By Tim Van Milligan
This article is available in printable form in two parts:
Introduction: If you've been in rocketry for a while, then this article will be pretty basic; but you might learn one or two new things. It tells how two stage rockets work, and how to design your own multi-stage rockets. I've decided to write this article because people have been telling me that web based information is lacking on this subject. So hopefully this article will help someone that wants to build a two (or three) stage rocket.
From the book: Model Rocket Design & Construction, we see this definition: "A rocket having two or more engines, stacked one on top of another and firing in succession is called a multi-stage. Normally each unit, or stage, is jettisoned after completing its firing. The reason rocketeers stage models is to enable the uppermost stage to attain a very high altitude. This is accomplished by dropping mass throughout the burn so the top stage can be very light and coast a long way upward."
There are two methods of staging rocket motor. They describe the way the upper stage(s) are ignited, and will be described in this article. The easiest method is called "direct" staging, where the lower stage motor ignites the upper motor. Most of this article will describe "direct" staging.
The second method is called indirect staging. In this method, the upper stage motor is ignited by some other device (not the lower stage). The device used to ignite the motor is a separate ignition system that is carried on the rocket. This method was discussed in Apogee e-zine newsletter 91 (Oct 28, 2002). http://www.ApogeeRockets.com/education/
Indirect staging is used on rockets that are larger than a D engine; because the lack of large special booster engines required for the direct-staging technique.
In direct staging, the lower "booster" stage motor ignites the top motor in the rocket. From the modeler's perspective, direct staging is simple and cheap. You don't need any complicated electronics or launch support equipment. The reason it works is explained by the physical make-up of the rocket motors.
The drawing in Figure 2 shows a cut-a-way drawing of a typical black-powder propellant rocket engine. The typical rocket engine has a special slow-burning propellant that burns after the propellant is consumed. This is called the "delay grain." It burns slow, which allows the rocket to coast upward before the parachute is blown out of the rocket by the ejection charge. The delay also spews out a lot of smoke while it burns, which makes the rocket easier to track as it ascends into
In the special "Booster" stage motor, there is no delay grain, nor ejection charge. It only contains the fast-burning propellant.
When the propellant burns upward toward the top of the motor, it throws a lot of heat and burning particles forward as it finishes its burn (see Figure 3). The hot gases and the burning particles go forward into the nozzle of the upper stage. There is so much heat that comes out of the booster motor, that the top stage instantly ignites (see Figure 4). It doesn't need a separate starter, because the heat from the lower motor supplies the energy to get it to
Really, the black-powder propellant "booster" motor is exactly the same as an upper stage motor. The only difference is that the booster motor does not contain the special delay composition. If you look into the front end of a booster motor, you'll see the hard black surface of the propellant. In comparison, a regular rocket motor that has a delay will have a top end that is capped with grayish looking clay (see Figure 2).
By not having a delay element incorporated in the booster motor, we get ignition of the top stage nearly instantaneously after all the propellant in the booster has burned out. There is a good safety reason for this. If there were a delay between burnout of the booster, and ignition of the upper stage, the model could arc over. So it might not be pointed vertically when it ignites. This is a serious safety hazard, and should be avoided.
For direct staging to work properly, there must be several conditions that have to be met.
To start, the two motors in the rocket have to use "Black Powder" propellant. Why? Because black powder motors burn linear; from the nozzle end toward the front end. This is important, particularly for the special booster motor. The propellant itself becomes a bulkhead; which is needed to hold the pressure inside the rocket engine. Without internal pressure, thrust wouldn't be created.
In a booster stage motor, the propellant that hasn't burned yet becomes the bulkhead that holds the pressure inside the motor. As it burns, the bulkhead becomes thinner and thinner. When the flame nears the top, bulkhead becomes so thin that it can't hold the pressure, and the bulkhead bursts. This is what throws the hot gases and the burning chunks of propellant forward (see Figure 3).
In a composite propellant motor, the actual propellant is soft and rubbery. It can't hold back any internal pressure. That means it can't be used as its own bulkhead like the rock-hard black powder propellant. Composite propellant motors always need to have a solid bulkhead made from another material to hold the internal pressure of the motor. This solid bulkhead prevents composite propellant motors from being able to be used as "direct" staging booster motors.
Another problem associated with composite propellant motors is that they require high pressure to sustain the burning process. You've probably seen a cato of a composite motor that ruptures right at ignition. When this happens, the motor snuffs out. The remaining propellant doesn't burn. It just falls to the ground as a chunk of rubber.
What this means is that even if the propellant could act like a structural bulkhead, as soon as the flame reached the front end and broke through; it would immediately snuff out. The likelihood of hot gases and burning chunks being thrown forward out the top is greatly reduced.
The reason the top stage must have a black powder propellant rocket engine for direct staging to work is because the flammable substance inside the upper motor must be near the nozzle. The gases and the burning chunks eject forward from the booster motor have to come into contact with the propellant of the top stage. In a black powder motor, the propellant is right inside the nozzle opening.
Compare this to a composite propellant motor. Here, the propellant has a hole right through the middle -- from the nozzle all the way to the forward bulkhead. So there is less of a likelihood that the gasses are going to make it up into the motor. You'd think it would be possible to ignite, because the gases are so hot. But it doesn't.
An example is easily illustrated by blowing through a straw. If the straw is open all the way through, you can easily blow air through it. But if you block the front end, no matter how hard you try, you can't get any new air to go into it. This is very similar to a composite propellant motor. The hot exhaust gases coming up from the booster stage never make it into the middle of the motor. (Figure 5)
But a black-powder motor has propellant that is very close to the nozzle end. So some hot gases and burning chunks have a very high likelihood of making it into the top stage to ignite the propellant.
The other condition that needs to be met with direct staging to work is that the distance between the motors has to be fairly short. The hot gases from the bottom motor have to stay hot until it reaches the top stage. If the distance between motors is too great, the gases may cool to the point where it isn't hot enough to start the top stage burning. So the closer the motors are together, the easier it is to get a successful staging.
If the motors are in direct contact like shown in Figure 4, then it is customary to tape the ends of the motors together using cellophane tape. This prevents separation of the motors for a split second, allowing the gases enough time to ignite the upper stage motor. When staging occurs, the tape simply melts apart, allowing the stages to separate after a successful ignition of the upper stage.
The vent hole should be about 6.35 mm (0.25 inches) in diameter, and even smaller if you use more than one hole. Place the hole as close to the bottom of the upper stage as possible. This will allow the hot gases to push all the cool air out of the inter-stage tube.
When the rocket is "minimum diameter" the method of coupling the stages together can only be done one way. That is the aft end of the upper motor must be inserted into the front end of the lower stage. This is shown in figure 7.
Since we have to insert the booster stage from the forward end, we might as well put a engine block in the back end of the stage to prevent the booster motor from spitting out the back when the rocket stages. This is much simpler than trying to install an engine hook on the booster stage.
The other advantage of this method is that it allows us to tape the motors together. The practice of taping them together goes way back to the beginnings of model rocketry. The tape holds the motors together insuring that the top stage ignites prior to the bottom stage falling away. The heat and flame coming out of the top stage is what melts the tape in half, which allows the bottom stage to fall away.
The procedure for installing the motors then would go like this:
First, tape the motors together, with the booster engine on the bottom. Use only one layer of tape. Note: Cellophane tape is preferred over masking tape, because it melts at a lower temperature.
Second, add masking tape around the outside of the booster stage motor. The purpose of the tape is to create just a little bit of friction to prevent the booster engine from falling out of the stage as it tumbles to the ground. It isn't like friction fitting to keep the motor from popping out at ejection; since the thrust ring does that. It is just keep it from sliding forward as it tumbles to the ground.
Third; friction fit the upper stage motor into the tube of the top stage using masking tape. This time, you'll need a lot of tape to make sure the motor doesn't move reward when the parachute comes out of the top stage.
Because of the friction fitting of the motor into the upper stage, this method does have a drawback. It may be hard to remove that motor after you get the rocket back. It would be better to secure the motor differently.
What this means you'll have to make the diameter of the upper stage bigger to accommodate some type of engine restraint. Personally, I prefer to tape the upper stage into the engine mount tube as shown in Figure 9. If you used any type of engine hook, the nozzle would be just that little bit more further away from the lower motor.
This method of using a coupler on the lower stage that enters in the base of the top stage is the one that I prefer. The big advantage is that the stages are aligned straighter than if you just use the engine as the coupler (See Figure 7). In that method, the bottom stage can decouple too easily and the rocket may have excessive tip-off at the point of staging.
The biggest drawback is that the tube has to be larger in diameter to accommodate the coupler. The larger the diameter, the more drag the rocket will experience; so it won't fly as high.
Many competition modelers have discovered that they can still make rockets that are fairly small diameter to minimize the drag. See Figure 10.
The key to the design are the engine mount tubes. In the bottom stage, the engine mount tube extends out both the front and the back. The front portion acts as a tube coupler. It is inserted into the top stage to join the parts together. Since this tube fits over the aft end of the upper stage's rocket motor, the coupler joint is twice as strong. It grips the outside of the motor, and the inside of the tube.
Because of this arrangement, the motor mount tube of the upper stage has to be recessed deep into the top stage (even though the aft end of the engine hangs out the back). This really isn't much of a problem. It just means that the front part of the engine is holding the motor in place.
The only drawback in this near minimum diameter design is that the top stage engine has to use the friction fit method to hold it in the stage. I would prefer a mechanical method of engine restraint, but it is acceptable for most small motors like those used in rocketry competitions.
In the last issue, we talked about using gap staging when the motors were not in direct contact with each other. Figure 11 shows how this is accomplished when you are using larger diameter tubes.
The first thing to note is that there are holes in both the outside tube, and the motor mount tube. This allows the gasses of the booster stage to exit the rocket, instead of pressurizing the volume between the two stages. If there were no holes in the outside tube, the stage would pop off without igniting the top stage motor.
The other thing to notice is that the rear centering ring in the top stage is recessed deep within the tube. This is done to allow the tube coupler to be inserted into the top stage to join the stages together.
The motor in the top stage can be taped into the mount, like is shown in figure 9. Just be certain to design it so that the tape doesn't interfere with inserting the engine into the tube in the bottom stage.
Whenever we add more engines into a rocket, we introduce more chances for things to go wrong. Since we want to maintain a safe flight, we should do everything possible to increase the reliability of the flight. First off, we want to make sure the rocket does actually stage. We don't want the top stage coming in ballistic. For this reason, we never use more than three stages in a model rocket design. Also, the more stages in a rocket the more likely it will weathercock in windy conditions. Therefore, a four-stage rocket is just too risky, and should never be flown.
As mentioned previously, we should also make sure the stages are joined together correctly, and they can only separate in a straight line. This will prevent tip-off. Whenever possible, have a coupler join the stages together, instead of just using the end of the rocket motor.
Rocket motor selection is of critical importance. If your model comes off the launch rod with insufficient speed, it will weathercock severely. From a safety standpoint, we desire the rocket to go straight up, not horizontally. The motors you select for your rocket will determine the trajectory of the flight.
For more information on how to select rocket motors, please read the short series of articles that appeared in this e-zine beginning with Peak of Flight Issue #38.
Another element that will affect the trajectory of the rocket is the size of the fins. The determine the Center-of-Pressure (CP) of the model.
The way to determine the fin size on multi-stage rockets was also presented previously in the Apogee e-zine newsletter beginning with Peak of Flight issue #96.
Launching multi-stage rockets always requires more caution and attention to detail than single stage models. Here are some general tips:
1. Have a larger flying field. These models will fly higher, and therefore drift further with the wind. The larger the field, the better your chances of getting the model back to fly it again.
If you use RockSim to estimate the drift distance of the model, you'll quickly see that on a day with a 10 mph wind, the rocket will land roughly two times further away than it goes straight up. So if you expect the rocket to fly 1000 feet into the air, it will most likely land 2000 feet down range. You can reduce this by using a smaller recovery device in the top stage, or by angling the rocket slightly into the wind.
2. Multi-stage rockets are significantly more susceptible to weathercocking than single stage models. So use caution when there is even the slightest breeze. You may want to cant the fins on the booster stage slightly to give it some rotation. While this will lower the predicted altitude, it will give you a straighter flight.
3. A trick that modelers have been using for decades is putting a spill hole in the parachute of the top stage. This allows the rocket to descent faster, so it doesn't drift as far.
4. To help make your rocket easier to spot, you should use tracking powder in the top stage. Tracking powder is any nonflammable powder placed inside the rocket that is ejected at apogee into a large puff or cloud. The cloud can help you to locate your rocket at a very high altitude. Some powders that work well for this include tempera paint, chalk dust, and talcum powder. The colors that seem to work best are black for cloudy days and red when the sky is blue.
In the book "Model Rocket Design and Construction," you'll find additional information about staging model rockets. The book gives helpful information on: booster stage recovery devices, C.H.A.D. Staging, gliding booster stages, and finally indirect staging techniques
It should also be noted that we have previously discussed how to design the stage so it tumbles to the ground, and how big we can make the booster stage (in case we want to up-scale an old design). These articles can be found listed in the bibliography at the end of this article.
Apogee's Educational Information - You should always start at this web site first. It has lots of links to other sites that have information about staging model rockets. http://www.apogeerockets.com/How_2-Stage_Rockets_Work
How rocket engines work. http://www.apogeerockets.com/education/Education/How_Rocket_Engines_Work
How To Make Your Own Rocket Motors - Are you looking for formulas and instructions for home-brew rocket engines?
How composite propellant rocket engines work. http://www.apogeerockets.com/education/How_Composite_Rocket_Engines_Work
How to select rocket engines - a step-by-step guide. Click Here. This report tells you how to use the RockSim software to pick the "best" rocket motor for your own designs.
Design, Construction, and Flying Strategies for Achieving Maximum Altitudes. While this article doesn't directly deal with multi-stage rockets, it does have lots of information that carries over to multi-stage rockets. Apogee E-zine newsletter #75. http://www.ApogeeRockets.com/downloads/Newsletter75.pdf
Electronic Staging of Composite Propellant Rocket Motors - This article explains how to do indirect staging Apogee E-zine newsletter #91. http://www.ApogeeRockets.com/downloads/Newsletter91.pdf
How To Design Tumble Recovery Booster Stages - This article talks about how to arrange the parts so the stage will begin tumbling on its own. Apogee E-zine newsletter #96. http://www.ApogeeRockets.com/downloads/Newsletter96.pdf
How To Design Tumble Recovery Booster Stages - Part 2 - This article shows you how to determine the rate of descent of the booster stage. It is particularly useful when up scaling old kits into larger high-powered rockets. Apogee E-zine newsletter #97. http://www.ApogeeRockets.com/downloads/Newsletter97.pdf
In-line vs interdigitated fins: which is better for multi-stage rockets? Apogee E-zine newsletter #97. http://www.ApogeeRockets.com/downloads/Newsletter97.pdf
Optimum Mass - Squeezing Out Every Inch Of Altitude. - This article talks about using the delayed staging technique to get higher altitudes out of multi-stage model rockets. Apogee E-zine newsletter #84. http://www.ApogeeRockets.com/downloads/Newsletter84.pdf
Parallel Staging - Apogee E-zine newsletter #94. http://www.ApogeeRockets.com/downloads/Newsletter94.pdf
Model Rocket Design & Construction. By Timothy S. Van Milligan. Published by Apogee Components, Inc. ©2001. Available at: http://www.ApogeeRockets.com/Rocket_Books_Videos/Books/Model_Rocket_Design_And_Construction
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