Select to expand quote
mr love said..
Andrew...That would be great. All I am trying to find out is if there is a difference in bend curve characteristic between an RDM and SDM when they are deflected more than when tested with 30 kg. I am suspecting that an RDM starts to bend more at the bottom 1/4 point relative to an SDM the further you bend it. But I may be completely wrong.
Thanks
I'd guess it would be would be close enough to linear that the differences would come in smoothly.
I happen have an SDM and RDM 400. The SDM has outer diameter at the base of 52.0 mm and ID of 48.8 mm. The SDM has OD of 39.8mm and ID of 33.0 at the base end.
The formula for Area Moment of Inertia of a tube which is Ih = Pi( OD^4 - ID^4)/64.
(Why the engineers pinched the term "inertia" from the physicists in this application I don't know? But that's what they call it)
The "Area Moment of Inertia" is the measure of a cross section's resistance to bending.
For the SDM it is 89,536 and for the RDM it is 64,955.
(Sorry to leave out units, but I've calculated in mm, should use metres to get real numbers, treat the figures as just comparative.)
So according to the formulas used by engineers the SDM will bend less at the bottom. That's if the material's the same, the RDM has 90% on it, the SDM 97%, then there's the bias to the wrap, but 39% down on stiffness is a lot for the RDM to catch up by fiddling with the layup.
But that's for a free bending mast. The bend is constrained by the sail cloth. If the bend wasn't constrained no tension would be imparted to the sail, just a thin line of tension between the head cap and downhaul. Like a bow (and arrow).
Here comes a thought experiment. if you rigged a mast with a piece of string between tip and downhaul it would bend in a natural curve. If you sewed sailcloth onto it at this point there'd be no tension in the sail.
Then when you derigged the sail the luff curve would exactly match the natural bend curve of the mast. We don't want that.
So if you rig a sail on a skinny that is comparatively less stiff at the bottom then it would want to bend further than the SDM in the same sail. So the skinny would be trying harder to stretch the lower section of sail because the luff is constraining it to be further from its natural curve. Even though it's softer down there! A rigged sail is a very, very complicated piece of kit!
A question for the engineers. Does a tube being bent distort to being a little out-of-round? The formula suggests no, I always imagined it would?