The maths behind cutting these bevels?

[uziwood786]

Hi all,

I'm trying to recreate the base (ignore the name) but don't know how to do it.

All I know is my finished size of the piece I want is 29cm x 5.5cm x 2.4cm, and the main thing is the part on top in the middle where the name is sitting I want to be 3cm.

While I want to re-create it, I want both sides to be equal in how they are cut unlike the example.

I've tried to play around with some different angled bevel cuts but it's just not working, 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!

 

[johna.clements]

Correct me if I am wrong but you are starting with a piece that is 290 long by 55 wide by 24 deep.

The top wants to be 30 wide after the bevels are cut and you want the bevels on the ends to have the same slope as the sides..


55 wide less 30 leaves 25 or 12.5mm horizontal slope distance on each side.

290 long less 25 (or 12.5mm horizontal slope distance on each side) leaves 265 length along the top.


You have not stated how high the vertical section is before the bottom of the bevel. If you assume it is 5mm.

24 deep less 5 leaves 19mm vertical distance on each side.

Tangent of the angle = 19 divided by 12.5 = 1.52

Therefore the angle of the bevels are 56.7 degrees. or 33.3 if cutting the other way.

 

[Jacob]

45º?
You don't need maths - draw lines at the top and the bottom edges of the bevel exactly where you want them on the blank, then join them up by eye, with your TS, bandsaw, hand saw, plane, axe, teeth, whatever.
If planing it's easier if you do the long grain first and then the short bevels across the grain last.

 

[Woody2Shoes]

What tools do you have at your disposal?

I think that simply drawing it may be easier than 'maths' - TBH I'm struggling to understand what your difficulty is - where exactly in the process (you are going through some kind of process, aren't you?) do you get stuck?

Cheers,

 

[Woody2Shoes]

......
If planing it's easier if you do the long grain first and then the short bevels across the grain last.

Personally, I'd do the end grain first because tear-out...

 

[Jacob]

Personally, I'd do the end grain first because tear-out...

It's counter intuitive, but it works better the other way, assuming moderate competence with a plane

 

[Hornbeam]

It's counter intuitive, but it works better the other way, assuming moderate competence with a plane

Really?

 

[uziwood786]

Correct me if I am wrong but you are starting with a piece that is 290 long by 55 wide by 24 deep.

The top wants to be 30 wide after the bevels are cut and you want the bevels on the ends to have the same slope as the sides..


55 wide less 30 leaves 25 or 12.5mm horizontal slope distance on each side.

290 long less 25 (or 12.5mm horizontal slope distance on each side) leaves 265 length along the top.


You have not stated how high the vertical section is before the bottom of the bevel. If you assume it is 5mm.

24 deep less 5 leaves 19mm vertical distance on each side.

Tangent of the angle = 19 divided by 12.5 = 1.52

Therefore the angle of the bevels are 56.7 degrees. or 33.3 if cutting the other way.

Thanks Jonah, so the 290 x 55 x 24 with 30 wide is what i want the finished piece to be, my question i guess is what size piece should i start with to achieve that? The vertical section is 6mm. Also, how did you get 56.7 degrees from the 1.52? And if i was cutting the angle at 56.7, where would I set the fence on the tablesaw for that?

Also i'm unsure how i'd get the vertical height of 6mm? If I cut straight bevels it of course doesn't give me that so i'm a bit confused

 

[uziwood786]

What tools do you have at your disposal?

I think that simply drawing it may be easier than 'maths' - TBH I'm struggling to understand what your difficulty is - where exactly in the process (you are going through some kind of process, aren't you?) do you get stuck?

Cheers,

I go to a professional workshop so they have every machine you can think of,

So if I draw a straight line of where i want the bevel to finish, where do I set the fence, that's one thing i'm unsure about, and secondly I don't know how to get that vertical height of 6mm as jonah mentioned?

 

[Jacob]

Really?

Yes. Done it often. Mind you somebody else might get it wrong I suppose.
If in doubt try it on a bit of scrap first!

 

[johna.clements]

Thanks Jonah, so the 290 x 55 x 24 with 30 wide is what i want the finished piece to be, my question i guess is what size piece should i start with to achieve that? The vertical section is 6mm. Also, how did you get 56.7 degrees from the 1.52? And if i was cutting the angle at 56.7, where would I set the fence on the tablesaw for that?

Also i'm unsure how i'd get the vertical height of 6mm? If I cut straight bevels it of course doesn't give me that so i'm a bit confused

You have to decide on the horizontal and vertical dimensions of the bevel or the angle and one of the other dimensions. As @Jacob notes deciding on a 45 degree angle would be far easier to set up as it will be a preset angle on most machines.

If a 45 degree angle was used then the vertical height of the bevel would obviously be the same as the horizontal 12.5mm to give your required width of 30mm across the top.

I assumed you wanted to use a non standard angle rather than 45 degree which is why you are having difficulties. I just guessed 5mm because the height below the bevel looks to be about that in your photos. Do you want it to be 6mm instead, that will change the angle too 55.2 degrees.

Tangent is a trigonometry function. If you put in the ratio of the sides into the the tan-1 box it will give you the angle. A ratio of 1.52 gives 56.7 degrees when you "tan-1" it.

https://www.rapidtables.com/calc/math/Tan_Calculator.html
As Jacob notes cut up a piece of scarp first to make sure you have set the angle correctly if you do not want to make life easy and use 45 degrees.

 

[johnnyb]

forget maths take a stick that's wider than you need and 4square but twice as long as you need. rip a 45 along one edge(either a full 45( to a point or leave a small flat. do the same on one end. then put a line indicating how wide you need the flat. then adjust the fence by eye as close as you can then take small cut( say 1/2 inch) and withdraw. check the cut against the line. adjust to suit. when right do the full pass. chop the other end to size. finally saw the flat(use the stick offcut( as long as its 8inch or so) to adjust the saw.
ps I've no idea if you've got a saw!

 

[uziwood786]

I go to a professional workshop so they have every machine you can think of

You have to decide on the horizontal and vertical dimensions of the bevel or the angle and one of the other dimensions. As @Jacob notes deciding on a 45 degree angle would be far easier to set up as it will be a preset angle on most machines.

If a 45 degree angle was used then the vertical height of the bevel would obviously be the same as the horizontal 12.5mm to give your required width of 30mm across the top.

I assumed you wanted to use a non standard angle rather than 45 degree which is why you are having difficulties. I just guessed 5mm because the height below the bevel looks to be about that in your photos. Do you want it to be 6mm instead, that will change the angle too 55.2 degrees.

Tangent is a trigonometry function. If you put in the ratio of the sides into the the tan-1 box it will give you the angle. A ratio of 1.52 gives 56.7 degrees when you "tan-1" it.

https://www.rapidtables.com/calc/math/Tan_Calculator.html
As Jacob notes cut up a piece of scarp first to make sure you have set the angle correctly if you do not want to make life easy and use 45 degrees.

Okay I should have been clearer, firstly i'm an amateur woodworker starting off so excuse the elementary nature of my questions. 45 degrees and 5mm is perfect, i'm trying to recreate it but i don't need it exact. When you say 12.5mm is that the what i'd set the fence to?

Would you mind detailing the steps if I was to do this on a table saw? I know it's relatively straightforward but nothing is straightforward if you don't know what you're doing..

 

[uziwood786]

forget maths take a stick that's wider than you need and 4square but twice as long as you need. rip a 45 along one edge(either a full 45( to a point or leave a small flat. do the same on one end. then put a line indicating how wide you need the flat. then adjust the fence by eye as close as you can then take small cut( say 1/2 inch) and withdraw. check the cut against the line. adjust to suit. when right do the full pass. chop the other end to size. finally saw the flat(use the stick offcut( as long as its 8inch or so) to adjust the saw.
ps I've no idea if you've got a saw!

Okay I feel like this is what I need but could you break it down into simpler terms and I also don't know what a 4square is...

 

[baldkev]

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?

 

[TRITON]

Sorry Jacob. Endgrain first.

'Counterintuitive you're being controversial again

 

[Jacob]

Sorry Jacob. Endgrain first.

'Counterintuitive you're being controversial again

Well no, I've done it often with fielded panels. Familiar routine, endgrain last, no problem.
It's a shallower angle; OK perhaps I'd have a go at 45º first.
Might have a go later - I'm into practice practice!

Scroll down for planing end grain last, here: Sad story of my uneven bench top

 

[Doug71]

I'm thinking along the same lines as @baldkev, it sounds like you might be best avoiding the table saw for the sake of your fingers.

If I was making a one off of these I would start with a piece twice as long as I need, set the fence on my planer to 45 degrees and make a few passes then cut to length and the end angles on my mitre saw.

Despite being allergic to hand tools I might even blow the dust off my hand plane and just use that for a bit of fun, think even I could manage it.

 

[MorrisWoodman12]

Sorry Jacob. Endgrain first.

'Counterintuitive you're being controversial again

Although I agree @Jacob is being his usual controversial self - thank goodness, cos someone has to be - and while I would normally agree end grain first surely it depend upon what you are doing. In this case its probably easier to plane the end grain 'from the top' as it were rather than across the end. That way it probably doesn't matter.
Martin

 

[Jacob]

Although I agree @Jacob is being his usual controversial self - ...

Not at all I've done it often. But yes it is "counter intuitive" and it is possible to do it badly.
The angle might be a bit steep though.
Our OP really needs to sketch it out on a drawing board first - if you look at the figures given they look different from the samples in the photos.
And yes - doing it on a table saw not at all easy - a skilled operation for an experienced user, plus two push sticks etc