Graphical method for calculating mast section length

In previous posts I used a table for working out how long mast sections (main tube, strengthener, topmast) should be. Here’s a graphical way to do the same thing. It has the advantage of greater precision plus it is hopefully easier to see what is going on.

Mast strength vs height

The black line shows the required strength.

The horizontal red lines show the strength of the sections – Douglas Fir (strengthener and topmast), the Aluminium main tube, and the combination of Aluminium tube and Douglas Fir.

The vertical red lines are where the horizontal red lines intersect with the required strength lines.

The green lines show the required combinations of Douglas Fir and Aluminium. Thus we have:

  • Douglas Fir from 0 to 270mm
  • Douglas Fir and Aluminium from 270 to 1897mm
  • Aluminium from 1897 to 2913mm
  • Douglas Fir and Aluminium from 2913 to 3213mm (top mast bury or overlap)
  • Douglas Fir from 3213 to 5600mm

Putting it in the same form as a previous post:

TubeStart (m)End (m)Length (m)Weight (kg)
Main0.273.2132.9435.4
Stren01.91.93.1
Top2.9135.62.6873.3

Total weight = 11.8kg

One thing that is missing from this design is a gradual change in stiffness between each section. The abrupt changes will cause stress concentrations leading to early failure of the mast at these points. Fortunately it is easy to avoid this issue – I just need to make sure the stiffness of the wood tapers off. I could taper the wall thickness internally, or add a barrel-taper externally so that the aluminium can flex gently over a reasonable distance as the mast bends. The ideal is to use internal tapers to reduce weight as much as possible, if I can figure out a sane way to cut them out.

The upper sections of this mast might be a bit strong as some of the loading of the sail is applied below the mast head. However, there is debate on whether it is possible to treat the load as uniformly distributed or not – currently it is considered safer to work on the basis that all load is at the mast head.

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