# 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.

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 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.

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.

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.

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.

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.

# August 2020 virtual meeting

By Dave Nordling, Reaction Research Society

In the absence of our secretary, I took a few notes from the meeting. This is what I recorded. Contact the RRS secretary for updates and corrections.

The Reaction Research Society held its monthly meeting by teleconference on August 14, 2020. Our monthly meetings are always held on the 2nd Friday of every month. We’ve had a lot of success with holding our meetings remotely and we will likely continue for the next coming months to continue our commitment to safety in light of the pandemic. Our membership is in regular contact with our community which has allowed us to promote and hold events including our first launch at the Mojave Test Area (MTA) on July 25, 2020. You can read the details in the firing report posted on this website.

Our members are doing well and thus far no one has reported being infected with COVID-19 which we hope continues to be the case. Frank is in regular contact with the Los Angeles Police Department’s (LAPD) Community Safety Partnership (CSP) but under current circumstances, the next school event may not be until next year. Options are being considered on how to continue our educational programs while maintaining social distancing.

## REVIEW OF THE 7/25/2020 LAUNCH EVENT OPERATIONS

The first topic was the recent launch event we held on July 25th at the Mojave Test Area for the first time since the start of the pandemic. We had some difficulties in operating under the summer heat (106 Fahenheit at the peak) but this is nothing unusual for this time of year. Many of us were well prepared for the hot sun with our hats, sunscreen and iced beverages and chilled water. We also did a good job of watching out for each other. Still, the heat was responsible for leaving all but one of the micrograin rockets downrange. It also underscores the importance good planning, coordination and putting safety over all other considerations. We had several mis-fires which we were able to resolve, but maintaining discipline during the event proved to be a larger challenge. The launch protocols will be explained more thoroughly in the next safety briefing. The meeting highlighted that every member and pyro-op attending the event holds a joint responsibilty for the safety of all and it starts with self-discipline and patience by all.

We also discussed proper protocols such as announcing the pyro-op in charge well before the event and the necessity of providing detailed information about the intended operations to the pyro-op in charge in advance. Most of the planned projects were well understood as they were micrograin rockets and the previous hybrid rocket attempted at the last launch event.

## DATA REVIEW OF THE STANDARD ALPHA FLIGHT OF 7/25/2020

The only micrograin rocket to be recovered from the launch event of 7/25/2020 was the standard alpha with plain steel nozzle. John Krell has been developing progressively better and more powerful avionics payloads designed to fit the narrow confines of the RRS standard alpha payload tube. John was able to spot and recover one of his payloads and process the flight data captured that day. The avionics payload was intact after being extracted from the desert floor including the solid-state data chip. John was able to recover the data and accurately reveal the huge acceleration of the RRS standard alpha with unprecedented accuracy. A peak acceleration of 114 G’s was recorded at roughly 0.3 seconds just before tail-off and burn-out at 0.4 seconds from launch. I was able to screen capture his plot below.

The second plot shows the velocity derived from the accelerometer readings in the half-second which captures burnout at 0.4 seconds. Burnout velocity was measured at 670 feet/second which is consistent with prior data and trajectory predictions. The alpha is subsonic but travels at substantial speed from the swift acceleration. Given the high air temperature that day, 106 Fahrenheit, the speed of sound was 1165 ft/sec. The altitude of burnout was determined to be 130 feet which is consistent with prior flight data and high speed video footage.

The third plot was made for the whole flight of standard alpha from the 7/25/2020 event from launch to impact at 35 seconds. Given the roets were impacting 2000 to 3000 feet downrange, the sound delay matches with the time to impact witnessed in the observation bunker. The maximum altitude was just over 4,400 feet based on the barometric pressure measurements using the 1976 standard atmosphere model. Base atmospheric pressure reading at the start of the flight shows the elevation of alpha launch rail platform is 2,048 feet.

John Krell has really accomplished something with these custom avionics packages. He has been mentoring some of our other RRS members and the society encourages other members to build and fly their own payloads to spread the knowledge.

The society hopes to recover the other two alphas and the beta for further data analysis. Both of the unrecovered alphas from this last launch event had ceramic coated nozzles which should not erode. This should result in a more ideal performance as the throat area will not open up. The actual effect of this design improvement can best be assessed with recorded flight data. Also, we hope to compare the trajectory of the four-foot propellant tube with the standard length. Lastly. if the beta is recovered with recorded flight data, we may be able to assess its performance in unprecedented detail. The society hopes to report this flight data soon.

## IMPROVEMENTS TO THE NITROUS OXIDE FILL/DRAIN MANIFOLD

The failure to launch the second build of the hybrid rocket was discussed at the August 2020 meeting. After discussing the launch procedures and corrective actions followed during the attempt to launch the nitrous oxide hybrid at the MTA with Osvaldo (the Level 1 pyro-op in charge) and racing experts at Nitrous Supply Inc., Huntington Beach, California, the cause of the fill valve’s failure to open became clear.

nitroussupply.com

In the racing industry, these normally-closed direct-acting solenoid valves are commonly used to open the flow of stored nitrous oxide bottles against the full supply pressure in the storage bottle. These are called “purge solenoid valves” among racers because it is this solenoid valve that opens the flow of nitrous oxide which displaces or purges out the air in the engine lines during the race. Buying these 12-volt DC high pressure solenoid valves from racing suppliers is much cheaper given they are made in greater numbers for the racing industry. (~\$120 each versus \$400+ each from reputable solenoid valve manufacturers).

In researching common designs for normally closed (NC) solenoid valves, the excessive heat of that day simply created too much inlet pressure against the internal valve seat for the electromagnetic solenoid coil to overcome and open the flow path. 1000 psig is likely the limit to reliably open these valves according to advice given by Nitrous Supply Inc. who has decades of practical experience at racing tracks around the country using purge solenoid valves for an application nearly identical to the needs of hybrid rocketry fill and drain operations. The ambient temperature at the MTA on launch day was creating a bottle temperature of 1400 psig accordling to the bottle pressure gauge and the separate pressure gauge in the manifold when the bottle was opened. This is well above the 900 psi recommended pressure range seen by marking on the gauge. The bottle, valve body and fittings are rated for these higher pressures, but opening mechanism of the solenoid valve was not.

A color-coded example of direct-acting normally closed solenoid valve is below. Blue shows the high pressure fluid path which is holding the seat down along with some assistance from an internal spring only for low inlet pressure conditions. With current applied to the electromagnetic solenoid (Orange), it pulls up on the moving armature (in red) which then allows the fluid to slip past the seal and through the flow control orifice when commanded open. Only a slight amount of movement is necessary to lift open the valve. However, if the fluid inlet pressure is too great, the solenoid can not provide enough force to lift and open the seal, therefore the valve stays shut.

To understand the relationship between pressure and temperature of the nitrous oxide you must consult the vapor pressure curve for nitrous oxide. This set of data points spans between the triple point and critical point of any pure fluid. NIST provides accurate data to generate such a curve.

webbook.nist.gov

The critical point of any pure fluid is where the distinction between gas and liquid phases disappears. This is not necessarily hazardous but it does mark a fundamental change in fluid behavior. The critical point of nitrous oxide (N2O) is 1053.3 psia and 97.6 degrees Fahrenheit according to Air Products company literature. This means the nitrous oxide conditions in the bottle at the launch (1400 psig as read on the gauges with an fluid temperature of 106 Fahrenheit or more) was well in the supercritical range, but again, this is only hazardous if the pressure vessels and plumbing connections aren’t able to safely contain the pressure. If the solenoid valve could have been opened, the pressure drop would have returned the supercritical fluid back to normal conitions and would flow dense liquid into the rocket when the fluid naturally chills down from the expansion.

Keeping the bottle pressure below 1000 psia means controlling the external temperature of the bottle to a lower temperature. Below is a tabulation of state points along the vapor pressure curve for nitrous oxide (N2O) for common ambient temperatures. You can see that small shifts in ambient temperature can greatly affect the vapor pressure of the pressurized liquid. Keeping nitrous oxide under pressure is the key to retaining its denser liquid state. As long as the tank pressure is above the vapor pressure at that fluid temperature, you will have a liquid phase in the tank. If the pressure on the fluid drops below the vapor pressure, the liquid will begin to boil away.

• 30 F, 440.05 psia
• 40 F, 506.63 psia
• 50 F, 580.33 psia
• 60 F, 661.71 psia
• 70 F, 751.46 psia; liquid density 48.21 lbm/ft3, vapor density 0.1145 lbm/ft3
• 80 F, 850.46 psia
• 90 F, 960.09 psia
• 97.6 F, 1053.3 psia; density 28.22 lbm/ft3, CRITICAL POINT
• Molecular weight = 44.01 lbm/lb-mol

At first, it was thought that there wasn’t sufficient current from the lawnmower lead-acid battery we use. The summer heat can cause batteries to fail, but even after switching to a car battery, the failure to open was the same. Having a 12-volt solenoid requires greater current to actuate the solenoid valve, but it is a common standard for automotive grade parts which can be less expensive yet reliable. A current draw of 15 Amps over the long cable runs of a few hundred feet can be taxing to the firing circuit battery. This was not the cause of the problem, but it is a regular concern making sure sufficient voltage and current is available to both ignition and valve control.

To exclude outright failure of the solenoid valve, Osvaldo brought the unit home, allowed it to cool to room temperature then dry-cycled the valve from a battery to see if it still actuated. This simple test was successful and the filling valve in our nitrous oxide manifold continues to operate. At the next launch attempt, we will be prepared to chill the nitrous oxide supply bottle with an ice bath if necessary as was originally suggested at the prior launch event. Keeping the bottle pressure in an appropriate pressure range for fill operations is dependent on controlling the fluid temperature (60 to 90 F) under extreme heat or cold environments.

In researching purge solenoid valves, a second 12 VDC normally-closed valve was found and purchased. Nitrous Supply Inc., was out of purge solenoid valves but offered many alternative suppliers in the Los Angeles area. After some searching, I selected a high flow purge solenoid valve sold by Motorcycle Performance Specialties (MPS) Racing in Casselbury, Florida, for the purge solenoid valve used for venting our nitrous oxide manifold. The control panel is already equipped with the second command channel to open the vent from the blockhouse should it be necessary in launch operations. A schematic illustration is provided in this article.

mpsracing.com

The previous drain solenoid valve equipped with the nitrous manifold I bought was not deisgned for the full bottle pressure in the manifold so it quickly failed during initial checkouts. A manual valve was used in its place to carefully bleed out the remaining pressure in the line after the main bottle valve was tightly closed. This second solenoid valve will be used for draining the nitrous in the event of a launch scrub. Although the Contrails hybrid motor already has a small orifice and vent tube at the head end of the nitrous tank to provide slow release of pressure buildup, it is better to have a remote option to quickly depressurize the vehicle if the need arises.

With some re-plumbing of the nitrous oxide manifold to include the new vent solenoid, a soap-bubble leak check would be needed to prove the system before use. Given the significant overhanging weight of two solenoid valves, it may be wise to mount both valves on a separate plate structure to avoid excessive bending loads on the bottle connection. Design changes like this will be considered in preparation for the next launch event.

PYROTECHNIC OPERATOR TRAINING SESSION BY FRIENDS OF AMATEUR ROCKETRY

Mark Holthaus of the Friends of Amateur Rocketry (FAR) organization is offering an online training session for those interested in becoming licensed pyrotechnic operators in the state of California. The event requires registration on the FAR website and a fee paid to FAR (\$10) to attend this two-hour introduction to the licensing and application process to be held on August 26th.

Amateur rocketry in California is controlled by the same laws governing fireworks which require licensing by a state exam. The application forms and guidelines are available through the Office of the State Fire Marshal in the state of California (CALFIRE).

https://osfm.fire.ca.gov/divisions/fire-engineering-and-investigations/fireworks/

This training course for pyro-op applicants is another example of FAR and the RRS partnering to help the cause of amateur rocketry. The RRS, FAR and Rocketry Organization of California (ROC) last year met to create a joint set of recommendations to help CALFIRE improve the definitions used to govern amateur rocketry when CALFIRE they were seeking input from rocketry organizations. It is to the mutual benefit of the whole rocketry community and the public that there be more licensed pyro-op’s in amateur rocketry to both increase awareness of state laws and improve the culture of safety in our hobby and professions.

This FAR training course only serves to provide applicants with basic guidance on how to begin the application process and prepare to take the examination. Members of FAR, the RRS, ROC and any other amateur or model rocketry organization are welcome to apply. Several members of the RRS have already applied as the society continues its campaign to grow our ranks of licensed pyro-op’s at all three levels.

Completion of this training course does not substitute for any part of the pyro-op application process set by CALFIRE. As each applicant is required to pay their own fees including fingerprinting, they must also provide five letters of recommendation from licensed pyro-ops at or above the level of license being sought. After this class, each applicant must formally request these letters from state licensed pyro-ops in writing. For a licensed pyro-op to offer a letter of recommendation to an applicant, they must be willing to endorse their skills, knowledge and character to the state of California based on their personal experience with that individual. This is done through active participation at launch events through rocketry organizations having licensed pyro-ops leading their operations. Apprenticing, studying and attentiveness are all ways that a pyro-op can get to know an applicant personally and thus build confidence that the applicant is ready to have the responsibility of being licensed in rocketry. A letter of recommendation is given solely at the discretion of the licensed pyro-op which means their standards and expectations may vary significantly from others. It is important to establish a working relationship with both the society and the specific pyrotechnic operator over several projects to demonstrate skills and learn best practices through active participation.

As the RRS has more licensed pyro-ops than FAR at this time, this training course will be successful if both organizations support it. Some of the RRS pyro-ops have already offered their support as this means more people will need to become active with the RRS and conduct their projects at the MTA.

## ROCKET LABORATORY AT THE COMPTON AIRPORT

Keith Yoerg announced that there is a tentative plan to create a rocket laboratory in a hangar at the Compton Airport, Although, the hangar will be used from time to time to store or service light aircraft, there is a great deal of working space which will help the RRS continue their liquid rocket project already underway. Several members of the RRS are also active with civil aviation and are members of Chapter 96 of the Experimental Aircraft Association (EAA 96). The EAA has generously supported the RRS over the last two years and we hope to continue and expand this partnership.

## NEXT EVENT AT THE MOJAVE TEST AREA

The RRS has been planning the next event at the Mojave Test Area which will be dedicated to repairing some of our facilities including the adjustable rail launcher damaged in solid rocket launch explosion in August 2019. The consensus at the meeting was that we should not to return to the MTA for a formal launch event until the seasonal temperatures decrease from the excruciating desert summer. October 3rd was selected for this work event, Our hope is the weather will be cooler and we can accomplish more on that day. We may also take some time to search for more rockets planted downrange from past launch events.

The RRS may also conduct a few static firings or even a launch if member projects are ready. All such proposed hot-fire and launch activities must be proposed to the RRS president and the selected pyro-op in charge for that day. Some of our member projects such as Wolfram Blume’s Gas Guzzler two-stage ramjet and my second-build of the high-powered hybrid rocket are both still works in progress and may be ready for the early October launch date. Larry Hoffing has been working on an improved solid motor chemistry which he may want to test at the MTA.

The RRS is available for private events before that time, but one must make their request to the RRS president as usual. Some have indicated interest in returning to the site for just a few hours to recover more rockets downrange. Its our policy that at least two members be present for any excursions to the MTA and the RRS president must be notified in advance.

## IN CLOSING

Some topics were not able to be covered including the overview of the new RRS Constitution as it gets ready for administrative membership review. Also, facility improvement plans at the RRS MTA including new restroom facilities and blockhouse should be discussed.

The next RRS meeting will be held by teleconference on September 11, 2020 as it is unlikely we will be permitted to return to the Ken Nakaoka Community Center by then. We hope everyone continues to stay safe during these days of the pandemic and try to stay in touch as we are planning another event at the MTA for October 3, 2020.

secretary@rrs.org

# July 2019 meeting

Dave Nordling, RRS Secretary

The RRS held their monthly meeting on July 12, 2019, at the Ken Nakaoka Community Center in Gardena. We had a very large turnout with over 26 people coming in to see the three different presentations we had and catch up on the latest news.

After our reading of the treasury report, we had a special announcement of the induction of five new administrative members to the RRS. Our society is growing and this is in large part to the great participation we’ve been having and the dedication of the many talented people at the RRS.

Larry Hoffing gave us a short summary of the UCLA Rockets project he supervised at the RRS MTA. This Wednesday, July 10th, event was the first since the pair of earthquakes that rattled the nearby town of Ridgecrest in the Mojave. The RRS is happy to report none of our structures had any significant damage and the MTA is very much ready to operate.

We next discussed the upcoming launch event at the MTA tomorrow with Operation Progress in Watts with the LAPD CSP. We’ll have several alphas and a beta launch. We also plan to have an alpha with a parachute recovery system put together by new member, Kent Schwitkis and his friend Brian.

RRS vice president, Frank Miuccio, has started a new educational program this week with the students of Boyle Heights. There will be 10 teams launching their rockets from the MTA in September.

Our first presenter was Kent Schwitkis who brought several of his students from Compton College to our Friday night meeting. Kent is a member of the Sierra Club and Ski Patrol and has many years of experience with wilderness survival and first aid. His presentation outlined the important of planning for many kinds of potential emergencies. One of the important results from this discussion was the need for the RRS to form a safety committee to begin preparing emergency plans and establish contact with the regional authorities in preparing to handle serious emergencies if the need would ever arise.

The second presenter we had at the meeting was Sam Austin, a senior at MIT. Sam presented his two-stage solid rocket design to reach the von Karman line.

Sam also detailed the kerosene-LOX liquid rocket design that was test-fired at FAR in January 2019. Although the test was short (3 seconds), his results were impressive and his injector survived intact..

The last presentation was by RRS members, Jack Oswald and Cooper Eastwood. They have been steadily improving their solid motor design and have fabricated their improved motor based on prior tests. Their goal is to reach the 50,000 foot altitude limit at the RRS MTA on July 20th. His “50 for 50” rocket is 12 feet tall and 5-inches in diameter built entirely from scratch. The launch is to be timed with the 50th anniversary of the Apollo 11 moon landing.

The solid rocket holds 30 lbm of APCP propellant with an estimated burn time of 3 to 4 seconds generating an impulse of 7000 lbf-sec. The rocket fully loaded is 84 lbm and should reach a peak acceleration of 30 G’s and a burnout velocity of Mach 2.5 as it reaches 50,000 feet.

A 100-foot drogue streamer will deploy from the recovery system followed by a 9-foot Apollo 11 replica parachute at 2000 feet. The flight events are driven by an upgraded classic flight computer from Eggtimer and an RRC3 dual deployment system from MissileWorks. The von Karman nosecone is 3D printed and the aluminum fin can was rolled onto the aluminum body to be painted in polished black and white pattern of the Apollo 11 vehicle.

The RRS looks forward to the successful flights of Sam and Jack’s rocket from FAR and the RRS MTA, respectively. Both will be on the 50th anniversary of mankind’s greatest achievement on July 20th.

If there are any questions or corrections, please contact the RRS secretary. The next meeting of the RRS will be August 9, 2019.