Designing Amateur Rocket Motors (Engines)

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Designing Rocket Motors

What is your motive?

What is your reason for wanting to build your own rocket motors? Is it to save money because model rocket motors or high power motors are SO EXPENSIVE? If that is your reason, you are wasting your time. If it is because you like the challenge of building something yourself, and you don't mind spending some money doing it, you might be on the right track. You don't have to spend thousands of dollars to get started building rocket motors but you might end up spending hundreds down the road because you want to either make more efficient motors or more powerful motors. One thing leads to another and you will soon be unsatisfied with what you are doing and will want to do something more. Many people eventually (if not sooner) decide they want a lathe so they can build their own reloadable casings. Then they wish they had a mill for making tools and test equipment and so on. Others have been content to build PVC motors with sucrose or sorbitol and potassium nitrate propellants. Note: sucrose propellant will crack from the pressure and stresses of accelerated rocket flight in larger motors. Sorbitol propellant is not as susceptible to cracking. Also, sucrose propellant motors are not allowed at Tripoli research launches.

What is your purpose?

Do you just want to build your own rocket motors and it isn't that important that they are the absolute most efficient? Then all you need is PVC motors and sucrose-KN propellant. Do you want the most efficient and most powerful motor to try for records or for contests? Then you want a metal casing and composite propellant. You can either build your own metal casings or you can buy your casings and nozzles and just make your own fuel loads. For now, I am going to focus on the simplest and easiest -- single use PVC motor casings with concrete nozzles and caramel candy propellant.

Design Tables Instead of Motor Design

For those in a hurry to try making some motors or who don't want to do the design but still want to experiment, I have listed all the specifications you need to know to build a variety of motors with one to six BATES grains and from 1/2" PVC through 1-1/2". To date, only the 1/2" and 3/4" have been tested. The larger motors may have a tendency to crack and CATO, so extra caution should be used while experimenting. The tables are the product of specific inputs to FPRE software. Click here for the tables.

Three approaches to motor design

If you are going to design everything from scratch, then you need to know a little engineering. You don't need to be an engineer, but you need to be mechanically minded and good at math. You can calculate everything by hand but since this is the age of computers, most everyone uses computer programs for the more difficult of the calculations.

You can approach design from three directions.

Design the rocket first, its dimensions, weight and the altitude and/or velocity you want it to achieve. From that you can calculate the total impulse needed for your rocket and from the dimensions of the rocket, figure out the maximum dimensions your motor can have. Finally, you have to figure out what propellant, will give you that impulse within those dimensions, and last, design the motor. This is a pretty complicated process.
Next option is to do the design in the opposite order. Decide on a total impulse and a motor type, design the motor, then design a rocket for the motor.
The easiest and the more normal route for beginners is to just decide what kind of motor you are going to build such as a PVC sugar propellant motor or reloads for a commercial reloadable motor, build some and see what you get. Actually, you can calculate everything about the motor and then see how close your motor performs to your calculations. This is the approach I will explain.

The first two design approaches are actually re-iterative. You will go through the calculations more than once, each time refining the design until you get what you want. In the first approach you may find you can't achieve what you want with the dimensions of the rocket and then you have to go back and try again. On the second approach you may find you can't build a rocket to attain the desired results with the motor you have designed. With either method, you need to have a ball park idea of what you can achieve. Obviously, you can't put a rocket into orbit with an ounce of propellant.

What you need to know

What kind of propellant are you going to make?
What kind of casing will you use?
What will you use for the nozzle?
Will your motor have a time delay and ejection charge?
What type of grains will you use -- Bates, C-slot, Moon-burner, etc.?
What, if any, surfaces will be inhibited?
What is the maximum designed chamber pressure?
What is the grain configuration and dimensions -- OD, ID, length?
How many grains will you use?
What is the area required for the nozzle throat?
Will the propellant be case-bonded?
Will you use a liner?
How will you seal the nozzle and header from the hot gases?

Design a 1" PVC Motor

Let's design a motor. Refer to the "What you need to know" and we'll answer those questions.

Propellant. We are going to design a motor using sugar and potassium nitrate. These are the easiest ingredients to get normally and have been used for scores of years.
Casing. For the casing we will use standard schedule 40 PVC pipe.
Nozzle Material. The nozzle and header will use Rockite anchor cement. It is very easy to work with, sets quick but not too quick (20 minutes), gives a nice surface finish on the nozzle, expands when it cures to make a better seal and is readily available. All cements and clays erode and so we will also use one or more steel washers so the throat diameter will remain fairly constant.
Time Delay & Ejection Charge. None. Since we are just getting started and want to just see if we can make a motor that works, we are not going to design in a time delay and ejection charge. We can do that later. For high power rockets, people usually end up getting altimeters or electronic timers anyway which both are much more reliable and precise than time delays built into the motor.
Grain Type. The standard type of grain used is a Bates grain and this is what we will use. (the name BATES is made from the BA of "ballistic" and the TES from "test" in BAlistic evaluation TESt motor). A bates grain is a cylindrical grain with a round core running through its length. The outside is inhibited so that it will not burn. Burning takes place on both ends and in the core. The grain dimensions are designed such that the total thrust is relatively constant. Actually, the beginning and ending thrust are about equal but is a curve that increases a little and then decreases in an arc between the two end points. The idea is to have the burn area as constant as possible since the area of the grain that is burning is directly related to the motor case pressure and so the thrust.
Inhibited Surfaces. Since a Bates grain by definition means that only the OD is inhibited, that answers question #6.
Chamber Pressure. The higher the pressure, the more efficient the motor will be (the higher the specific impulse will be). So we want the pressure as high as the motor will stand without rupturing or blowing out the nozzle or header. Looking at the pressures for 1" PVC pipe in the Misc. Tables, Schedule 40 PVC pipe, we find a maximum working pressure of 450 psi, a required minimum burst pressure of 1440 psi and a calculated burst pressure of 2220 psi. The working pressure is the industry standard maximum pressure the pipe is supposed to be subjected to at normal temperature. This is supposed to give a healthy factor of safety so that if the pressure goes some over that pressure, the pipe won't burst. The minimum required burst pressure is the industry standard minimum value of pressure at which the pipe will burst. Actually, this pressure is also lower than what the pipe will normally burst at. The calculated burst pressure is the pressure that has been calculated at which the pipe will actually burst under ideal conditions and this pressure is likely to be too high. Also, at elevated temperature, the strength goes down rapidly. Fortunately, these motors burn less than one second and so there isn't time for the heat to weaken the pipe very much. The larger the motor, the more affect the heat will have and at a certain point, the pvc pipe must be insulated with rubber to prevent the heat from weakening the pipe wall. At 1", the pipe does not need insulation. Also, the fact that the grain is inhibited and so won't burn on the outside helps to prevent the pipe from getting too hot, although the hot gases can still seep between the grain and motor wall. In the case of PVC motors and quick setting concrete nozzles, the nozzles will actually fail before the pipe will burst and the nozzle will be ejected. At higher pressures, the exhaust gasses can also start leaking around the nozzle and header and the motor wall. A good pressure to run in 1" PVC pipe is going to be around 350 to 400 psi and it will still depend on how the nozzle and header are retained and how well it is sealed against the pipe wall.

Grain Configuration. This is the point at which we actually have to make some decisions and do a little calculation. As a first motor, we are going to start with grains for a 1" PVC pipe motor. You can make motors from 1/2" or 3/4" PVC pipe but the smaller they get, the harder it is to load the propellant into them. A two grain 1" PVC pipe motor will make a motor in the high F range which may be higher than what you want for starters but is actually easier to make. A Bates grain has the OD inhibited so we are going to make a glued paper inhibitor sleeve and cast the propellant into that. For 1" PVC, you can use regular typing paper but card stock is better and easier because it takes less wraps. The larger the grains, the longer the burn time and the thicker a paper inhibitor sleeve must be. 90# card stock is .005" thick. Regular typing paper or printer paper is about .002 thick. The inhibitor sleeve should be around 3%-5% the thickness of the web of the grain (distance from the inside surface to the outside surface of the grain. From Misc. Tables, Schedule 40 PVC pipe we find the ID of a 1" PVC pipe is 1.033". For a .25 It also depends on the pressure. It is not worth doing all the calculating yourself. You need a program that will calculate the pressure and thrust given a certain geometry of grain. I use FPRED by CP Technologies (John Wickman's Company) which you can get for $19.95 at http://www.space-rockets.com/fpred.html. A free online calculator is available from Scott Fintel. I find the thrust and impulse results from his to be higher than what I actually achieve with sucrose potassium nitrate motors. He doesn't have a place to input efficiency and the efficiency he uses in his equations seem to be high. See the links page for more software sources. I have compiled some information taken from this software that you can use without the program or to get some starting values for the program (see Motor Design Tables). Using the program is an iterative process. You plug in values, click on calculate and see what the pressure is for the parameters you put in. If it is not what you want, you adjust the parameters and try again. Normally, you will choose the number of grains, the OD of the grain, the length of the grain and the core diameter. Then you will try a nozzle throat diameter and calculate. You then adjust the nozzle diameter up or down to change the pressure. If the throat diameter becomes larger than the core diameter, you have to increase the core diameter. When you have the right pressure, you plug in the optimal exit cone diameter that the program calculates for you back into the exit cone diameter in the Nozzle Properties section and do one last calculate. If you are doing Bates grains, you ignore the C-Slot width & depth and Moon burner offset. You also click on "No Ends" under "End Restrictions". Once you have the OD and Bore Diameter, you can click on "Neutral Length" and it will calculate the proper length of the core for you and put that number in the "Bore Length" cell. I usually adjust this to an even 1/8" just to make it easier to make and measure. The neutral length for a bates grain (OD inhibited, full length core, no ends inhibited) is easily calculated. It is 1.5D + 0.5d where "D" is the outside diameter and "d" is the inside diameter. So for a 1" OD, .25 ID you calculate 1.5 X 1 + .5 X .25 = 1.5 + .125 = 1.625" long.

To use this software, you need the following information:

Sucrose Sorbitol Dextrose

Propellant Properties Density (lb/in³) .0683 .0658 .0679

C-Star (ft/sec) 3106 3076 2993

Gamma (or "k") ratio of specific heats 1.044 1.042 1.043

Burn Rate Coeff. (in/sec) .0665 .0400 .02485

Burn Rate Exponent .319 .348 .4531

Comb Eff. (%) 75 75 75

Nozzle Properties Throat Dia (In.) Experiment to get the right pressure.

Exit cone Dia. (In.) Pick a number about 1.5 times larger than your throat diameter and then when you have the pressure you want, move the optimal calculated exit cone diameter to this field and do one last calculation.

Exit Cone Angle (Deg)
15

Fixed Cf
0

Ambient Pressure (psia)
14.7

Radial Throat Erosion (Mils/Sec) 0 if you use washers, will vary if you don't. Try 15 and then measure from experiments

Exit Cone Eff. (%) 90 is a good guess

Grain Properties Outer Dia. (In.) The ID of the PVC pipe you are using minus twice the inhibitor sleeve thickness. 90% of the ID should be close.

Bore Diameter (In.) A little larger than your nozzle throat diameter -- pick a size that you can get material for, usually 1/16" increments up to 3/8" and then 1/8" increments.

Bore Length (In.) Calculate using formula or "Neutral Length" button in software.

Number of Cartridges 1 to usually a max of 6 -- your choice

Erosive Burn Click on if your core area is close to your throat area. The rule is you have erosive burning if your core cross sectional area is less than twice your throat cross sectional area. It doesn't actually change the calculated output much.

Ignition Time (Sec) Use 0. If you put a value in, the software will spread out the total burn time and will calculate a lower pressure and thrust. You want to know the highest pressure possible to make sure that is low enough to not burst your case.

Number of grains. Start testing with just one or two. As you increase the number of grains, your nozzle throat diameter will increase and you will also have to increase the core diameter. Alternatively, if you plan on testing a maximum number of grains, say, six, then figure out the minimum core size that will be larger than the throat with that number of grains and then make all your grains with that core diameter. It is surprising that you won't loose that much total impulse over the minimum core diameter for just one grain.
Nozzle throat diameter. Get an idea of the throat diameter for what you are designing by looking at the design tables page and then modify that until the software calculates a pressure that is appropriate.
Case Bonding. Case bonding is a different style of grain and is not a bates grain except if the overall length is the neutral length for one Bates grain. Case bonding is when you don't use an inhibitor sleeve or a liner. You cast your propellant directly into your motor case so that the propellant sticks to the inside surface of your case. If the grain is longer than the neutral length, your motor will have a progressive burn which doesn't necessarily mean your rocket won't go as high. This is not an uncommon practice and is much simpler because you don't have to deal with liners. However, for a longer motor, it is more difficult to get the propellant evenly distributed without voids, especially with smaller motors.
Nozzle and Header sealing. Part of the experimenting is to see if you can make a motor that doesn't leak exhaust gasses around the header or nozzle. The higher the pressure, the more likely this will happen. Just a little more pressure and you will usually eject the nozzle or header or both. The most common method of sealing a PVC motor with concrete nozzles and headers is to use RTV which is the high temperature red silicone like sealant you can get at any auto parts store for use with gaskets. This is a little tricky to apply (and messy). You have to get a bead around the junction of the concrete with the PVC case on the inside. This is done with a long stick. You have to be careful not to get it up on the wall or you won't be able to get your grains all the way in. After you put your grains in, you can put a piece of foil on top of the last grain and then put a ring of seal around that and let it dry before you pour in your header concrete.

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