Fisher's Wife's Rake: at an angle on an inclined plane

This is Fisher's Wife's Rake on Clough Head. Apparently Mr Fisher cut peat above and it was his wife's job to get it back to the farm on sleds down this wickedly sloping narrow path. The start (above), which is beyond the famous tree, is clear enough but then we had to keep to the left along the line of the crags to stay on the path.

The path itself goes up at a steep angle but it also cuts across an inclined plane. I wondered how the geometry affected the actual slope climbed. I find that the steepest slope for walkers to be OK is about 45 degrees so I've modelled it at a 30 degree slope.

First of all I drew a 100m line going up a 30 degree slope across a vertical face. I've said it is 100m above the ground. The height gain from A to B would be 100sin(30) = 50 metres. The slope is said to be 1 in 2 (or 50%) because you go up 1 metre for every 2 metres along the path.

Then I took the diagram and tilted it over to an angle of 30 degrees to mimic the situation on Fisher's Wife's Rake. Now A would be 50 metres above the ground and B would be 75 metres, so by walking 100 metres you would end up 25 metres higher. That's a slope of 1 in 4 or 25%. By angling across a plane, the gradient can be reduced.