• Nose Cone: Estes Reliant/Viking BT-20
• Nose Weight: 1/2 oz. clay
• Body Tube: QCR 18mm, 24" long
• Engine Block: Estes EST 3085
• Parachute: 6" mylar or equivalent
• Shock Cord 130 lb. test Kevlar 48" long
• Fins: 3/32" Balsa, trapezoidal Root chord: 6" Tip chord: 6" Span: 3" Sweep: 3"
• Launch Lug: drinking straw, 1/8"-1/4" dia., 6" long

Observations: Evan Ross' entry last DesCon reminded me of some speculative calculations I'd done earlier and laid aside. I had wondered what was the minimum number of conventional fins that would stabilize a rocket, but I took a different approach. Yes, you can make a two-finned rocket, or even a finless rocket, stable by spinning it, but can you make a two-finned rocket stable without spinning it? Rockets have been flying with a single stick fin for thousands of years, but on rockets more than a few inches long, they become unwieldy. I suspected there was also a weight penalty. A ring fin could arguably be called a single fin, but because in profile, one side is "behind" the other, I didn't see how it could readily be compared with conventional fins. Three fins obviously work, but what about two? On rockets with three or more fins, the fins are equally spaced around the body because a fin offers no stabilizing force parallel to its surface. Four-finned rockets have two pairs of fins perpendicular to each other, so in the direction one pair presents minimum stabilizing surface to the airstream, the other presents its maximum surface. On a three-finned rocket, in the direction one fin presents minimum surface, the other two fins combine vectored forces to make up for it. Two fins opposite each other can't do this. So, if a stable two-finnned rocket is possible, what is the optimum angle between fins? I predicted that the optimum angle would be the one that presented the greatest minimum lateral area. That is to say, position the fins so that, if you turn the rocket so the least fin area is visible, you have the most visible area left. If you put the fins opposite each other, and turn the rocket so the least fin area is visible, you are looking at a fin edge-on, for practically zero area. As you reduce the angle between the fins, the minimum area increases to a point, then decreases until, as the fins become nearly parallel, the minimum area again approaches zero. I calculated that the "maximum minimum" area would be found when the angle between the fins, theta, was such that cos theta=2 sin theta. So theta should equal the arc cosine of twice the sine of theta, or 53 degrees. (See sketch.) How big should the fins be? I didn't know, so I took the size that RockSim said would stabilize a four-finned rocket and doubled it. I used a long body tube, plenty of nose weight, and big enough fins to make the rocket stable by the most conservative estimate, the cardboard cutout method. In a proof of concept model, a marginally stable rocket wouldn't prove much. This rocket should be clearly stable or clearly unstable.

Aft View click image to enlarge   Sketch click on image to enlarge

Assembly Instructions:

Building the rocket was straightforward; I used mainly conventional techniques. I used a 24" length of 18 mm body tube, because that was the longest piece I had on hand. I used a long NC-20 nose cone to allow plenty of room for nose weight. I added half an ounce of clay, which almost completely filled the nose cone, then I glued the base in place with plastic model cement. I cut the fins with the grain parallel to the root edge because I couldn't find any balsa sheet large enough to lay them out any other way.

How to ensure that the fins were the angle I wanted? I took the span of the fins, added the radius of the tube, and found that the distance between the tips of the fins just happened to equal their span -- 3"! I glued one fin in place, then used an extra piece of 3" wide balsa sheet to set the correct spacing. "Hmm," I thought, "53 degrees is awfully close to 60. Maybe an equilateral triangle would have given a fin spacing just as good or better."

Because the fins were rather large for their thickness, I used an external shock cord mount to make the rocket come down horizontally, and, I hoped, protect them from damage. I cut 48" of 130 lb. test Kevlar. Then I made a hole with a toothpick just inside the angle of the root edge and the trailing edge. I threaded the Kevlar through the hole, and used CA to tack one end to the fin fillet just behind the leading edge. When this was dry, I pulled the cord taut along the fillets on both sides of the fin, and CA'd it down. (Epoxy might work better here.) Then I put an expended casing in the rocket to find the balance point, which just happened to be at the leading edge of the fins. I tied the other end of the shock cord to the nose cone, and tied a swivel to the cord near the nose end for a parachute. I wanted this rocket to get a smooth start off the launch rod, so I ran a launch lug between the fins the full six inch length of the fillet of the fin that wasn't attached to the shock cord.

My rocket was complete. Now I needed a highly visible finish. I colored it with Magnum 44 permanent markers -- body and one fin red, for visibility, and the other fin black, so I could easily see if the rocket spun on its way up. I left the nose cone white because I thought it looked cool.

Per the NAR Model Rocket Safety Code, I tried to determine stability before flying it. I did a swing test, and it appeared quite stable. Just to be on the safe side, (and to avoid embarrassment if anything went wrong) I conducted the first test flight in complete isolation from persons not participating in the actual launching. I did bring my wife, so I'd have another witness to confirm that the rocket had made a stable flight. I had already been appointed RSO of the next club launch, and I wanted to fly the model there. I anticipated having some difficulty convincing certain members that I should be allowed to fly it.

The day of the test flight was windy, so I selected a six inch mylar chute to avoid having the rocket drift out of the launch field. I set up my rocket with the rod slightly angled into the wind, counted down, and pressed the button. The rocket surged smoothly off the pad and into the air. I could see it rolling as it climbed, but certainly not enough spin to stabilize an unstable rocket. It coasted to a good altitude, ejected exactly at apogee -- nose horizontal, and drifted down on its chute. I ran after it, and found it well within the field, with no damage. Success!

The next weekend was our club's big meet. After I'd gotten all my competition flights in, I prepped TFNK and brought it to the safety check-in. The SCO said, "You can't fly a rocket with only two fins!" "But it swing tests stable, and it's had a safe flight before." I argued. "A rocket can't be stable without at least three fins!" he said. I reminded him that some aerodynamic experts had insisted that the WAC-Corporal couldn't be stable because it didn't have four fins, until someone pointed out that arrows are stable with only three feathers. (Handbook of Model Rocketry, 6th ed. p. 154) I heard another old-timer mutter, "Not on MY field!" (Which it wasn't.) and "Not in this lifetime!"

It didn't matter. He had already made up his mind not to let that rocket fly, so he said that it couldn't fly because the grain wasn't parallel to the leading edge of the fins. That's not in the safety code. It hadn't been a problem on the earlier flight. It was only a rather strong suggestion in the Handbook, (6th ed. p. 52) but without the force of law, and no evidence to support it.

Although, as RSO, I could have overruled him, (HMR pp. 286-287, 298-299) I got the distinct impression that I'd end up flying all my rockets alone. So now I have this really cool rocket that I hardly ever get to fly.

I still have questions. Now that I know that a two-finned rocket can be stable, how do you calculate its center of pressure? Is the optimum angle 53 degrees, 60 degrees, 90 degrees, or some other angle? Can the optimum angle be proven mathematically or tested experimentally? Do I see a potential RD project here?