Biconic Nosecone Geometry and Sizing

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

June 2022 Virtual Meeting

by Dave Nordling, President, Reaction Research Society

The Reaction Research Society held its monthly meeting by teleconference on June 10, 2022. The meeting covered several recent topics and we welcomed new member, Rushd Julfiker.:

We discussed the two recent events at the RRS MTA. Firing reports have been posted for each.

5/21: YMCA student launch event

6/4: UCLA Senior Capstone project launches

The society has had a few groups interested in using the MTA in the next month. Formal requests to use the MTA must be sent by email to the RRS president with specific dates requested.

Wilbur Owens’ loader in action on 5/21/2022 at the RRS MTA.

Dimitri Timohovich and Osvaldo Tarditti went to the MTA on Sunday, 6/5/22 to disassemble and examine the condition of the loader used at the MTA and owned by member, Wilbur Owens. The hydraulic cylinders will require a complete rebuild to return the machine to working order. The backhoe and loader has been a very useful asset to the society and as such the repairs will be paid by the society. Our security cameras are working well to monitor the site in our absence.

The 40th annual Large and Dangerous Rocket Ships (LDRS40) event by the Tripoli Rocketry Association is being hosted by the Rocketry Organization of California (ROC) in Lucerne Valley this weekend. Some of the RRS will be attending. it is an excellent event that brings many groups together and this year it is back in southern California.

Progress is being made on the new restroom facility. The septic system and leach field will go in soon. Dimitri provided updates on the container interior which should be finished by month’s end. The next step will be adding the roof platform and water tanks followed by completing the electrical systems.

Site maintenance and upgrades were discussed for projects after the new restroom facility is complete including more water storage and fire suppression gear. We could also use some metal cabinets and industrial shelving to better organize the contents of our new 40-foot storage container.

We have had a persistent problem with nails and metal debris puncturing tires at the MTA. One solution to this problem is a magentic sweeper which can pull up and remove any iron pieces left in the shallow layers of sand and dust.

Magnetic sweepers make picking up nails, bolts and other iron debris simple.

The society has bought two of these devices. With some dedicated and coordinated efforts, our site can be cleaned of this hazard. We will be asking our membership to spend some time sweeping the MTA, collecting the findings and disposing of them in the burn pit.

The north pad (foreground) by the Dosa Building is a convenient spot for loading and unloading.

The society has bought a new 1-ton gantry crane, trolley and chain hoist. This equipment will be useful in loading and unloaiding heavy materials on and off pickup trucks. Items such as cryogenic liquid cylinders would benefit from having a simple means of lifting them on and off with no power source required. The gantry crane will have the wheels removed and will be permanently mounted to a fixed foundation at the north pad by the Dosa Building.

An example of a gantry crane, trolley and chain hoist lfiting a heavy article on or off a pickup truck.

After some consideration, the executive council decided it would be best to postpone the next RRS Symposium until the spring of 2023. It takes a significant amount of preparation and we felt it best to wait to begin in the new year when we will celebrate our 80th anniversary. Before the pandemic, we had three increasingly successful annual events and we look forward to restarting them soon.

Next meeting will be July 8th as they happen on every 2nd Friday of the month. Our meetings will remain by teleconference but we are checking with the Ken Nakaoka Community Center about returning to in-person meetings soon. We will continue to have the teleconference feature even after we return to in-person meetings.

To attend our meetings, contact the RRS secretary.

MTA Launch Event, 2022-06-04

By Dave Nordling, President, Reaction Research Society

The RRS held a launch event on Saturday, June 4, 2022, at our Mojave Test Area (MTA). I was the pyro-op in charge. Winds were brisk and steady, but still under the 25 MPH limit. We had two operations that day.

The first was the UCLA Senior Capstone project led by Professor Brett Lopez. This quarterly class has seniors build and balance their own rockets from scratch. They load F-sized motors and fly them at the end of the quarter to prove their team’s skills in flight.

The UCLA students gather their materials in the propellant loading area.

Secondly, RRS member Wolfram Blume returned to the MTA with the latest rebuild of the Gas Guzzler. He had concerns about flying in the strong winds that day so he limited his work to testing the staging system with both halves on the 1515 rail. Bill Inman and new member, Dale, offered their assistamce in positioning the rocket on the rail.

Dale, Wolfram and Bill Inman

Bill Inman and Dale assisted Wolfram in trying out the new staging system in the Gas Guzzler. The old system (e.g., last December) was a hassle and required assembling the upper stage (main body tube, cowling, nose cone) on the rail with a screw driver and a step ladder. The mating of the booster thrust rods into the upper stage was very difficult. So after December, he redesigned and rebuilt the thrust rods and the staging system. The result was a successful design. The new system is fairly easy to stage on the rail, does not require any assembly (with the ever-present danger of losing small screws) and does not require a ladder. Wolfram feels good about this system for future launches.

The Gas Guzzler during its fit check on 6/4/2022

Wolfram doesn’t think he’ll make it back to the MTA until the summer heat is over. His goals for the summer both involve the fuel system:

  • The flameholder is the ramjet needs to ignite every time.
  • The ramjet slows down very quickly after stage separation (25m/sec/sec = 60mph/sec), so the ramjet must ignite within less than 2 seconds after stage separation; less than 1 second would be better.

Using the 270-volt, 3-phase electricity at Wolfram’s laboratory, he can run a 20hp air blower which can mimic the air flow at stage separation with a K-motor in the booster (175 m/sec). The blower can be run higher to mimic stage-separation flight speeds of about 250 m/sec which is just below the separation speed of an L-motor in the booster (280-300 m/sec).

Wolfram’s workshop is good for the tuning and testing the flameholder. but running the main burner would require returning to the MTA. The main fuel flow could be tuned using water. After the summer’s heat is over, he will return to the MTA and finish testing the parachute system. The first powered flight of the ramjet with a short – 5 second burn is under discussion.

This short event was also a good time to clean up the site a bit. The society has big plans for the summer including some much anticipated facility upgrades.

The next monthly meeting will be June 10th (2nd Friday of each month) by teleconference. Contact the RRS secretary for details.