Maths question...

[holdennut]

Does anyone know the formula that is used to calculate the radius of the arc in the picture below?

I have seen it before somewhere, using the distance between the two points of the arc and the height to that line and something about dividing by 8

Any help would be appreciated.

[CheffoJeffo]

Does anyone know the formula that is used to calculate the radius of the arc in the picture below?

Pic ?

[holdennut]

Sorry, pic attached...

[Dustin Mustangs]

http://mathforum.org/library/drmath/view/55146.html

 

[holdennut]

Cheers Dustin, that's the one but I can't get it to work. What does ^ represent? (multiply, divide)

                4h^2 + c^2
       r   =  ----------------
                      8h

h = 95
c = 685
r = ?

Maybe I'm having a blond moment but every way I twist it the result is way off.

Cheers

[CheffoJeffo]

Cheers Dustin, that's the one but I can't get it to work. What does ^ represent? (multiply, divide)

"To the power of" ? (e.g. squared)

Cheers.

[holdennut]

Cheers Cheffo, this time r = 807 which sounds just about right!

I really should have paid more attention at school. 

[ahofle]

http://mathpwned.ytmnd.com/

 

[jbullfrog]

The formula that was given assumes that you're starting your cut at a 90 degree angle (perpendicular) to the top edge (should the top edge have been parallel to the ground); from your pic it doesn't look as though you wanted a cut that was 90 degrees from being parallel to the ground, but wanted something that was a bit more sloped at the top.  If I'm wrong about this, please disregard everything that follows...

Because you don't want a 90 degree cut at the top, the formula will give you an 'r' that is a bit too small...  if you don't feel the need to be exact, just increase 'r' an inch or two from what the formula gives you...  draw it out for one inch, then draw it out for two inches...

Does this all make sense?

[Quarters]

If you want a more hands on approach, you can use circles to figure it out. See pic below.

1.) Draw 2 dot anywhere on your arc.
2.) Make small identical circles centered on each dot.
3.) Make larger circles centered where your small ones cross the arc.
4.) Make strait lines though where your larger circles intersect.
5.) Measure from where your 2 lines cross to your arc. this is your radius. (the green line)

hope this helps.

[Dustin Mustangs]

The formula that was given assumes that you're starting your cut at a 90 degree angle (perpendicular) to the top edge (should the top edge have been parallel to the ground)...

Just to set the record straight, the formula linked has nothing to do with anything surrounding the circle (or radius), just the circle itself.  The cut coming into or going out of the desired radius has no effect on the radius itself or the formula used to calculate it, so what was quoted above is incorrect.

Oh, and that's quite an interesting approach you have there Quarters...

[hbm*rais]

Holden,

Are you trying to draw some plans or to plot that curve down for sawing?

As you probably noticed in my plans, I didn't marked the radius of those curves clearly. I didn't because that information was lacking in the pictures/measurements I got from Stuzza at first place. So, after defining some "anchor point" (top of the marquee,  front of the CP and bottom of the cabinet), I just tweaked the curves freely using Illustrator to what I considered more aesthetic pleasing.

As my plans were 1:1, I just used Illustrator to measure the deepth of the side panel at various height point (each 10cm or so). Then I plotted this points on a big piece of paper, used a flexible ruler to smooth the curve out and used it as a template for cutting.

What I'm trying to say is, if you just want to get down to cutting, the template might be an easier way. If you want to draw plans, then God bless you. The world needs some nicely done lowboy plans  . Good luck anyway!

[hbm*rais]

Holden,

Just one more thing. I'm not sure if the curve you posted is taken from my plans or from the lowboy you're using as a model, but... have you considered it might not even be an arc of a circle? The way Illustrator works I'm pretty sure the curves in mine lowboy are an arc of an ellipse or something even more complex...

[holdennut]

Hmmm... back to the drawing board, since I still have the original panel I'll try out these suggestions and let you know which worked the best.

Ahofle: That's the answer I needed in my year 10 maths exam, awesome...

hbm*rais: I'll have to take your Illustrator file to work today and take a look. And yes I'm working on some plans for the Lowboy, a bigger mission than I first thought.

[NoOne=NBA=]

I would second the "flexible ruler" idea.
I usually use a long scrap of 1/8" Lexan, put two nails to hold the ends where I want them, and then just pull the center until it "looks right".

The easiest way to actually mark the piece is with a can of spray paint.
The nice thing about this method is that you can hold the Lexan in place, and not have to worry about it moving while you are drawing with a pencil.

[jbullfrog]

The formula that was given assumes that you're starting your cut at a 90 degree angle (perpendicular) to the top edge (should the top edge have been parallel to the ground)...

Just to set the record straight, the formula linked has nothing to do with anything surrounding the circle (or radius), just the circle itself.  The cut coming into or going out of the desired radius has no effect on the radius itself or the formula used to calculate it, so what was quoted above is incorrect.

Oh, and that's quite an interesting approach you have there Quarters...

Sorry for any confusion I might be causing, but what I'm describing is a concern...  although a fairly small one...

Hopefully the attached picture will help my explanation... 'h' and 'c/2' are given as they would need to be for the equation in question.  The problem is that the derivation of the equation relies on 'h' being a part of the radius of the circle while a radius will intersect the circle's circumference at a right angle.  This would mean that the angle 'A' shown in the attached picture would have to be a right angle which it is not (even very near where 'h' and the circumference intersect).  Given that 'A' is not a right angle, the equation would lead to an incorrect value for 'r'.

as stated before, to get an angle of 'A' that is a bit less than 90 degrees, increase whatever 'r' the equation gives you by a little bit and you should be good.

then again, maybe I'm not "looking at the same picture" you guys are:  maybe you guys are using a different 'c' and 'h' and I'm just confused 

I would also use the flexible ruler idea... you'd just be using a big protractor then

[holdennut]

Thanks for your concern jbullfrog but "h" in the equation isn't the radius. "h" is actually the height of the chord which is given as "c". (the picture in the link done in ASCII is a little confusing)

[Dustin Mustangs]

Not to mention that assuming line 'h', as drawn by bullfrog, goes through the center point of the circle (which if it doesn't I have no idea what it would be useful for), angle 'A' will always be the same for any given circle so worrying about what 'A' is really doesn't make any sense.

[jbullfrog]

Thanks for your concern jbullfrog but "h" in the equation isn't the radius. "h" is actually the height of the chord which is given as "c". (the picture in the link done in ASCII is a little confusing)

Yes, 'h' is the height of the chord, I understand that perfectly well... and because 'h' is the height of the chord, it goes through the center of the circle, as Dustin Mustangs points out (making it part of a line that describes a radius).  Also, just as Dustin Mustangs points out, any line that goes through the center of the circle will make the same angle with the circumference of the circle as any other line that goes through the center of the circle...  no matter what circle you are describing...

This angle will be a right angle.

really guys, go ahead and use the formula...  the radius it gives won't be that far off because the angle 'A' in the picture I linked to before is very close to 90 degrees...

have fun.