Build a High Power Rocket Nozzle

Experimental High Power Rocketry is an extreme sport which offers makers a variety of opportunities to utilize their skills, obtain new skills, and explore...well, rocket science! In this Instructable I will introduce one method of making nozzles for Experimental High Power Rocket motors. I will also show a bit about the construction of the motor itself. The attached images of an in-flight rocket are the results of flying with a custom made nozzle following the steps I will outline. That rocket, it's motor including the nozzle, it's propellant, and all of the constituent parts other than the electronics were 100% made from scratch.

Disclaimer and Plea

As I outlined in my previous Instructable on characterizing rocket propellant, High Power Rocketry is dangerous. In some places it is illegal. Please DO NOT experiment with High Power rocketry without first following all applicable laws and safety practices! If you intend to produce your own rocket motors, first join the Tripoli Rocketry Association and obtain your level 2 certification. Then and only then will you be able to fly experimental motors at Tripoli insured launches. Work with others that have experience in this hobby. You will find most are happy to mentor and guide you through this exciting part of hobby rocketry. Understand that safety reigns supreme! Your accident can endanger the entire hobby! All bad publicity for the sport puts it in constant jeopardy, potentially cutting off millions from the hobby they love, and the education they need to become aerospace leaders of the future. Our local school rocketry programs depend upon volunteers from NAR and Tripoli, whose sport depends upon the good will of the community and authorities having jurisdiction. Land owners willing to support our hobby are difficult to find. It is imperative that we retain a high safety record.

With that said, be advised that I will not disclose any propellant formulas in this Instructable. If you can prove a level-2 Tripoli certification and association with other experimental rocketry enthusiasts, you will have access to the necessary formulas, or you can contact me and I can point you to forums where such formulas are disclosed to certified members.

Not everything has to be made...

It is also important to note that while I will provide details on making rocket nozzles, as with all other aspects of High Power, Mid Power, and Model Rocketry, the components can be purchased by many reputable and committed vendors. If you are new to rocketry, don't start by making nozzles, or your own propellant! Start by working with a local club, and buying kits and parts from vendors. If you don't have access to all of the tools needed, many of the vendors will custom make parts such as nozzles to your specifications. Prior to making my own nozzles, I have purchased several from Tru-Core. I also have one or more nozzles from Gorilla Rocket Motors provided by another vendor.

Most High Power Rocket Nozzles are made from graphite. Graphite is an excellent material for nozzles for many reasons. Graphite rods come in many sizes and densities. I recommend purchasing lower density graphite to learn on! Then, when you are confident in the machining process, step up to higher quality graphite.

Becker Graphite

The nozzle shown in the in-flight photos was made from a 2.75" diameter JC3 graphite rod obtained from Becker Graphite. At the time I purchased it, 24 inches of 2.75" diameter JC3 graphite rod cost $88 with shipping. This will make several 75mm nozzles.

Graphite Store

Another excellent source of graphite or nozzles is the Graphite Store. Medium density graphite will work fine for learning to build nozzles and can even be used for a few flights and for test motors. Step up to the superfine isomolded graphite rods for longer lasting production nozzles. Graphite is subject to erosion. The better the graphite you use, the less erosion you are likely to see.

Selecting the size

When selecting a diameter I recommend that you find the one closest to the inside diameter of your motor tube. For a 75mm motor, 2.75" diameter is the best. 3" diameter may be less expensive in some cases, but you will have to do more work to cut it down to size. For 54mm motors, you will likely have to start with 2" diameter rods.

If you have successfully used other materials for multiple-use nozzles, please comment on your experiences.

Caveat

One additional note about working with graphite: Graphite is messy. You'll notice the latex gloves I wear in the photos. It saves a lot of scrubbing! A good, strong shop vacuum is mandatory for working with graphite. Always position it so that as much of the dust as possible is immediately sucked away. Use a vacuum bag designed to catch fine particles. Remember that graphite also conducts electricity! If you allow the dust to collect inside the motor of your lathe, you may short it out! From personal experience I can warn you that it will cling to everything if not vacuumed away as it is cut. It will stick to your shoes! Your wife will not appreciate you dragging it into the house!!!

A lathe is required for making rocket nozzles. You can get by without a lot of the tools I will use, but not without a lathe. I own two lathes, but because of the mess made by graphite, I only use the cheap Harbor Freight 7 x 10 mini-lathe for making rocket nozzles. Despite what you may have heard or read in forums, a 7 x 10 mini lathe is perfectly adequate for making nozzles for 75mm motors. Obviously smaller nozzles, such as those for 54mm and 38mm are even easier on a small lathe.

The 7 x 10 lathe chucks will open just wide enough to grip a 2.75" diameter graphite rod. If the rod is only a few inches long (e.g. 3" long) the 7 x 10 works great.

If you are working with 98mm motors or even with 3" rods for 75mm nozzles you may need a larger lathe, or you can use a jig to hold the graphite. (e.g. A smaller diameter rod of aluminum or steel with a center hole through which a bolt can extend through it and through the graphite rod to hold it tight. The smaller diameter rod is held in the chuck jaws.) This will require you to mark and drill a hole through the center of the graphite rod. A drill press will be required, along with a drill bit long enough to go all the way through the blank.

While it not necessary to have a larger lathe, it will make some things easier. Though I use my 7 x 10 for making nozzles, I always drill out the throat (the entire core through the center of the rod) on the larger lathe. It is easier than using the drill press for nozzles too large to be drilled on the 7 x 10.

Other required tools:

1. Drill bits
   • Nozzles throats are usually measured 1/64". Select a set of bits that covers the full range you may need to drill, and which are long enough to cut through the length of the nozzle if possible. I spent just under $120 for a 32 piece set of Silver & Deming drill bits on e-Bay, ranging from 38/64" to 1". These have a 1/2" shank for use in the chuck on my larger lathe.
2. Cone Cutters or boring bars
   • In the next step I will include a video on how to make the custom cone cutters. Without these or commercial end-mills, the cones will need to be cut with a boring bar and the lathe set to cut at the proper angle (which is far more time consuming.)
3. Parting Tool
   • The parting tool is especially useful for cutting o-ring grooves.
4. Band saw or hack saw
   • A band saw (metal cutting) is ideal for cutting the graphite rods. A hacksaw could be used instead.
5. Drill Press
   • A Drill Press may be required depending on the size of the lathe used.
6. Measuring tools
   • Calipers and other measuring tools are a must
7. Masking tape
   • This will be helpful in marking cutters to obtain the proper depths
8. Turning Tools
   • Turning tools will reduce the outside diameter or the graphite rod to the proper size and will be used to face the ends.
9. A powerful shop vac
   • Mine is a 14 gallon, 6.0 HP peak RIGID vacuum with the best available dust collection bag.

As seen in the previous step, I made custom cutters to cut the divergent cone and convergent cone of the nozzles. The convergent cone cutter cuts a 45 degree half-angle and the divergent cone cutter cuts a 15 degree half-angle.

Commercial end mills are available for this purpose too, and they will cut much faster than the custom made cutters, but they are very expensive and come in a variety of sizes. It is difficult to find one that can produce the full range of exit diameters needed or that end in a fine point. If you have a better source please leave a comment!

This video will demonstrate how my custom made cutters were made. It shows the 15 degree half-angle cutter, but the process is identical to that used for the 45 degree half-angle cutter -- with the exception that I used a 1/2" shank on the 45 degree cutter and a 1" shank on the 15 degree cutter.

Propellant Characteristics

In order to design an optimal nozzle there are certain pieces of information that are necessary. First details of the propellant to be used must be known. This includes its theoretical "Specific Heat" and density. The propellant will have to have been previously characterized in order to obtain average ISP, Burn Rate Coefficient, and Burn Rate Exponent. For more information on characterizing rocket motors and capturing and processing data from test burns please see my Instructable on that topic. That data is used by BurnSim to design a flight motor. The Specific Heat of "Chamber CP/CV" of the formula is also needed to design a nozzle.

Motor Design

In addition to propellant characteristics, a motor must be planned and designed. BurnSim is the author's tool of choice for designing a rocket motor. Once propellant characteristics are entered, the number of propellant grains can be entered along with the core size (and shape). To calculate the expected initial and maximum Kn and pressure of the motor BurnSim needs to know the Nozzle throat diameter. You use Burnsim, and adjust throat diameters until your motor will function as desired. The most important issue is the maximum case pressure (Max Pc). Exceeding the pressure capabilities of your hardware will result in a CATO (catastrophic failure of the motor, a.k.a. an explosion). The nozzle throat diameter, along with the amount of burn surface area in the grain design will have the biggest affect on pressure. Some propellants burn faster than others, and some with higher pressure sensitivity. Almost all APCP propellants burn faster under higher pressure, and this in turn can lead to out of control pressure.

Though this is a somewhat controversial topic, the author prefers to keep pressure well under 1000 PSI. Others will say that less than 1000 PSI is a waste. Due to the possibility of erosive burning (which further increases surface area and pressure), and the highly pressure sensitive nature of most APCP propellants, I prefer to reduce the risk of a CATO by keeping pressure closer to the 600 to 700 PSI range, with some variations depending on the propellant used. My hardware for 75mm motors does not use snap rings and could theoretically handle much higher pressures, but I find that I get suitable performance for my targeted altitudes running at lower pressures. Note that our testing has shown that with 54mm hardware, snap rings are prone to failure when pressure exceeds 1200 PSI.

It is also important to have sufficient pressure for the motor to start and run without chuffing. Characterization of the propellant will help to identify the minimum Kn required for the motor to start without chuffing. Generally speaking, propellants with a small percentage of lampblack or other char added have proven to start more readily at lower pressures. Also formulas containing copper compounds tend to start easily but they burn rapidly and tend to be more pressure sensitive.

Collecting Data

With all of this in mind, design your motor in BurnSim. (See the attached photos for details on the motor used for the in-flight photos shown on the Intro page.) The following information from Burnsim will be needed to calculate the nozzle:

• * Max Case Pressure (Pc) called - Max Pc in BurnSim
• * Atmospheric Pressure (Pe) or use 14.7 PSI - called Ambient PSI in BurnSim
• * Nozzle Throat Diameter - labeled Nozzle Throat Dia in BurnSum

• --Note that BurnSim can also calculate the "best" Exit Diameter but details of that calculation are not provided.

In addition to this information from BurnSim, the following information from the propellant formula is needed:

• * Specific Heat (k), called Chamber CP/CV in ProPEP 3

ProPEP 3 can calculate the Specific Heat based on the formula. The attached images show this information from ProPEP 3. You will notice that the formula is blocked out for purposes outlined in the introduction.

The Theory

With the information obtained in the last step you are now ready to calculate the dimensions of your nozzle! For details on the science behind how the nozzle works and how these calculations are made I recommend reading Chapter 3 of the 8th Edition of Rocket Propulsion Elements by George P. Sutton and Oscar Biblarz.

The Pragmatic Approach

For the sake of simplicity, and because I am no math or physics genius I will forego a detailed discussion of the math involved in designing your nozzle. Instead note that a formula is used to calculate the optimal nozzle for a rocket that will operate under 10,000 feet above ground level. The results of this formula will allow us to derive the nozzle's exit diameter. Given the diameter of the throat from the previous step, the exit diameter, and the angle of the cone we can determine the length of divergent cone and where it intersects with the nozzle throat.

Similarly, given the diameter of the nozzle, the width of the shoulder which determines the inside diameter of the convergent cone, and the diameter of the throat we can determine the depth (or length) of the convergent cone as well as the point where it intersects with the throat.

These two lengths (or depths) added to the desired depth of the throat will give us the overall length of the graphite rod we will use to make the nozzle.

Note that the throat depth ideal is kept to a minimum. Most commercially available nozzles will have some depth to the throat. You will likely find as you machine nozzles that having some room allocated to the throat alone will cover any mistakes in cutting the divergent or convergent cones slightly too deep. Otherwise you may end up expanding the throat diameter.

Most nozzles have a divergent cone with a approximately a 15 degree half-angle. Most also have a convergent (or entrance) cone with either a 45 degree half-angle or a 60 degree half-angle. The 60 degree half-angle cone is shallower and is used to keep the overall length of the nozzle shorter. When I make nozzles though, I stick with 15 degrees for the divergent cone and 45 degrees for the convergent cone because as you've already seen, I've made cutters for these two half-angles.

The Nozzle Designer App

Rather than explain and require you to work out all of the math behind the nozzle design, I've written a program for designing nozzles. It is available on the Windows 10 Store at the following URL:

https://www.microsoft.com/store/apps/9NBLGGH68GFZ. This app will work on all Windows 10 devices. It will allow you to enter all of the parameters we've discussed and will calculate the dimensions of your nozzle. You can then print those dimensions out and machine your nozzle, or send it to a machinist such as Ed Romani at Tru-Core to have a custom nozzle made.

The Alternative

If you do not have access to Windows 10 device (e.g. desktop, phone, or tablet), borrow one or upgrade! Alternatively, I have attached a spreadsheet produced by my friend and mentor in all things Rocketry, Raymond Kinsel. This is the spreadsheet that I used to make the nozzle shown in the in-flight photos. I made the Windows 10 universal app only in preparation for this article. I selected Windows 10, because as a programmer I had not yet written a Windows 10 Universal App in C++. At some future point I may back port this to Windows 8 or even to OS X or iOS, but for now this is it! Producing an App, regardless of the platform takes a substantial amount of work, no matter how simple the application. There are always gotchas with UIs, always. Printing under Windows 10 is not as straightforward or simple as it should be -- or as it is with Win32 GDI printing, because it seems to be designed to print screen content without knowledge of device characteristics such as DPI. Of course, that will likely improve in time -- or else my knowledge of how it is supposed to work will improve and so someday I may even be able to produce one-to-one drawings in the printouts.

With all of the measurements needed in hand it is time to cut the blank. For this I use a metal cutting bandsaw which allows me to clamp the graphite rod in place to make the cut. The blank should be slightly longer than the "Overall Length" determined by the High Power Rocket Nozzle Designer app. This will allow some excess material to be removed while facing the ends.

The next step is to secure the blank in the lathe chucks, face each end, and then turn down the outside until it is the correct diameter. The video attached to this step attempts to speed up the playback a bit and shows facing and turning of a 75mm nozzle. (My apologies for the wobble in the first minute.)

After turning down the outside diameter, turn one end to make the shoulder that will fit into the liner tube.

This step as with the remaining steps do not need to occur in any certain order, but it is a good idea to cut your O-ring grooves before investing a lot of other work. Why? If you cut too deep and have no space for additional grooves you have to start over at the beginning. And it is very easy to cut the grooves too deep.

The grooves must be deep enough that the nozzle with the rings can slide into the motor tube with effort, but not so deep that the nozzle moves freely. The rings need to form a seal between the nozzle and the motor tube.

A parting tool usually works well for cutting grooves. Use calipers on a commercial nozzle to get an idea of what is needed for your nozzle. If you don't have a commercial nozzle, buy or barrow one -- or simply experiment until you get good fit. Each groove should be wide enough for the o-ring to fit inside, no wider, and about half of the width of the ring deep -- maybe more depending on your motor tubes and the O-rings you select.

If you go too deep on one and have enough space left, add another one or two grooves. In the 75mm nozzle I made for the flight shown in the video, I cut the second groove too deep and so added a third. A 54mm nozzle or smaller usually only has one groove.

After cutting the grooves, use a file to lightly round the edges of the cuts. This is not shown in the video.

Using the lathe and a center drill bit, mark the center of the nozzle with a pilot hole. If you have a large enough lathe to hold the nozzle and the drill bit and chuck simply drill through the entire length with the bit that is the same as the desired throat diameter.

If you don't have a large enough lathe, use a drill press to drill all the way through the nozzle blank using the pilot hole as a guide.

In the video I am using a larger lathe for this task.

Cutting the divergent cone can be a very time consuming task. You can use a boring bar with the lathe's compound angle set to the appropriate half-angle, or you can use an end-mill with the correct half-angle, or you can make a tool like that shown in the video which will cut the cone at the correct angle.

The most expensive and fastest cutting tool will be the end mill, but it is difficult to find these large enough for 75mm and up nozzles.

If you make a tool like that shown in the video, go slow. The tool cuts quickly through medium density graphite, but slowly through higher density material. In the video you will see at least once where the lathe stopped because I pushed it too hard and had to shut it off and restart it.

A piece of masking tape is showing in the video to mark the stopping point. Not shown in the video was the need to run a piece of sand paper briefly though the cone to smooth it slightly. There is some initial chatter in the video as the cutting starts, but that subsides quickly.

Cutting the convergent cone is almost identical to the process of cutting the exit or divergent cone. The same types of tools can be used. The video will show this being done (partial-speed-up and partially cut) using a homemade cutting tool with a 45 degree half-angle.

The cut is made until only the "Shoulder Width" remains.

It is a good idea to use sandpaper to round the edges between the convergent cone and the throat as well as the that of the divergent cone and the throat. If you did not allow for a "throat depth" be careful not to increase the throat diameter while rounding or cutting the cones.

You can use some 600, 800, or finer sandpaper to polish the nozzle gently while turning it in the lathe. After this the nozzle is complete. Double check the fit in the motor tube and if necessary *carefully* deepen the O-ring grooves.

The photos attached to this step show the nozzle that is now complete as well as how it is used to measure the liner tube and the motor tube. An inside view of the motor is provided as well.

Though the remaining details of building a motor are beyond the scope of this Instructable, I've added this step to show photos of the flight that utilized this nozzle that was made for this article.

Enjoy, and please always practice safety in all rocketry and making endeavors!