I got a surprise gift in the mail from my friend Joe Barnard this week - a Signal Alpha thrust vectoring kit!
This was such a nice surprise, and I'm not sure what I'm going to do with it yet. I have no experience with this sort of technology, apart from watching Joe launch his rockets. This is a new frontier in hobby rocketry, and I had to do something right away.
I met Joe about a year and a half ago, while he was trying to build a model rocket which would not only stabilize itself through thrust vectoring - the kind of finless, active stabilization used by real space launch vehicles, where the rocket adjusts the direction its engines are pointing, to keep the rocket upright in flight, like balancing a broomstick on your fingertip - but also land under thrust, using a second hobby rocket motor. The idea was to create a working model rocket which flew and landed a bit like SpaceX's Falcon rockets.
Joe Barnard prepping an early version of Scout at the first launch I witnessed.
The landing legs
An early version of the gimballed motor mount with ascent and descent motors.
Other than that one obsessive project, he wasn't really into model rocketry.
But I got to tag along to a few test launches, some more successful than others.
Eventually, Joe came with me to a few NAR club launches, and to my surprise, decided to go for a Level 1 high power certification, which he successfully completed with his scratch built rocket, Thrusty McThrustface, on his first attempt.
We've been working on a story about Joe for some time on The Rocketry Show podcast. As he got better and better at thrust vectoring, he eventually decided to see if he couldn't make a commercial thrust vectoring kit available.
Well, guess what - he's done it.
Signal Avionics, his thrust vectoring system, is apparently ready for a limited, experimental release to the public. A small run of 30 units will soon be ready to ship! The system costs $299, and is only available in the United States for now. But this is some exciting stuff. To reserve a unit, click here and fill out the form.
(For the curious and the cautious out there, sometimes folks in online forums have suggested that active stabilization violates the NAR Model Rocket Safety Code - or worse, the law. Neither of those is true. While aiming for a target is against the rules, active stabilization is not. The Signal Avionics isn't a "guidance" system, and can only be used to keep a low to mid power rocket upright in flight. Joe has had discussions on this subject with the leadership of both the National Association of Rocketry and the Tripoli Rocketry Association, and there simply is no safety code or legal violation here. Of course, all other MRSC guidelines should be followed when flying an actively stabilized model rocket, but the homework has been done. Also note, Signal Avionics is not currently available for high power rocketry - baby steps!)
I'm really glad I got to witness a lot of this firsthand. It's been really exciting to see!
Illustration from the cover of Centuri TIR-33, by James S. Barrowman
This is a continuation of a series on model rocket stability for beginners. Click here to go to the beginning of the series. Click here to go to the last post.
Each year, since 1958, the National Association of Rocketry holds an event called NARAM - the NAR's Annual Meet. This is a large competition, with fly offs for things like altitude, duration (how long a rocket can stay in the air on a parachute or streamer), scale modeling, craftsmanship, etc.
There's also a Research and Development competition, or R&D. Competitors present research projects into some aspect of model rocketry they've been examining.
Research topics can be very basic or pretty esoteric. They may be focused on a highly technical aspect of rocketry, or perhaps on the craft of rocket building. An R&D project might examine some very specific problem only of interest to competition rocketeers, - for example, the effect of a piston launch pads in altitude competitions, or new exotic building materials for boost wing gliders - while others are more general and concern issues many modelers face.
NAR R&D reports have added much to the knowledge base of model rocketeers and expanded our horizons. While some reports are of interest to only a few people, there are others which really make a large impact on the hobby.
In the next couple of posts, we're going to discuss the one research project that has probably benefited every single rocketeer since it's submission in 1966.
* * *
In the early days of model rocketry, as we've discussed in the previous posts, rocketeers ensured that their designs would be stable by using a somewhat crude but effective method using a two-dimensional cutout drawing of their designs. By balancing the cutout, the center of lateral area could be found, which was also what the center of pressure would be if the rocket were flying at an angle of attack of 90 degrees - sideways into the wind, in other words.
We also saw hints, through the pictures, that the true center of pressure during flight is in fact far aft of what the cutout method indicated.
But if the cutout method worked, why bother with a different method? It may have been crude, sure, but it worked, and the rockets resulting from its use were stable, so what's the problem? And how do we know where the true Center of Pressure is, anyway?
Well, it turns out that the engine driving the search for a new method of determining CP was competition. Specifically, NAR competition rocketry.
While a model built using the cutout method is certainly stable, it is actually quite unlikely to fly as high as it might. There are three main reasons why: weight, drag, and weathercocking.
Weight
The cutout method shows the hypothetical center of pressure much further forward than it actually is. In our illustration, using a quickly designed model - Sounder IB - we saw that while the Center of Gravity (CG) was a ahead of the CP in our simulated design and the rocket would therefore be stable, if I'd simply used the cutout method, the CP would have seemed to be so far forward that it was ahead of the CG. If all I had to go on for finding the CP was the cutout method, I'd worry the rocket would be unstable, and I'd have to modify the design.
One way to fix this would be to shift the CG forward, until it was at least one body tube diameter (or caliber) ahead of the CP. To do this, I'd need to add some weight to the nose end of the rocket. I could do this a number of ways. If I had a plastic nose cone, I could stuff it with clay and ram it into place with a dowel rod until the rocket balanced where I wanted it to. (If you have built certain Estes kits, you may be familiar with this method). With a balsa nose cone, I might drill a hole in the shoulder of the nose cone, and fill the hole with either clay or fishing weights, and then some glue to keep everything in place.
With 15 grams of nose weight, the CG shifts forward, but the rocket pays a penalty by losing altitude -
a little over 100 feet. If this were a competition model, those extra feet could make a big difference.
The point is that in order to know my rocket would be stable, I'd have to add a significant amount of weight to the rocket - probably 10 grams or more - and with a rocket as small as Sounder IB, that would add up to a significant weight gain - and altitude loss.
Drag
Another way I might fix Sounder IB's stability problem would be to shift the CP aftward. To do this, I would need to increase the size of the fins. (I could also increase the number of fins, but as we saw with the quickie designs I drew up with the three, four, and six trapezoidal fins, the cutout method might not indicate a change in CP.)
Increasing the size of the fins would, though. I'd have to make a new drawing with larger fins, cut that out, find the new CP, and hope the CG of the finished model would be forward of that.
Increasing the fin span would shift the CP aftward, but the increased
aerodynamic drag would again cost the rocket over 100 feet in altitude.
Using larger fins creates more drag, or wind resistance (as does adding more fins). Drag can be a powerful force which tries to stop a rocket in flight. Because of that, a rocket with larger fins will not fly as high as one with smaller fins.
Weathercocking
All model rockets will tend to arc into the wind somewhat. Some do it only a little, and fly mostly straight until they get near apogee, when the rocket is slowing down, and then arcs into the wind.
Other rockets arc into the wind much more, so that flights are rarely straight up, and more often form a large bow in the sky.
This phenomenon is known as weathercocking, and is caused by the same things which make the rocket stable in the first place.
As a rocket flies upward, its angle of attack is near zero degrees. But in reality, it's never completely zero degrees. Crosswinds flowing parallel to the ground combine with the apparent wind coming directly nose-on to the rocket. If a rocket is flying 200 miles per hour upwards, and the wind is only, say 10 miles per hour from the east, you might think the wind felt by the rocket from the front would overwhelm the wind coming from the side, and the rocket would only experience wind from straight ahead. The rocket may oscillate back and forth as it stabilizes itself, but generally it's only going to feel wind coming from one direction - upwards.
In fact, a consistent, light breeze from one direction will combine with the wind from the front, and as the rocket oscillates back and forth, it will tend to curve into the wind. This happens to some degree with most rockets on most flights. However, it's more apparent on 1) really windy days, or with 2) slow-lifting rockets, or on 3) overstable rockets.
In Part 4, we mentioned that the ideal static margin of stability is 1-2 caliber. A higher caliber of stability is usually OK, but it will lead to more weathercocking. Why?
Think of a rocket as a lever. The Center of Gravity is the fulcrum. The CP is where you grab the lever to do the lifting.
If you have a short lever, it's harder to lift things with it. But a longer distance between your hand and the fulcrum means it takes less force to move the lever.
Archimedes claimed that with a long enough lever and a place to stand, he could move the Earth.
So a rocket with a longer distance between the CG and CP means it takes a lot less force for the wind at a slight angle of attack to cause the rocket to arc over.
Going by the cutout method, you're going to build a rocket with a much longer lever than you think. You might think you have a 1.5 caliber static margin, but it may in fact be 3 or 4 caliber. You're giving the wind a much easier task of weathercocking the rocket.
And of course, a rocket which expends all its energy in going straight up is going to reach a much higher altitude than one which arcs over into the wind.
Note: While weathercocking is normal in rockets, sometimes it's bad enough that it can be a little scary. The first time I flew my Estes Big Bertha, I was unfamiliar with this concept. The Bertha has very large fins, and it was a pretty windy day. The rocket flew almost horizontally before taking a nose dive - straight at a dog park! Fortunately, the chute opened at the last minute, and the rocket drifted back to the field.
The Bertha is pretty lightweight, and I actually don't think there were any dogs at the park at the time, so it was probably not a dangerous situation - but it certainly scared me at the time! I enjoy looking back at that video now, because my reaction was pretty funny, but I've never posted it online, because in my panic, I used a lot of language.
We'll talk more about weathercocking and how to minimize it in an upcoming post.
* * *
With these limitations, it was clear we needed a better method of reliably finding the CP on a rocket design before building. For competition modelers, this was vital.
One particular section of the National Association of Rocketry - NARHAMS, of Maryland - had a lot of competitive rocketeers. They also had one huge advantage - a particular club member they could turn to to ask for help.
His name was James S. Barrowman. Not only was he a member of the National Association of Rocketry, he also happened to work for NASA, with the sounding rocket program. Perhaps he would be able to help.
We'll talk more about James Barrowman and his solution in the next post.
This is a continuation of a series on model rocket stability for beginners. Click here to go go the beginning of the series. Click here to read the last post.
Last time, we discussed the earliest method of finding the Center of Pressure (CP) on a model rocket - the cutout method. This simple method ensured stable flights on every model in the early days of model rocketry. Finding the CP is a crucial problem to solve, because in order for stable rocket flight,the CP must be behind the Center of Gravity (CG).
But, of course, the cutout method had drawbacks. Rocketeers had to be reasonably skilled at drawing an accurate representation of the rocket on stiff paper or cardboard, with all the parts in correct proportion. In other words, in order for the cutout method to work the drawing had to look just like the real thing.
Since I'm not a skilled draftsman, I cheated a little. I illustrated the cutout method with a design I'd created in OpenRocket - Sounder IB - which I printed on heavy card stock, cut out, and balanced on a piece of aluminum angle.
This showed us another drawback of the cutout method - accuracy. While balancing the two-dimensional cutout of Sounder IB did find the center of area for the rocket, that point was far forward of the red CP mark on the drawing itself. In other words, OpenRocket told me that the CP was in one spot, but the cutout method indicated that the CP was a good two inches further forward. So far, in fact, that the CP as determined by the cutout method was in front of the CG, as calculated by OpenRocket.
So, while the OpenRocket design showed the rocket to be perfectly stable, the cutout method showed me a dangerously unstable rocket - one which would flip violently around if it were launched!
So, does the cutout method represent the Center of Pressure at all? Or were rocketeers merely fooling themselves? And how do we - how does OpenRocket - know where the CP actually is? Who's right, who's wrong, and why?
The answer is that they're both right - kind of.
In the cutout method, we're balancing a 2D representation of the rocket - on its side. The cutout is resting on its balance point, so as the force of gravity pulls on it, the force is equally distributed in front of and behind the aluminum angle. This force - gravity - is acting a substitute for another force - air pressure - in the real rocket. So, for the cutout method to represent reality, the air pressure would have to be hitting the rocket directly from the side. The cutout method shows you were the CP would be if the rocket were flying sideways!
In this case, that means that all the air is hitting the rocket from the side - at an angle of 90 degrees. The angle the wind is hitting a rocket is known as angle of attack.
Alpha represents the angle of attack. Image from Centuri TIR-30, by James Barrowman.
In The Handbook of Model Rocketry, a 90-degree angle of attack is described as "the worst possible flying condition." In fact, it's an imaginary flying condition, because rockets do not fly sideways. They fly pointy end first!
Under normal flying conditions, with the proper motor (providing enough thrust for the weight of the rocket), model rockets fly at or near zero degrees angle of attack. While the ambient wind tends to blow horizontally along the ground, the rocket flies fast enough upward that the effect of the wind is minimized. If the wind on launch day is, say, 8 miles per hour, and the rocket is flying upward at, say, 200 miles per hour, the rocket will barely notice the wind coming from the side.
Under those conditions, the determination of the Center of Pressure is dominated much more by the fins and nose cone than by the surface area of the body of the rocket. As the rocket wobbles during flight - totally normal for a model rocket - the angle of attack will swing back and forth between zero and a few degrees. As this happens, the fins, which stick out from the body of the rocket, use the oncoming air pressure to correct the rocket's path, causing the back end to rotate away from the wind.
The pressure on the body tube at or near zero degrees angle of attach is much lower, and has much less effect on the CP.
But if the angle of attack were to suddenly increase significantly, then the air pressure on the nose cone and body tube becomes much more significant. The effect is that, at high angle of attack, the Center of Pressure moves forward. If, due to some (imaginary) catastrophic event in flight, the rocket were to fly sideways, then the CP would move forward enough that it would be where we see it when we do the cutout method.
As angle of attack increases, the influence of the nose cone and body tube increase -
the CP moves forward! Image from Centuri TIR-30, by James Barrowman
There are only two situations I know of when a normal rocket experiences these conditions. The first is when the rocket is sitting on the launch pad, and the breeze is blowing across the field. But when the rocket is sitting still on the pad, it's not flying, so this doesn't count.
The other is a rare, pretty strange event, which I've seen twice - recovery.
Once in a while, a rocket will launch, fly to apogee, and then due either to an ejection charge failure or a nose cone which is stuck on too tight, the nose cone doesn't eject. The rocket stays intact, the parachute does not come out, and the rocket begins to fall back to Earth.
Normally, when this happens, it's pretty frightening. Because the rocket is stable, with its CG in front of its CP, it will tend to fly nose first. So a rocket which has an ejection failure usually comes in ballistic - taking a nose dive straight at the ground with increasing speed. This usually destroys the rocket.
Sometimes, very rarely, an odd thing will happen. The rocket will go up, tip over at apogee, and begin falling back down. In rare instances, the CP at 90 degrees angle of attack will be the same spot as the rocket's CG. The rocket is then neutrally stable. The forces of gravity and air pressure are both centered on the same spot. The rocket descends sideways. Since the Center of Gravity is the point of rotation, and the Center of Pressure is the balance point of the force of the air of the rocket, the whole thing is in balance - just like a balanced scale.
If she weighs the same as a duck...
Both times this happened, the rocket fell very slowly, and came to a soft landing. Both times, I was filming, but both times, I was so stunned, I missed getting the slowly descending sideways rocket in frame. But it was pretty cool - and certainly a relief not to have the rocket come in ballistic.
I should mention that you shouldn't try to replicate this, by gluing on a nose cone or something. It's a chance event when it happens, and the same rocket might not do it twice - a slight difference in Center of Gravity could change everything, and the rocket would come in ballistic. But if you do see it, it's kind of amazing.
* * *
The fact that the CP can shift forward is really important. It means that the CG and CP could be too close together for the rocket to remain stable. If the angle of attack suddenly increases, due to a gust of wind, or off-center thrust of the motor, or any number of things, having the CG too close to the CP means that under certain circumstances, the CP could move forward of the CG! If these two switch position, you now have a dangerous, unstable rocket.
This brings us to the question How far forward of the CP chould the CG be? I was going to save this for a later part of this series, but I think it makes sense to mention it here.
In general, the rule of thumb is that the CG should be at least one body tube diameter ahead of the CP. That means that if the rocket is, say, 1 inch in diameter, the CG must be at least 1 inch forward of the CP. This margin is known as caliber, and refers to the diameter of the rocket.
Sounder 1B is 0.976 inches or 24.8 millimeters in diameter. If the CG is exactly 0.976 inches or 24.8 mm ahead of the CP, we say the rocket has a stability margin (sometimes called the static margin) of 1 caliber. If the CG and CP are 1.952 inches or 49.6mm apart - twice the diameter of the body tube - the margin is 2 caliber.
As you see, Sounder 1B has a static margin of 1.63 caliber. The CG is 40 millimeters forward of the CP. Since the minimum static margin is 1 caliber stability, this is fine. The ideal, especially if you want to fly as high as you can, is a static margin between 1 and 2 caliber. More is usually OK, up to a point. Less is generally not enough for safety, except in the case of some short, stubby rockets.
For most model rockets, however, the minimum safe static margin is 1 caliber. Having a static margin of 1 caliber or more ensures that, even if the rocket encounters a high-degree angle of attack for a moment, the CP isn't likely to shift forward of the CG. The rocket should remain stable.
* * *
To be clear, the cutout method does work to make stable rockets. But it's what we could call overly conservative with its CP location. A rocket designed using the cutout method would certainly be stable and safe, but it errs so far on the safe side, that you may end up building rockets which are far heavier in the nose cone than they need to be, or with more fins or larger fins than you need. That means you may rob yourself of performance, or you may shy away from building a rocket which is perfectly safe and stable, because you worry it might not be.
A better, more accurate method of finding the Center of Pressure was called for. We'll discuss that method in the next post.
In the previous posts on model rocket stability, we talked about Center of Gravity (CG) and Center of Pressure (CP) on a rocket, and where the two should be in relation to one another (CG ahead of CP). We learned that the purpose of fins is twofold: to move the CP aftward - behind the CG - and to correct a rocket's trajectory and dampen the back-and-forth oscillation you naturally get in rocket flight through the air.
But how do we know where the Center of Pressure is? How far behind the Center of Gravity should it be - can the CP be too close or too far from the CG? And what can we do to fix an unstable or understable rocket?
We're going to devote the next few posts to different ways of finding the Center of Pressure, then move on to other questions on stability. This is exciting stuff, because once you understand the basics of model rocket stability, you can do some interesting things. You can design and build your own rockets, knowing they'll fly safely. Even if you mainly prefer to build kits, understanding stability will enable you to modify those kits - such as building them to fly with larger, more powerful motors, or converting single-stage rockets to high-flying multistage rockets by adding a booster section.
An upcoming project - an Estes Photon Probe* kit with a booster - now a two-stage rocket!
* * *
First, finding the Center of Gravity - also known as the Center of Mass - is simple enough. All you have to do is balance the rocket on its side. You can do this on a finger, the back of a chair, or the edge of a ruler (if you can get it to stay still). I like to use a piece of string with a loop tied in the end. Balancing a model rocket on a chair back, which I have done, you run the risk of it falling off and breaking. With a string, I don't worry about the rocket falling to the floor.
Finding the CG on an Apogee Avion rocket
When locating the CG for checking stability, it's important to have the rocket prepped to fly. In other words, you need to install a motor, recovery wadding, and the parachute.
Once you've located the point where the rocket balances without tipping one way or another, you've found the Center of Gravity. The CG is the rocket's balance point, and as it flies, the rocket will rotate back and forth around this point as the fins keep the rocket pointed upward.
Well, the Center of Pressure is another kind of balance point, but rather than being a balance point of all the mass or weight of the parts of the rocket, it's an aerodynamic balance point. It's the theoretical point on the rocket where the sum of all the aerodynamic pressure is in balance. It has to do with surface area rather than the relative weight of the rocket's parts.
So, while a heavier nose cone might change the CG, its weight has no bearing on the CP. It has to do with the shapes and sizes of all the external parts of the rocket. How on earth do you figure out where that point is?
That question plagued rocketeers in the early days of model rocketry. They knew what the CP was, and knew it had to be behind the CG, but how were you supposed to know where the CP would be on a given rocket design?
There are three basic methods. Today, we'll look at the earliest and most basic one.
In the early days of model rocketry, people knew that the CP had to do with surface area, and needed to find a simple way of locating the center of the surface area of their rockets. Specifically, the center of lateral area - the center of the area of the rocket as viewed from the side. It would be easy to find the center of area looking at the rocket from straight on - it's the tip of the nose cone.
How do you find the center of lateral area of a 3-dimensional rocket-shaped object? The answer is to simplify things a bit.
It's actually simple to find the center of area of an oddly-shaped two-dimensional object. You balance it. If we had a two-dimensional representation of our rocket, we could find its geometric center or centroid.
Using the plumb line method to
find the centroid of an odd shape
The cutout method involved making an accurate drawing of a rocket on a stiff material such as card stock or cardboard, cutting the drawing out, and balancing it. Since the card stock is of uniform thickness and density throughout, its Center of Gravity and Center of Area are the same thing!
Here's a cutout of a simple model rocket - Sounder IB - balanced on a piece of aluminum angle.
Once we've found the center of lateral area for our rocket design, we know that as wind hits that object, it should be balanced at the geometric center. Because the air pressure would be equal on all sides of that point, that's our CP. If you were to balance the rocket at that point and hold it in the fast moving air of a fan, you could point the rocket sideways, but it wouldn't pivot - the air pressure would be equal in front of and behind the CP.
As long as when we build the rocket, we make sure that the CG is ahead of that point, we should have a stable rocket.
From Centuri technical report TIR-30, by James Barrowman
Of course, the cutout method has some drawbacks, a couple of which can be deduced from the photo above.
The first is that it requires that you be able to draw an accurate representation of your rocket design, with all parts correctly proportional and in exactly the place they will be on the finished model. Not everyone is terribly gifted at drawing these days, so you'd have to be able to draft an accurate design with tools - rulers, curves, maybe a compass, etc. (Since am not skilled at drafting, I used a printout from an OpenRocket design just to show you the cutout method above. And since I have OpenRocket, I really don't need to use the cutout method - but I wanted to show it, and since I can't draw, I cheated here.)
Another drawback is this: Drawing a two-dimensional representation of your three-dimensional rocket may not tell the whole story. A rocket seen only in silhouette is not the same as the real, 3D thing.
As an illustration, here are three very similar - but significantly different - model rocket designs.
Sounder IB is a four-finned rocket, so it's simple to create a symmetrical, reasonably accurate drawing of it.
The three rockets above - which I haven't named - are all the same design. They have 18-inch long body tubes, a 4-inch plastic nose cone, and trapezoidal fins. The only difference is the number of fins - three, four, and eight.
Let's start with the four-finned rocket, since that's symmetrical in multiple directions. Here's what the drawing we would make of it on cardboard would be shaped like.
Pretty simple.
For the moment, ignore the blue and white CG marking and the red and white CP marking. We'll get to those in a bit. Also, ignore that I've done this drawing using model rocket design software. Let's pretend - just for now - that we're looking at a good drawing done by hand.
If we cut out along all the lines of our drawing, we can see that the end of our two-dimensional cardboard cutout with the fins on it will be heavier, and that the CP of the rocket will be closer to that end than to the nose cone end. As we look at the design, we see two of the fins directly from the side - in other words, we can see their full outline straight on.
Of course, if we turn the rocket 45 degrees, then our two-dimensional drawing looks a little bit different.
The fins of the rocket are the same size as they were before, but in our two-dimensional representation, they look smaller. That means that, if we were to use this drawing to find our CP, it would seem like it was further forward than if we used the first drawing. But, of course, the actual CP on the rocket isn't dependent on which way you look at the rocket.
Of course, most likely nobody would have drawn their rocket like this to find the CP, so this might seem a bit silly. But it does begin to give an idea of the limitations of the cutout method.
So, let's look at a three-finned model.
Now, with this drawing, we're looking at two of three fins, which would be 120 degrees apart on a rocket. Since we're seeing one fin directly face on, we're seeing another one at an angle, and so in this drawing, the fins are lopsided. That's OK, of course, because we're not trying to balance our cutout along the rocket's vertical axis - from nose tip through the motor nozzle. And, of course, we could rotate the view of the rocket by 30 degrees and see it like this:
Now we're seeing two fins at an angle, so they're smaller than they would look face on. The third fin is on the opposite side of the rocket, pointed directly away from us.
Because the fins in this drawing look smaller, a cutout of this balanced on a ruler would indicate that the CP is further forward than on the four-finned rocket - which would be correct. If you add more fins, there is more surface area on the back of the rocket, and the CP moves aftward.
So, which way should you draw your rocket if it has three fins? Well, it might not matter. Perhaps you'd find that both drawings have the same area, and the balance point of the cutout would be the same. But, in fact, I've found no explicit instructions about what to do for a three-finned rocket when using the cutout method. Again, either one will work, and if you build your rocket with the CG forward where the balance point is on the two-dimensional cutout, the rocket will be stable.
Since we've established that adding more fins moves the CP toward the rear of the rocket, let's go in the opposite direction. Instead of three or four fins, let's build a rocket with eight.
If you draw a two-dimensional outline of the four-finned rocket seen above, you get this:
Because you're creating a two-dimensional outline of this rocket, the four-finned version and the eight-finned version look exactly the same, which means that the cutout method suggests that these two rockets have the same Center of Pressure, despite one having twice the fins of the other!
Now, of course, you may well already know that, in OpenRocket or RockSim, the Center of Pressure is indicated by the red circle with the red dot in the middle, seen above in all the designs. And the CP on the cutout of Sounder is far behind the spot where it is balancing on the aluminum angle.
You probably also know that the CG is indicated with the blue and white checkerboard circle. The CG in these designs is an estimate, calculated based on what I've told the software each of the component parts weighs. You'll notice that, regardless of what the rocket looks like in silhouette, as I add more fins, the CP moves aftward.
You can see that all of these rocket designs have the CG well ahead of the CP, and are stable. That includes Sounder - even though the blue CG mark is behind the spot where my cutout balances on the aluminum angle! In order to make Sounder stable, according to the cutout method, it looks like I'd have to make the front end of the rocket much heavier, to move the CG further forward.
So, what gives? Can the cutout method be said to represent the CP of a rocket at all?
Well, the answer is yes - but only in certain circumstances. We'll talk about that in the next post.
*Original OpenRocket file by Jim Parsons - a.k.a. K'Tesh. His OpenRocket work can be found on The Rocketry Forum in this thread. It's helpful to have these, because you can take them and tweak them, which is a lot of fun.
In Part 1, I cut the damaged portion of the Quest Magnum Sport Loader off, shortening the airframe by about 1 3/4 inch. The rocket now looks good, despite being shorter, and because I drilled some static ports - vent holes for a barometric altimeter - into the fat payload section, I can now launch the rocket with an altimeter on board, which will tell me how high it flies.
Now, I have to make sure the rocket is safe to fly. Just looking at the shortened rocket, it looks fine. If I didn't know it had been altered from its original design and build, I would assume it was perfectly safe to fly.
The repaired, shortened, Sport Loader
But I don't want to guess or assume - I want to make sure. That requires a few easy steps.
If you've read my posts on stability, or if you've read the Handbook of Model Rocketry by G. Harry Stine and Bill Stine, then you know that rocket stability depends on the relationship of the Center of Gravity (CG) and the Center of Pressure (CP). In short, the Center of Gravity must be forward - closer to the nose of the rocket - of the Center of Pressure. How do we know where the CG and CP are? How far forward does the CG have to be from the CP? And if the CG is too close to the CP - or, even worse, behind the CP, how do we fix that?
The picture above is a simulation of the rocket, as seen in OpenRocket, free, downloadable rocket simulation/design software. In the picture, the blue and white circle represents the CG, and the red circle represents the CP. As you can see, the CG is ahead of the CP, which means that the rocket is stable.
We'll come back to rocket simulation software in a bit. For now, let's concentrate on the actual, physical rocket in question: The shortened Sport Loader.
Finding the Center of Gravity is simple, so let's start with that.
Another term sometimes used to describe the Center of Gravity is its balance point. This is because when you've found the CG, the rocket will balance perfectly. (Center of Gravity is also sometimes referred to as Center of Mass, because that's really what it is.)
To find the CG of a rocket, simply balance the rocket. You can balance it on your finger, or the back of a chair, or anything you have handy. My preferred method is to use a loop of thick string.
I used to use the back of a chair, but it was hard to balance the rocket perfectly. Sometimes it would roll, and I had to make the tiniest little adjustments so it wouldn't fall off. Sometimes it tries to roll off my finger as well. The string holds the rocket in place, so you can really see where it balances.
Above, you can see that I've found the CG of the rocket - but this is the CG of the rocket with no motors installed. I'm going to mark that spot, and plug it into my simulation file later.
The forward edge of the blue tape marks the CG of the Sport Loader with no motors installed.
I'll explain why the rocket's nose is against the wall in a bit.
But for determining stability, we need to find the CG of the rocket from the moment it lifts off. That means we need to find out where the CG is when the motors are installed. Since this is a two-motor cluster rocket, the two motors should shift the CG significantly backwards.
To do this, you load the motor(s) into the rocket, as well as the parachute and recovery wadding - anything that goes into the flying rocket goes in when checking stability.
Once again, I balanced the rocket to find the new CG.
You can see the CG has shifted aftward dramatically. I'll mark that spot with blue tape as well, and compare them.
In this photo, the nose is beyond the left hand side of the picture. You can see the
difference in CG when the rocket is loaded with motors, compared with when it is empty.
* * *
Now that we've found the CG for the rocket, with everything loaded in it for flight, I'm going to interrupt this post for a moment, and I figure this is the right place to do it. If I don't, then after reading this whole post, someone is sure to write in the comments, "Just do a swing test."
What is a swing test? It's a simple (and fun) test to check whether a model rocket will be stable in flight.
To do a swing test - sometimes known as a string test, you'll need the loaded rocket and a long piece of string. The longer the string, the better, so long as you can actually get the rocket swinging. At least six feet long is recommended.
Simply find the CG, as above, with the loop of string - the string I'm using here is a strong piece of Kevlar, but any sturdy string, such as kite string, will do. What you then do is tape the string in place to the underside of the rocket, so that the loop will not slip, and the rocket will stay in place.
Go outside, hold the string in one hand above your head, and hold the rocket out at arm's length, with the nose pointed forward. Make sure nobody is standing too close to you. Begin turning your body in the direction of the nose and give the rocket a little push with your hand to get it started. Swing the rocket around and around, letting the string out to its full length. If the rocket flies nose first, you know it's going to be stable in flight. It might take a few tries to get it to fly right, but if it does, you can skip the whole CG/CP measurement if you want to.
It's also a fun test to do, because you get to see kind of what the rocket would look like in flight, but from a close vantage point, which you never get to do when the rocket is actually launched.
Here's a good video with a swing test in it.
So, why not "just" do a swing test? There are a few reasons. For one, maybe you don't have the room. As I write this, it's winter, so it's cold outside, and I don't have a lot of space outside that isn't populated by cars, houses or shrubbery.
Another reason is that some rockets do not pass the swing test, yet are perfectly stable. I'll elaborate on this point when I write Part 3 of my stability series, but I'll just briefly say that long rockets or rockets with large fins sometimes have a hard time flying straight on a swing test. And larger rockets are harder to get swinging at a fast enough speed for the swing test to work, especially without hitting something.
Yet another reason for going beyond swing testing your rocket is that perhaps you're interested in understanding the rocket's stability in a more theoretical way. Calculating the CG/CP relationship is interesting - it's the theoretical part of rocketry. Then, swing testing or launching the rocket once you've determined stability is the experimental part. That's fun science! I find the swing test useful as a way of double-checking my work. A failed swing test prompts me to take careful measurements, to see if I really do need to modify the rocket.
If your rocket passes the swing test, it will be stable. If it doesn't, then you need to go on to the next step.
* * *
Now we need to find the Center of Pressure - CP.
The easiest and most reliable way to do this today is with rocket simulation/design software. There are several kinds, but the most common are RockSim and OpenRocket.
RockSim is sold by Apogee Components. It's a fine software, quite sophisticated, and a lot of rocketeers swear by it. If you get serious about rocketry - especially scratch building and high power rocketry - it's a good investment. But it does cost over $123. You can download a free three-month trial of RockSim if you're curious about it.
OpenRocket is free to download and use. It uses Java, so you'll need to have that installed on your computer. It lacks some of the bells and whistles of RockSim, but it's a good place to start for beginners, and some rocketeers simply stick with it, because they don't necessarily need the few extras RockSim provides. One of my fellow club members, an experienced rocketeer who flies lots of high power rockets, uses both software to run simulations before he launches. As he puts it, "Sometimes it's good to have a second opinion."
Center of Pressure is determined by the shapes and sizes of all the external components. It has to do with the relative surface areas of all the parts. As such, it doesn't matter whether your nose cone is heavy or light, or what materials your fins are made of - just what size things are and where they are placed on the rocket. Most specifically, what puts the CP toward the aft of the rocket, where it should be, is the fins.
If you're very meticulous about measuring all parts of your rocket, getting the shapes and angles of the fins correct, figuring out the exact length-to-diameter ratio of your nose cone, etc., you can create a pretty good simulation of your rocket on your own. But if you are using a kit, such as from Estes or Quest, you can very likely find a good sim file somewhere online of your very rocket.
Since the Sport Loader is sold by Apogee Components, I was in luck. Apogee has kindly put free RockSim files of most of the rockets they sell on their website. I use OpenRocket, but I can still open and modify RockSim files with it. The two software are mostly compatible.
I open the Sport Loader RockSim file, and here's what I see.
You can see that the CG is well forward of the CP. In the top right corner of this image, you see the following information:
Stability:2.48 cal
CG:35.6 cm
CP:47.7 cm
This is the stability information for the original rocket without motors. CG and CP locations are measured from the tip of the nose cone. So, in this instance, the CG is 35.6 centimeters from the tip of the nose cone, and the CP is 47.7 centimeters from the tip of the nose.
Incidentally, when taking stability measurements, I always use the metric system. It's much easier, since everything is divided by 10 (how do you measure 15.655 inches with a ruler?), and millimeters are small enough units that if you get a measurement to within less than a millimeter of accuracy, you're probably going to be just fine.
"Cal" is short for caliber, and it refers to the distance between the CG and CP. Caliber is based on the diameter of the rocket itself - more precisely, on the diameter of the widest part of the rocket, which, in this case, is the payload section. This distance between the CG and CP is called its static margin of stability.
In order for a rocket to remain stable in flight, the static margin must be at least 1 caliber. The reason for this is that the Center of Pressure can move forward, depending on the flight conditions. If the CG moves too close to the CP, the rocket will be neutrally stable, and if it goes forward of the CG, the rocket will be unstable, and will flail around in flight.
With the Sport Loader, we have a rocket whose widest diameter is 4.9 centimeters, or 49 millimeters. That means that in order to maintain a minimum static margin of 1 caliber, the CG must be at least 49 millimeters forward of the CP. Anything less than 1 caliber stability is referred to as marginally stable, and is not safe enough for flight. In the image above, the CP is 12.1 cm forward of the CP, giving us a static margin of 2.48 caliber.
Of course, rockets do not fly without motors, so let's see what the static margin is with the motors installed.
The CG has shifted aftward to 42.1 cm from the tip of the nose, and we still have a safe static margin of 1.14.
Well, that's great for our original rocket, but what about our newly-shortened, repaired rocket? We'll need to re-measure that.
I want to make my simulation as accurate to the real rocket as possible, so I need to measure the new, shorter length of the tube.
Looks like I've cut the body tube down to about 33.2 centimeters in length. Why don't I just change the design in OpenRocket and see if the rocket is stable? That should work, right?
Let's take a look.
Whoa, what?? I take off an inch and three quarters, and suddenly the rocket has a stability margin of 0.627? The rocket looks like it should be stable, so why is it now marginal?
Here's a clue - the Sport Loader with a very short, stubby tube:
I've shortened the body tube to about 7 centimeters or so, and now the CG is behind the rocket!
Of course, this doesn't make sense. But I'm showing it to you, because it took me some thinking to figure out what the problem was. OpenRocket doesn't come with instructions, and for about a year, there were two important functions I was completely unaware of: the ability to override both the mass of the rocket, and the rocket's Center of Gravity. That's what's going on here: the CG in the RockSim file has been overridden.
The design elements box in OpenRocket. The CG symbol means that the
Center of Gravity has been overridden. The little weight symbol
means that the mass has been overridden.
This is because when you build a rocket in simulation software, it calculates roughly where the CG will be by finding the CG of the individual components. But it doesn't take into account certain key components - namely, the kind and amount of glue or epoxy you use to build the rocket, and the weight and thickness of paint. Often, a person will build a simulation of a rocket, then compare the calculated CG with the CG of the real, built rocket, then override the CG in the simulation. This will help you to get better simulations.
The fact is, no matter how accurate a simulation may be, you still need to verify the measurements on the actual rocket, when making repairs or modifications. So, while simulations can be useful, for now, let's get back to the real rocket. What we need to do is find, measure, and mark the CP on the rocket we have.
The simulation tells us that our new Center of Pressure is located 43.8 cm from the tip of the nose cone. You could take a cloth tape measure, put it on the tip of the nose cone, and measure from there. But to be truly accurate, you need to measure straight back from where the tip of the nose cone. That's why I placed the nose cone against the wall in the pictures above. I'm going to measure from the wall, which will be on the same plane as the tip of the nose, back to the CG and CP.
It's kind of like when you go to the doctor and they measure your height - they use a straightedge to find the top of your head.
So, from the wall, where the tip of the nose cone is placed, I used a rigid, metal tape measure to mark a spot on the rocket 43.8 cm from the tip of the nose cone.
I've already marked and measured the CG for the rocket, both with no motors, and with motors installed.
With the motors (and parachute and recovery wadding) installed, the real CG of the rocket is about 36.1 cm from the nose.
That's a difference of about 7.7 cm.
The rocket is about 4.9 cm in diameter at its widest point - the payload section. The static margin is larger than 1 caliber - I have now verified that the rocket will be stable, and is safe to fly.
So, why did I bother checking the CG on the simulation, instead of just using it to find the CP, which is all I needed to do here? And why did I mark the CP of the rocket with no motors installed, if I only needed to find the CP with the motors in to check stability?
The answer is that I wanted to be able to run accurate simulations of my rocket in the future. We'll talk briefly about that in the next post.
For now, though, if you alter a rocket in any way, through repair, or through upgrading a kit to take a larger motor - which I have done, and it's been a lot of fun - take these steps, and you can be sure your rocket will be stable.
