Skip to content
Snippets Groups Projects
Commit 128af25d authored by Thomas Lambert's avatar Thomas Lambert :helicopter:
Browse files

Fix: Column misalignment

parent 65999db2
No related branches found
No related tags found
No related merge requests found
Hide whitespace changes
Inline Side-by-side
APRI0004-ADP/BEMT/bemt_helico_slides.tex
+ 40
− 30
View file @ 128af25d
......@@ -106,8 +106,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\vspace{0.5cm}
\begin{columns}
\column{0.55\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.53\textwidth}
\textbf{Principle}
\begin{itemize}
\item Momentum theory
......@@ -123,7 +123,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\end{itemize}
\column{0.45\textwidth}
\hfill
\column{0.42\textwidth}
\center
\incfig{}{rotor}
\end{columns}
......@@ -161,8 +162,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Blade Element}
\begin{columns}
\column{0.45\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.43\textwidth}
\vfill
\only<1|handout:0>{\incfig{blade_element}{be_helico1}}
\only<2|handout:0>{\incfig{blade_element}{be_helico2}}
......@@ -172,7 +173,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\only<6>{\incfig{blade_element}{be_helico5}}
\vfill
\column{0.55\textwidth}
\hfill
\column{0.53\textwidth}
Angles
\begin{itemize}[<+->]
\item Blade pitch: $\theta$
......@@ -203,13 +205,14 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Blade Element}
\begin{columns}
\column{0.45\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.43\textwidth}
\vfill
\incfig{blade_element}{be_helico6}
\vfill
\column{0.55\textwidth}
\hfill
\column{0.53\textwidth}
\begin{itemize}[<+->]
\item Force perpendicular to rotor disk\\[0.2cm]
$dF_z = dL \cos\phi - dD \sin\phi$
......@@ -256,8 +259,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Non-dimensionalizations}
\begin{columns}
\column{0.5\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.48\textwidth}
\begin{itemize}
\item Relative position element\\[0.2cm]
$r = \dfrac{y}{R} \approx \dfrac{U}{\Omega R}$
......@@ -270,7 +273,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\pause
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\begin{itemize}
\item Thrust coefficient\footnotemark\\[0.2cm]
$dC_T = \dfrac{dT}{\rho A (\Omega R)^2}$
......@@ -355,11 +359,12 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Momentum equations}
\begin{columns}
\column{0.3\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.28\textwidth}
\incfig{}{annulus}
\column{0.7\textwidth}
\hfill
\column{0.68\textwidth}
The incremental thrust on the rotor annulus can be derived from the mass
flow rate through the annulus and twice the velocity at that section:
$$d\dot{m} = \rho dA (V_c + v_i) = 2\pi \rho(V_c+v_i)y \, dy$$
......@@ -401,15 +406,16 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\bigskip
\begin{columns}
\column{0.45\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.43\textwidth}
\textbf{Example}
\begin{itemize}
\item No twist: $\theta = \theta_\text{tip}$
\item Linear twist: $\theta = \theta_\text{tip} + \theta_\text{tw} (r-1)$
\end{itemize}
\column{0.55\textwidth}
\hfill
\column{0.53\textwidth}
\setlength\fwidth{0.7\textwidth}
\input{figures/matlab/twisteffect.tex}
\end{columns}
......@@ -449,13 +455,14 @@ sectionstyle=style2, sectionpage=none]{trigon}
Same blades ($\sigma=0.10$), different twist at constant rotor thrust $C_T = 0.008$.
\vfill
\begin{columns}
\column{0.5\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.48\textwidth}
\setlength\fwidth{0.7\textwidth}
\centering
\input{figures/matlab/idealTwist_lambda.tex}
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\setlength\fwidth{0.7\textwidth}
\centering
\input{figures/matlab/idealTwist_cl.tex}
......@@ -498,8 +505,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\vfill
\begin{columns}
\column{0.4\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.38\textwidth}
\textbf{Prandtl's tip-loss function}
\begin{itemize}
\item Correction factor $F$\\[0.2cm]
......@@ -509,7 +516,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
$f = \dfrac{N_b}{2} \cdot \left(\dfrac{1-r}{r \phi}\right)$
\end{itemize}
\column{0.6\textwidth}
\hfill
\column{0.58\textwidth}
\setlength\fwidth{0.6\textwidth}
\input{figures/matlab/prandtl.tex}
\end{columns}
......@@ -591,12 +599,13 @@ sectionstyle=style2, sectionpage=none]{trigon}
Caradonna and Tung, 1981. [NASA TM-81232]
\vfill
\begin{columns}
\column{0.5\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/caradoCL.tex}
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/caradoCT.tex}
\end{columns}
......@@ -612,12 +621,13 @@ sectionstyle=style2, sectionpage=none]{trigon}
Knight and Hefner, 1937. [NACA TN-626]
\vfill
\begin{columns}
\column{0.5\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/knightCTCQ.tex}
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/knightFM.tex}
\end{columns}
......
APRI0004-ADP/BEMT/bemt_prop_slides.tex
+ 44
− 35
View file @ 128af25d
......@@ -106,9 +106,9 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\vspace{0.5cm}
\begin{columns}
\begin{columns}[c,onlytextwidth]
%------------------------------------------------
\column{0.55\textwidth}
\column{0.53\textwidth}
\textbf{Principle}
\begin{itemize}
\item Momentum theory
......@@ -124,7 +124,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\end{itemize}
\column{0.45\textwidth}
\hfill
\column{0.42\textwidth}
\center
\incfig{}{rotor}
\end{columns}
......@@ -161,8 +162,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Blade Element}
\begin{columns}
\column{0.4\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.38\textwidth}
\vfill
\only<1|handout:0>{\incfig{blade_element}{be_prop1}}
\only<2|handout:0>{\incfig{blade_element}{be_prop2}}
......@@ -171,8 +172,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\only<5|handout:0>{\incfig{blade_element}{be_prop5}}
\only<6>{\incfig{blade_element}{be_prop5}}
\vfill
\column{0.6\textwidth}
\hfill
\column{0.58\textwidth}
Angles
\begin{itemize}[<+->]
\item Blade pitch: $\theta$
......@@ -204,13 +205,14 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Blade Element}
\begin{columns}
\column{0.4\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.38\textwidth}
\vfill
\incfig{blade_element}{be_prop6}
\vfill
\column{0.6\textwidth}
\hfill
\column{0.58\textwidth}
\begin{itemize}[<+->]
\item Force perpendicular to rotor disk\\[0.2cm]
$dF_z = dL \cos\phi - dD \sin\phi$
......@@ -233,9 +235,9 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Non-dimensionalizations}
\begin{columns}
\begin{columns}[c,onlytextwidth]
%------------------------------------------------
\column{0.5\textwidth}
\column{0.48\textwidth}
\begin{itemize}
\item Element rel. position\\[0.2cm]
$r = \dfrac{y}{R} \approx \dfrac{U}{\Omega R}$
......@@ -245,7 +247,8 @@ sectionstyle=style2, sectionpage=none]{trigon}
\end{itemize}
\pause
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\begin{itemize}
\item Thrust coefficient\footnotemark\\[0.2cm]
$dC_T = \dfrac{dT}{\rho A (\Omega R)^2}$
......@@ -291,10 +294,11 @@ sectionstyle=style2, sectionpage=none]{trigon}
\begin{frame}{Momentum equations}
\begin{columns}
\column{0.3\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.28\textwidth}
\incfig{}{annulus}
\column{0.7\textwidth}
\hfill
\column{0.68\textwidth}
The incremental thrust on the rotor annulus can be derived from the mass
flow rate through the annulus and twice the velocity at that section:
$$d\dot{m} = \rho dA (V_\infty + v_i) = 2\pi \rho(V_\infty+v_i)y \, dy$$
......@@ -465,11 +469,12 @@ Assume
\begin{frame}{Momentum equations}
\begin{columns}
\column{0.3\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.28\textwidth}
\incfig{}{annulus}
\column{0.7\textwidth}
\hfill
\column{0.68\textwidth}
Incremental thrust on the annulus is still
$$dT = 2\rho (V_\infty + v_i) v_i dA = 4\pi \rho(V_\infty+v_i)v_i y \, dy$$
or in non-dimensional form
......@@ -507,15 +512,16 @@ Assume
\end{itemize}
\bigskip
\begin{columns}
\column{0.45\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.43\textwidth}
\textbf{Example}
\begin{itemize}
\item No twist: $\theta = \theta_\text{tip}$
\item Linear twist: $\theta = \theta_\text{tip} + \theta_\text{tw} (r-1)$
\end{itemize}
\column{0.55\textwidth}
\hfill
\column{0.53\textwidth}
\setlength\fwidth{0.7\textwidth}
\input{figures/matlab/twisteffect.tex}
\end{columns}
......@@ -555,13 +561,13 @@ Assume
Same blades ($\sigma=0.10$), different twist at constant rotor thrust $C_T = 0.008$.
\vfill
\begin{columns}
\column{0.5\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.48\textwidth}
\setlength\fwidth{0.7\textwidth}
\centering
\input{figures/matlab/idealTwist_lambda.tex}
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\setlength\fwidth{0.7\textwidth}
\centering
\input{figures/matlab/idealTwist_cl.tex}
......@@ -581,8 +587,8 @@ Assume
\end{itemize}
\vfill
\begin{columns}
\column{0.4\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.38\textwidth}
\textbf{Prandtl's tip-loss function}
\begin{itemize}
\item Correction factor $F$\\[0.2cm]
......@@ -592,7 +598,8 @@ Assume
$f = \dfrac{N_b}{2} \cdot \left(\dfrac{1-r}{r \phi}\right)$
\end{itemize}
\column{0.6\textwidth}
\hfill
\column{0.58\textwidth}
\setlength\fwidth{0.6\textwidth}
\input{figures/matlab/prandtl.tex}
\end{columns}
......@@ -686,12 +693,13 @@ Assume
Caradonna and Tung, 1981. [NASA TM-81232]
\vfill
\begin{columns}
\column{0.5\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/caradoCL.tex}
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/caradoCT.tex}
\end{columns}
......@@ -707,12 +715,13 @@ Assume
Knight and Hefner, 1937. [NACA TN-626]
\vfill
\begin{columns}
\column{0.5\textwidth}
\begin{columns}[c,onlytextwidth]
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/knightCTCQ.tex}
\column{0.5\textwidth}
\hfill
\column{0.48\textwidth}
\setlength\fwidth{0.75\textwidth}
\input{figures/matlab/knightFM.tex}
\end{columns}
......
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment