Asked and Answered: 3.1
There is a ten-foot long alcove in our lower-level hallway — we call it the gallery. This is the one place in our house I can hang whatever I want (i.e., my own art) and switch it out whenever I want. To facilitate this, I installed a hanging system — basically a slotted rail mounted near the ceiling, with sliding wires and height-adjustable hooks. These systems cost more than you think they should, but AS Hanging has some more affordable ones. (You’re welcome for the plug, AS Hanging.)
I was a bit surprised when I hung my first piece and saw how far forward it tilted (see photo at right). It was not intuitive to me why hanging a fairly light 12″ x 16″ frame on a long wire should cause this. So naturally, I googled it.
Unlike Fifty Shades of Grey, the topic of tilting picture frames is not discussed a lot on the web. Where it is mentioned, some surprisingly bad and/or misleading advice is often provided. For example, take this article from the San Fransisco Chronicle, “How to Keep Heavy Paintings Flush Against the Wall.” Written by a crafter, the article asserts: “A heavy painting tends to lean forward under its own weight, which isn’t attractive and can cause wall damage if it pulls its hanger from the wall.”
The second part of that sentence is true enough, but the notion that only heavy items lean forward is false, as my own experience shows. Furthermore, the solution offered by the author may be well-intentioned but is half-baked at best. She instructs the reader to cut a piece of wire slightly wider than the frame, attach it to eye hooks on the sides of the frame, and then, “ensure the wire is taut to minimize the chances of the picture leaning forward.” Sounds reasonable, until you consider the stress this puts on the frame.
The diagram at left shows how tension in the wire increases dramatically as you make the wire taut. A 7-lb frame creates exactly 7 lbs of tension in a vertical wire, but if you string a wire tightly across it, that same 7-lb frame will produce over 40 lbs of tension in the wire, pulling the sides of the frame inward and possibly crushing the art.
Stretching a wire tightly across a frame is about the worst thing you can do, especially with a heavy piece of art, says The Fine Art Trade Guild. This has not prevented people — even decorators and sellers of gallery systems — from recommending the practice. It is much better for the integrity of the frame (and the art) if you leave some slack in the wire and hang the item from two widely-spaced hooks at 45-degree angles, as shown later.
All well and good, but it does not really answer my question: why do frames tilt forward? Having failed to find a good explanation on the internet, I decided to answer this myself. Bear with me, fascinated readers.
This side-view (click to open a larger version) may help you understand what is going on. Figure A shows a frame hung on a wire attached to its top-center. Now this is a really bad idea, because the entire weight of the frame would pull on the threads of the hook. But I show this just to illustrate that there would be no cause for this frame to tilt. The real reason that a frame tilts forward (see Figure B) is because the wire is attached to the back of the frame, while the center-of-mass of the frame is in front of the attachment point. This creates a torque that causes the frame to rotate.
The frame will rotate until its center-of-mass reaches the lowest possible point. In the case of the free-hanging frame, it is where the center-of-mass is directly below the attachment point. Figure B shows how the center-of-mass of the tilted frame (black arrow) is slightly lower than when the frame is held straight up-and-down (red arrow).
Most people in the Northern Hemisphere hang their pictures against a wall — I know I do. The wall changes the equilibrium position of the frame (Figure C) such that the frame does not tilt as much as it would otherwise. This is because the wall pushes against the base of the frame, counteracting some of the torque.
Where one attaches the wire makes a difference in the amount of tilt (compare Figure C to Figure D). Websites offer various guidance on this. Most advise you to attach the wire to the frame one-third of the way down. A few say, one-quarter of the way down, or a certain number of inches from the top. Is there a definitive answer or only opinions? Or, as Mitch Hedberg asked, who is the real hero?
The hero in this post is geometry, along with a small dose of physics and calculus. We are going to solve this problem for the benefit of man-and-womankind. Don’t worry, there are no equations involved… until the appendix.
Here is the setup (click image to enlarge). A frame of length f is attached to a wall by a wire. The slack in the wire (the maximum distance one can pull the wire away from the back of the frame) is w. The wire is attached to the frame b inches from the bottom of the frame and pivots freely at the wall and the frame. The center-of-mass of the frame is halfway down the frame and distance d from the back of the frame, where I assume the glass is mounted. We know f, w, b and d, and we want to find g, the gap between the top of the frame and the wall, at its equilibrium position — the lowest possible location of the center-of-mass. This would be the maximum value of y1 + y2 + y3 given f, w, b and d.
It took me a few hours (and a second try) to find the right approach and eliminate errors in my calculations, but I got there. The chart at right (click to zoom) shows how slack in the wire and the position of the glass affects forward tilt, for frames of various heights. Here, I assumed that the wire was attached one-third of the way down from the top of the frame, as most so-called experts advise.
The solid lines in this chart correspond to 10-inch, 20-inch and 40-inch-high frames with a center-of-mass 1/2-inch from the back of the frame. You may be surprised to see that short frames tilt forward more than tall ones, when one follows the “one-third rule” and provides the same slack in the wire in each case.
The dashed lines show how moving the center-of-mass 1/8-inch to the front or back affects forward tilt, for a 20-inch high frame. This may seem insignificant, but a 1/8-inch change in the depth of the rabbet could increase the gap at the top of the frame by 25 percent. It is simple physics — the farther the center-of-mass is from the back of the frame, the greater the torque and the more the frame tilts.
The next chart (click to zoom) shows how fastening the wire at various distances from the top of the frame affects forward tilt. For a given amount of slack, attaching the wire closer to the top reduces tilt. Knowing this, one may ask, why shouldn’t we just forget the “one-third rule” and attach the wire one-sixth of the way down from the top?
Here is one reason: the closer to the top that the wire is attached, the less slack you can allow without the wire being visible. So the “one-third rule” represents a compromise solution for traditional one-hook installations — some forward tilt is accepted for the sake of having more slack and lower tension in the wire.
Interestingly, the weight of the frame did not enter into my calculations. This means that a sheet of foamboard having the same dimensions and the same center-of-mass as a wood frame would tilt the same amount when hung the same way. I have not physically tested this, but you are welcome to disprove it.
So it is not true that “heavy” frames tilt just because they are heavy. Frames tilt forward more when the wire is attached closer to the center, when the slack in the wire increases, and when the frame is front-heavy. In typical hanging situations the forward tilt is usually less than 1/4-inch. But when the frame is suspended on a long wire, as gallery systems do, the tilt can be noticeable — 1 inch or more for a 20-inch-tall frame.
The Bottom Line
So what have we learned and what do I recommend? If you want to use hooks and wires and you want to hang pictures close to the wall without undue stress on the wire or frame, I suggest using two hooks and 45° wire angles, as illustrated in the diagram at right. This may look a little complicated but it is do-able.
In the original version of this post, I provided a formula to help you with the installation, but in practice, it didn’t go far enough. So I programmed a two-hook frame hanging calculator and posted it in a companion article titled (what else) The “Hang It with Two Hooks” Calculator. This online calculator suggests where to fasten the D-rings, how to install the wall hooks, and the length of wire to cut. This makes the task much easier.
Yes, two hooks present the added challenge of ensuring they are level, but this post is all about reducing forward tilt without stressing the wire or frame. If you are up to the task of carefully positioning two hooks, you might consider eliminating the wire altogether and hang the frame directly onto the D-rings. One drawback to this method is the visibility of the hardware; the other is the extra precision that is needed in mounting the hardware.
But what about my gallery hanging system with the long cables? Here, since we have to rely on a single hook, I suggest wiring the frame according to the one-third rule, with just enough slack so that the cable hook will engage the wire close to the top rail of the frame. Then attach an offset clip to the top rail, slightly off-center, and tuck the cable behind the clip. For a 20-inch-tall frame hanging 30 inches below a cable track, this will reduce forward tilt from nearly 1-1/4 inches to less than 1/2-inch.
By reader request, I have added a photo (click to enlarge) of how the offset clip, cable, and cable hook are installed. This shows the rear of the frame with the cable threaded behind the offset clip. Here I have used a clear 1/8″ mirror clip instead of a metal clip.
Others have used Velcro strips for this purpose instead of offset clips, which is a nifty idea if you don’t mind attaching something to the dust cover with adhesive.
So now you know and so do I. Asked and answered.
Appendix: Calculating the Forward Tilt in a Frame Hanging on a Wall
I provide a full derivation of the problem here. If you would rather not go there, please refer to the diagram above. We want to find the gap g between the frame and the wall, given the known variables w, d, f and b. To get there, we first need to find an expression for y = (y1 + y2 + y3), then use calculus to find the max value for y and back-calculate g.
I found it easier to solve for y in terms of the angle θ formed by the bottom of the frame and the wall, and then replace sin θ and cos θ with our known variables. This ultimately led to the following expression for y:
To find the maximum value of y, and the gap between the top of the frame and the wall at that location, we need to differentiate this equation with respect to g, then set dy/dg = 0 and solve for g by iteration:
This is how I generated the data for the graphs in the body of this report.
[This post was updated October 4, 2015, with simplified expressions, updated charts, and a link to the complete solution. This is Part One of a three-part series on hanging frames with wall hooks and wires. You may also be interested in the follow-up articles, namely The “Hang It with Two Hooks” Calculator and The Physics of Hanging Pictures. – CHC]