HSE said one of the cows ran towards David Clark (pictured), causing a fatal blow to his chest after crossing a right of way at a farm in North Yorkshire.
Íæż½ã½ã from North Yorkshire have been sentenced for failing to protect members of the public from cattle.
An investigation by the Health and Safety Executive (HSE) found that Andrew and David Turnbull had failed to offer and display signs of an alternative route in a public right of way where cattle were grazing.
HSE prosecuted the brothers, who farm at Low Gingerfield Farm in Richmond, following the death of former teacher David Clark, who was killed by a herd of cows while crossing the right of way on September 21 2020.
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Mr Clark, 59, had been running with his two dogs when he was surrounded by a number of cows.
According to witnesses at the scene, the father-of-three was then struck to the ground by a cow, causing a blow to the chest.
Paramedics pronounced Mr Clark dead at the scene.
Appearing at Teeside Crown Court on Monday (March 3), the Turnbull brothers pleaded guilty to breaching health and safety legislation.
Andrew Turnbull was fined £1,589 and ordered to pay £1,500 in costs.
David Turnbull was fined £1,390 and ordered to pay £1,500 in costs.
HSE inspector Elliot Archer said: "Andrew and David Turnbull failed to do all that was reasonably practicable to prevent members of the public being put at risk by their cattle.
"Íæż½ã½ã, landowners and other livestock keepers need to be aware of the risk their cattle pose to members of the public and take suitable protective and preventive measures to mitigate that risk."
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HSE said farmers, landowners and other livestock keepers should adopt control hazards for walkers when keeping cattle in fields where the public have access; by assessing the risks posed by cattle to users of public footpaths and implementing suitable protective and preventive measures to minimise those risks so far as is reasonably practicable.
Government advice in the Countryside Code requires members of the public to give livestock plenty of space as their behaviour can be unpredictable and keep dogs under effective control.
