--- /dev/null
+
+
+\chapter{Basics of model rocket flight}
+\label{chap-basics}
+
+
+As rockets and rocket motors come in a huge variety of shapes and
+sizes, different categories are defined for different levels of
+rocketry. {\it Model rocketry} itself is governed by the NAR Model
+Rocket Safety Code~\cite{nar-safety-code} in the U.S. and other
+similar regulations in other countries. The safety code requires that
+the model rockets be constructed only of light-weight materials
+without any metal structural parts, and have a maximum lift-off weight
+of 1.5~kg. They may only used pre-manufactured motors of classes A--G
+(see Section~\ref{sec-motor-classes} for the classification).
+
+{\it High power rocketry} (HPR) is basically scaled up model
+rocketry. There are no weight restrictions, and they can use
+pre-manufactured solid or hybrid rocket motors in the range of H--O.
+The combined total impulse of all motors may not exceed 81\s920~Ns.
+
+{\it Experimental} or {\it amateur rocketry} includes any rocketry
+activities beyond model and high power rocketry. This may include
+for example using motor combinations that exceed the limits placed by
+high power rocketry, building self-made motors or utilizing liquid
+fueled motors. Finally there is {\it professional rocketry} which is
+conducted for profit, usually by governments or large corporations.
+
+Even though rockets come in many different sizes, the same principles
+apply to all of them. In this thesis the emphasis will be on model
+rocketry, but the results are just as valid for larger rockets as long
+as the assumptions of for example the speed range remain valid. In
+this chapter the basics of model rocketry and differences to high
+power rocketry are explained.
+
+
+\section{Model rocket flight}
+
+A typical flight of a model rocket can be characterized by the four
+phases depicted in Figure~\ref{fig-model-flight}:
+%
+\begin{enumerate}
+\item Launch: The model rocket is launched from a vertical launch
+ guide.
+\item Powered flight: The motor accelerates the rocket during the
+ powered flight period.
+\item Coasting flight: The rocket coasts freely until approximately
+ at its apogee.
+\item Recovery: The recovery device opens and the rocket descends
+ slowly to the ground.
+\end{enumerate}
+
+\begin{figure}
+\centering
+\epsfig{file=figures/model-flight,scale=0.8}
+\caption{The basic phases of a typical model rocket flight:
+ 1.~Launch, 2.~Powered flight, 3.~Coasting and 4.~Recovery.}
+\label{fig-model-flight}
+\end{figure}
+
+Model rockets are launched from a vertical launch guide that keeps the
+rocket in an upright position until it has sufficient velocity for the
+fins to aerodynamically stabilize the flight. The NAR safety code
+forbids launching a model rocket at an angle greater than
+$30^\circ$ from vertical. A typical launch guide for small rockets is
+a metal rod about 3-5~mm in diameter, and the launch lug is a short
+piece of plastic tube glued to the body tube. Especially in
+larger rockets this may be replaced by two extruding bolts, the ends
+of which slide along a metal rail. Use of a launch lug can be avoided
+by a tower launcher, which has 3--4 metal bars around the rocket
+that hold it in an upright position.
+
+After clearing the launch guide, the rocket is in free, powered flight.
+During this phase the motor accelerates the rocket while it is
+aerodynamically stabilized to keep its vertical orientation. When the
+propellant has been used, the rocket is typically at its maximum
+velocity. It then coasts freely for a short period while the motor
+produces smoke to help follow the rocket, but provides no
+additional thrust. Finally, at approximately the point of apogee, a
+small pyrotechnical ejection charge is fired upwards from the motor
+which pressurizes the model rocket and opens the recovery device.
+
+High-power rocket motors usually have no ejection charges incorporated
+in them. Instead, the rocket carries a small flight computer that
+measures the acceleration of the rocket or the outside pressure change
+to detect the point of apogee and to open the recovery device.
+Frequently only a small drogue parachute is opened at apogee, and the
+main parachute is opened at some pre-defined lower altitude around
+100--300 meters.
+
+The typical recovery device of a model rocket is either a parachute or
+a {\it streamer}. The parachutes are usually a simple planar circle
+of plastic or fabric with 4--10 shroud lines attached. A streamer is
+a strip of plastic or fabric connected to the rocket, intended to
+flutter in the air and thus slow down the descent of the rocket.
+Especially small rockets often use streamers as their recovery device,
+since even light wind can cause a light-weight rocket with a
+parachute to drift a significant distance.
+
+
+
+
+\section{Rocket motor classification}
+\label{sec-motors}
+\label{sec-motor-classes}
+
+The motors used in model and high power rocketry are categorized based
+on their total impulse. A class `A' motor may have a total impulse in
+the range of 1.26--2.50~Ns. Every consecutive class doubles the
+allowed total impulse of the motor. Thus, a B-motor can have an
+impulse in the range 2.51--5.00~Ns and a C-motor in the range
+5.01--10.0~Ns. There are also classes \half A and \quarter A which
+have impulse ranges half and one quarter of those of an A-motor,
+respectively. Commercial rocket motors are available up to
+class~O with a total impulse of 30\s000~Ns~\cite{all-certified-motors}.
+Table~\ref{tab-motor-classes} lists the impulse ranges for model
+and high-power rocket motors.
+
+\begin{table}
+\caption{Total impulse ranges for motor classes \quarter A--O.}
+\label{tab-motor-classes}
+\begin{center}
+\begin{tabular}{cr@{--}l|cr@{--}l|cr@{--}l}
+\hline
+\quarter A & 0.0 & 0.625~Ns & E & 20.01 & 40.0~Ns & K & 1280.01 & 2560~Ns \\
+\half A & 0.626 & 1.25~Ns & F & 40.01 & 80.0~Ns & L & 2560.01 & 5120~Ns \\
+A & 1.26 & 2.50~Ns & G & 80.01 & 160~Ns & M & 5120.01 & 10240~Ns \\
+B & 2.51 & 5.00~Ns & H & 160.01 & 320~Ns & N & 10240.01 & 20480~Ns \\
+C & 5.01 & 10.0~Ns & I & 320.01 & 640~Ns & O & 20480.01 & 40960~Ns \\
+D & 10.01 & 20.0~Ns & J & 640.01 & 1280~Ns & \\
+\hline
+\end{tabular}
+\end{center}
+\end{table}
+
+Another important parameter of a rocket motor is the thrust given by
+the motor. This defines the mass that may be lifted by the motor and
+the acceleration achieved. Small model rocket motors typically have
+an average thrust of about 3--10~N, while high-power rocket motors can
+have thrusts in excess of 5\s000~N.
+
+The third parameter used to classify a model rocket motor is the
+length of the delay between the motor burnout and the ignition of the
+ejection charge. Since the maximum velocity of different rockets
+using the same type of motor can be vastly different, also the length
+of the coasting phase varies. Therefore motors with otherwise the
+same specifications are often manufactured with several different
+delay lengths. These delay lengths do not apply to high-power rocket
+motors, since they do not have ejections charges incorporated in them.
+
+Model rocket motors are given a classification code based on these
+three parameters, for example ``D7-3''. The letter specifies the
+total impulse range of the motor, while the first number specifies the
+average thrust in Newtons and the second number the delay of the
+ejection charge in seconds. The delay number can also be replaced by
+`P', which stands for {\it plugged}, \ie the motor does not have an
+ejection charge. Some manufacturers may also use an additional letter
+at the end of the classification code specifying the
+propellant type used in the motor.
+
+Even motors with the same classification code may have slight
+variations to them. First, the classification only specifies the
+impulse range of the motor, not the exact impulse. In principle, a
+D-motor in the lower end of the range might have a total impulse only
+1~Ns larger than a C-motor in the upper end of its range. Second,
+the code only specifies the average thrust of the motor. The thrust
+rarely is constant, but varies with time.
+Figure~\ref{fig-thrust-curve} shows the typical thrust curve of a
+small black powder rocket motor. The motors typically have a short
+thrust peak at ignition that gives the rocket an initial acceleration
+boost before stabilizing to a thrust level a little below the average
+thrust. Statically measured thrust curves of most commercial rocket
+motors are readily available on the
+Internet~\cite{thrust-curve-database}.
+
+\begin{figure}
+\centering
+\epsfig{file=figures/motors/D12-thrustcurve,width=9cm}
+\caption{A typical thrust curve of an Estes D12-3 rocket motor and
+ its average thrust.~\cite{D12-curve}}
+\label{fig-thrust-curve}
+\end{figure}
+
+Also the propellant type may affect the characteristics of the motor.
+Most model rocket motors are made up of a solid, pyrotechnical
+propellant---typically black powder---that is cast into a suitable
+shape and ignited on launch. Since the propellant burns on its
+surface, different thrust curves can be achieved by different mold
+shapes.
+
+% vesiraketit!
+
+A significantly different motor type, {\it hybrid motors}, were
+commercially introduced in 1995. These motors typically include the
+propellant and oxidizer in different states, typically a composite
+plastic as the fuel and a separate tank of liquid nitrous oxide
+($\rm N_2O$) as the oxidizer. The plastic on its own does not
+burn very well, but provides ample thrust when the nitrous oxide is
+fed through its core. The nitrous oxide tank is
+self-pressurized by its natural vapor pressure. However, since
+temperature greatly affects the vapor pressure of nitrous oxide, the
+thrust of a hybrid motor is also diminished if the oxidizer is cold.
+On the other hand, the motor will burn longer in this case, and since
+nitrous oxide is denser when cold, the motor may even yield a greater
+total impulse.
+
+The significance of this effect was observed when analyzing the video
+footage of the launch of the first Finnish hybrid rocket,
+``Haisunäätä''~\cite{haisunaata-launch}. The average thrust during the
+first 0.5~seconds was determined to be only about 70~N, whereas the
+static tests suggest the thrust should have been over 200~N.
+Instead, the motor burned for over 10~seconds, while the normal thrust
+curves indicate a burning time of 5--6~seconds. This shows that the
+temperature of the hybrid motor oxidizer can have a dramatic effect on
+the thrust given by the motor, and the static test curve should be
+assumed to be valid only in similar operating conditions as during the
+test.
+
+One further non-pyrotechnical rocket type is {\it water rockets}.
+These are especially popular first rockets, as they require no special
+permits and are easy to construct. The water rocket includes a bottle
+or other chamber that has water and pressurized air inside it. On
+launch the pressure forces the water out of a nozzle, providing thrust
+to the rocket. While simulating water rockets is beyond the scope of
+this thesis, it is the aim that methods for modeling water rockets can
+be added to the produced software in the future.
+
+
+
+\section{Clustering and staging}
+
+Two common methods used to achieve greater altitudes with model
+rockets are {\it clustering} and {\it staging}. A cluster has two or
+more rocket motors burning concurrently, while staging uses motors
+that burn consecutively. The motor configuration of a cluster and
+staged rocket is depicted in Figure~\ref{fig-cluster-stages}.
+
+When a cluster is launched, the total thrust is the sum of the thrust
+curves of the separate motors. This allows greater acceleration and
+a greater liftoff weight. Staging is usually performed by using
+zero-delay motors, that ignite the ejection charge immediately at
+burnout. The ejection charge fires towards the upper stage motor and
+ignites the next motor. High power motors with no ejection charges
+can be clustered by using an onboard accelerometer or timer that
+ignites the subsequent stages. Staging provides a longer duration of
+powered flight, thus increasing the altitude.
+
+
+\begin{figure}
+\centering
+\parbox{65mm}{\centering
+\epsfig{file=figures/motors/cluster,width=60mm} \\ (a)}
+\hspace{10mm}
+\parbox{40mm}{\centering
+\epsfig{file=figures/motors/staged,width=30mm} \\ (b)}
+\caption{The motor configuration for (a) a cluster rocket and (b) a
+ two-staged rocket.}
+\label{fig-cluster-stages}
+\end{figure}
+
+Clustering provides a greater acceleration at launch, but staging
+typically provides greater altitude than a cluster with similar
+motors. This is because a clustered rocket accelerates quickly to a
+greater speed thus also increasing the aerodynamic drag. A staged
+rocket has a smaller thrust for a longer period of time, which reduces
+the overall effect of drag during the flight.
+
+
+\section{Stability of a rocket}
+\label{sec-stability}
+
+When designing a new rocket, its stability is of paramount
+importance. A small gust of wind or some other disturbance may cause
+the rocket to tilt slightly from its current orientation. When this
+occurs, the rocket centerline is no longer parallel to the
+velocity of the rocket. This condition is called flying at an
+{\it angle of attack $\alpha$}, where $\alpha$ is the angle between
+the rocket centerline and the velocity vector.
+
+When a stable rocket flies at an angle of attack, its fins produce a
+moment to correct the rocket's flight. The corrective moment is
+produced by the aerodynamic forces perpendicular to the axis of the
+rocket. Each component of the rocket can be seen as producing a
+separate normal force component originating from the component's CP,
+as depicted in Figure~\ref{fig-normal-forces}.
+
+\begin{figure}
+\centering
+\epsfig{file=figures/aerodynamics/component-normal-forces,width=130mm}
+\caption{Normal forces produced by the rocket components.}
+\label{fig-normal-forces}
+\end{figure}
+
+The effect of the separate normal forces can be combined into a single
+force, the magnitude of which is the sum of the separate forces and
+which effects the same moment as the separate forces. The point on
+which the total force acts is defined as the center of pressure or the
+rocket. As
+can be seen from Figure~\ref{fig-normal-forces}, the moment produced
+attempts to correct the rocket's flight only if the CP is located aft
+of the CG. If this condition holds, the rocket is said to be
+{\it statically stable}. A statically stable rocket always produces a
+corrective moment when flying at a small angle of attack.
+
+The argument for static stability above may fail in two conditions:
+First, the normal forces might cancel each other out exactly, in which
+case a moment would be produced but with zero total force. Second,
+the normal force at the CP might be in the wrong direction (downward
+in the figure), yielding an uncorrective moment. However, we shall
+see that the only component to produce a downward force is a boattail,
+and the force is equivalent to the corresponding broadening of the
+body. Therefore the total force acting on the rocket cannot be zero
+nor in a direction to produce an uncorrective moment when aft of the
+CG.
+
+The {\it stability margin} of a rocket is defined as the distance between
+the CP and CG, measured in {\it calibers}, where one caliber is the
+maximum body diameter of the rocket. A rule of thumb among model
+rocketeers is that the CP should be approximately 1--2 calibers aft of
+the CG. However, the CP of a rocket typically moves upwards as the
+angle of attack increases. In some cases, a 1--2 caliber stability
+margin may totally disappear at an angle of attack of only a few
+degrees. As side wind is the primary cause of angles of attack, this
+effect is called
+{\it wind caused instability}~\cite{galejs}.
+
+Another stability issue concerning rocketeers is the
+{\it dynamic stability} of a rocket. A rocket that is statically
+stable may still be poor at returning the rocket to the original
+orientation quickly enough. Model rockets may encounter several types of
+dynamic instability depending on their shape, size and
+mass~\cite[pp.~140--141]{stine}:
+%
+\begin{enumerate}
+\item {\it Too little oscillation damping.} In short, light-weight
+ rockets the corrective moment may significantly over-correct the
+ perturbation, requiring a corrective moment in the opposite
+ direction. This may lead to continuous oscillation during the
+ flight.
+\item {\it Too small corrective moment.} This is the case of over-damped
+ oscillation, where the corrective moment is too small compared to
+ the moment of inertia of the rocket. Before the rocket has been
+ able to correct its orientation, the thrust of the motors may have
+ already significantly affected the direction of flight.
+\item {\it Roll-pitch coupling.} If the model has a natural roll
+ frequency (caused \eg by canting the fins) close to the oscillation
+ frequency of the rocket, roll-pitch resonance may occur and cause
+ the model to go unstable.
+\end{enumerate}
+
+By definition, dynamic stability issues are such that they occur over
+time during the flight of the rocket. A full flight simulation that
+takes into account all corrective moments automatically also simulates
+the possible dynamic stability problems. Therefore the dynamic
+stability of rockets will not be further considered in this
+thesis. For an analytical consideration of the problem, refer to
+\cite{advanced-model-rocketry}.
+
+
+
projects / debian / openrocket / blobdiff