# finding the arc between two points

Discussion in 'Boat Design' started by Mcgyver, Aug 8, 2007.

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### McgyverNew Member

Im starting to build a hydroplane from the 60's (sporthydro) that I found on the net, and I can't figure out how to find out the curve of the BOWPLATE. I have all of the dimensions that I need but cant figure out the curve. I know I can just wing it and get something close but I want it to be a little bit more precise. is there a more precise way of doing this or do I have to guess. I have also clipped a picture from the plans so you can see what I'm talking about

The New Guy

Mcgyver

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### LPFlying Boatman

Without going into detail, I just drew it up at a 62" radius.

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### PericlesSenior Member

Use a batten to create the curve, using the measurements given on the blueprint.

Pericles

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### McgyverNew Member

So string and a pencil is the simplest way to do this? if there is a better way to do this, can you point me in the right direction?

Mcgyver

5. ### lazeyjackGuest

take the beam, and divide by 3
then take the crown height and mutliply by these factors
at 1/3 beam out from centre, multiply height by .8818, and 2/3 out by .5393
draw straight line between outside ponts and divide into the thirds, now square up and mark the heights you obtained , I do all my decks this way, if there are 40 beams I do each and everyone separately, makes very fair deck and beam,
you can then use a batten to draw in the line from points or do it in rhino or something
is this what you are wanting?

6. ### lazeyjackGuest

here in rhino

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7. ### lazeyjackGuest

here it is split up, it is a very accurate and fast way

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### Michael ChudyYacht Designer

If you want the math, here it is.

To find the radius of an arc when you know the height and the length:

You know the height of the arc = 4.5"

The length is 48 " minus twice the length of the opposite side of the triangle whose adjacent side is 3" and angle is 15 Degrees.

Opp = Adj * tan angle. So Opp = 3" * tan 15. Opp = .804"

Length = 48 - (2* .804) = 46.392

Using Pythagorean theorem:

Radius = (4h^2 + L^2) / 8h

All this information and more is available online at

http://mathcentral.uregina.ca/

Have fun,
Michael

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### McgyverNew Member

Thank you very much for your help guys. I got the desired arc for the bow plate and it came out perfect.

Thank you

Mcgyver

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### BWDSenior Member

Glad the deck arc came out right.
Wanted to ask if anyone has used the method from Gougeon's book, getting ready to do so myself.
Very simple, draw circle with radius equal to deck camber, measure arc heights above diameter, transfer to template/stock and spring batten. Seems straightforward, but no reason not to ask before cutting...

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### SkipperSkiJunior Member

Mcgyver,

I assume the picture is from a magazine, the easiest way is first determine the scale of the drawing, using the 6" dimension, on a scale ruler it's say, 3/8" which is a half foot of 3/4" scale.

Now tape the picture to a sheet of paper, and using only a drawing compass, pick two points along the arc. place the compass on one point, and scribe a 180 degree right arc, perpendicular to the arc, place the compass neddle at the intersection, and scribe a 180 degree left arc, the intersection points of the two scribed arc's, place a straight edge on these points and draw a line, out on the drawing paper, this drawn line is perpendicluar to the design arc, do the same at a wider point of the design arc, this second line drawn to intersect with the first, is the vertex of the designs radius, measure the design radius from the found drawing scale. Or draw it out full size on your material.

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### tom28571Senior Member

The formula is: r = 4(h^2) + (c^2)/ 8h

h = height of arc = 4 1/2
c = span of arc = 48

If the span is far greater than the height, a close enough answer is r = c^2/8h which give 64". close enough and easy enough to remember.

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### lewisboatsObsessed Member

I take it no one reads the entire post...he already has the darn thing done!

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### SkipperSkiJunior Member

Aye, Aye, Mate !

But someone may learn from it next year !

The compass method is fool proof, when doing a boat part copy/restoration.
by drawing out the arc full size, and find the center of the arc/circle (s)

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### tom28571Senior Member

Aye Lewis, but knowing the simple formula will work at small scale on paper or at any scale next time anyone wants to do this. The true mensuration formula from a math book is much more involved but this one works well enough.

Of course if anyone just likes to plug numbers into an internet table, just look here:http://www.handymath.com/cgi-bin/rad2.cgi?submit=Entry

Also kicks out the length of the arc.

Good knowledge never wasted.

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