Help with mathematics please.

[richardda1st]

Can someone show me how to find 'X', which is the required clearance for a door/gate with a known thickness but with a variable range of widths (door swing). It's easy using cad software but I need a formula instead. :question::help::shrug::confused2:

Please refer to attached pdf file.

Thanks
Richard

[DarkRevenge]

Hi Richard.
I can resolve it by making a function (but in fact idk if it's the shortest way). You just need to know the Pythagorean theorem and how to work with functions. I'll write a .doc about how to do it and I'll post it.

[DarkRevenge]

Here it is. I hope someone can check it to see if the solution is ok. If it is and you don't understand something (I think I haven't explained it well :confused2:) comment, and I'll try to do everything possible to help you.

Cheers, Luis.

[richardda1st]

Hi Luis.

Thanks for such a rapid reply. :D

Yes your answer is correct:thumbsup: (but you probably knew that;))

Can you expand your steps as you work through it. Thanks to cad software I have been able to switch my brain of for the last 30 years:confused2:

Richard:thanx:

[Robh]

I'm not clear about your clearance. Are you talking about the door's clearance from the door jamb recess? Why do you need x?
The clearance is always going to be a few mms (e.g. pick 3 mm) more than the door width (door swing) regardless of the size of the door.

Regards, Rob

[DarkRevenge]

I think here it's a bit better. I don't know very well the "technical words" as I speak spanish and I've never been taught about "maths in english" lol So I'm sorry if it isn't very clear :question:

Cheers, Luis.

P.S.: I know... the pics are horrible! :sadeyes:

[richardda1st]

Luis, as soon as I looked at your 2nd diagram it all became obvious.:screwy:
If only I drew a triangle of what I knew. My brain has been switched of for to long.:ashamed::doh::screwy::rofl:

Muchas gracias:thanx:
Richard

[richardda1st]

Hi Rob.
Where have you been?:)

As to these doors/gates. They are very thick (like me), range from 178mm to 200mm and as the door opens the corner furthest from the hinge kicks out. The narrower the door but same thickness the more clearance you need, can be anything up to 30mm.

Cheers
Richard

[sheeny]

For fairly narrow doors (compared to the width)

x = t * t / w

will give a reasonable clearance. (That is determined by applying similar triangles). For very narrow or thick doors this may give too much clearance however, so the precise formula based on Pythagora's theorem is:

x = sqrt(w² + t²) - w

where:

t = thickness
w = width

You need to allow a bit extra to have "clearance" with this formula.

Al.

[Robh]

I get it. In that case, Al (sheeny) is spot on.
I tune in from time to time.

Regards, Rob.

[scopemankit]

I see it as sagitta maths. Sag (x) = r^2/2R
eg 1 - 178x178/2(700) = 31684 divided by 1400 =22.63
eg 2 - = 31684 divided by 2000 =15.84
eg 3 - = 31684divided by 3000 =10.56

That's my theory

[richardda1st]

Thanks Al, that seems to agree with Luis, except in your case I think 'W' is the radius (door swing arc) not the width of the door, do you agree.:question:

Hi Chris, I googled Sagitta and found this link very interesting.http://liutaiomottola.com/formulae/sag.htm
sets it out clearly, also boils down to Pythagora's theorem.

By the way;
Luis result for 700mm radius is X = 23.01
Al's X = 22.28
Chris's X = 22.63
Sagitta S = 23.01

I can't see why there is 3 slightly different answers!:question:

BTW I also add 5mm to the answer to allow for sag and build quality.

Thanks all:thumbsup:
Richard

[Jen]

Jen flies straight past this post as i wasn't any good at maths :lol:

But i use autocad everyday LOVE IT :P

[richardda1st]

Wot the hell! Don,t tell me you are a female draughtsman, oops sorry Jen, a "Draftsperson". :lol:
Maths :sadeyes::confused2::help::zzz2::zz z2::zzz2:

[Jen]

:lol:
I draw up houseplans and sewer plans using autocad :lol: but i also have a calculator :rofl:

[scopemankit]

My difference was due to finger trouble. 23.01 is correct.

[Robh]

Sorry, but your model is incorrect.
Al (sheeny) has the only correct answer.
The first diagram shows the correct model with w the width of the door and t the thickness of the door.
In your model you are using w as the door's internal hypotenuse (second diagram). Hence, the larger incorrect value.

Regards, Rob

[GeoffW1]

Hi,

We are fortunate :lol:

I think that only works in the Southern Hemisphere :rofl:

Cheers

[richardda1st]

I think I may have confused a few.:rofl::P sorry.:P

Here is a better diagram of what's going on, attached pdf file.

The main aim is to choose a door width to clear the jamb.
The opening is set, the door/gate thickness is chosen and the final clearance is also chosen.


Thanks to all especially Pythagoras
Richard

Ps How embarrassing.:screwy: