The maths behind cutting these bevels?

[Phill05]

Wow!!! don't you two know how to put off a newcomer to woodworking you should be helping not arguing with each other, could it not be said there are more than one way of getting the job done.

 

[johna.clements]

Wow!!! don't you two know how to put off a newcomer to woodworking you should be helping not arguing with each other, could it not be said there are more than one way of getting the job done.

Hopefully @uziwood786 looks at @J-G drawings in post 34 and see which option he wants. Then takes up @Jacob kind offer.

 

[baldkev]

Happy to!
But binned it already and it was only redwood.
Send me your address uziwood786 and all dimensions and I'll pop one in the post today.
FOC, have it for Christmas!
Choice of sycamore, beech, ash, various hardwood odds and ends.

That's very nice of you jacob

 

[uziwood786]

Do you have someone to supervise your tablesaw adventure? If so, just show them the pictures and they'll help. If no, use pushsticks, we hate seeing those posts with fingers missing.

On the photos, it looks like they had the angles the same all round, then trimmed the back off, maybe to get it closer to the wall?

I hadn't delved too deeply into the OP's question as I thought that it had been adquately answered but now I look back I see that is far from the case. It seems that no one has answered the subsequent question about how @johna.clements got the angle from the 1.52 calculation.

This is simply 'Maths' - 1.52 is the tangent of the angle and the actual value (in degrees) has to be 'looked up' from a table of Trig values - or today - keyed into a calculator/phone app.

Now the real question is what does the OP really want? - He has specified 2 criteria : the 'platform' should be 30mm wide and the 'skirt' should be 6mm. @Jacob's suggestion to set the saw at 45° would not achieve this without reducing the total height of the plinth.

Here is a drawing showing three posibilities :
View attachment 147956
[ A ] shows exactly what the OP has specified and to achieve this the angle Alpha needs to be 34.778° - which makes Beta 55.222° - both of which are cumbersome to set up on any type of saw. If the 6mm is not sacrosanct (and I cannot see any reason for it to be so) then making Alpha 35° would force the skirt to be 6.148mm.

To maintain the 30mm table width and use a 45° angle, the skirt would be 11.5mm as shown in Fig. [ B ] The alternative of maintaining the 6mm skirt would make the table width 19mm as Fig [ C ]

Given that the OP knows that the total height is 24mm and that he wants a 6mm skirt the he must use arithmetic to determine the 18mm dimension. Similarly knowing the width is 55mm and he wants 30mm left, only use of arithmetic can determine the 12.5mm dimension. Simply guessing a setting on any sort of marking stick and scribing that same value on each face (to get a 45° chamfer) will never achieve any of the criteria specified.

Personally I would settle for a 35°/55° setting - though as far as suggesting a location for a fence is concerned, we simply don't have sufficient information to give an unqualified opinion, but assuming the 35°/55° option is taken and that the job will be done on a table saw, then here is a drawing showing the figures :

View attachment 147957
This (hopefully) shows the two posible methods and I'm sure there will be equal support/opposition for each

Naturally, the precise width (nominally 55mm) height ( 24mm) and length (290mm) of the initial blank will have a bearing upon the final outcome.

[EDIT] - apologies to @johna.clements - I missed your responce detailing the Tan-1 explanation (though I doubt that the OP would have really understood the true implications!)

Hi,

I'm not sure what i've walked into with all of the debates, but firstly thanks for going to the trouble of drawing the diagrams they actually make everything a lot clearer.

Here's what I understand. A 35 degree bevel cut on my piece should automatically give me a skirt of 6.1mm which is perfect. I'm not precious about the angle whether it's 35 or anything else, I just want a nice bevel. What it then sounds like is Jacob's method of marking and keep cutting until you meet the bevel lines on each side will be the way to go, and adjust the fence accordingly

I do want to stick to doing it on the table saw because I may be experimenting doing it on acrylic as well. Am I correct in what i'm thinking above?

 

[baldkev]

I would be very very cautious about the acrylic bit. I might be wrong, having never tried acrylic on a tablesaw, but it sounds like disaster waiting to happen
A bandsaw is the best, safest option with acrylic, but of course you'll have to sand the cut faces progressively through the grits to about 1500 wet n dry, maybe 2k

Edit to add, i have cut acrylic sheet both with bandsaw and a jigsaw, which worked, but you have to keep the heat down, so feed rate is important, as is a sharp blade. A tablesaw blade would almost certainly spin so fast it would be melting the acrylic as it cuts, causing it to bind and shatter. Bandsaw was better than jigsaw, but jigsaw worked ok

 

[uziwood786]

I would be very very cautious about the acrylic bit. I might be wrong, having never tried acrylic on a tablesaw, but it sounds like disaster waiting to happen
A bandsaw is the best, safest option with acrylic, but of course you'll have to sand the cut faces progressively through the grits to about 1500 wet n dry, maybe 2k

I checked that with the technician at the workshop and he said it's not a problem. At the workshop they have a Panhans 690-100 TS which cuts through Zebrano like paper.

 

[baldkev]

Ok, cool, id be interested to hear how you get on

 

[Jacob]

...... keep cutting until you meet the bevel lines on each side will be the way to go, and adjust the fence accordingly

Well yes - if you don't cut to lines you'd have to do a trial cut or two anyway.

There is a serious point here which is that there's a tendency to resort to gadgets, CAD, Sketchup, calculators, maths, to solve simple problems which have much easier traditional solutions. Graphic projections is one, the rod is another, and so on.
Not to mention sharpening!

 

[Woody2Shoes]

I checked that with the technician at the workshop and he said it's not a problem. At the workshop they have a Panhans 690-100 TS which cuts through Zebrano like paper.

I'd be concerned that the acrylic might melt/burn.
This is a relatively small workpiece that would need correct procedure on a tablesaw without which there is significant risk of injury. Forgive me op, but will your use of these professional machines be supervised at all times?

 

[Jacob]

I'd be concerned that the acrylic might melt/burn.
This is a relatively small workpiece that would need correct procedure on a tablesaw without which there is significant risk of injury. Forgive me op, but will your use of these professional machines be supervised at all times?

I've cut acrylic, perspex, formica etc on a TS with no problem so far.
I agree about the risks though!

 

[baldkev]

I've cut acrylic, perspex, formica etc on a TS with no problem so far.
I agree about the risks though!

Hi jacob, what thicknesses of acrylic / perspex and what blade did you use?

 

[Jacob]

Hi jacob, what thicknesses of acrylic / perspex and what blade did you use?

Probably a medium sort of blade and not very thick perspex about 6 mm I guess. Some time ago can't remember. Clean cut. Formica no prob as long as it's firmly down on the bed.

 

[Jacob]

Well yes - if you don't cut to lines you'd have to do a trial cut or two anyway.

There is a serious point here which is that there's a tendency to resort to gadgets, CAD, Sketchup, calculators, maths, to solve simple problems which have much easier traditional solutions. Graphic projections is one, the rod is another, and so on.
Not to mention sharpening!

Or to put it another way - assuming a roughly dimensioned workpiece to start with this is a very easy job, few minutes work, with just a pencil and a plane. Every step towards using cleverer, more sophisticated, mathematical, technological methods, makes it more difficult and much slower. Not always the case of course!

 

[TRITON]

Are those sanding marks ?

 

[Adam W.]

Er, they were still using maths. Might not have using modern nomenclature, symbols or even methods, but it was still mathematics.

Off topic /

It's practical geometry, not maths, and let's not forget the power of proportion either. The vault I'm building doesn't require any maths or measurements, just a compass, a straightedge and a bit of geometrical savvy.........And.......geometry is art, not maths, before you number based freaks start to try and claim it.

Here's a picture of it so far and I might get my hands on it very soon for a winter of fun in the shed.

Those joints in the middle need a bit of a tweak, I wouldn't want to get accused of doing too much rough work.

/ off topic.

 

[Scruples]

That's even more pedantic than your maths!
Before he even mentioned TS he said "i'd really appreciate some guidance on this because i've tried for about 4 days and I haven't made any headway. Please help"
n.b. You wouldn't use arithmetic for the marking out you'd use a combination square. Even if it had no numbers on it you could just set it by eye. Or a marking gauge. Or just roughly gauge it with a pencil and your thumb.
Nuff said, this is getting boring.

There are many paths to the same result. Having allowed the OP to view a few on here, together with the accompanying rhetoric, he should be in a better postion to understand the concepts of cutting bevels.

 

[Jacob]

Are those sanding marks ?

No, just a slightly blunt blade.
It's easier than you think!
Probably took about 15 minutes from the point where I had a blank to the right size.

 

[mudman]

Off topic /

It's practical geometry, not maths, and let's not forget the power of proportion either. The vault I'm building doesn't require any maths or measurements, just a compass, a straightedge and a bit of geometrical savvy.........And.......geometry is art, not maths, before you number based freaks start to try and claim it.

Here's a picture of it so far and I might get my hands on it very soon for a winter of fun in the shed.


View attachment 148035

Those joints in the middle need a bit of a tweak, I wouldn't want to get accused of doing too much rough work.

/ off topic.

No, geometry is an area of mathematics that concerns the properties of shapes and space. Geometry can be used to create art but it is mathematics.

 

[Jacob]

Off topic /

It's practical geometry, not maths, and let's not forget the power of proportion either. The vault I'm building doesn't require any maths or measurements, just a compass, a straightedge and a bit of geometrical savvy.........And.......geometry is art, not maths, before you number based freaks start to try and claim it.

Here's a picture of it so far and I might get my hands on it very soon for a winter of fun in the shed.


View attachment 148035

Those joints in the middle need a bit of a tweak, I wouldn't want to get accused of doing too much rough work.

/ off topic.

I was going to mention Adam's work! Somewhat beyond anything you could do with the aid of maths, a calculator or even with Sketchup!

 

[Jacob]

I've cut acrylic, perspex, formica etc on a TS with no problem so far.
I agree about the risks though!

Basically the thinner and the more fragile the more you have to hold down the workpiece or it can chatter and start shattering. A bendy bit of Formica is better done with a sliding table and a board on top of it