How safe is safe enough? Since I acquired an elderly 26’ Norman Cross-design trimaran two years ago, I have been learning to sail and reading lots about blue-water cruising (which I expect never to do!). Scanning my bookshelf, I see Sensible Cruising, The Coastal Cruiser, Cruising in Comfort, The Case For the Cruising Trimaran, The Finely Fitted Yacht, and so on. Even though I expect never to need tips from Heavy Weather Sailing, I figure there is no premium on ignorance or poor preparation.

Part of safe sailing is to be visible to commercial traffic so a freighter does not run you down without even noticing. Here on Northumberland Strait just north of Nova Scotia, heavy commercial traffic is not really a problem—perhaps one barge tow goes by in a day and the ferry from Wood Islands (where I moor) runs on a 90-minute interval. I am quite confident the ferry has someone looking out all the time as well as looking at the radar, and a sailboat is highly visible during the day. Still, a radar reflector seems like a good idea. When I got my sailboat, the previous owner tossed in a 3-plate radar reflector (an “octahedral” reflector which was, by hindsight, too small at 4 ¾” to be at all effective), which I hung near the mast top. Unfortunately, it flopped around and clanged horribly up there even in calm weather, so this Spring I was going to mount it rigidly at the mast top, but then I started to think about how it works and figured it wasn’t going to reflect all the way around.

When I got my sailboat, the previous owner tossed in a 3-plate radar reflector (an “octahedral” reflector) which was, by hindsight, too small at 4 ¾” to be at all effective. click image to enlarge

Comparing Reflectors

I was reading my way through my West Marine Catalog and came to radar reflectors (page 205 in the 2007 catalog). The catalog makes a great read just for the little bits of information they scatter through it even if you are not shopping at the moment. It may seem odd to you, but then I knew a fellow who used to read the encyclopedia for entertainment. I found they sold reflectors at prices from $25 to $600. Being on a strict boat budget, I decided I could make a better, and hopefully cheaper, reflector.

I discovered in a web search that US Sailing did an evaluation study of commercial radar reflectors in 1995. It is an excellent article. It defines terms and establishes a goal for an acceptable reflector. The authors decided a RCS (Radar Cross Section) of 2.5m2 was the minimum to be useful—the reflection that comes back from a sphere with a viewed area of 2.5 square meters—about 6 feet in diameter! Fortunately, there are much more effective shapes for reflecting radar. (I know, everybody wants a shape to make their car invisible to police radar!) The study was very revealing in that almost none of the reflectors tested gave what they considered a minimum acceptable performance. My tiny triangular one was there, totally insufficient! An ideal reflector would return a strong signal to a distant ship’s radar detector when the ship is on the horizon anywhere around the boat. Actually, unless your reflector is gimballed, if you have a monohull

Figure 1: Trihedral corner reflector

sailboat that works best at about a 30 degree heel, or are travelling in a rough sea, you really want a reflector to return even if it is tipped! For uniformity at all angles, you cannot do better than a sphere, but for some reason no one wants a 6’ sphere at the top of their mast!

Trihedral Basics

Years ago, a friend who loves astronomy talked about a corner cube reflector set up by the astronauts on the moon. You could do experiments bouncing a laser beam off the moon. The reflector is the thing of interest here. It did not have to be set up precisely—if it did, the distance to the moon would certainly exaggerate any errors! The secret is a corner cube. Imagine cutting off a corner of a cube, getting three triangles that are at right angles to each other (“orthogonal”). It turns out that they will bounce light back in the direction from which it came as shown in figure 1. The shape is a “triangular trihedral”. With these three perpendicular surfaces, no matter what angle the light arrives from (as long as it is still “seeing” all 3 surfaces) bounces in turn off all three surfaces and returns at just the angle from which it arrived. As the reflector turns less and less light bounces back until at angles outside the corner, nothing

Figure 2: Octahedral radar reflector

bounces back. Conversely, the closer the beam is to the axis (the point where all 3 sides are the same angle to the beam) the more light bounces back. Replace the mirrors with almost any metal and you have a shape that reflects radar signals about the same way a corner cube mirror reflects light.

Applying this to my tiny 3-plate unit in figure 2 (called an “octahedral” because the plates form eight trihedral corners), the reflection as shown would vary greatly as I walk around it. Remember, unless the path hits all three surfaces, the radar beam bounces off at some other angle and lost. The most return comes when the corner is straight on, and almost nothing comes when one of the sides is in line—even though I can see a lot of surface, the reflector is not sending the signal back unless all three surfaces are involved. That means that positioning my octahedral unit with one plate horizontal is the worst possible orientation. Unless it is exactly horizontal, a slight tip, projected over several miles, will send the return far above or below the distant ship.

Figure 3: Sheet metal layout

Much better is to position one corner up and one down (called the “holds water” position because, if it you seal the joints, the unused upper corner would do just that). I do not need to worry about radar coming from overhead! With one useless corner pointing up and one pointing down the remaining six corners have to cover 360 degrees—each corner is responsible for 60 degrees. Unfortunately, with this orientation the corners are not facing straight out—one axis is up by about 16 degrees and the next axis points down by the same angle.

The US Boating article liked the “double hold water” orientation. With one plate oriented vertically with an edge along the top (build a model and try it!), you get four corners facing out each covering 90 degrees, but their axes are exactly horizontal—not tipped up and down—which gives the largest reflections. That orientation gives four very strong peaks but drops to almost no reflection in-between.

Designing your own

Scratching my head, I decided that stacking two separate octahedral reflectors with one rotated 45 degrees to the other would give eight straight-on reflectors and fill in the nulls around the circle. Might there be a better way than the 3-plate design? I started with construction paper, making up individual trihedral corners and fitting them together. To save space it seemed that one set of four could have points up and the second set could have points down. The corners could fit into each other. The paper model revealed that, if you accept some up and down tip of the corners, I could build the whole reflector with 3 pieces of sheet metal, given the right tabs and bends. My current design (see figure 3) uses a 24" x 29" sheet of aluminum roof flashing to make a unit about 8 1/2 inches high.

- TOP VIEW - The top rectangular plate is removed so this view looks into the inside, showing the inside ends of each corner. click images to enlarge

The finished unit, figure 4, looks like a loudspeaker array you might find on a pole at some sporting event. I like the idea that a very good reflector can be made for perhaps $15 in materials when the “unacceptable” ones are $55 (or $25 for a foam-core plastic one) and $250 for a lens-type reflector in West Marine's catalog.I would hesitate to call this reflector an invention—it is just a convenient way of bending sheet aluminium and may already have been “invented”. I intend to stick my prototype up on the mast at least for a season (I'm sure it is better than the simple 3-plate units), but I have now gotten to the point of doing some calculations that say it could be improved.

Construction Hints

I started to build the reflector to the pattern of figure 3 using 14 gauge aluminum (which cost me almost $4 a square foot) but I found it too difficult to cut—I had to use a metal blade in a jigsaw rather than tin snips—and I found it very difficult to bend. If I had the right sheet metal tools it would be a different story, but the folds are still difficult and I found that using the thinner metal still gives sufficient strength once all the bends are in place.

I easily cut out the pieces of figure 3 from aluminum flashing with ordinary tin snips. Then I set out to make all the folds. I suggest you practice with a small model cut from construction paper (my models were dark blue and black because my grandson cannot draw in crayons on the dark pieces in the package) and assembled with Scotch® tape. Getting the folds took some head scratching again. A vice can almost work if the jaws are wide enough or if you put longer sticks of wood between the jaws and the metal. Or you could clamp the metal to a table with C-clamps and a piece of wood. I happened to have an antique saw sharpening vice which I’m told my grandfather used to sharpen hand saws—now that goes back at least 70 years! You can make the bends with your bare (or gloved) hands or help it out with a mallet or hammer. As you look at the pattern, the two long strips are the bending challenges (you could make individual corners and fasten them together if you prefer, but that takes more sheet metal and I hate waste). The sequence that worked for me was to bend the left-most straight (short) side toward me to 90 degrees (it would become the boundary between two orthogonal sides of a corner), and then bend the next diagonal back flat (180 degrees). The intersections did not end up at quite that angle in the end but it was easier to work with that way. Then I bent the first two tabs forward 90 degrees. I continued the process on down the strip and ended up with half of the center pieces. I did the same with the second strip and had the full 360 degree center. Next, I fastened the two pieces together at the ends (into a sort of circle). I did all the fastening of the aluminum pieces with short 1/8” aluminum blind pop® rivets. I figured aluminum sheet and aluminum rivets would avoid galvanic interactions. I had to drill 1/8” holes through the two pieces I was joining but the rivets made it easy to fasten from either side—not everything was very accessible as it took shape. Once I had connected the center strips together, I fastened the eight remaining individual triangle pieces to the side tabs to form the eight trihedral corners. The result was quite stiff. The top and bottom surfaces are 10" x 10" squares and while you can use plywood or heavier aluminum, I chose the latter because I hated to waste all that 14-gauge aluminum from the first attempt! In order to get wiring up through fro the radio antenna and the anchor light (as well as my weather station), I fastened the top surface with sheet metal screws (stainless since I could not find any aluminum screws such as were used for add-on aluminum storm windows in the old days).

How Well Should It Work?

Figure 5: Graphical model of off-axis effective area

The US Boating article is excellent in that it gives a way to get a calculation of real effectiveness. Figure 1 of their article, when blown up to be readable, gives formulae for a variety of shapes including the triangular trihedral (you can also calculate for circular and square trihedrals). For my triangular design, the maximum RCS (on axis) is:

where is the length of one side of the triangle sides (about 7" in my case) and, for X-band radar, is about 2.5 cm. Converting units and cranking out the numbers (its been a long time since I’ve used scientific notation!) I get a maximum (on axis) of about 7 m2 as the RCS of my 7” corner. A little piece of aluminum about 10” on the long edges looks to distant radar like a sphere almost 10’ in diameter! Notice that the RCS goes up with the fourth power of the side length. Size matters.

So how well does my design work? Setting the finished reflector on the kitchen table and staring at it as I turned it around, I began to see that the key is to find how much of the part I’m seeing still gives 3-bounce return—on axis a beam arriving anywhere within the projected equilateral triangle makes the requisite 3 bounces, but as it rotates, less and less of the projected triangle represents 3-bounce region.. After a lot of head scratching again, I think I have a way to calculate the relative off-axis reflectance. Look at figure 5, which shows a hypothetical reflector at some angle off-axis. If, for one side, I draw lines from the outer corners at the same angle on the other side of the back edges, I mark off the area that works for the reflection from one side. Think of it as the reflected shadow of the one side. Then do the same for the other two sides and get the area that is shared by the reflection of all three surfaces. Now I have the area that will have three reflections—anywhere else in my view of the reflector will miss at least one reflection and send that incoming signal off somewhere else. In figure 5 I brought out the striped area as the only valid reflector area for that orientation—at a guess it looks like about 40% of the on-axis orientation. If this were a view of my 7” (7 m² RCS) that would mean that this orientation gives an RCS of 40% of 7 or 2.8 m².

For A First Cut, Measure - Don't Calculate

How can I get all the areas? By the time I could re-learn all the solid geometry and trigonometry that I almost learned in college that I would need to direct-calculate the angles and areas, I would have ceased to care! Instead, putting the finished reflector on my kitchen table, I measured the projected width and apparent angles of the outer edges and the inner sides with a protractor. This was not high precision, but I needed some ballpark numbers to go on. Searching the web, I found a SITE that solves angle-side-angle and side-angle-side triangles (again, it looked like too much work to do it all with the ½bh formula). The results are shown in Figure 6 for the 7.5 degree angle intervals I measured and computed areas. Bad news! Even though straight on should give 7m2 for the RCS, because of the up/down tip, the best I get is 31%—12 degrees off axis had dropped off 70%. The good news is that the adjacent corners pick up the slack as I had hoped and the fluctuation is about 2:1 around the reflector. The reflection is present all the way around—just not enough.

A Little Bigger Is A Lot Better

Figure 6: RCS for my design vs. angle

Now, do you remember that fourth power? If, as the article says, I need a minimum of 2.5m2 for the RCS, I can just make it enough bigger so the minimum 1.18m2 RCS scales up to 2.5. How much bigger? With a fourth power I need the fourth root of 2.12 or a scale up of 1.2. My 7” edge dimension can go up to 8.46” (or 10” diagonals go to 12”). That is hardly enough to see and can easily be done with a longer piece of roof flashing. Scaling up to fit still on 24” wide flashing, if I go to 60” instead of 29” I can fit two widths of 10” sides (14” diagonal) and fit the extra corners at the end for less waste. That is better than a fourfold increase—my next reflector could have a minimum of 5m2 RCS or, as you rotate it, double to quadruple the minimum!. I expect by next season I will be restless enough to build the larger reflector—going from 10” wide to 14” will hardly be visible from the dock.

What About Rough Seas And Heeling Sailboats?

I have not really analyzed the reflection as the mast tips. I can say that the fact that the corners are tilted up and down means that some would do better when the mast is tipped away and some would do better when the mast is tipped toward the source. The gain would be a factor of 3 or 30m² for straight on axis! In that orientation, a 24 degree tip would bring the value back down to original horizontal value. On the other hand the corners pointing the wrong way would now be 36 degrees off axis—almost no return at all. In a tossing sea, hopefully the motion will occasionally bring the reflector to a good position at the moment the radar beam sweeps past the boat. I suppose I could study the period of rotation of radar antennas as well as the periodicity of the sea to get a probability of getting a good reflection, but again, life is too short. I will function on the theory that the time I need the reflector the most is in a thick fog when the sea is calm and even monohulls are not heeling much.

Conclusion

I liked the end of the US Sailing article where they say something like, "Even though they barely work, you should still stick one up there—it can't hurt and might help.” I think my design is simpler than the lens units and can be fabricated at home without any special skills. Made a little bigger, it should be far better than the units on the market for small boats. I can’t imagine making it gimballed to give better heeling when the boat heels or bounces on the waves, but then a few months ago I couldn’t imagine designing a reflector myself dither. Who knows?
Thomas Schultz
schultz@pei.sympatico.ca

Addendum
Dec, 2008

In my article last year about making your own radar reflector, I may have mentioned that the design is probably not new. Later that year I happened to notice the markers on each side of the channel leading into the harbour here on PEI. There is a large neon-orange surface as well as a light, but additionally, at the top is an aluminum structure shown in the attached picture. If it isn’t the same structure as I described!  Clearly I cannot apply for a patent (I had no intention of doing so) and someone else had thought the same series of thoughts before me. I suspect the Coast Guard buys them from someone else, and the design may be patented by whoever constructs them, but I can’t imagine that an individual making one for their own use would be at any risk of a lawsuit. I have never seen the design advertised for use on boats in any of the marine supply catalogs, but I would think that the patent-holder (if any) ought to go into business for the marine pleasure market since the other devices are so totally inadequate.

Tom Schultz

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