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How far is it to the top and back to the car park and are dogs allowed of the lead?
Used to take me about 20 mins to walk to the top from the carpark when I was younger and slimmer. Coming down takes less time.
Can't answer the dog part of the question.
No livestock in the specific area normally although sheep have been rescued from the cliff before.
Give yourself a bit longer and on the way down wander through the woods you will have climbed up through.
Assuming you come up the direct route up the front (west) head back down the south which intesects a wall and turn west back past the folley thing and into the woods and then bear left for a bit and then turn back right down the hill in the woods (multiple options) which get you back to the main track to the car park.
I'm pretty sure our dogs have been up there more than once.
About 2 miles from car park, 20 mins is about right.
Last little bit is quite steep, dogs allowed but as far as off the lead is concerned they should be on a lead but mine used to go up regularly off the lead with no issue.
Another nice walk is to walk from Gt Ayton where the old tip used to be and walk along the bottom of the tree line, or across the top of the quarry. This brings you out about half way up the hill.