I can’t believe that the rising gate calculation is original – it should have been well known since geometry was invented – so I’ve published the rising gate calculator source on Github under an MIT Licence. Feel free to fix my bugs!
I was looking for a way to put a true, opening gate on the web as a 3D model – I was thinking about fancy SVG. But, poking around, I tripped over Sketchfab. They provide a free service (with paid-for upgrades) to upload a 3D model and host a version of it that can be seen on a 2D browser. It took just a few minutes to sign up and upload the Sketchup gate model. I love the modern web, it provides free and easy technology that once would have been so hard. Thank you, Sketchlab!
The rising gate model can be seen, using a modern desktop browser, here. You can move around it and zoom in. In that model, there are two gates, one in the closed position, one in the fully open. I’ve actually forgotten quite what dimensions that model was designed to model, but it looks OK to me.
I’m still looking for a way of putting a real working 3D opening gate on the web, so please let me know if you find one.
I added some 2D pictures of Sketchup models, with annotation, to try to explain how the calculator worked more clearly. It was a difficult day waiting for downloads and phone calls, so I filled in the time adding a random-woodworking-aphorism feature to the rising gate calculator. Some of the sayings are my own, and some are from here and here and here.
The source for the Rising Gate Calculator is released under an MIT licence at Github. I may be foolish for releasing it without trying to make any money, since I can’t see it anywhere else. However, I can’t imagine this technique hasn’t been familiar to every carpenter since the time of Pythagoras, so, for better or worse, it’s out there as free source, in all senses.
Having struggled all day with dying laptops, dying software, a complete inability to understand VAT rules on intra-EU software downloads (except Ireland), and Adobe Creative Cloud (about which my opinions had better remain unexpressed), I have given up trying to do work and present…
That’s a page that allows you to put in the gate dimensions and get out the required hinge offsets and angles to make the gate sit neatly, so it is vertical both when closed and when fully open.
That page still needs some extra help-features to explain just how it works, but it seems OK as far as it goes. It was vastly less work than the birthdate calculator!
The previous post demonstrated that gate hinges should lie in a vertical plane normal to the bisector of the open and closed gate positions. Here’s the plan view of the hinges in the open position: (click for a bigger version)
Plan view of hinges, gate fully open
Triangles BFG and BFK, lying in the horizontal plane, are mirror images. So, length FK must be ONS
The points labelled here are exactly the same as the ones in the previous diagram. Length FK in the horizontal BFK plane is ONS, because triangle BFK and BFG are mirror images. Length KM is also ONS, because that’s how we made the spacer for the gate. Triangles AFK and AMK are therefore mirror images, because they are both right triangles, they share a hypotenuse and have side KM equal to side KF. So, angle KAF is equal to angle KAM. Let’s call this angle θ. And, call distance AF, the vertical distance between the hinges, OUD.
tan θ = KF / AF = ONS / OUD
θ = tan-1 (ONS / OUD)
Here’s how the gate looks when fully open.
The gate rises up at an angle 2θ from the horizontal. The effective length of the gate, JK, is OGATE + ONS.
JN / JK = sin (2θ)
Rise = JN = (OGATE + ONS) * sin (2θ)
Rise = (OGATE + ONS) * sin(2 * tan-1 (ONS / OUD)) ♦ Equation 2
Oddly, this doesn’t depend on β. Is that right?
So now I have some equations for the variables ONS and OWE. Here are the parameters fixed by the requirements of the gate design:
| Symbol | Meaning |
| OUD | Vertical pitch between gate hinges |
| OGATE | Width of gate when closed, measured from centre of top hinge pin to outside edge of gate |
| Rise | Required Rise of gate when fully open |
| β | Angle between gate open and gate closed |
Here are the parameters I’m trying to determine:
| Symbol | Meaning |
| ONS | Offset of bottom hinge parallel to the gate |
| OWE | Outset of bottom hinge at right angles to the gate |
And here are my equations:
OWE = ONS * tan (90° – β/2) ♦ Equation 1, from previous post
Rise = (OGATE + ONS) * sin(2 * tan-1 (ONS / OUD)) ♦ Equation 2
I don’t actually know of a symbolic solution of (2) for ONS. Fortunately, that doesn’t stop me solving it numerically, which will come in a post real soon now.
This post is a geometry exercise to work out the hinge offsets needed to make a gate rise from its closed to open position, but sit vertical at both closed and open positions. Between closed and open, it won’t be vertical.
You shouldn’t need to understand all this post just to hang a gate. I’ll be posting a calculator for this later. Click any of these diagrams for a bigger version.
Plan view of hinges, gate fully closed.
The diagram above shows a view looking down on the top of the gatepost when the gate is closed. Point A is the top hinge pin and point B is the bottom hinge pin. The gate is exactly vertical, although B is not directly below A, because the bottom hinge includes spacers to offset the hinge. The spacers offset the Hinge ONS in the north-south direction (parallel to the gate) and OWE in the east-west direction (perpendicular to the gate).
Plan view of hinges, gate half-open
This diagram shows the gate partially open, neither open nor closed, looking from above. The bottom bar of the gate, where the bottom hinge sits, is no longer directly underneath the top bar. The gate does not sit in a vertical plane. That’s OK. Only when the gate is fully open will it lie in a vertical plane again.
Plan view of hinges, gate fully open
The above diagram shows the gate fully open. This gate has been designed to be fully open at an angle β to its closed position. The diagram is confusing (sorry) because it’s a vertical plan view, and the gate has risen out of a 2D plane. Points B, K and F all lie in the horizontal plane through the lower hinge pin. Points M and H are in a horizontal plane raised above the plane BKF. It’s clear that M and H lie in a horizontal plane because
The line MH has a length OWE when the gate is closed and MH is horizontal in the same plane as hinge pin B. MH is again horizontal with the gate open to angle β, so again the projection of line MH on the horizontal plane containing points BKF still has length OWE.
The projection of the line MH in the plane BKF is at right angles to the intersection of the vertical gate plane and BKF. This is true however much the gate rotates in the vertical plane containing F and J, because MH is normal to the gate plane. So, line KB, parallel to MH but in the horizontal plane BKF, is at right angles to line FK, and also has length OWE.
Triangles BFG and BFK are mirror images, because are both right triangles, they share a hypotenuse and side BG is the same length as BK. So, angle BFK is the same as angle BFG – let’s call this α.
Point G, F and L lie on a straight line:
β + α + α = 180°
α = 90° – β/2
or, in other words, the vertical plane containing the hinges must lie at a right angle to the vertical plane containing the bisector of the angle between the open and closed gate positions.
Or, in yet other words:
And, equivalently,
OWE / ONS = tan α
OWE = ONS * tan (90° – β/2) ♦ Equation 1
This is the sort of gate I usually think about, although the same method applies to any sort of hinged mechanism.
That’s a picture of a Sketchup model made from a hinge by Matthew Miller and a gate by Adam J. Having fooled around with Sketchup for a couple of hours, I did wonder if it would have been easier to go outside and find a real gate. But, I got there in the end.
With the gate in its closed and latched position, everything is true and square. Here’s a picture of the hinged end of the gate, without its gatepost. The top hinge is directly above the bottom one, so this gate will open level, not rising.
The surfaces marked “horizontal” and “vertical” in the picture are, not surprisingly, vertical and horizontal. This is true for ordinary gates and for rising gates too.
Here is the gate modified to make it rising.
click the picture to enlarge
The gate hasn’t moved 1mm from the previous picture. Only the bottom hinge has moved. I added the white spacer screwed to the gate, and I drilled a different hole in the gatepost to match. The whole bottom hinge has moved out and left compared to the previous picture. But the gatepost is still vertical and the gate is still all vertical. Because of the slight offset of the hinges, they should be twisted a little so pins of the two hinges line up exactly straight (but tilted). However, this sort of gate hinge is usually made very loose, and the hinges work fine with the hinges out of line. If I’m being very pedantic, I twist everything to line up precisely. I find that easier to do with a power drill in my hand than I do with Sketchup 🙁
As a reminder from the previous blog post, what I’m trying to avoid with this design is this:
This picture shows how the gate skews as it opens and doesn’t sit vertical. I want the gate to be vertical both in the closed position and the open position.
Now, the real trick is to understand how much the bottom hinge has to move out and move left for any particular gate. That will be the subject of the next post.
Much to my surprise, I found that the best way to hang a rising gate is not common knowledge. In fact, I’ve found it nowhere, and I had to work it out from scratch when I first needed to use the technique.
To make a rising gate, one hinge needs to be offset. The hinges aren’t one above the other.
When the gate is closed, the uprights of the gate need to be vertical, and the top bar of the gate needs to be vertical.
When the gate is open, the top bar of the gate needs to be rising up at an angle. That’s what we want, that’s why it’s called a rising gate.
But, when the gate is open, it’s very nice if the gate is still upright, and is not skewed off at some odd angle. That looks much neater when the gate is hooked back open. That’s the real trick to rising gate hinges, and that’s what this post is about. (No, not a gate post, a blog post.)
The rule for rising gate hinges is:
The hinge axes must lie in the vertical plane at right angles to the vertical plane which bisects the vertical planes in which the gate lies when it is open and when it is closed.
More to follow!