Naismiths Rule For Height Gain

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Originally Posted by Naismith's rule

Allow 1 hour for every 3 miles (5 km) forward, plus ½ hour for every 1000 feet (300 metres) of ascent.

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See the following website : Naismiths Rule For Height Gain or from Wikipedia

Here is an equivalent formula for fell runners from:

Running uphill: energy needs and Naismith's Rule

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In this note we make two points, from which follows a suggestion for running uphill: .... (2) corresponding to Naismith's rule of 1 to 8, in whole numbers, for walking or running in mountainous country (1 foot of ascent is equivalent to 8 feet on the level), the rule for running on a treadmill is 1 to 3 and the rule for running on roads is 1 to 4 or 5.

This result suggests that, if possible, a runner should zigzag up slopes steeper than 1 in 8 on the fells and zigzag up slopes greater than 1 in 4 or 5 on roads.

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Naismith's Rule is very good formula used when walking.

I'm not sure how it relates to running but for those who have never heard of it the above post might be helpful.