How do I calculate these angles?

[Johnwa]

Afternoon all, I've been asked to make a decorative lantern for christmas decoration (yes, early I know but at the speed I move at these days I need plenty of time !) The lantern body is no problem I've worked that out but then I came to the 4 sided pyramid top and hit a wall! How do I calculate the bevel angles to set my saws at? Maths has never been my strong point and for the life of me I can't figure it out. Can one of our more gifted members explain in language for mathmatical illiterates how these angles are calculated and help an old feller out please?

 

[Inspector]

You can do some searches for pyramid cutting calculators and all you need to do is fill in the boxes with the sizes you are playing with and they spit out the angles you set your saw to. If you have your heart set on relearning and remembering how to do it with pencil and paper there are likely members that can describe it in detail.

https://www.blocklayer.com/pyramid-calculator
https://www.1728.org/volpyrmd.htm
https://jansson.us/jcompound.html
There are a ton or tonne if you prefer, more.
Pete

 

[Jacob]

Afternoon all, I've been asked to make a decorative lantern for christmas decoration (yes, early I know but at the speed I move at these days I need plenty of time !) The lantern body is no problem I've worked that out but then I came to the 4 sided pyramid top and hit a wall! How do I calculate the bevel angles to set my saws at? Maths has never been my strong point and for the life of me I can't figure it out. Can one of our more gifted members explain in language for mathmatical illiterates how these angles are calculated and help an old feller out please?

Is this a pyramid shape cut on the end of a 4 sided block, or something dIfferent?
You can probably avoid maths altogether if you just slice off each of the 4 pyramid sides at the same angle, whatever it is. Might as well be 45º if you want a number.
Or if I've misunderstood you could draw a little sketch?

 

[Yojevol]

Is this a solid pyramid or is it a shell and you are trying to calculate the mitre angles for the 4 sides?
Brian

 

[Johnwa]

Sorry for my ambiguity guys. I was intending to make the pyramid hollow out of of ply, thats why I needed to calculate the compound bevel angle. I envisage something square about 180 mm each side and around 25/30mm high. Cheers. John

 

[Peter Sefton]

As its four sided it will have the standard 45 degrees mitres in one plain, so setting your saw arbour to 45 and you are half way there. The other angle will depend on how tall the pyramid is.

Cheers

Peter

 

[Peter Sefton]

Sorry for my ambiguity guys. I was intending to make the pyramid hollow out of of ply, thats why I needed to calculate the compound bevel angle. I envisage something square about 180 mm each side and around 25/30mm high. Cheers. John

I assume you mean 180mm wide at the base by 250 to 300mm high?

 

[Jacob]

Sorry for my ambiguity guys. I was intending to make the pyramid hollow out of of ply, thats why I needed to calculate the compound bevel angle. I envisage something square about 180 mm each side and around 25/30mm high. Cheers. John

Very shallow angle! How thick the ply and how would you finish the 4 exposed edges - just leave them square?
I'd be inclined just to plane it from a single solid 180mm square piece 25 to 30 mm thick You could taper the eaves down to say 5mm.

 

[Jacob]

I assume you mean 180mm wide at the base by 250 to 300mm high?

That'd be getting on for a steeple!

 

[Rewound]

If it is what I am thinking of, then it is a very very complex calculation and unless you are very good at trignometry and aljebra you will need to find an online resource.
I will see if I can fin my workings out. I made a spreadsheet as I had to make a number of these last year, very intersting project

Is this the angle you are needing ?

and this was the final article, an eight or nine sider, I can't remember

if you tell me what size you want I can do the numbers for you, here is a screenshot of my calculator

 

[Jacob]

There is a very easy way to do it graphically with no calculations, however many sides (within reason).
I'll see if I can do a demo tomorrow (after I've been to the dentist and one or two other things!)

 

[Adam W.]

You need to state the height and length of one the sides first.

Anyway here it is

https://www.omnicalculator.com/math/pyramid-angle

Anyway, quite what you do with all those complicated numbers and bits of numbers, I don't know.

 

[Peter Sefton]

@Johnwa What type of saw or kit do you have, a table saw with a sliding table or mitre slot and mitre gauge?

 

[J-G]

There have been some useful 'pointers' to the correct solution but none that take account of all the details. The calculations are a little more than trivial but dertainly not 'very very complex'; As usual Jacob will suggest that no calculations are necessary but if you want to get the job done, Mathematics is the only solution

I've done the calculations and then checked them against a 3D drawing (SketchUp).

Adams figures are correct but don't go quite far enough - only because he doesn't take account of the 5mm thickness.

The Green Triangle shows the figures from a simple front elevation. The Blue triangle shows the elevation looking square on at the corner.

Both of these confirm Adam's figures,

To determine the real angle for the edge which will produce a totally mating fit to the second and subsequent faces you need to determine the angle when viewed - not square on - but looking along the 'ridge' - this is shown in the Red Triangle.

The black triangle confirms the angles looking perpendicular to the face of each pyramid side.

I've shown the results to 3dp but achieving that is a mere pipe dream

 

[Yojevol]

Here is a brilliant visually interactive calculator for any number of sides and infinitely variable height
Enjoy
Brian

 

[Yojevol]

he doesn't take account of the 5mm thickness.

I don't think @Johnwa mentions a thickness and anyway the bevel or mitre angle for saw setting is independent of material thickness.
Brian

 

[J-G]

Here is a brilliant visually interactive calculator for any number of sides and infinitely variable height
Enjoy
Brian

Once I managed to persuade that to work in 'Metric' it confirms my ultimate figures, which came from simple mathematics (that'll annoy Jacob!!)

 

[J-G]

I don't think @Johnwa mentions a thickness and anyway the bevel or mitre angle for saw setting is independent of material thickness.
Brian

Once you have a 'thickness' then you must take account of it. If you were making it from paper or thin card then the extra adjustment isn't necessary. The calculator you linked to said this specifically, I new from past experience that it needed to be addressed.

I think the OP said in a later post that he was making a 'hollow' Pyramid and that's where I picked up the 5mm.

 

[Jacob]

There have been some useful 'pointers' to the correct solution but none that take account of all the details. The calculations are a little more than trivial but dertainly not 'very very complex'; As usual Jacob will suggest that no calculations are necessary but if you want to get the job done, Mathematics is the only solution

Wrong.
This happens to be a very simple roof structure and graphic projections are the ancient, classical well established non mathematical way of working out roof structures particularly, and other things too. And it can be a lot faster.
I'll do a demo tomorrow, can't be bothered to get the drawing board out now.
It used to feature in all the old books and was taught until relatively recently. Not entirely forgotten - it's too useful, but dropped right off the radar of the new boys! A bit like sharpening really.

 

[J-G]

Wrong.
This happens to be a very simple roof structure and graphic projections are the ancient, classical well established non mathematical way of working out roof structures particularly, and other things too. And it can be a lot faster.
I'll do a demo tomorrow, can't be bothered to get the drawing board out now.
It used to feature in all the old books and was taught until relatively recently. Not entirely forgotten - it's too useful, but dropped right off the radar of the new boys! A bit like sharpening really.

My 'mathemaical' solution - from first principles - took me less than 30 minutes. It'll probably take you longer than that to set your drawing board up !!

Using the calculator @Yojevol linked to took me less than a minute - even changing it to Metric!