Tale of the Un Level Shelf

I had an interesting problem a while back. It seems our Bose radio needed
improved reception. I tried just about everything. I thought it strange that the coax antenna cable did not improve the reception. I searched the internet and discovered that the problem I was experiencing had a name, multi-path distortion. The speech sound of the letter s sounded like ssss. All of the antenna in the world would not solve the problem. Antenna location would.

This meant I really needed to move the radio more than I had been moving it. There weren't many "nice" locations in the room. We have a cabinet with a hutch in the room that would be nice. I moved the radio around and found a location that eliminated, at least to our ears, the distortion. The "sweet" spot was on the top of a bookcase that rested on a hutch. That shelf was 6-12 feet above the floor!

This presented a unique problem. If the radio rested on the shelf, it would be near to impossible to read the display. After some thought and experimentation I found that tilting the radio about 20 degrees would allow display viewing from the bed.

That being said it was easy to create a shelf. I simply used one leg at the back of the shelf. I even went so far as to create a profile for the shelf that played on the geometry of the Bose. The radio sat on the shelf just fine. However there is one problem, gravity.

Gravity creates a force on everything, mass times acceleration. The magnitude of this acceleration is 32.2 ft./sec/sec. For those metrically inclined, 9.8 meters per sec /sec. Granted, I mentioned the metric value for gravity, but I will not make any further conversions for the metrically inclined. I will leave that for an exercise. With this thought in mind, and a little trigonometry and an engineering concept, friction, or lack thereof, it was determined that the radio just might slide down the inclined shelf.

Did I say that the shelf was about 6-1/2 feet above the floor? Once the radio slid off of the shelf there would be little to break its fall save for the counter top of the hutch, approximately 3-1/2 feet below. After possibly damaging the hutch the radio would continue on its fall to the floor another 3 feet below. Yes, there is another engineering concept called "potential energy". The radio has a potential energy relative to the floor. With the aforementioned concept of gravity, the astute reader can calculate the velocity the radio would attain at hutch elevation and again at floor elevation. This is where it, the radio would eventually come to rest. Its potential energy relative to the floor would then be basically zero. This paragraph has been quite useless, for the condition of the radio would be rather poor at that point.

To counteract this gravity thingy, I decided to counterbore the shelf surface directly under the feet of the Bose radio. This would surely hold the radio in place, save for a possible earthquake. I say it would hold it in place for the shearing stress on the rubber feet is definitely below that which the rubber can handle. Determination of that stress, I leave, yet again, to the engineering inclined for there is yet another physical property, center of mass, that needs to be determined.

Let’s get back to the counter bores. To determine where these counterbores would be located presented yet another problem. This would be an interesting exercise in reverse engineering, to determine in x-y coordinates for each foot, no, I didn't want to use polar coordinates.

I could have swabbed the feet with a slow drying ink and then carefully set on a piece of paper. I could then determine the relationship of the feet. save for one problem. I would not be able to determine the orientation of this geometry to that of the radio case and hence to the inclined shelf. Then there was my trusty scanner. It could create an image of the feet and the bottom geometry of the radio case. Scaling the image the location of the feet relative to the radio case and transfer this data to the shelf while updating my CAD drawing. Yes, I like CAD. Although I am well versed in drafting, I like the chance to forgo my diminishing ability, or desire, to utilize this capability. Why? There is a lot of math involved in drafting in 2-D. CAD takes that task to heart. No, inanimate objects do not have a heart, save for the tin man after he met the Wizard.

Now for the rest of the story.

That's how the un-level shelf came into fruition.
As I mentioned 20 degrees was tried and it proved out quite nicely. This was not till I considered 15 degrees. No, I did not examine the angle 16 degrees, 14 minutes and 7 seconds. Yes, 3-D CAD would calculate the required dimensions without destroying a transistor. Math and Trig tables would be required at the drafting table. I would like to add here to those that have never heard of a drafting board, let alone a T–square, or circular slide rule, there have been many many thingies that have been designed with a T-square. I used TurboCAD 15 as my 3D design software of choice. I add here that all of this could be down in 2-D. Yes, using a drafting table and auxiliary views, The picture here is the side view displaying the 20 degree slope of the shelf.

This is the scanned image I mention earlier.

After finishing with Danish oil and, yes, sanding with 220 wet/dry sandpaper it was done.
Or was I? All along I was worried about the radio sliding down the shelf and then falling to the cabinet’s top and then finally to the floor. Not a pleasant thought. I decided to bore a shallow hole for each of the four feet. The only problem is that the locations of the feet were somewhat difficult to locate accurately. Nothing is square on the Bose. This is when I decided to use my tried and true method. So, I threw (not literally) the Bose onto my flatbed scanner upside down and 2D scanned the bottom of the radio, utilizing "scale". The figure shown here is not the scan. This is a brochure image. The feet on the brochure are not indicative of the locations of the feet on our radio. Bose had made a change since we bought our used Bose. Scaling shouldn't be necessary. I use a "scale" capability just in case, to cover any mistakes. There are several ways to incorporate scale. One is to simply measure a feature on the scanned item and then using that measurement to scale the same feature when in the CAD program. Another method is to place an actual scale with the item prior to the actual scan. This is the most accurate method. A mention here is that you might find that the scanner distorts the scale of the working axis. The direction of travel of the scan bar. To help correct for this, two scales would need to be added during the scan. One set parallel to the scan bar travel and one set perpendicular to the travel.

Now with the feet accurately located, I printed a template which I placed onto the shelf to transfer the locations to the wood. I used a Forstner bit to create the counterbores. Please do not mention spade bits. I leave that for another discussion. A bull nose router bit would be a good choice.

The template required paper slightly larger than 8-1/2 X 11 paper so I needed to utilize my HP450C E-size plotter.

After finishing with Danish oil and, yes, sanding with 220 wet/dry sandpaper it was done.

I learned this many years ago that it creates a silky smooth and scratch free finish.

There is no need to work up from 220 grit to 10000 grit sandpaper, which I have read many using.