Going Supersonic – Building a Model Rocket That Exceeds Mach 1

I have discovered that it isn’t hard to design a rocket to go supersonic. I’m guessing the most challenging part of this project would be building it to withstand high airspeeds, yet still light enough to go that fast. Thus, here is the goal of this project:

Goal—To build a rocket that flies faster than the speed of sound and creates an audible sonic boom, built strong enough to withstand such high airspeeds.

To Fly Faster Than the Speed of Sound
Model rocketry is probably the only hobby that can travel faster than the speed of sound (mach 1). But you can’t just build any old model rocket and expect it to break the sound barrier. It has to be a sleek, lightweight, high-thrust rocket. I’ve had to tweak my design several times to get it just right, and I probably will tweak it now and then in the future. However, there are 4 essential design features:

1)High-thrust rocket engine

2)Minimum diameter (That means the rocket should be no bigger around than is necessary to fit the high-thrust rocket engine

3)1-2 caliber stability (<-- What’s that supposed to mean?)

4)Light as a feather. Almost. Not so light that it flies like a feather!

So what is the speed of sound? It’s hard to design a rocket to go faster than a certain speed when that speed is unknown! Typically the speed of sound is about 761 miles per hour at sea level. But as it turns out, the speed of sound varies by a few factors. Here is the equation:

V = [331.5 + 0.606(T)]m/sec

In this equation, V is the speed of sound, and T is the temperature of the air in Celsius.

It is actually a lot more complicated than that, but this equation is accurate enough for my simple needs.


To Create an Audible Sonic Boom
The science behind a sonic boom is rather fascinating:

When a rocket flies at subsonic speeds (less than mach 1, the sound waves emulating from it might look like this:

Notice that the sound waves are rather bunched up toward the nose of the rocket. The faster it goes, the more exaggerated it becomes, until
This is when the rocket is going the same speed as the sound waves; so all those sound waves get bunched up at the nose of the rocket creating a shock wave.

Once the rocket exceeds the speed of sound, it outruns the shock wave, which we hear as a sonic boom.

Anything faster than mach 5 is termed “Hypersonic.”

…but that’s more of a “spacecraft” field of study.

It used to be common to hear a sonic boom from aircraft (until the government passed a law prohibiting mach near populous), but you rarly ever hear sonic booms from rockets. I've seen numerous rocket launches that have gone over mach 1, but have only heard one boom from a rocket. As it turns out, even though rockets routinely break the sound barrier, and even though they make sonic booms, the booms are hardly ever heard, and there are a few reasons for this:

1) An airplane flies horizontally, a rocket flies vertically. On an airplane the shock wave is deflected off toward the ground, on a rocket it is deflected out horizontally, which we don't hear. Unless the rocket is on the same lateral plane (geometric, not airplane) as the observers listening for a sonic boom.

2) The small boom it does make could be drowned out by the roar of the high-thrust rocket motor.

3) The rocket is traveling away from you, so according to the Doppler Effect, sound from objects moving away from you will undergo a redshift, where the wavelengths increase which will both lower the pitch and mute the sound slightly.

So… to help the likelihood of hearing a boom, my current design crosses over to transonic speed at about 0.5 seconds after ignition at an altitude of 300 feet. My idea is that if I can get it to accelerate to to the speed of sound fast enough, it will be at a low enough altitude that the sonic boom will be deflected out toward the spectators, and not over their heads.

To Withstand High Airspeeds
Here is why this is a challenge: drag and lift forces increase as the square of the airspeed. This means that if the average speed of a smaller model rocket is about 250 feet per second, a rocket that flies at the speed of sound is going to have about 20 times more drag force! How do you get cardboard and balsa wood to hold together going that fast?

Most large model rockets employ a certain method to help secure the fins on the rocket, and that is through-the-wall fin attachment. As its name implies, a tab on the fins goes through a slit in the rocket body and attaches to the motor mount. It is the single best way to secure the fins so that they can withstand almost any flight condition.

However, my design has no space between the rocket body and motor mount for through-the-wall fin attachment—the rocket body is the motor mount. So it will be tricky getting a strong bond using only a simple butt-joint.

Here are 4 ways to help keep the fins attached and secure:

1) Double-wedge airfoil: A good airfoil on the fins of a supersonic vehicle is double wedge, or a “diamond” airfoil. This has sharp-pointed leading and trailing edges.

2) Paper skins: Even though balsa wood has a higher strength-to-weight ratio than carbon steel, it is only so strong. One of the biggest things you can do to increase the durability of balsa wood fins is to laminate them with paper skins.

3) Double-dry glue joint: To really make a good glue joint, you need to coat both surfaces with a thin coat of glue and let it dry before bonding them. Then apply a second coat and bond the two surfaces. The first coat penetrates the pores of the balsa wood, and the second coat bonds glue to glue. When it comes to porous materials this is the strongest glue joint out there.

4) Good fillet with epoxy: If you spread a bead of glue in the intersection of the fin and the rocket body the force will be distributed better. Not to mention this is better for aerodynamics.

Summing It Up
I will probably build 4 or 5 identical vehicles, because I don’t expect that I will ever find them again after launch. I have not yet started building them (waiting for funds to come in. Actually, I have to go earn them). But the materials to build it are simple: paper, cardboard, balsa wood, plastic, elastic, polyethylene LDPE, wood glue, epoxy, white glue, ammonium perchlorate, and a phenolic casing. I mean, who would have thought that such materials could be made into such a complex vehicle?

I see God in my field of study. I sometimes wonder how in the world some scientists could be atheists. How on earth could you not see God in His Creation? I mean, just look at this photo!

Yuri Gagarin was either a liar or a nut when he said "I don't see any God up here."

Improving Aerodynamics: 5 Types of Drag

What Makes an Aerodynamic Rocket?

Well, for one thing: patience. If you try to slap a rocket together because you're under a deadline, or just can't wait to finish it, the rocket will turn out sloppy and unfinished.

There are 5 types of aerodynamic drag:

-Friction drag

-Interference drag

-Parasite drag

-Pressure drag

-Induced drag

Now, I know what you're thinking. "Uh! What a drag!" Well, it is, and that is why it is certainly worth doing something about! I will go over the effects of each of these types individually.

Friction Drag

There is always a layer of turbulent air surrounding a speeding model. The velocity of the air relative to the rocket increases with distance from it. This layer is only a few thousandths of and inch thick, and it only takes .0005 inches to transition the laminar boundary layer to turbulent. That’s why it is crucial to keep the model as smooth and glossy as humanly possible. While it is impossible to keep the boundry layer from turning turbulent, a good idea is to trip the boundry layer manually near the nose of the rocket so that the boundry layer will be tripped in exactly the same position all the way around the rocket. Some claim this helps reduce drag.

Interference Drag

Interference drag is the result of an interruption of the boundary layer. The abrupt disturbance causes much drag. Such causes of interference drag are as follows: a protrusion, cavity/gap, joint, bump, or wavy surface. The most prominent source of interference drag is from the fins. Obviously, a rocket with triform (3 fins) fin configuration will have 25% less interference drag than a rocket with cruciform (4 fins) configuration. Also, interference drag will be reduced with a fillet in the fin root connection to make the interruption less sharp.

Pressure Drag

In order for a model rocket to fly through the air it has to force the air aside and let it slip back into place with as little disturbance as possible. To minimize positive pressure drag, you can either fly on very hot days or high altitudes, or select nose shapes with low drag coefficient (Cd). The nose shapes with the lowest pressure Cd’s are parabola and hemispherical.

Also, the air has to close behind the speeding model with as little disruption as possible. If the rocket is going faster than the air can close behind it there will be a negative pressure drag due to the partial vacuum tugging at the back side of the rocket. So sometimes a boat tail or transition to narrower diameter will reduce these effects.

Parasite Drag

This form of drag is actually just another facet of pressure drag. It is caused primarly by the launch lug, or any other protrusion sticking out the side of the rocket's body. Parasite drag can be as much as 35% of the entire drag on a model rocket. It can be reduced by ~25% when the launch lug is positioned in a fin root connection. Or, you can build a tower launcher, and remove the launch lug entirely!

Induced Drag

Induced drag is the drag that occurs when the fins generate lift. More specifically it is called the lift-induced drag. This type of drag is the hardest to picture.

The induced drag occurs at the tip of the fin. If the fin had no finite length, there would be no induced drag. The way this happens is when the airflow around the fins “leaks” around the fin tip to the opposite side creating vortices of swirling air in its wake:

The drag due to lift can be expressed with the following diagram:

The induced drag becomes greater if:

-The fins are swept back

-The fin span is shorter

-The fins have a rounded tip (leave the very tip square, but give the leading and trailing edges a good airfoil)

Summing It All Up

When studying drag, one realizes that there is no "correct" or "ideal" way to make a rocket. When you include a feature that is supposed to help in one area in aerodynamics, you're going to have to make a compromise in another area. But with insight as to what causes drag, you should be able to come up with a happy medium.

Rocket Design Software

Rocket design software uses the aid of a computer to determine the design of a rocket, static and dynamic stability, altitude, drag coefficient, and more.

While it is possible (and probably good) to do all the calculations with paper, pencil and calculator, if you deside you want to make one small change to see what effect it would have, your going to have to do it all over again by hand. There are many benefits to rocket design software, but that is probably the best.

Which program is the best? There are two main competetors that I know of:

-RockSim
-SpaceCAD

Comparison of RockSim and SpaceCAD

What I'll do is design and run a simulation of the same rocket using RockSim and SpaceCAD to compare features.

First let's take a look at the overall interface of each program.

RockSim:

The interface of RockSim is very user-friendly and intuitive. The user inputs the rocket specs in the upper portion of the window, and the program draws it in the graphic box below. It is very easy to run simulations by loading a motor file and clicking the launch button. That's all you have to do, and the program does everything else.

There are many controls on the main screen of SpaceCAD. At a first glance it is harder to assess how to use the program, but with a little bit of tinkering it becomes apparent.

I have come to think that SpaceCAD's interface is a little more complicated than RockSim's, and it isn't even as powerful. (I may be biased: I really like RockSim). But SpaceCAD is much cheaper than RockSim, and so still might be just as good a deal as - if not better than - RockSim.

SpaceCAD design file

RockSim design file

Also, the simulation results aren't as easy to read in SpaceCAD, but you can do it. RockSim even goes as far as to provide the user with an animation of their rocket's flight profile!

In short, I suggest that SpaceCAD can do most of the things RockSim can do, but RockSim does them better.

Price:

-SpaceCAD - $59.90

-RockSim - $108.95

Static Stability

The problem of stability was my biggest challenge in the early days. It wasn't something I paid much attention to, and then I wondered why my rockets weren't flying upwards.

There are two points on a rocket one must look at when dealing with stability:

The center of gravity is simply the balancing point on the rocket. The center of pressure is the point where the drag forces are equalized. This can be visualized by imagining a weathervane:

The reason the weathervane points into the wind is because there is more drag on the rear when the wind blows, so the rear swings backwards. However, if the CP was in the same place as the CG:there would be no rotation, because the drag on one side of the CG would equal the drag on the other side.

THUS, IN ORDER TO MAKE A ROCKET FLY STRAIGHT THE CP SHOULD BE FARTHER AFT THAN THE CG.

But how large should the margin between them be?

There are a few guidelines to go by for a stable rocket:

-The CG should be at least one diameter of the rocket forward of the CP. This is called caliber stability, and 1 caliber equals 1 body diameter:

However, it won't help any to have the stability be more than 2 or 3 calibers. In fact, it could hurt stability (but that's getting into dynamic stability, which would have to be another post).

-The length of the rocket should be at least 10 calibers, but some say 12. In other words, the length to diameter ratio should be greater than 10:1.

-There are 3 ways to increase the margin between the CG and CP: 1) Add more weight to the nose (not a very good way, unless you're dealing with a scale model) 2) Increase the fin are (Tip: The best way is to increase the span, not the length. The farther from the rocket body, the less turbulent the air, so the fin is more effective). 3) Lengthen the body tube.

So how do you find out what the CG/CP margin is on a rocket? Well, to find the CG all you have to do is balance the rocket on a straight edge. But finding the location of the CP is a little more complicated...

One not very accurate way is to use the center of lateral area as the CP. To do this, make a 2D cardboard cutout of the rocket, and then balance it to find the CG. Then compare it with the CG of the actual rocket. This is an okay way to calculate stability. However, it turns out that the CP is even more complex than that.

You see, the center of lateral area is the CP when the rocket is flying at an angle of attack of 90 degrees (i.e. the aiflow is perpendicular to the rocket). That's the concept of dynamic stability: When the rocket is exposed to real flight conditions, the CP location will travel, depending upon the angle of attack.

There are equations that determine the position of the CP under actual flight conditions, known as the Barrowman equations. To learn how to use these equations, click here. They look complicated at first, but they're pretty straightforward if you know how to use simple arithmetic. Just plug in the numbers and the location of the CP appears.

As a third alternative, download some rocket design software to aid you with stability calculation. Rocket design software usually does much more than this, but they are an excellent and pretty reliable way of determining stability. To learn more about rocket design software, click here.