The maths behind cutting these bevels?

[johna.clements]

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..

You can not have a 45 degrees bevel and 5mm vertical height to bottom of bevel and still have 30 across the top. A 45 degree bevel would increase (edit not reduce) the vertical height and or reduce the width of the top.

Have you tried drawing out to scale the profile you want to produce so that you can see what is possible.

I can not tell you were to put your fence. I would suggest you talk to the people in the workshop.

 

[Jacob]

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

Thought I'd better check incase I'm going senile or something.
Yes it is easier to do the end grain last, not least because the long side bevels have already removed a lot of wood.
There is a slight knack - skew the plane slightly as you go across. Also has to be very sharp and, as ever, a slight camber is good.

This is quick demo on a bit of scrap, to our OPs measurements.
One end:

Skew the plane (a No.5)

T'other end, not quite down to the line yet

 

[Jacob]

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..

It isn't straightforward on a table saw, it'd be quite problematic and you'd need some practice and training.
Band saw with tilting table better. Or just hand plane alone.
1 Cut and plane the blank to your chosen size
2 Gauge mark all the lines where you want your bevels to end
3 Remove the waste - easiest just to plane it off. Be very careful to leave the lines in place until the last cleaning up pass.
That's it really.
Problem is, you are asking much more than how to do this little project - you are actually asking how to do very basic simple woodwork. But keep asking that's how you find out, if you are lucky!
And avoid maths you don't need it.

 

[J-G]

And avoid maths you don't need it.

!!! - everything in life needs Maths - !!!!

 

[Jacob]

!!! - everything in life needs Maths - !!!!

It's probably the one biggest cause of error for woodworkers, from just misreading a tape measure onwards!
Marking up and graphical layout (the rod etc) is simpler and relatively fool proof.

 

[J-G]

It's probably the one biggest cause of error for woodworkers, from just misreading a tape measure onwards!
Marking up and graphical layout (the rod etc) is simpler and relatively fool proof.

Mis-reading a tape measure has nothing whatever to do with Maths!

A good understanding of Maths - or even basic Arithmetic (they are NOT the same !!) - will always be beneficial to any endevour.

 

[Jacob]

Mis-reading a tape measure has nothing whatever to do with Maths!

A good understanding of Maths - or even basic Arithmetic (they are NOT the same !!) - will always be beneficial to any endevour.

If there are numbers it's maths. Useful yes but not always the easiest way.
They built marvellous stuff before maths was invented - striding things out for measurements, string lines for straight or radii, dividers for precision etc
This project a good example. No maths needed just pick up a piece of wood and make marks in the right places. Only have to count to 1! (unless you want to make 2 if them, or more of them than you have fingers - which could be where the trouble starts)

 

[mudman]

If there are numbers it's maths. Useful yes but not always the easiest way.
They built marvellous stuff before maths was invented - striding things out for measurements, string lines for straight or radii, dividers for precision etc

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

 

[J-G]

If there are numbers it's maths.

You are (dare I say 'as usual') disingenuous --- Arithmetic is concerned with the four basic operations of + - x & / .

Mathematics is concidered to be concerned with the higher problems involving Trigonometry, Geometry, Algebra, Calculus and even more specifically 'Proofs' of theorems.

 

[J-G]

before maths was invented

It will no doubt surprise you to appreciate that 'Maths' (which was not 'invented' but 'discovered') was in use in 3000BC

 

[Jacob]

You are (dare I say 'as usual') disingenuous --- Arithmetic is concerned with the four basic operations of + - x & / .

Mathematics is concidered to be concerned with the higher problems involving Trigonometry, Geometry, Algebra, Calculus and even more specifically 'Proofs' of theorems.

So do you think our OP would be better off using maths/arithmetic to make his plinth thing?

It will no doubt surprise you to appreciate that 'Maths' (which was not 'invented' but 'discovered') was in use in 3000BC

It will no doubt surprise you to appreciate that there are many non mathematical, and often not even arithmetical, ways of setting out and marking up of craft work of many sorts. It's a bit of a lost art.
The classic first exercise in roofing layout was to make a sawhorse, and this featured in many of the older text books. I wrote it up here Making perfect trestles . Made the trestles too.

Never got beyond howto 2 but I've still got a little list!

 

[baldkev]

Thought I'd better check incase I'm going senile or something.
Yes it is easier to do the end grain last, not least because the long side bevels have already removed a lot of wood.
There is a slight knack - skew the plane slightly as you go across. Also has to be very sharp and, as ever, a slight camber is good.

This is quick demo on a bit of scrap, to our OPs measurements.
One end:

View attachment 147919

Skew the plane (a No.5)

View attachment 147920

T'other end, not quite down to the line yet

View attachment 147921

Sorry to interrupt your thread @Jacob , but maybe you could ask for the o.p's address..... then you can send him the part you kindly made for him

 

[J-G]

So do you think our OP would be better off using maths/arithmetic to make his plinth thing?

My 'beef' was never with the OP or that he did or didn't need to understand Arithmetic to enable him to accomplish his task - it was with your assertion that Maths is irrelevant and can be ignored, which may be the silliest thing that you have uttered (though even that is debateable )

 

[J-G]

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 :

[ 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 :

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!)

 

[Jacob]

My 'beef' was never with the OP or that he did or didn't need to understand Arithmetic to enable him to accomplish his task - it was with your assertion that Maths is irrelevant and can be ignored, which may be the silliest thing that you have uttered (though even that is debateable )

I assert again: Maths is irrelevant and can be ignored - as a solution to this problem that is.
As evidence, compare and contrast my offering (below) with your long-winded meanderings above.
The job could be done 10 times over in the time it has taken you to even start thinking about it!

1 Cut and plane the blank to your chosen size
2 Gauge mark all the lines where you want your bevels to end
3 Remove the waste - easiest just to plane it off. Be very careful to leave the lines in place until the last cleaning up pass.

 

[Jacob]

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

Definitely not. See below

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!)

In your drawing the left hand option is potentially dangerous and the workpiece could be picked up and flung out violently. It's a classic mistake which many people make, once only!
The right hand option is safer as long as two push sticks are used, but the slightest tremor will leave a trace and the thing would need planing.
Either way it'd have to be done with the crown guard off, which is not advisable except in very experienced hands.
But the biggest problem you have ignored altogether - how to trim the angle at the ends?
Maybe make a little sledge or something?
Still going to have to clean up with a plane or sand paper.
Easier to start and finish with plane alone?
Basically you could have it done 10 times over instead of fiddling about setting up and sorting out the various TS issues.
They'd be worth sorting out if you were going into production of a run bigger than say 10 off, but not for just one.

 

[Jacob]

Sorry to interrupt your thread @Jacob , but maybe you could ask for the o.p's address..... then you can send him the part you kindly made for him

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.

 

[J-G]

In your drawing the left hand option is potentially dangerous and the workpiece could be picked up and flung out violently. It's a classic mistake which many people make, once only!
The right hand option is safer as long as two push sticks are used, but the slightest tremor will leave a trace and the thing would need planing.

This is precicely why I said that there would be opposing views. Personally, I would use the right hand option but that doesn't make me right (or wrong).

But the biggest problem you have ignored altogether - how to trim the angle at the ends?

I haven't - I've shown the information for both 'Sides' and 'Ends' - did you not see the two anotations?

Maybe make a little sledge or something?
Still going to have to clean up with a plane or sand paper.
Easier to start and finish with plane alone?
Basically you could have it done 10 times over instead of fiddling about setting up and sorting out the various TS issues.
They'd be worth sorting out if you were going into production of a run bigger than say 10 off, but not for just one.

You again have your own agenda and completely ignor the OPs request for the distance that a fence should be from the saw when using a TS.

I actually agree that the problem is trivial and that marking out (still using arithmetic!!) and removing the waste material with whatever tools you have might be the quickest method, but that doesn't answer the OP's question.

 

[J-G]

I assert again: Maths is irrelevant and can be ignored - as a solution to this problem that is.
As evidence, compare and contrast my offering (below) with your long-winded meanderings above.
The job could be done 10 times over in the time it has taken you to even start thinking about it!

And I again assert that Maths is never irrelevant.

You were not asked "How would YOU do this task" the question was "What is the distance that I should set the fence on my TS to to achieve this result".

 

[Jacob]

marking out (still using arithmetic!!) ........

And I again assert that Maths is never irrelevant.

You were not asked "How would YOU do this task" the question was "What is the distance that I should set the fence on my TS to to achieve this result".

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.