Another way of calculating the load on the mast
Deciding on the right dimension on a freestanding mast (or any sort of mast) appears to be a bit of a black art.
In the early days of commercial junks in Britain, the masts (from Needlespar) appeared to be terribly slim. Several photos show Sunbird 27 and 32 sailing along with a lot of bend in their masts. Some of these appear to have ended up with fatigue problems and eventually snapped.
(..the photo below shows a Sunbird 27 with the mast bending quite a bit in moderate conditions....)
At the other end of the scale are the scantlings specified for wooden masts in Practical Junk Rig. Their formulas needed to be adjusted for lighter craft with the generous sail areas that I use, or the resulting masts would end up much stronger than needed - and much heavier than could be tolerated.
Nowadays I have tried to base my calculations of aluminium masts on the calculated ultimate righting moment of the vessel. See Chapter 6b of TCPJR.
There is another way to roughly find the load on a mast, based on the calculated wind pressure at maximum wind strength before reefing.
About the wind pressure, we know that it varies with the square of the wind velocity.
A place to start is to find the wind pressure at wind speed 10m/s. This turns out to be 6.1kp/sqm
Case Ingeborg:
SA = 35sqm and CE is sitting 4.4m above the partners. At a wind strength of 10m/s (about 20 knots), the bending moment should be around (roughly)...
Mb35 = 6.1kp/m2 x 35m2 x 4.4m = 939kpm
However, I know that at this wind strength, my Ingeborg will be down at 5 panels ( 25sqm) and the CE will now only sit only 3.4m above the partners, so the bending moment should come out at
Mb25 = 6.1kp/m2 x 25m2 x 3.4m = 519kpm.
This is about a quarter of the designed strength of Ingeborg’s lower mast section (Ø150 x 5mm). Practical sailing has shown that there hardly is any discernible mast bend at all, much unlike on the shown photo.
My conclusion is that my way of calculating mast scantlings based on the boat’s ultimate righting moment, probably results in slightly over-strong masts. Still, I will rather be there than sailing under very flimsy under-size masts.
Arne
PS: For weekend sailing, I guess I could safely use masts that are only 2/3 as strong as the strength I calculate while using the righting moment method.
