MegaSack DRAW - This year's winner is user - rgwb
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A rectangle, length x, height y, corners ABCD where A is top left, B is top right, C is bottom left, D is bottom right.
AC and BD are initially vertical, AB and CD horizontal.
The rectangle is rotated around A resulting in
- a horizontal distance (h1) and vertical distance (v1) between the new position of C and the original line of AC.
- a horizontal distance (h2) and vertical distance (v2) between the new position of D and the original line of CD.
This is all about levelling up a gate. I could just prop it up and measure it, but it's got to be mathematically workoutable
I'd just model it in CAD. Lots easier than messing around with sums.
v1 = AC * cos(angle)
h1 = AC * sin(angle)
v2 = AB * sin(angle)
h2 = AB * cos(angle)
This might not be exactly the measurements you're after as your definition of h1, v1 etc isn't completely clear and it's not entirely obvious (to me) what calculation you actually need to perform. This will give you the horizontal and vertical distances from corner A to the new positions of corners C and B respectively (a diagram would probably help here)
v1 and h2 will be almost the same as the lengths of AC and AB if it's only tilted a little bit
What are you trying to work out? Do you know how much you need to rotate it by, eg is it 15 degrees out of level or, more likely, 20mm out left to right?
I assume your mountings are plumb vertical?
What are you trying to work out?
The 8ft-ish wooden gate across the drive has dropped a bit. Probably a combination of possibly wasn't quite straight in the first place, time, the gate itself drooping a bit, post settling etc etc. It needs lifting about 50/60mm at the 'open' end. Ideally it would have been fitted with an adjustable hinge on the bottom, which would have made this a doddle, but it wasn't.
So, I could buy and fit an adjustable hinge, but I was looking at it and I think I can get away with removing the existing bottom hinge, adding a piece of timber as a packer, and refitting the hinge over the packer which will have the effect of pushing the bottom corner out a bit, so lifting the open end. I was just trying to work out how much I need to pack it out by. As I say, it'll be easy enough to do by eye when I'm actually doing it, but I'm here idly thinking about it, and the gates out there...
You need the distance between the top and bottom hinges, work out the ratio between that and your gate width and multiply that by the drop. eg 5ft between hinges, 8ft gate so 5/8. 60mm drop means 60 x 5/8 = 37.5mm packer. The closer the hinges, the smaller the packer. It's not exact but close enough for small angles of drop.
I had a feeling it'd be some kind of height/width ratio thing. Ta
Lets call the length of the gate L, the distance between the hinges H, the drop at the end D and the width of timber to pack the lower hinge P
Using small angle equivance, we can say the angle of the dropped gate in radians is D/L
We want a value of P that results in a change of the same angle. We can also say this angle = H/P
Therefore using these two equations, D/L = H/P
Rearranging gives P = (H*L)/D
So for your 8ft gate (approx 2440mm) with a 50-60mm drop (lets call it 55mm)
P = (H * 2440)/55, or simplifying, P = H/44
I've done a lot of rounding here, plus your measurements are approximate and I don't have a value for H so I'd check the dimensions and use the equation for P above.
The equation is based on small angle equivance - basically for small angles, the cosine of the angle is approximately 1. On the off chance any mathematicians take issue with this, yes it will give a slight innacuracy in the results, but for the dimensions involved it'll be in the order of hundredths of a mm compared to using calculating "properly", plus this method is very simple to apply.
Edit: typed this before I saw nickjb's post, which explains it a lot more simply
What nickjb said.
However, has the post moved or the gate itself sagged? If the hinges aren't aligned vertically, the gate will tend to swing around to its lowest point. If you want the gate to stay put when it's open, you need to get the hinges aligned vertically first. If the post has moved, then digging around it, realigning it, and putting a few inches of concrete in should sort it out permanently.
If the gate itself has sagged (i.e. it's not rectangular anymore), just put a jack under the end, jack it up until it's rectangular, then fit a diagonal brace. Just a length of wire running diagonally from the top hinge corner to the bottom non-hinge corner will do it if it's just an old farm gate. If you want it to look pretty, you'll need to get something that matches the gate.
Cracking, so, having nipped out with a tape measure, the gate is 3m wide and the distance between the hinges is 1m.
So, nice and easy, for every 10mm I pack it out, the other end will rise 30mm, yeah?
However, has the post moved or the gate itself sagged?
Sorry, missed this. Tiny bit of everything I think, as per my post up there^. Can't (well don't want to) dig around the post though as it's tarmaced all around it, and the gate may have sagged a bit but not by much, as it's got 4x cross braces on it. Staying put doesn't matter, as it's either bolted shut or bolted open
Packing out will work well enough I reckon. Cheers all.
So, nice and easy, for every 10mm I pack it out, the other end will rise 30mm, yeah?
Yep that's exactly right
If the hinges aren’t aligned vertically, the gate will tend to swing around to its lowest point.
This. If the gate has dropped because the post has leaned, packing the hinge out brings it back into line, all good. But if the gate has sagged, and you pack the hinge so it's not directly below the top one, the gate will want to swing open when not latched - which might also be good, but might not be.
But if the gate has sagged, and you pack the hinge so it’s not directly below the top one, the gate will want to swing open when not latched
The hinge itself won't move. It's one of these, it wraps around the bottom corner of the gate:
I'll just undo the carriage bolt and screws that are attaching it to the gate, pack out the closed end of 'U' portion of the hinge a little so the bottom corner of the gate sits slightly further away from the pivot, re-drill the holes for the bolt/screws and put it all back together again.
Ah, understood. So that won't change anything about its self closing or self opening properties.
You've made me think about the self closing thing. If the post is now inclined so that it leans into the gate then the gate will become self closing as the non-himge end will rise slightly as it opens.
If doing the above fix what is stopping the post slumping further and the same fix being needed again but likely sooner?
If the gate slump is due to gate becoming a parallelogram then a diagonal brace is the solution.
Do it by eye. Undo bottom hinge and pack the end of the gate so it's the right height (level?). Refit bottom hinge.
Just a thought, is the hinge pin that’s installed in the gate post on a plate or the sort that’s hammered through the post? If it’s a bolt on plate version you could perhaps loosen and place a packer behind, rather than drill holes in your gate. Careful mind, the coach screws that sometimes are used can be brittle and in tight if in a green oak post...
Alternatively an adjustable bottom hinge assembly could be fitted - in case of future droopage...