It’s amazing what maths you see when you go for a walk along a canal on a beautiful afternoon. After helping a canal boat through a lock, the following problem occurred to me: how many times must you turn the handle to raise the sluice gate?

Fact: The sluice is controlled by a series of cogs. The handle turns a ratcheted cog with eight teeth.

Fact: The handle turns a small cog with thirteen teeth.

Question: The next cog has ten teeth on a quarter of it’s circumference. How many is this in total?

Fact: This large cog is attached to a small cog with ten teeth, which lifts the vertical post.

Question: From the picture can you estimate how many teeth are on the vertical post?

Question: Given all this information how many turns does the handle need?
Extension: Look at this picture. What is the angle between the foot supports?