Reviewed the pBallSin setting.

doc/report/report_philip/thesisPage__experiments__pBallSin.tex

@@ -26,12 +26,12 @@ Additionally, the object does not move at constant speed any more, instead its v
 		\end{minipage}
 	\end{figure}
 	%
-	The situation is illustrated in figure \ref{sec:experiments:pBallSin:genSetting:sketch}, which looks similar to the \constBall{} setting, but there are some differences.
+	The situation is illustrated in figure \ref{sec:experiments:pBallSin:genSetting:sketch}, and looks similar to the \constBall{} setting, but there are some differences.
 	First of all, the box is larger, its height is $\SI{2}{\meter}$ instead of just one meter and it is also $\SI{50}{\centi\meter}$ longer.
 	%
 	\\
 	But the main difference is the velocity we are imposing on the ball.
-	Instead of a constant movement, it is now depending on time $t$ as 
+	Instead of a constant velocity, it now depends on time $t$ as 
 	%
 	\begin{align}
 		\Fkt{v_{x}}{t} = -\alpha \cdot \left( 1 + \Sin{\frac{2 \pi}{\omega} \left( t - t_{0} \right) } \right)	,	\label{eq:experiments:pBallSin:genSetting:vx}
@@ -41,7 +41,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 	$\alpha$ describes how fast the ball moves, and $\omega$ how strong it shakes back and forth, we require $\alpha > 0$ and $\omega > 0$.
 	Because of the minus in front of \eqref{eq:experiments:pBallSin:genSetting:vx} and the ``$+1$'', the velocity will always be negative and the ball will move towards the left.
 	%
-	As we have done it before, we will consider the \emph{speed} in the following discussion, ignoring the sign.
+	As we have done it before, we will consider the \emph{absolute speed} of the ball in the following discussion, ignoring the sign.
 	
 	$\alpha$ and $\omega$ are parameters that describe the system.
 	As default value we have selected
@@ -73,7 +73,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 		
 		\item[\pBallSinRet ]
 		As its name indicates, the Reynolds number is $\approx 180$.
-		The density of the fluid was increased for this to $\rho_{F} = \SI{1}{\kilogram\per\cubic\meter}$, and for the ball we have $\rho_{B} = \SI{3.2}{\kilogram\per\cubic\meter}$.
+		The density of the fluid was increased to $\rho_{F} = \SI{1}{\kilogram\per\cubic\meter}$, and for the ball we have $\rho_{B} = \SI{3.2}{\kilogram\per\cubic\meter}$.
 		
 		\item[\pBallSinOrg ]
 		This is the original setting, that uses the real densities.
@@ -124,13 +124,13 @@ Additionally, the object does not move at constant speed any more, instead its v
 	
 	
 		\subsubsection{Measuring}~\label{sec:experiments:pBallSin:Goal:Measuringoal}
-		The acceleration of the body will lead to a ``collision'' with the fluid and will generate a pressure.
+		The acceleration of the body will lead to a ``collision'' with the fluid and will generate a pressure on the ball's surface.
 		This means that \eqref{eq:experiments:pBallSin:Goal:Ff} is actually a pressure.
 		
 		We will measure this force in two ways.
 		%
 		In the \emph{indirect} way, we will measure the change in the fluid's momentum.
-		This method was used in \ref{sec:experiments:linMom:linMod:slowDown}.
+		This method was also used in \ref{sec:experiments:linMom:linMod:slowDown}.
 		%
 		\\
 		In the second method, we will use the convex hull, see section \ref{sec:experiments:methodology:calculation:ConvexHull} on page \pageref{sec:experiments:methodology:calculation:ConvexHull}, as an approximation of the surface and \emph{directly} integrate pressure over it.
@@ -173,7 +173,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 		
 			\paragraph{Indirect Way}~\label{sec:experiments:pBallSin:Results:Sin:Indirect}
 			As we see in the plot, we have almost a perfect match, and we also see that the lines are smooth, and we only have small fluctuations.
-			We would like to emphasize, that the plot was not smoothed.
+			We would like to emphasize, that the lines were not smoothed.
 						
 			% END:		Indirect
 			%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -184,7 +184,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 			To be honest, they are terrible.
 			%
 			What is worth noting is, that the \NoBC{} method is ``approximately'' right.
-			For example it is able to capture the periodic nature of the force, but it has some problems.
+			For example it is able to capture the periodic nature of the force, but it has some other problems.
 			%
 			Especially from the other systems, except \StokesBC , we see, that the mean value of the curves is not zero, instead they seam to be shifted downwards.
 			%
@@ -235,7 +235,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 			In figure \ref{fig:experiments:pBallSin:Results:Sin:pressForce:pressDistNoBC} we again show the pressure distribution in a \pBallSinSin{} model, but this time the \NoBC{} method is used.
 			We do not see the spikes from before.
 			%
-			If we look at the two figures we also see, that we have additional pressure artefacts for the \FullImp{} method.
+			If we compare the two figures, we also see, that we have additional pressure artefacts for the \FullImp{} method.
 			They are located near the surface, but on the \emph{inside} of the ball.
 			%
 			\\
@@ -290,7 +290,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 		%
 		\\
 		We think that the stronger forces, that now acts on the ball, are responsible for this.
-		They penetrate the outer layer of the ball more efficient and are able to reach deeper levels.
+		They penetrate the outer layer of the ball more efficiently and are able to reach deeper levels.
 		This results in a less distorted pressure signal on the convex hull.
 		
 		% END:		RE3
@@ -323,7 +323,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 		%
 		The measured pressure is still more ``faithful'' than accurate, but more details are captured.
 		As usual the method is not able to accurately capture the onset of of the increasing phase.
-		However it is able to capture \emph{both} turning points, \emph{i.e.} it does not really under or over shoot and is no longer shifted.
+		However it is able to capture \emph{both} turning points, \emph{i.e.} it does not really under or over shoot and is no longer shifted down.
 		
 		As we have noted above, we think that the improvement, we saw in the \NoBC{} system, is related to the even larger forces, that are present in these systems.
 		%
@@ -393,7 +393,7 @@ Additionally, the object does not move at constant speed any more, instead its v
 		Which is probably due to continuity.
 		%
 		\\
-		But measuring the force directly, by integrating over the convex hull, shows that the value is basically zero for all four.
+		But measuring the force directly, by integrating over the convex hull, shows that the value is basically zero for all of them.
 		
 		
 		Above we have learned, that the convex hull, is not so reliable.