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`Demonstrates a technique for finding the angle where the RA is half of max.
    ` Demonstrates a technique for finding the angle where the RA is half of max.
    ` Also demonstrates how the RISE limit can be used to ensure that EQU is less
    ` than the angle where RA is half of the maximum RA.
    
    
    macro maxra2 `Finds the first heel angle where the RA is half of max.
     `create a constant heeling arm which is MaxRA/2
     `use solve to find intersection of RA curve and this heeling arm
     lim off |  hmmt off
     variable maxarm, maxmmt2, angmax2
     lim ra at max > 1
     ra 0 2 /lim /noprint
     set maxarm = {limmarg} div 100 plus 1
     `\ Maximum RA = {maxarm:3}
     set maxmmt2={maxarm} times {weight} div 2
     hmmt {maxmmt2}
     solve
     set angmax2 = {HEEL}
     \ Angle at half max RA = {angmax2:2}
     \\
     lim off | hmmt off
    /
    macro lim_HM  `set limits and heeling moment due to anchor towline
     lim(1) angle from equ to ABS {angmax2:2} >0
     lim(2) angle from equ to ABS 15 or DI0 > 0
     lim(3) rise > 1                               `this limit is equivalent to limit 1
     hmmt 123.0 /c1
    /
    
    
    proj maxra2
    read fv
    report
    weight 200 3f 0 10
    
    .maxra2
    .lim_HM
    angles 0 2
    heel 0
    ra /lim
    
    page
    solve maxvcg
    .maxra2
    .lim_HM
    heel 0
    ra /lim
    \Note that limits 1 & 3 both have zero limit margin.
    
    print preview
    report off
    
    
    

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