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Biconic Nosecone Geometry and Sizing

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by Dave Nordling, Reaction Research Society

One of the most common nosecone geometries I have seen in model and amateur rocketry is the tangent ogive. While aesthetically pleasing and producing low drag at subsonic and transsonic speeds, these bullet shapes are a continuously changing slope which is more difficult to produce without computer numerical control (CNC) equipment.

Tangent ogive shape with a rounded tip

Although CNC is much more available than ever before, there are many who use manually controlled lathes. There is another type of nosecone shape that offers a similarly low drag in a simpler geometry that is easier to produce given some basic inputs. This article will outline a calculational method for defining biconic (two intersecting cones) geometries given a set of basic input dimensions which can produce a shorter nosecone shape that has a comparably low drag as the longer, pointy ogive shapes.

Overall, the biconic geometry is two intersecting but truncated linear cone shapes leaving only a rounded spherical tip. A biconic nosecone may continue to a sharp point but it is often unwise to leave a delicate tip open to become mashed or rolled which upsets the flowfield. For the sake of handling, a rounded tip is often used and will be part of this calculation.

It is important to follow the calculation steps in order. The variable names are given in the photos taken of the derivation.

The general sizing dimensions of a biconic nosecone.

The first input is the cone base diameter or radius ”R3”. This is what mates to the rocket body tube. Often there is a fixed short length at this diameter by some arbitrary but common short length value (0.25 inches, 6mm, etc.). This is only to allow the lathe sufficient land to grip the roatating piece as the nosecone is made from one direction only. The base radius, R3, would match common body tube sizes (e.g. 54mm diameter or 27mm radius).

The second input is the tip diameter or radius ”R1”. This is much smaller than the cone base, “R3”, but typical a modest fractional value. Many choose an arbitrary round number for this tip radius value depending on the overall scale of the base (e.g. 0.375 inches, 8mm).

The third input is the overall biconic length, ”H1+H2”. This does not include the extra rounded tip length. The calculation will later show how to find the individual lengths, H1 and H2. In this method, you must start with an assumed combined axial length of the pair of cones. It is likely to be significantly greater (1.5x, 2x, 2.5x) than the base radius, R3. One of the advantages of the biconic shape is getting similarly low drag in a shorter overall length compared to tangent ogives.

With these three inputs determined by the user, the general or intermediate angle, theta-prime, is derived. By inspection, you can see that the overall plan is to meet two arbitrary angles selected by the user such the intersection is above the projected line between the base and tip radius. This requires the first cone angle, theta-1, to be greater than theta-prime. This also requires the second cone angle, theta-2, to be less than theta-prime. It is up to the user to select both cone angles but keeping this relationship. Typically, round numbered angular values are selected (e.g. 5, 10, 15, 20, 25, 30…). Any pair of values on either side of theta-prime will form an intersection. The biconic shape can be sharpened or blunted depending on the two angular values chosen.

Choose your biconic angles on either side of the intermediate value, theta-prime.

Now that all three dimensions and the two cone angles are chosen, the phantom length, b, is calculated. This is a projected, fictional value that is useful in subsequent calculations but has no physical meaning. The user should notice that the left side is simplified to being only the difference in base radius to the tip radius (R3-R1). This will make the calculation easier.

Calculate the phamtom length, b.

With the phantom length (b), two cone angles, the biconic length (H1+H2) and the radius difference (R3-R1). the two cone lengths can be individually calculated (H1, H2) and the intermediate radius difference (R2-R1) determined. With intersection point determined, the travel distance to cut each cone is known.

Calculate the individual cone axial lengths and the middle radius, R2

The last segment of the calculation is to get the rounded tip. The tip radius is not the same as the spherical tip radius. Because the first cone intersects the sphere at a tangent point, the true center of the sphere is recessed inside the cone. The true spherical radius value, phi-1, is greater than the tip radius, R1. This recessed length or offset, H0, is calculated by trigonometry using the existing tip radius, R1, and the first cone angle, theta-1. The projected tip length, A1, is the result from the rest of the resulting geometry.

Get the nosecone radius, recess depth, and tip projected length

The biconic nose shape is still used on launch vehicles today likely for its ease of manufacture. This calculation process should make production of biconic nosecones easier to do. The actual drag from this family of shapes is a complex subject all its own, but it can be inferred that this family of shapes are useful to amateur rocketry.

Atlas V vehicles by United Launch Alliance, biconic and ogive fairing shapes

Poor Man’s Acoustic Analysis of Rocket Engines

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by Richard Garcia, Director of Research, Reaction Research Society

In this first month of the new year, 2022, a new technical article is now available to RRS members only. This article will be one in a quarterly series of technical subjects explored that are relevant to amateur rocketry.

Combustion instability is a common concern in the development of new liquid rocket engines and in solid motors. Although not as commonly found in the smaller engine designs of amateur rocketry, it has been seen in some cases. A simple and inexpensive method of conducting acoustic analysis of rocket engine behavior in hot-fire is discussed.

The article will be kept in the society library. Contact the director of research for inquiries.

research@rrs.org

Claybaugh 6-inch Rocket, Post-Flight Inspection

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by Bill Claybaugh, RRS.ORG

EDITOR’S NOTE: This is a continuation of the reporting from the 10-16-2021 flight of the 6-inch rocket design, built and flown by RRS member, Bill Claybaugh.

Post-Flight Motor Inspection

Recovery of the spent motor hardware allowed a detailed disassembly and inspection of the parts.  This revealed several useful observations:

Motor Tube

The recovered Motor Tube showed a dent just above the fins that was deep enough to have caused a pressure failure if it had been present while the motor was operating; we thus conclude that the dent occurred during or post impact.

Localized dent in the aluminum case, likely resulting from impact after burnout

Bulkhead

Inspection of the Forward Bulkhead showed it to be in good condition with no evidence of any gas leaks above the two O-rings.  The bottom of the Bulkhead showed some damage to the fiberglass heat shield from the ground impact of the rocket but showed plenty of fiberglass heat shield remaining after the about eight second burn.  The “nose” of the ignitor assembly remained in place in contrast to previous tests where this part had shattered upon ignition; the change to a steel “gun barrel” liner for the initiator appears to have resolved this issue.

The forward side of the bulkhead showing no leakage or damage.
Aft side of the bulkhead showing damage to fiberglass heatshield.

Fins

The four fins were intact and largely undamaged; they appear suitable for reuse in future flight vehicles.  Checking with a 0.002” feeler gauge showed there was no gap between the “nose” of any of the fins and the motor tube.  A further check using backlighting confirmed that there were no visible gaps between the fins and the motor tube at any location along the fin edges.

Nozzle

The graphite nozzle insert had broken free of its aluminum shell on impact; it was damaged at the exit end and is not suitable for reuse. The aluminum shell showed signs of erosion at the very top of the nozzle.  This area was covered by a ring-shaped fiberglass heat shield that was not present upon disassembly.  This suggests that the heat shield was fully consumed by hot gas erosion during motor operation; a thicker heat shield is evidently appropriate in future nozzles.

The titanium nozzle extension was undamaged and is suitable for reuse in future nozzles of the same design.

Nozzle was damaged in the impact.

Fin Can

The internal “Fin Can” showed some evidence of blow by of the O-ring that normally sits between the Fin Can and the phenolic liner at the base of the propellant grain.  No hot gas erosion was evident in the aluminum structure or in the O-ring, but soot was found on the downstream side of the O-ring.  If this O-ring were breeched, hot gas could—in principle—circulate between the liner and the motor wall; thus, this is a potentially significant issue.  Mitigating against circulation is the use of high temperature grease between the liner and the motor wall. There was no evidence of any soot or hot gas circulation along the interior of the motor wall. Likewise, there was no evidence of any hot gas leak between the fin can and the motor wall.  With minor refurbishment, the fin can does appear suitable for reuse excepting the potential change to two O-rings between the liner and the fin can.

Some “blow by” transient leakage past the seals was evident.
Opposite side of the fin can shows same pattern of the “blow by”.

Phenolic Liner

The propellant grain liner was partially consumed at the forward and bottom ends where the liner is exposed to hot gas for the full eight second duration of the burn.  There was no evidence of any hot gas contact with the motor tube wall and we thus conclude that the existing liner is of sufficient thickness to handle the current eight second burn time.

Conclusions

Based on this inspection it appears some minor redesign of the nozzle top heat shield is required.  It may likewise be prudent to replace the single O-ring used between the internal Fin Can and the phenolic liner with two O-rings.  The rest of the vehicle hardware appears to be in good shape and does not seem to require any design changes.

The lack of gap between the fins and the motor wall appears to rule out the possibility of part of the belly-band having become trapped on one of the fins and causing the unexplained turn to the Northeast.  The cause of that turn remains https://odellfamilychiro.com/phentermine-37-5-online/ a mystery.