The sine is dependant on the angle, and is the same for any radius. The
_percent_ changes in position are therefore correct as originally stated. To get
the actual distance moved, multiply the radius of the point you are interested
in times the sine or cosine of the angle. The center of resistance of the
centerboard will change slightly, as you pointed out, since the shape of the
exposed area is a little different with the change in angle, but it's not going
to be anything like a factor of two.
The overall center of resistance of the boat is going to be affected by more
factors than just the centerboard position. As Steve Barnes pointed out, moving
back in the cockpit will lift the forward part of the lee chine out of the water
and present more of the after section of the chine to the water. The effect is
to move the center of resistance aft.
Best regards,
Dave Kautz
P-15 #1632 Tilly Lucy
Palo Alto, CA
______________________________ Reply Separator _________________________________
Subject: Re: Raising Centerboard
Author: Non-HP-ajsallee (ajsallee@engin.umich.edu) at hp-boise,mimegw7
Date: 4/24/99 10:49 AM
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West Wight Potter Website at URL
http://www.lesbois.com/wwpotter/
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Gordon,
Just a little correction...
You're right about calculating depth, but for moving the CENTER of effort,
you need to figure out how far back the center of the area of the board
moves, not how far back the tip moves. This is actually a fairly
complicated calculation because of the way the amount of board 'hiding'
within the hull changes. You need to know how high the pivot is in addition
to the profile of the board. As a quick estimate, just use half of the sin,
since you're looking at the middle of the board. So it moves back ~12%.
Andy
Beatrix, P19-854
-----Original Message-----
From: Gordon <hlg@pacbell.net>
To: wwpotter@tscnet.com <wwpotter@tscnet.com>
Date: Saturday, April 17, 1999 12:26 PM
Subject: Re: Raising Centerboard
>- - - - - - - - - - - - - - - - - - - - - - - - - - -
> West Wight Potter Website at URL
> http://www.lesbois.com/wwpotter/
>- - - - - - - - - - - - - - - - - - - - - - - - - - -
>Great post, Dave. Thanks for doing the math. It does appear that 10 or 15
>degrees aft could be effective in reducing weather helm without affecting
>stability significantly.
>
>Harry
>
>>Soooo, heres a little table which should help us understand why "raising"
the
>>board slightly can change the way the boat handles without imposing
>>significant danger:
>>
>>Angle Cosine Sine
>>0 deg 1.0 0.0
>>5 deg .996 .087
>>10 deg .985 .174
>>15 deg. .966 .259
>>20 deg .939 .342
>>30 deg .866 .500
>>45 deg .707 .707
>>60 deg. .500 .866
>>75 deg. .259 .966
>>90 deg. 0.0 1.0
>>
>>We can multiply each of these entries by 100 to get a percent change in
>>height with angle - So "raising" the board by 15 degrees, as I suggested
>>before, actually leaves the board at 96% of it's original depth while
moving
>>it back 26%. 10 degrees would maintain 98.5% depth while moving the board
>>back by 17%. Going back 30 degrees leaves 86% of the board down while
moving
>>it back by 50% of it's length.
>>
>>At 45 degrees things become even (71% depth, 71%aft), the change in depth
the
>>same as the change in fore/aft position and after that the relationship
>>reverses and we are then quickly lifting the board out of the water.
>>
>>I hope it's obvious here that while raising the board a little is okay (in
my
>>opinion, anyway), raising it more than, say, 30 degrees will have
diminishing
>>returns in balancing the helm and will start to seriously compromise the
>>ability of the boat to "self-right". Coming from a background of sailing
>>dinghies with unballasted boards which are frequently raised all or part
way
>>may make me more cavalier with this than is prudent, so it is probably
better
>>that I suggest that readers of this not interpret it as advice or
>>recommendation. If there is any question in your mind, leave the board all
>>the way down.
>>
>>Best regards to all,
>>
>>Dave Kautz
>>P-15 #1632
>>Palo Alto, CA
>
>
>