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.
Hi,
This is an awesome idea. I cant believe this seems to be the only calculator i have ever laid eyes on for this application. I have put this formula to use a few times now, though have had some issues. Although the end rise does seem to be accurate, it does not seem to rise on a linear scale. In other words, it will finish with the right gap, though bottoms out because it seems to rise slowly at the start and kick up more toward the end of its travel.
The last 2 jobs where i have had issues both had fall across the driveway. Without getting overly technical, i just measured the total rise from centre stop to open position of the gate. I had to allow an extra 150mm of rise in the calculator to get it to open (thats on top of the original 50mm starting gap). It then just clears the ground for approximately the first third, then ends up with around 200mm + at the open position.
Any ideas on how to factor this in to get some sort of linear rise? is it something to do with the bottom hinge corner of the gate moving (in this case around 500mm) and needing to allow for the extra rise? Have you had anyone else with similar issues? Again, love your work. Thanks
I’ve never thought about whether the rise is linear – you raise a very good point. I’ll think about that. Thanks!
So glad I found your post about offset hinges. I had searched for ages without any luck. I am trying to hang a gate at the bottom of a slope built for my Dads mobility scooter. I’d rather it didn’t have to open outwards away from the slope as I’d have to place the hinges on the outside of the gate thus ruining the look for me. My Dad is ninety and has been trying to explain this method to me for quite a while (having used it many time before himself during his days ‘working on the land’) but age, speech and memory problems have made it difficult for him. It will now give me great pleasure to hang this gate the way he has been trying explain whilst secretly using your very clear instruction to fill in the gaps. Thank you. I believe this will make a very old man very happy.
Glad to be of help! Can you send a picture of the finished gate? I’ll start a collection of them!