a host of other such stopover tour firms (called "layover tours" in North America), have also been set up in recent years, and are equally seeing their businesses boom.

'Steak frites'

TripAside now has a team of five people working in its Paris office, plus 10 guides in Paris, three in London, two in Frankfurt, and one each in Brussels, Rome and Madrid.

One of its most popular trips is the Paris Day Tour. Costing €230 ($250; £180) per person, for visitors with at least seven hours before their connecting flights, it includes sightseeing at the Eiffel Tower and Notre Dame Cathedral, plus stops at a number of patisseries.

Image copyright Frankfurt on Foot Image caption Frankfurt on Foot guides travellers around the centre of the German city

Mr Rozenblum, 32, estimates that between 30% and 40% of his company's clients are business travellers, who can also order a more bespoke tour.

He says: "One time we had a business traveller from the US on his way to South Asia, and he just wanted to be picked up and brought to a restaurant to eat steak frites."

While the majority of stopover tour companies guide people around the main sights of a city, others - such as Frankfurt on Foot - offer to take customers off the beaten track.

The business was started in the German city back in 2008 by Jodean Ator and her husband David.

It devises walking tours based around the specific requests of a traveller, such as seeing the city's Jewish history, or trying Frankfurt's culinary specialities, such as veal schnitzel with green sauce - a blend sour cream, yoghurt, and seven herbs.

Image copyright Trip Aside Image caption Emmanuel Rozenblum (right) launched his business in Paris

"We can tailor it to whatever you want," says Mrs Ator, 60. "[For example], some people need to collect souvenirs before they head home, so we can go out on the hunt for a beer glass."

The Ators, who also employ three freelance guides, gave 131 stopover tours in 2015 alone, with prices from 115 euros per person.

'Time cushion'

Frankfurt is a user-friendly city for stopover tours because the airport is connected to the city centre by a regular 11-minute train ride.

Image copyright Catherine Lu Tours Image caption Stopover tours are now available from Beijing airport to the Great Wall of China

This means that short trips of a few hours are possible, without people fearing that they will miss their flights.

By contrast, for cities whose airports don't have such decent public transport links, and whose road are often gridlocked, transit can be a major concern.

Moscow and its often horrific traffic is just such a city.

Image caption Frankfurt on Foot also does rooftop tours

One firm which offers stopover tours in the Russian capital - Bridge to Moscow - gets around the problem by only offering trips to travellers who have at least eight hours to spare, and by allowing a lot of time for potential transport delays.

Co-founder Katerina Pigusova, 30, says that the business, which employs 10 guides, works hard so that clients "don't have to worry".

Back in Frankfurt, Mrs Ator says that despite the rail link, Frankfurt on Foot still always leaves "a nice cushion of time".

Image copyright Getty Images Image caption Air travel is a glamorous business

"We've been doing this for over seven years, and no-one has ever missed a flight," she says.

Steve Vranian, a chef from Minneapolis recently used TripAside when he had 22 hours to kill in Paris on his way back to the US from visiting his daughter in Armenia.

He says he so enjoyed the experience, that he now plans to deliberately select flights with long stopovers, so he can sample similar tours.

"Just think of the number of hours you spend sitting in airports, " says Mr Vranian. "Why not use that time to actually see something worthwhile?"