Water wheels once powered the nation’s flour mills, before Scots inventor James Watt’s revolutionary steam engine rendered them obsolete in the 18th century.

Now a Scots engineer has “reinvented” the water wheel with a new design which could power hundreds of homes.

The Carruthers Wheel, created by former maths lecturer turned civil engineer Penelope Carruthers, is the first water wheel to be patented in 138 years.

It is hoped her water wheels could eventually be brought into previously untapped river locations, opening up a new source of renewable energy for Scotland.

Carruthers, 47, is the daughter of renowned engineer David Carruthers, 71, who was involved in designing the first gas platforms.

She said: “I was looking at old water wheels and as a mathematician I found them rather ugly. I told my father I could do better, and at the very least I could make them mathematically elegant. He dared me to prove it, and I did. I must admit I didn’t realise I had invented something new, he spotted it.”

Unlike mill wheels, the Carruthers Wheel can operate at a range of speeds, dependent on river flow, and could help power remote communities with no access to the electrical grid.

Carruthers said: “It’s a simple design that can be scaled to any size. A 10-metre diameter wheel at Bannockburn Falls would supply enough electricity for 40 Scottish households. A 12-metre diameter wheel at Lindsay’s Mill Weir would supply enough electricity for 80 Scottish households.

“Smaller more domestic sized versions of the Carruthers Wheel may be profitable in those areas of Scotland where there is a limited grid supply.

“I can’t give names of rivers because we’re in negotiations, but we are looking at estates and farms, as well as small communities in the Highlands, where getting electricity to areas not attached to the grid would be worthwhile, because they would not need to use as much diesel or oil.”

The innovative design was tested at Abertay University’s hydrology lab by senior lecturer Rebecca Wade and her students.

Wade admitted she was sceptical when she first received a call from Carruthers three years ago. “When somebody phones you up and says they’ve reinvented the wheel of course you think hang on a minute, but I was intrigued,” said Wade.

Carruthers explained to Wade that her wheel can be used directly in river channels, rather than requiring a steady flow from a separate mill stream or mill lade.

The Carruthers Wheel can cope with four times the water volume of traditional models thanks to hydro-dynamically designed blades.

Wade said: “Penny applied her mathematical understanding to how you might literally reinvent the wheel, reshape the blades, and understand the way in which the forces and action of water was working on the blades to maximise the power output.

“It’s so exciting that she’s taken that pure mathematical knowledge and applied it in principal, just in the way the engineers hundreds of years ago were doing.

“This wheel differs from traditional water wheels in the same way that wind turbines differ from windmills – they are old technology with a modern twist, harnessing natural resources to produce electricity, rather than grinding flour.”

Following successful lab tests, the team is now investigating potential demonstration sites in the east of Scotland.

Wade said: “We’ve been looking at some sites in Dundee and Edinburgh. We’ve identified several sites that have existing weirs and we’re speaking to landowners at these sites at the moment.”

Carruthers has set up a Perth-based Carruthers Renewables Ltd with her father to market the design overseas.

She said: “We have the UK patent. It’s the first water wheel to be patented in 138 years. We now have to go for the international patent.”

Carruthers also revealed she only began studying engineering in 2010. “I’m in my forties and I was always steered towards maths because that’s what girls did when they showed an interest in science in engineering. I’m now gaining from the change in attitudes.

“I was just looking at water wheels as a mathematical exercise and it’s taken over my life. I now realise I probably should have been a civil engineer from day one.”

THE RISE AND FALL OF WATER WHEELS IN SCOTLAND

The first water wheels in Scotland are most likely to have been the type known as Norse Mills –simple horizontal wheels with no gearing which were used to grind corn.

These mills were in use in Europe more than 2000 years ago, but it is not known when they arrived in Scotland. The Norse Mill at Shawbost on the Isle of Lewis and the Dounby Click Mill on Orkney are restored examples.

The Romans brought with them the undershot, or stream wheel, and the overshot water wheel, both of which are vertical water wheels with gearing. One type of Roman mill once seen in Scotland was the tide mill. This was an early method of harnessing tidal power, and a growing number of archaeological remains are being found by drones over our coastline, such as at the Fife Ness ruins.

Prior to the industrial revolution the most common form of water wheel in Scotland was the undershot. One example is at the Preston Mill, East Lothian, which was seen in the television series Outlander. Another example of an overshot wheel is the 18th century New Abbey Mill in Dumfries.

In 1752 John Smeaton’s scientific paper on water wheels heralded both modern industrial water wheels and the modern profession of civil engineering. By this time there were 56 mills on the Dighty Water in Dundee, making it Europe’s hardest working river. At the peak of innovation, the increased output of water wheels powered the UNESCO World Heritage Site at New Lanark.

With the maturing of steam power, industrial wheels fell into disuse and the last commonly used water wheel, the Pelton Wheel, was patented in 1880. This wheel was further improved by putting the water under pressure and the first high-efficiency water turbine was born.