Need 3D functions for Uhden Boom Vang

[john.uhden]

I haven't seen one of these contraptions anywhere, but I am imagining it.

The goal is that by tightening the vang (from either side of the boat), not only do you pull the boom down but also pull it forward to optimize the sail shape and outward position mainly on a run.  Conventional vangs attached to the base of the mast don't pull the boom forward.

Rather than trial and error by drawing the thing a number of times with the boom in or out, I want to calculate the height above the deck.  I am pretty sure that the XY force vector is the bisector of the two legs of the vang, but calculating the Z will indicate to me the relative downward pull that the vang will exert on the boom at its point of attachment to the boom.  With this daydream design, I am assuming that the closer hauled the sail (boom being almost midships) that the downward pull will be the minimum, which is what you want when sailing upwind because the mainsheet should control the downward pull in that condition.

Anyone got any functions that will help me calculate the Z for various boom angles and tightness on the vang?

My premonition is that the force directions are simple (x y z) vectors and that the Z value is just a matter of applying the sine of the vertical part of the vector.  But I could spend days on this and spin myself in circles (just like many sailors do on the water after they have fouled another boat.)  I would like to build and use it (if it mathematically works) before the end of the racing season, just three weeks away.  Even better for the next races this coming Friday.

Now it's probably not that important because I lapped the rest of the fleet twice in the last race.  I'm not a sore loser, but winning is fun.

For those of you who have read this far and are familiar with yacht racing rules, for fun I suggested to the committee that the 360° penalty is too severe and should be cut in half.😆

[leeminardi]

The weather has cooled down a bit so I was able to get back onto my CAD computer.

I had some fun with this task.  The program prompts the user for the following:

- the elevation of the point on the mast where the boom connects (P2).

- the angle between the mast and the boom (alpha)

- the angle of the boom with the boat centerline as viewed in a plan view (i.e., parallel to the XY plane) (gamma)

- the length of the line connecting the boom to the B3 pulley (d)

Note, the location of the deck cleats are defined in the program.  This could be changed to user input.

From this information the program determines the connection point on the boom (P1) and the location of B3.  It outputs the location of P1 and P2 and delta z then draws the boom and connecting lines in 3D.

 To calculate B3 thr program uses a numerical technique (trial and error) by making an initial guess that the line from P1 passes through the midpoint between the 2 cleats (B1 and B2). Additional guesses are made by halving the distance from the last guess.

To tryout the program open the file boat.dwg and load the program boat-rigging.lsp. Give the command rigboat.

For a test case use the following values.

Elevation of point P2:  2.0

Alpha: 85 

Gamma: 35

Distance P1 B3:   4.3

I have not closed the program variables in the listing as I use them for debugging.

(defun c:rigboat	(/)
; calculates rigging for sailboat.  Use with drawing boat.dwg
; L. Minardi 8/14/2020
;  
  (setvar "cmdecho" 0)
  (setq P2Z (getreal "\nEnter elevation of point P2, where boom connects to mast."))
  (setq P2 (list 9.5 0 P2Z))
  (setq alpha (getreal "\nEnter alpha, angle of boom with mast."))
  (setq	gamma (getreal
		"\nEnter gamma, angle of boom with boat centerline."
	      )
  )
  (setq d (getreal "\nEnter distance from P1 to B3"))
  (setq dXY  (* d (cos (- (/ pi 2) (d2r alpha)))))
  (setq	P1 (mapcar '+
		   p2
		   (list
		     (* dXY (cos (d2r gamma)))
		     (* dXY (sin (d2r gamma)))
		     (* d (sin (- (/ pi 2.) (d2r alpha))))
		   )
	   )
  )
(findb3)
(princ "\n\nP1 = ") (princ p1)
(princ "\nP2 = ") (princ p2)
(setq dz (- (caddr p1) (caddr p2)))
(princ "\ndelta z P1 to P2 = ") (princ dz)
(princ "\n")  
(command "_point" p1 "")
(command "_text" p1 "0.4" 0. "P1" "")
(setq PBoom (mapcar '+ P2 (mapcar '* (mapcar '- P1 P2) '(3. 3. 3.))))  
(command "_line" P2 PBoom "")
(command "_cylinder" P2 0.2 "A" PBoom)  ; draw boom  
(setvar "cmdecho" 1)
  (princ)  
)

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun findb3 (/)
  (setvar "osmode" 0)
; location of cleats on deck  
  (setq	B1 '(7.75 3.35 0)
	B2 '(7.75 -3.35 0)
  )
; initial guess for v vector from P1 to midpoint of B1 B2
  (setq pguess (mapcar '/ (mapcar '+ B1 B2) '(2. 2. 2.)))
; set initial step size for next guess  
  (setq delta (/ (distance pguess B1) 2.))
  (setq	cont T
	pold B1 i 50
  )
  (while cont
    (setq i (1+ i))
    (if (> i 50) (setq cont nil)) ; quit if no convergence in 50 iterations 
    (setq v  (mapcar '- pguess P1)
	  s  (distance pguess P1)
	  uv (mapcar '/ v (list s s s)) ; unit vector from P1 to pguess
    )
    (setq B3 (mapcar '+ p1 (mapcar '* uv (list d d d))))
    ; calculate cosine of the angle B1 B3 Pguess and angle B2 B3 Pguess
    (setq s	(distance B1 B3)
	  uB3B1	(mapcar '/ (mapcar '- B1 B3) (list s s s))
	  beta1	(dot uv uB3B1)
    )
    (setq s	(distance B2 B3)
	  uB3B2	(mapcar '/ (mapcar '- B2 B3) (list s s s))
	  beta2	(dot uv uB3B2)
    )
    (setq pold pguess)
    (if	(< beta1 beta2) ; adjust point pguess 
      (setq pguess (mapcar '+ pguess (list 0 delta 0)))
      (setq pguess (mapcar '- pguess (list 0 delta 0)))
    )					; end if
    (setq delta (/ delta 2.)) 
;;;  uncomment to see convergence of b3
;;;    (command "_point" pguess "")
;;;    (command "_point" B3 "")
;;;    (command "_text" B3 0.4 0. "B3" "")
    (if	(< (distance pold pguess) 0.01) ; adjust tolerance if necessary  
      (setq cont nil)
    )
    )					;end while
(command "_point" B3 "")
(command "_text" B3 0.4 0. "B3" "")
(command "_line" P1 B3 B1 "")
(command "_line" B3 B2 "")  
(princ)
)					; defun

; degrees to radians
       (defun d2r (deg / )
(* (/ (float deg) 180.) pi)
  )  

;;; dot product of 2 vectors a and b
(defun dot (a b / dd)
  (setq dd (mapcar '* a b))
  (setq dd (+ (nth 0 dd) (nth 1 dd) (nth 2 dd)))
)

[john.uhden]

WOW!  Thanks, Lee.

I've been working in the same direction, but not as far as you.

My urgency is diminished because the next race is this evening and there's no way I can complete and confirm and install my design by then.  I don't think it matters though because the last time out I lapped the rest of the fleet twice, without any vang gadgets.  I think it's another two weeks until the next races after today's.

What we both need to add is accounting for when the boom is far enough out that the vang rope wraps around the windward side of the mast.

That dot product stuff has me baffled.  I'll have to learn it.  Right now I'm using a lot of sines and cosines and quadratics.

I am relieved to hear that things have cooled off a little in Boston.

[leeminardi · Accepted solution]

I find working with vectors much easier than dealing with x,y,z and trig functions.  The mapcar function makes it much easier to work with vectors.  For example, to add 3 vectors just write (mapcar '+ P1 P2 P3)

The dot product of 2 unit vectors is the cosine of the angle between them.  Rather than converting the cosine to an angle (there's no intrinsic acos function in vlisp) the program just compares the dot product result (the cosines) to see which angle is bigger and adjust the guess point accordingly.

I never got into sailing boats.  Hang gliding has been my passion for 45 years.  Here's a vid of me flying the dunes at the Cape Cod National seashore.

[john.uhden]

That was so cool. I can't figure out how you fly downwind without falling
out of the sky. But I guess that, thanks to Bernoulli, the momentum keeps
you up.
Bernoulli's Theorem applies to sailing up wind as well. I did not catch
how you steer the thing, but I enjoyed your face-plant landings.
If you ever go down to the Cape Hatteras area (Outer Banks), you'll have to
check out the sail boarders (board sailors?) on the bay side roughly
between Avon and Buxton. They're mostly all Frenchies from Canada and the
locals don't like them, but boy can they sail.
Also, you will have to get some Apple Uglies from the Orange Blossom Cafe.
If you keep the uneaten ones (a rare occurrence) in a paper bag overnight,
they are just as good the next day. Do NOT refrigerate.

[leeminardi]

When flying at a site like the Cape you use the wind that rises as it hits the hits the cliffs.  The wind must be coming in off the water and as it hits the cliffs goes up and over.  The maximum lift is usually found just in front and above the cliff edge. Outer Cape Cod has about 14 miles of east facing cliffs with just a few gaps.  You require an east of at least 18 mph to soar. The wind was about 25 mph +/- on my light run flight. Since the wind that day had a bit of a northern component the flight going south was much faster than going north.  You steer a hang glider by shifting your body.  Forward to dive, left to turn left.  Of course, there's a bit more to it.  Most of my flying these days is in NH getting into the air via a tow plane.  I'm getting too old and weak to carry the glider to mountain launch sites.

I went  to the Outer Banks years ago and had a good time with a Hobie Cat on Currituck Sound.

[Sea-Haven]

Have you thought about using two vangs one on each side of mast with quick release hitch do in say red and green ropes, hint boat lights. Both attached at same end points should be some Yacht hardware to suit larger D.

Lee nice image clarifies task.

[john.uhden]

Thanks for all that info.
Yeah, I used to sail Hobie 16s years ago too.
We literally sailed rings around the E Scows, trapped out and everything.

[dbroad]

dot alternative:

(defun dot (a b)
  (apply '+ (mapcar '* a b))
)

[leeminardi]

@dbroad  dot alternative, I like it!  Very clean.

[john.uhden]

I thought I had mentioned the two-vang approach which I had on my Barnegat Bay Sneakbox.  That's great if you have a crew to release the tight one before you snap the boom, but Sunfish are almost always sailed singlehandedly.  Maybe if I had a third arm with hand, but I don't.

Along with that issue is my desire to add a hiking strap.  Most of the world runs one fore and aft, down the centerline of the boat.  But my oldest brother decided that running them across the boat is better, so I have done that for years on my Sneakboxes and M Scows.  The problem I have is that I would have to mount each end to the side wall of the cockpit, which on the Sunfish appears to be about 3/16" of some kind of plastic.  Hollow wall fasteners (aka molly bolts) are either too deep of are made of zink which won't take the salt water environment for very long.

The solution may come to me in my nightly dreams, which usually wake me up laughing uproariously.

I think I entertain myself as much as The Big Bang Theory does, though not quite as much as Johnny Carson and SCTV and Ernie Kovacs and Victor Borge did.  Befive I nine my dessert I was sure three have finished my meal.

[john.uhden]

Being more comfortable with trigonometry than vector math, I muddled through my own tedious code, and instead of solving for Z, I tested various boom angles and plus and minus Zs to find the associated lengths of vang.

I am happy to report that the shortest vang length is when the boom is out more and the longest is when the boom is midships.  That translates to the vang being tighter (more force) with the boom out than in, which I had imagined and hoped for, and that there is a forward force on the boom when the vang is not slack.  However, there will also be a component of the force perpendicular to the boat which will tend to force the boom inward, which I don't want.

I hope I can presume that if the angle of the vector is less than 45° from the centerline of the boat then the forward component is greater than the perpendicular component, which it must be in all angles of the boom except zero.

Of course I still have to add the code for when the boom is out far enough that the windward leg of the vang is wrapping around the mast.  That will probably impact my results negatively.

Many thanks to all those who took interest and contributed their valuable thoughts.  You kept me going.

Now if I can just relearn how to get my @$$ across the boat on a gybe so I don't go for another swim in the river and have to get rescued.

Everyone is welcomed to criticize my thoughts (constructively, please).

BTW, does anyone know what you call an eye that looks like this...

     __________

__|                     |__

and not this...

     ___

__|     |__   ?   I'd say a bar eye, but I think that's something you would find in a pub.

[john.uhden]

@john.uhden wrote:

"BTW, does anyone know what you call an eye that looks like this...

     __________

__|                     |__

and not this...

     ___

__|     |__   ?   I'd say a bar eye, but I think that's something you would find in a pub."

I found it.  It's called a footman loop, and you can get it in stainless.

[leeminardi]

@john.uhden I'm not sure what forces you want to calculate but referencing the labels in my drawing of post #12 if the force in the cable from B3 to P1 is T then the force in the VANG line is:

Tvang = T / ( 2 * cos(angle))

in vlisp for my program since beta1 is the cosine of the angle the statement becomes:

(setq Tvang (/ T (* 2 beta1)))

You can enter !beta1 to output the cos(beta).

[Sea-Haven]

Had a look at Sunfish would it be easier to have the vang not go to base of mast but rather a track on inside so could set to middle at base of mast or for downwind out to side of hull and so pulls down. Did the Hobie have this for Boom ? 

[john.uhden]

For years I have thought of using a track for a vang because all the force
would be vertically down. But it would have to be curved in an arc whose
center is the mast. That design is very popular for travelers (the first
block/pulley near the end of the boom), but the radius for a vang would be
too small to work. Plus, my primary goal is to force the boom forward. In
a very light wind going downwind (on a run) you try to heal the boat to
windward to get the sail up in the air more. But when you do that gravity
pulls it back in when you want it out all the way. In moderate air you
still want to heal the boat to windward on a run but you want to keep the
boom down so there is more sail area perpendicular to the wind direction.
Then again, an old friend of mine who I grabbed as a 3rd crew in my
Sneakbox decades ago on a very windy day taught me to pull the sail in more
on a run to reduce the sail area apparent to the wind direction, giving you
more control of the helm. Sneakboxes and other boats want to balloon gybe
when a heavy wind is coming directly from behind which is likely to capsize
you and/or break spars.
A balloon gybe is when the boom is lifted high by the wind and comes
rapidly over your head to the other side of the boat. *Thwunk!*
I can't sail without telltales (light yarn or cassette tape) attached to
each side stay. They show you the wind direction. Sunfish don't have any
stays so I invented a way to add them to the sprit by attaching coat
hangers that stick out from a spring clamp that clamps onto the sprit. One
of the gals at the club suggested sacrificing a Barry Manilow tape. 😂 I
certainly wouldn't sacrifice a Beatles or Stones or Billy Joel or Eagles
tape, though I don't have a tape player anymore.

[Sea-Haven]

The hire hobie cats had a couple of big plastic 1gallon bottles on the top of mast not sure how they helped work out wind direction.

[john.uhden]

C'mon, Alan.
The plastic milk bottles are attached to keep the top of the mast afloat in
case the sailor capsizes. Otherwise a Hobie will turn turtle and get the
mast stuck in the mud. Most often, getting it out of the mud will bend the
mast permanently.

[Sea-Haven]

I knew that just having a laugh at tell tails. When dead straight HANG ON.

[john.uhden]

A little ribbing from down under, eh?

Well I finished my code, including wrapping around the mast, only to find my assumption was wrong.  The lowest Z of the boom attachment point falls when the boom is midships, not when it's out.  But at least I found that the range of Z is smaller when I move the deck blocks closer to midships, yet there is always a forward force on the boom.  So I just may employ it after all.  I can always release the vang when heading upwind and tighten it going downwind.  Most sailors do that with a conventional vang anyway.

[john.uhden]

BTW, with more testing I found that if I set the deck blocks just 1 inch ahead of the mast and 1 inch offset each side I get the most forward force and only a 1 inch vertical range.  But I have to add the arc length when the vang wraps around the mast.  I had just been using a point.  The arc radius is half the mast diameter plus half the vang rope diameter.  Back to Textpad...