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Dr. Robin Loscombe
APPENDIX A - Rough check on currency of ISO Pb1 and
Pb2 equations
As a matter of interest, I have compared Pb1 and Pb2 formulations (with Kar =1,0 and K1 =1,0) against GL's pleasure craft rules ('95), LR SSC rules and VTT ('97).
It is always said that you cannot compare loads from different methods, but if the scantling equation for plating is the same (t = s√kp/ησ) then this can easily be done by adjusting the pressure in the ratio of ISO stress factor to a given rule stress factor).
On this basis, I've carried out a few comparisons...
Sailing Yacht
Sailboat bottom pressures (corrected to ISO stress factor)
Motor Boats (30 knots)
Pb1 (corrected for ISO stress factors) 30 knots)
Motor Boats (40 knots)
Pb1 (corrected for ISO stress factors) 40 knots)
I don't suppose this is 100% reliable, but it does seem to support the view that the ISO loads are not unduly pessimistic and might even be on the low size. This is why I don't believe we need to be unduly worried about 'boats failing the standard'. This may not be due entirely to loads. For example, if metal boats pass and GRP boats don't, it could be the allowable stress factors that we need to look at (I know Rob Scholfield did talk about 0,67 instead of 0,5).
Preliminary ideas - Monday, 13 May 2002 Robin Loscombe
Following the Baltimore meeting, it appears that there is a strong desire to simplify the Kar formulation. such that Kar becomes a function of shortest unsupported span (b) or stiffener span (1u). This would alleviate the need for an Ar formula.
An initial formula was put forward by Paul Handley. Although initially reluctant to see more changes to the load algorithms, if the WG require a simpler formulation, then this must be developed.
The following represents post-Baltimore preliminary development work undertaken by Robin L.
1. ABS 'F' FACTOR BASED
・Based revised formula on the ABS Offshore Racing Yacht Rules (1994) where the design head reduction factor (F) is based only on b or 1u and scantling length {(LOA+LWL)/2}.
・Only one equation required for panels and stiffeners
・Fits in with Pb2 which is the ABS design head equation
・ABS formula is linear (i.e. not based on area)
Kar = 1,14 - 0,0019 (b/L0,4)
Comparison between actual ABS F values (using CF and Table 7.4 and Table 8.1b) and simple approximation is shown below.
ABS F Factor PLATING & STIFFENERS (Actual v Approx)
2. ISO (Draft) Kar FACTOR BASED
・ISO formula is area-based. Different equations are required for panels and for stiffeners and aspect ratio also needs to be fixed
Panel (AD = 2,5 b2)
Kar = 8,2L0,36/b0,6
Stiffeners.(AD = 0,33 1u2)
Kar = 0,25 (lu/L0,6)-0,6
Comparison between actual ISO values (eqns. 6 & 7) and simple approximation is shown below.
Kar PLATING (ISO v Approx)
Kar STIFFENERS (ISO v Approx)
3. ARGUMENTS FOR AND AGAINST
・Use ABS F factor approximation - One equation only needed and is easily 'auditable'
・Use Kar approximation - Gives lower values
The figure below compares F v Kar.
ABS F v ISO Kar (PLATING)
For plating, Kar is roughly 0,77 F. Please note, for stiffeners, the opposite is true and F is typically about 0,7 Kar.
If the WG like the form of the equations, the SIMPLEST approach would be;
・Use ABS approximation on the basis that the actual (as per ABS 'ORY '94) and approximation are the same - i.e. NEITHER is area based.
・The ABS is less onerous on stiffeners
・It may not be necessary to impose the (1,02 - 0,0006 b) formula limitation, since the approximation is not far off this for practical boat lengths
・Equation for Pb2 is then 'straight-ABS' (is it actually correct to use the ISO Kar formula with the ABS displacement pressure head?)
・Adjust Pb1 to reflect more onerous Kar requirement. If Kar/F = 0,77 then this could be justifiable done by reducing the 0,078 (eqn 2 - 1/100th highest) to 0,046 (1/10th highest as per the ABS 1990 Motor Yacht Rules).
・Replace term Area Reduction Factor by something else (why not F)
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