Facts, Fun and Fallacies about Fin-less Model Rocket Design

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1 Facts, Fun and Fallacies about Fin-less Model Rocket Design Introduction Fin-less model rocket design has long been a subject of debate among rocketeers wishing to build and fly true scale models of space launch vehicles and large military rockets which do not normally possess the large fins characteristic of typical tail-heavy model rockets. The methods of building and flying such fin-less scale rockets already exist but are not widely understood and accepted among model rocket builders. The purpose of this paper is to bring these methods to the attention of rocket builders and to explain the differences between techniques which actually work and those which are claimed to work but do not. The methods that will be explained involve passive stabilization of rockets (not requiring active guidance systems based on gyroscopic sensors and activation of aerodynamic or thrust vectoring controls). These passive stabilization systems allow scale models to be built and flown without fins and if desired even without the use of launch rails. Stabilizing tail cones such as those employed on blow-gun darts and some rockets will not be considered as fin-less designs since flared tail-cones contribute to the dimensions and appearance of the vehicle or projectile as do fins. Spin-stabilized rockets will be mentioned in the discussions, but non-spinning rockets stabilized by 1) fin-less re-direction of air or by 2) designed-in angular momentum management are the principal subjects of this paper. Both fin-less re-direction of air and designed-in angular momentum management use engine exhaust to achieve their different (or combined) stabilizing effects.

2 Finless Re-direction of Air Flow Air Inlet at or Near the Exhaust Finless redirection of air uses the engine exhaust and tail end of the body tube to deflect ambient air flow without the use of fins. Experiments conducted by Dan Hall in 2014 demonstrated that the fin-less redirection of ambient airflow can be achieved as easily as recessing the rocket motor into the base of the body tube of the rocket. Nose weight is required. Turbulent mixing of exhaust flow with air inside the body tube results in a cone of expanding diameter (yellow) that leaves the body tube along the longitudinal axis of the rocket. The ambient air drawn into the exhaust has a velocity and a radius of action (R wind ) about the center of gravity of the rocket, defining how much angular momentum the captured ambient air brings to the rocket. Since the captured air leaves the rocket along its longitudinal axis (R=0), the angular momentum leaving with the captured air is reduced to near zero. The net captured angular momentum turns the rocket in the direction which aligns the rocket with the relative wind. That is to say, it aligns the rocket into the relative wind and thus stabilizes it. This is also what fins do: receive the ambient air at the angle of attack, θ, from which it approaches and then directs the air to the rear down the rocket s longitudinal axis. The recessed rocket motor thus works like fins, but unfortunately at the expense of a considerable decrease in thrust. The suction required to draw in the ambient air (light blue) increases as the motor is recessed at greater depths within the body tube. If the motor is recessed too deeply, the suction becomes great enough that the drop in pressure expands the (yellow) cone until it cuts off the intake flow (blue) of ambient air. This Krushnic collapse results in an almost complete loss of thrust. Hall was able to insert his motor 1.75 into a 3 diameter rocket body without triggering the Krushnic collapse, but there is an easier way to prevent the intake and exhaust flows from having to compete with each other for flow area: keep them physically separated.

3 David Hall's 3 inch diameter finless rocket demonstrated that a recessed motor could stabilize a finless rocket by ingesting ambient air and then expelling it along the longitudinal axis of the rocket, much as fins re-direct air flow in conventional model rockets. Hall reasoned that stability was a result of the center of gravity being ahead of the center of pressure, based on the knife-edge balancing of a paper cutout of the rocket. This, however, is a fallacy based on a long-standing theory in the model rocket community that centers of pressure (or lift) correspond to centers of area. In fact, for shallow angles of attack the forces exerted by the airflow on a finless, constant diameter rocket are limited primarily to the rocket s forward facing surfaces (i.e. the nose cone) and tail suction on the rear of the rocket, which taken together will not stabilize the rocket. Despite the questionable theoretical explanation, Hall s rocket clearly demonstrated a practical means of stabilizing finless models. Simple modifications based on a more complete picture of what is taking place improve the efficiency of this technique. Photo and drawing supplied by David Hall.

4 Holes punched in the body tube near the base of the motor allow ambient air to enter the body tube from the sides without passing thru the base of the body tube where it flows counter to the expanding cone of mixed exhaust gases and entrained air. A Krushnic collapse is no longer possible and thrust losses can be kept small with adequate flow areas for the entering ambient air. This technique of using entrained air to provide pseudo-fin behavior is a major improvement over the use of clear plastic fins to stabilize scale models of fin-less rockets. These rockets still require a launch rail to get up to an adequate air speed before the fins, or pseudo-fins in this case, will stabilize the rocket. There is, however, an even more capable technique called induction tube stabilization that allows the launch of rockets without launch rails. (Induction rockets require larger and more conspicuous air intakes; the choice of a pseudo-fin rocket may be preferable in individual cases.) Induction Tube Stabilization Induction tube stabilization of rockets has been in limited use for at least 50 years. Induction tube stabilization differs from pseudo-fin stabilization in that it is a more capable system, not dependent on the speed of the rocket into the wind to provide stability. Induction tube stabilization is enabled by engine thrust, not air speed, and it stabilizes the rocket by freezing its pitch and yaw angles rather than by aligning the rocket into the wind. The outward difference in appearance between pseudo-fin rockets and induction rockets is the placement and size of the air intake. For induction rockets the intake is larger and it is placed at the center of gravity rather than near the base of the rocket. An intake at the center of gravity has near-zero radius of action for any momentum in the ambient air entering the intake. Nose weight is not required.

5 The major elements of a basic induction tube rocket are a forward body tube, an aft body tube, and a forward engine mount, all seen here. The open intake is between the fore and aft body tubes. No launch lug or fins are needed. Basic induction stabilized rocket assembled and painted, with rail-less launch pad The purpose of the large induction tube (lower body tube) is to maximize the gas flow out the exhaust. It is this flow which extracts angular momentum from the rocket s rotations about the yaw and pitch axes at a rate equal to the mass flow rate x the radius of rotation of the exhaust about the c. g. x the rocket s rate of rotation about the pitch or yaw axes. Purely induction stabilized rockets become unstable after thrust termination. For this reason hybrid stabilization is sometimes employed: an induction tube provides stability during lift-off, allowing launch without a rail, and small fins provide stability during high speed and coast. The small fins take advantage of the far forward center of gravity provided by the forward mounted engine. (Pseudo-fin rockets cannot be rendered stable by small fins due to the rear mounted engine.)

6 The requirements for a hybrid scale model are a bit more complex but manageable for Level 3 rocket builders. The following example is based on one of the United States historically most important launch vehicle developments, the USAF s Thor-Able which became the basis for Thor Delta, NASA s first standardized launch vehicle. This Thor-Able model is scaled to small size but has subsequently been scaled up to and flown in large sizes. Thor-Able and Thor Delta are examples of rockets suitable for hybrid induction tube and small fin stabilization.

7 THOR-ABLE and THOR DELTA Induction Stabilized Model Rockets Induction-stabilization has proven to be a robust alternative to the use of fins for the stabilization of scale model rockets. The need for an air inlet near the center of gravity to make inductionstabilization work is easy to accommodate for some models but problematic for others. In some cases the alternative may be a hybrid arrangement. Take, for example, Thor-Able and Thor Delta which have fins too small for traditional model rocket fin stabilization. It is possible to stabilize a Thor-Able or Thor Delta model with a combination of the existing small fins augmented with the use of a small induction tube. The arrangement appears something like this: This design assumes a Estes BT-60 body tube for the first stage and an A3-4T engine. The induction tube, to be in scale with the maximum engine bell diameter, should have an O.D. of about 20.4 mm. Nose weight required. Eight black rectangles are part of the regular Thor-Able and Thor Delta paint patterns. Four are located just above the fins. The other four rectangles are located at mid-body. If we cut out the four black rectangles at mid-body and 2 of the 4 rectangles above the fins, we will provide sufficient air inlet area to feed the induction tube. Painting the inside of the body tube black will keep the cut-out rectangles looking black. It is important to close off the base of the rocket to prevent air from entering near the exhaust. Such a small induction tube will be unable to stabilize the rocket on its own. The combination of the small induction tube and the small fins are sufficient. This assumes the induction tube slows any buildup of yaw and pitch rotation rates enough to give the rocket time to gain sufficient velocity for the fins to become effective aerodynamically. A 3-foot-long launch rail is then not needed. A short 6.5 rail sticking up vertically from the launch pad ring will steady the rocket against winds as it sits on the pad. The rail will fit into a paper straw of the same length that is

8 glued to the inside wall of the BT-60 body tube forming the lower half of the first stage. This short rail will delay the onset of pitch or roll rotations as the rocket begins to lift off. That is critical since the rocket takes about as long to travel the first 6 inches as it does to travel the next 2 feet. Thus the short rail will delay the onset of pitch and roll rotations for almost half the time it normally takes to travel to the end of a 3 foot launch rail making the induction tube s job much easier during the reduced time it takes to get the rocket the rest of the way up to fin speed. Confidence in this design is based on the robustness of the induction-stabilization demonstrated in the finless rockets that have been flown so far. Partial inductionstabilization in a hybrid induction/fin system is just the next step that needs to be taken if the limits of such systems are to be explored. A hybrid system which includes small fins also offers the possibility of the rocket remaining stable following thrust termination, allowing it to coast to the maximum possible altitude. Only the basics of this model design have been presented. If you are interested, take it and run with it. Induction-stabilization opens a range of new possibilities for scale model rocket builders. If changes in the competition rules can accommodate these new possibilities, the hobby will grow and be more interesting. Three-footlong launch rails and fake fins should no longer be requirements for the launching of scale models.

9 Thor Delta has similar shape and markings to Thor-Able. The same induction stabilized model rocket plan applies. The model may be scaled up to larger body tube diameters for larger diameter motors. On Able and Delta the fins extended out 30 inches from the base of the rocket and had a leading edge sweep of 60 degrees. Thor Able IV (not shown, but the rocket actually modeled) launched Pioneer 5 and had a total length of ft with a rounded nose on the 2 nd stage.