Reasons for diff between measured arc length and estimated arc length of a catenary curve?
A hanging chain is measured and its length, to nearest mm, is 36.0 cm. A catenary function is then developed to model this hanging chain. This function is then used to calculate arc length using length = definite integral (from a to b) of [(1+(f'(x)^2)^1/2]dx. The length is found to be 35.525cm (a difference of 1.319% from measured). What might be the reasons for this difference? The only one I have is that the figures used in the function were rounded meaning less accuracy. Are there any more?

Question

Reasons for diff between measured arc length and estimated arc length of a catenary curve?
A hanging chain is measured and its length, to nearest mm, is 36.0 cm. A catenary function is then developed to model this hanging chain. This function is then used to calculate arc length using  length = definite integral (from a to b) of [(1+(f'(x)^2)^1/2]dx. The length is found to be 35.525cm (a difference of 1.319% from measured). What might be the reasons for this difference? The only one I have is that the figures used in the function were rounded meaning less accuracy. Are there any more?

mrnood · Answer

A chain is made of links which are intrinsically straight.

The mathematical model assumes uniform flexibility at all points on the curve

mrnood · Answer

However - I would expect teh measured chain to be slightly SHORTER than the model...

so maybe there are other factors

mrnood · Answer

hmmm - it could go either way - depending on the parameters you used for the model...

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