trigonometry for saw horses

[mickthetree]

Pulling my hair out trying to get my head around this!!!

I need a couple of saw horses so thought I'd use the opportunity to get my head around some trigonometry. MISTAKE!!

I want the legs splayed at 15 degrees towards the ends and 15 degrees out to the sides.

I have read lots of articles but this is how I think it should be done. I'm struggling with thisthough!!

So I cut some test pieces. A leg cut at 15 degrees across the width and 15 degrees through the thickness:

View of it sat on the top

https://farm4.staticflickr.com/3902/14599875376_0d7c0fefc6.jpg

I tried cutting it into place on another test piece but its not 90 degrees to the sides.

If I draw around the leg as you can see it is a rhombus and not 90 degrees to the sides. Can anyone explain why this ends up like this? I need to understand so I can cut a housing into the side of the top or the leg.

 

[mickthetree]

Maybe sketchup can help here:

First off I create the top and a leg which is tilted at 15 degrees towards the end. I have beveled the top at 15 degrees too.

looking from the top the leg is parallel with the top:

But when I angle the leg out to the side at 15 degrees, all hell breaks loose and my brain melts out of my ears.

If I now cut the top of the leg so it is coplaner (correct term?) with top of the trestle then the resulting compound bevel, when laid flat and traced round, produces a rhombus (again correct me if I am wrong).

I want to house this into the top of the trestle slightly for added strength. I can probably work out with a bit of trial and error how to do this, but I'd really like to get my head around what this angle is, and if I can calculate it rather than trial and error.

Cheers!

 

[DTR]

Wow. I just drew out one leg to scale on the bench top, set a sliding bevel and marked the legs out from there.

 

[Random Orbital Bob]

I stole my method from a chippy mate of mine in 1990. Still going strong

The side splay is simply by taking a 15 deg slice off the side of the upper leg. The end to end splay is from the mortise as the pics show. The mortise is flat inside. The ends were cut level after construction by standing on a known level surface and scribing the level then cutting to the scribe.

 

[Jacob]

I wrote it up here
http://www.owdman.co.uk/howto/howto2.htm
No trigonometry involved - it's all done by graphical projection - basically you "unfold" the shapes to make them flat, as if they were cardboard boxes
(ignore rest of site it's due for a makeover)

 

[mickthetree]

Hi Jacob
Yes I read that page. It makes more sense now that I've made some test cuts and tried it. It was gobbeldegook to me before that

I am correct though arent I? In that when splaying the legs out to the sides, they are no longer parallel with the top edges?

It seems so simple in my head or on paper, but when I cut the pieces or do it in sketch up the pieces go out of alignment.

That picture shows what I want to achieve, and the bottom right sketch shows what is actually happening when I try to splay the legs out.

 

[Jacob]

Hi Jacob
Yes I read that page. It makes more sense now that I've made some test cuts and tried it. It was gobbeldegook to me before that

I am correct though arent I? In that when splaying the legs out to the sides, they are no longer parallel with the top edges?

It seems so simple in my head or on paper, but when I cut the pieces or do it in sketch up the pieces go out of alignment.

That picture shows what I want to achieve, and the bottom right sketch shows what is actually happening when I try to splay the legs out.

When you splay the legs you have 2 choices:
1. Keeping them rectangular in section means they either tilt outwards at the sides like your sketch, or tilt inwards at the ends (your sketch isn't quite right) which is a better option as the sides stay flush
2 Make the leg section rhomboid and they then are rectangular in plan and much neater looking. You have to "project" the cross section so you can get the angles of the bevels.

It's a bit of a head banger but you'll get there if you persist for long enough! It's tempting to cheat with a bit of trigonometry but in the end it probably won't help as you still have to make the step of visualising what's actually going on. When you've got it it's simple (ish) :roll:

 

[bugbear]

Maybe sketchup can help here:

First off I create the top and a leg which is tilted at 15 degrees towards the end. I have beveled the top at 15 degrees too.

looking from the top the leg is parallel with the top:

But when I angle the leg out to the side at 15 degrees, all hell breaks loose and my brain melts out of my ears.

That's because you angled the leg around the axis of the top. If you pivot the leg around it's own axis (which is also the plane of the mortise walls) everything stays simple, and no rhomboids appear.

Roy Underhill has a lovely episode (called "The Sawhorse" ) where he cuts one of these with no plan at all - just a sliding bevel which he sets at the start, by eye. After that it was all done using each prior stage as a marking or cutting tool for the next.

BugBear

 

[Fergal]

http://www.oneprojectcloser.com/how-to-build-sawhorses/

I recently made a pair of folding saw horses like the ones in the link above. They have legs with a 25 degree mitre and a 10 degree bevel. I followed the plans for the first one, but the notches for the top cross member didn't come out quite right. So for the second one, I clamped the legs to a chair in their final position and laid the cross member on top and used a rule to project the lines of the cross member on to the legs in order to mark the cuts.

Fergal

 

[Jacob]

...
That's because you angled the leg around the axis of the top. If you pivot the leg around it's own axis (which is also the plane of the mortise walls) everything stays simple, and no rhomboids appear.

Not so. That's the whole problem. You can't splay (tilt in two directions) rectangular section legs and have them sit square on plan.
Yes there's all sorts of ways of bodging it (quite neatly) but we are looking at the geometry here, and a basic setting out procedure

 

[Phil Pascoe]

+1 for BB's last paragraph - I did mine with no problem at all by doing exactly that. O.P. - you've possibly seen it somewhere, but a useful thing to do is to leave one end long enough to put a "V" in it about 60mm wide by 130mm (approx). This can be used to fix the edge of a door when sitting astride the horse to work on locks in situ.

 

[Jacob]

Useful tips - make three; much more useful than 2
Have the top finish short within the overall plan of the legs, for stability - you can balance on the very end without risk of tipping

 

[Eric The Viking]

Random Orbital Bob's approach (above) seems really straightforward.

There's no mechanical difference between that and keeping the legs straight (and the slots angled). If anything Bob's is stronger, as downwards pressure doesn't open the joints.

 

[Random Orbital Bob]

well its lasted 24 years so far I think I braced the ends after about 10 years with some old skirting that was lying around after a tiny wobble started. I also agree with making 3 at once which is what I did for extra support of sheet or awkward goods and I also wouldn't worry too much about either end of the legs. They can both be cut flush on the top and to a scribed level surface after construction. Then the only thing you have to worry about when sussing out the leg geometry is the joinery in the top which as already stated is really quite straight forward.

I used a sliding bevel to layout the angles. Only set it once.....job done

I've used them as platforms to paint from, plaster ceilings from (badly I might add). As can be seen by the delightful British Racing Green, to spray paint projects on, and of course all manner of sawing jobs and even as a table for the kids on one summer BBQ with a chipboard top covered in tablecloth. They stack and are basically indestructible. Tops on the pair were 4x2 and the bigger unsprayed one 5x2. Both nicked from offcuts of a roofing job we were doing at the time (my own wood I hasten to add).

The pair with the knackered old bit of veneer'd flooring nailed on has become blank creating station for the time being.

 

[bugbear]

...
That's because you angled the leg around the axis of the top. If you pivot the leg around it's own axis (which is also the plane of the mortise walls) everything stays simple, and no rhomboids appear.

Not so. That's the whole problem. You can't splay (tilt in two directions) rectangular section legs and have them sit square on plan.

Sorry, you're quite right. The simplest you can get it to is: vertical mortise walls (as sawn) and rectangular legs. But the mortise flank would have to be angled, and the leg-end would indeed show as a rhomboid.

BugBear

 

[Roughcut]

I was shown pretty much the same way as R.O.B has explained some years ago by a guy who had 40 odd years of chippy experience.
Can all be done with a hand saw, chisel and a sliding bevel.
For finishing the legs to correct length and bevel angle upturn the saw horse on a known flat surface, place a mark on one leg at the correct finished height by using a tape measure, then transfer the line to the other legs using a spirit level and pencil.
I was also told to put a vee in the end to accommodate doors etc. for hand planing.

 

[AnLasair]

I had to make a sawhorse at college and did it basically the same way that ROB and roughcut have described, complete with V cut in the end and also a peice of thick dowel sticing out vertically at one end to help hold stuff still for things like planing. Except mine have another bracing peice between the legs, which protudes slightly to be able to hold long planks and skirting board and such.


picture is easier than explaining in words I feel... not a great photo but best I have without going out to the garage and taking a new one

 

[Phil Pascoe]

Similar to mine, but as Jacob said it pays to splay the legs further so there's less risk of it's tipping if you're standing on it near the ends.

 

[merlin]

This is my way - I was going to post this on the jigs section but here goes -

I have made quite a few of these over the years for myself, other people and even as testers for a new job, they were never the same and each time I had to use the old one for a pattern, in the end I made a few templates to make life a bit easier.

I made the leg template out of some sheet brass and generally use 4x2, 2x2 and any off cut of ply for the gusset, I have never had one break so see little point in any thing bigger or heavier,

Once the leg joint is cut the rest will follow so easy really.

I don't bother cutting a door slot in the end, I just fix a piece of 4x1 on the top with a slot cut into that if I need to shoot a door edge.

Cheers, Merlin

 

[AnLasair]

i think is was a 1:6 splay in each dirrections that we were told was best. can't remember, but sure 1:6 was involed lol



I like the jig idea