Spar diameters

Here is an equation from Skene, rendered by Codecogs. Pretty nice.



I found a Beam Deflection Calculator that uses the same formula for a solid beam. If I put my 14' gaff into it with Skene's rule of thumb of 0.02 L as the diameter I can compare the deflection of a solid gaff with that of various different hollow gaffs.

So Skene says my gaff should be 3.36" max diameter if its solid. This gives a deflection of approx 1.5" for a 10 lb force.

I get about the same deflection for a 3.64" diameter gaff made with 1/2" walls or a 3.38" diameter gaff with 1" walls. So a 10% extra diameter and thin walls sounds like a real plan.

This calculation is perfect for relative strengths but it doesn't help much with deciding if scots pine is OK or do I need douglas fir.

I found a Young's modulus of 13 x10^9 N/m^2 on one site.

TRADA provides the following:

Douglas fir

Strength Properties (N/mm2)		Strength Class
		C14	C18
Bending Strength	f m,k	14	18
Tension Strength	f t,0,kf t,90,k	8 0.4	11 0.5
Compression Strength	f c,0,kf c,90,k	16 2.0	18 2.2
Shear Strength	f v,k	1.7	2.0
Modulus of Elasticity	E 0,meanE 0,05E 90,mean	7 4.7 0.23	9 6.0 0.30
Shear Modulus	G g,mean	0.44	0.56
Density	r kr mean	290 350	320 380

European Redwood

Strength Properties (N/mm2)		Strength Class
		C16	C24
Bending Strength	f m,k	16	24
Tension Strength	f t,0,kf t,90,k	10 0.5	14 0.5
Compression Strength	f c,0,kf c,90,k	17 2.2	24 2.5
Shear Strength	f v,k	1.8	2.5
Modulus of Elasticity	E 0,meanE 0,05E 90,mean	8 5.4 0.27	11 7.4 0.37
Shear Modulus	G g,mean	0.50	0.69
Density	rkr mean	310 370	350 420