Math Question - What Difference Does 1 Degree Make?

[Dennis Peacock]

Ok, I'm asking here because I KNOW there's a lot of smart people here. :)

Table base leg set - X shaped for farm style table.
Leg Overall height - 27.5"
Leg Overall width - 34"
Leg Intersection where both X pieces cross to for the "X" - 20" from the end of the long point of the leg-lower-section

Measuring the cross-section with 2 boards, I get about 91º for the cross section angle. If I changed that to 90º, what does that do to my "width" of he leg base? Design is 34" wide....
What is the difference 1º makes over the height of 27.5" and width of 34"???
419516

[Charlie Velasquez]

Check your measurements again. I get about 87° and hence 93° for your supplemental angles. As the angle may be off the easiest measurement you could give us is the width of the leg members, then we don’t need to mess with the angles.

[Stephen Tashiro]

Where the legs cross, there is a smaller pair of angles and a larger pair of angles. From the vertical dimension of 27 35/64 inches and the 20 inch sections of the legs, I get that the larger pair of angles should be about 93 degrees each. Do you want to reduce the larger pair of angles to 90 degrees each?

Is this a design for a new table? Or are you modifying an existing table, in which case you'd want to re-saw the bevels at the ends of the legs.

[Walter Plummer]

Above the "x" the short dimension is 16 15/32". Below it is 16 13/32". Is that throwing things off?

[Charlie Velasquez]

Edit to my previous.
If you want to maintain the 34” table top, and about 27.5” from floor to bottom of table, the base from inside edge to inside edge will be 21”, and from outside edge to outside would be 21”+(2*(2^.5)*w). w being the width of your leg members.

[Dennis Peacock]

Leg member width is 3.5" wide

In short.....the width at the TOP of the leg section is 34" wide.
The width at the BOTTOM of the leg section is 34".
The height of the leg section from the floor to the top of the "X" is 27.5"
Cross members are 3.5" wide x 3" thick

I included the drawing to give a visual of what I'm designing for. :)

[Charlie Velasquez]

With the width 3.5, the outside edge to outside edge of your base is 30.899”, height floor to bottom of the table is 27.5”, width at the top of the cross members from outside edge to outside edge is 34”

[Charlie Velasquez]

Labeled the vertices, added a couple of midpoints (F & G).
given: AB = 34: point F is midpoint and bisect angle ACB; segFB = 17”
triangle ABC is right isosceles. =>

Triangle FBC is also right isosceles; =>
segFB = segFC = 17.
segFC + segCG = 27.5 => segCG = 10.5

triangles DCE, DCG, GCE are all right isosceles =>
CG = DG =GE = 10.5
DG + GE = 21

Your cut off at the bottom is also a 45°, forming a right isosceles triangle.
The cut along the floor is the hypotenuse.
So the length is 3.5” x (square root of 2) ~4.949;
and there are two of them ~ 9.899
plus the 21 = 30.899”

edit, I like making all 45° cuts. If you want to keep the base at 34” consider changing your leg widths to 4.596”... or 4 5/8ths just a tad longer, but you could hit it with a couple extra swipes of the plane. If 4 5/8” is too massive for your design, consider starting with a 4 5/8” piece and do some scroll work in the middle 2/3 to reduce mass.

[andy bessette]

A rule of thumb is 0.0175" / inch.

[Dennis Peacock]

A rule of thumb is 0.0175" / inch.

This makes a lot of sense to me! Thank you!

[Kev Williams]

I'm not all that bright with angles so I cheat and use graphics programs :D

this is my reverse engineered version-- I drew a 27.5 x 34 inch box and made the legs fit, then took measurements-- then I changed the angles of the legs to 45 and then took more measurements...

419562
the right-most graphics are the 'to fit' layouts, the left is legs at 45...

Whenever I'm dumbfounded on angles and measurements, I just let Corel do it! ;)

[Jim Becker]

Dennis, I'm going to suggest you don't have the leg setup the same width as the table top, however..."IMHO", it's best to have the top slightly larger, both for appearance and comfort.

[Joe Bradshaw]

Dennis, I would get a large piece of paper and draw a full scale drawing of the end view of your table legs and take your angles from that. If necessary, lay the leg pieces on your drawing and mark your angles from that.
Joe

[Steven Cooper2]

I'm with Jim.

I plugged a few options into cad with similar geometries maintaining 90° to see how it looks, I have attached sketches below.

if you go to 90 degree crossin

I would tale the 27.5 and give some allowable .5 inch variation, and see how it looks. I prefer the look of the 36 inch top at 27.5ish with a 90 degree crossing. it has a nice round leg length for practical measurements as well. 34 works as well but insetting the legs a touch further looks better to me. =]

original

419588

90 ° crossing, new height
419590
90 degree crossing, original height
419587

90 degree crossing 36 inch top
419589

[David Buchhauser]

I vote for #4: 90 degree crossing 36 inch top. I think it looks better with more of an overhang.
David
https://sawmillcreek.org/attachment.php?attachmentid=419589&d=1573793169 (https://sawmillcreek.org/attachment.php?attachmentid=419589&d=1573793169)

[Jacob Reverb]

http://www.carbidedepot.com/formulas-trigright.asp

[Jim Becker]

I agree with David...

[Edward Dyas]

Ok, I'm asking here because I KNOW there's a lot of smart people here. :)

Table base leg set - X shaped for farm style table.
Leg Overall height - 27.5"
Leg Overall width - 34"
Leg Intersection where both X pieces cross to for the "X" - 20" from the end of the long point of the leg-lower-section

Measuring the cross-section with 2 boards, I get about 91º for the cross section angle. If I changed that to 90º, what does that do to my "width" of he leg base? Design is 34" wide....
What is the difference 1º makes over the height of 27.5" and width of 34"???
419516On a question like that I normally lay it out full scale on the back of a sheet of plywood. One degree can make a lot of difference on something that size. It's enough you could visually see it just mitering a piece of trim 1/2" wide and the longer the span the larger the difference gets.

[Dennis Peacock]

The table top will actually be 42" wide x 1.5" thick....solid white oak. I have 3 white oak boards that will go in this top that weigh in at 110 lbs each. The top is estimated to weigh about 350 lbs when assembled. The base is 34" wide which will give a total of 4" per side of clearance.

Last night, I forgot the "Math" and started cutting wood to make a prototype. Ended up with a 3º cut on the board that met at the center section and a 46.25º cut at the floor and at the top of the leg sections. I don't know if that's what the math would work out to, but it's what fit on my layout and the prototype. Tomorrow morning, I start the real wood working on the leg sections and expect to have them done by mid-day tomorrow. I really need to start on the top of the table next week!!

[Jim Becker]

The table top will actually be 42" wide x 1.5" thick....solid white oak. I have 3 white oak boards that will go in this top that weigh in at 110 lbs each. The top is estimated to weigh about 350 lbs when assembled. The base is 34" wide which will give a total of 4" per side of clearance.

That's very similar dimensions to the walnut table I recently did for a client, albeit the top is wood and the base is steel. But the design is similar with the "X". The top of the supports where they met the top were ironically 34" wide and the table top averaged 38-41" wide. (natural edge) So based on your description, I think your table is going to look great!

BTW, more than once I worked things out like you describe with scrap wood/MDF and then measured the angles. I did that for the "retro" vinyl record bin legs awhile back, as a matter of fact, as it had half-laps that were at oblique angles. Doing a flat mock up made the setups for the actual cutting to be really easy.

[Jack Frederick]

If there is anything that demonstrates the veracity of the "use it or loose it" theory it is mathematics. I envy the ability to handle these things so many have demonstrated here, but I'm, by necessity, with Joe. Get a large piece of paper, mdd or plywood and start drawing on it. That should be quite a table.