SD-S05-001-R-361
August 18, 2005
Main title
Project Number
Boris Karlof
A technical report submitted to the Aerospace Engineering faculty
in partial fulfillment of the requirements for the course
AerE 361 — Aerospace Numerical Methods and Design
Project Advisor: Dr. Ambar Mitra
TA: James Bond
Iowa State University
Ames, Iowa
c 2005 by the author. All rights reserved.
Copyright ii
Iowa State University of Science and Technology
Department of Aerospace Engineering
This is to certify that this is an original work of
Boris Karlof
There is no misappropriation of another author’s contributions,
including an author’s ideas, information, or words.
Author
This technical report has met the
English and technical content proficiency requirements
for a formal report and is hereby approved by:
Project Advisor
iii
TABLE OF CONTENTS
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2 Current Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
CHAPTER 1
AERODYNAMIC OF PARAFOIL AT IOWA STATE . . . . . . . . .
2
2.1 Vortex Panel Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
CHAPTER 2
CHAPTER 3
RESULT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
CHAPTER 4
CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
4.1 Referencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
APPENDIX A Importing figures into Latex . . . . . . . . . . . . . . . . . . . . . . . .
7
APPENDIX B SAMPLE CODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
1
CHAPTER 1
INTRODUCTION
Make sure you have an intro paragraph (2-3 lines at least). Then you may divide you intro into
sections.
1.1
Background
To steal ideas from one person is plagiarism; to steal from many is research.
1.2
Current Problem
2
CHAPTER 2
AERODYNAMIC OF PARAFOIL AT IOWA STATE
Always start with an intro paragraph to let the reader know what to expect. Don’t jump into section
right away.
2.1
Vortex Panel Method
According to Bertin [1], It is the location of these horse-shoe vortices on the wing camber which
gives the VLM it’s generality and accuracy. An illustration of the horse-shoe vortex distributions across
the planform is shown in Figure A.2 on page 8.
This is stuff stuff stuff stuff...
h
i
~r2
= [(~r2 × ~r2 ) · ı̂] ı̂ + [(~r1 × ~r2 ) · ̂] ̂ + (~r1 × ~r2 ) · k̂ k̂
~r1 ×
~r1
\begin{equation}
\left( \vec{r}_1\times \frac{\vec{r}_2}{\vec{r}_1}\right) =\left[
\left( \vec{r}_2\times \vec{r}_2\right) \cdot
\hat{\imath} \right]
\hat{\imath} + \left[ \left( \vec{r}_1\times
\vec{r}_2\right) \cdot \hat{\jmath}\right] \hat{\jmath}+\left[ \left( \vec{
r}_1\times \vec{r}_2\right) \cdot \hat{k}\right] \hat{k}
\label{abccc}
\end{equation}
(2.1)
3
2.2
Boundary Conditions
The lifting surface and the wake vortex sheet both induce a normal component of velocity at a point
CP. We want the wing mean camber line to be a stream surface of the flow such that it is as if there is
a body in the flow. For a horse-shoe vortex, there are three critical velocities which must be summed
in order to determine if the camber is a stream function of the flow. These include: freestream velocity,
induced velocity due to the bound vortices and the induced velocities due to the trailing vortices [1].
Please refer to Equation 2.1 on page 2

a11


 0



0
\begin{equation}
\begin{bmatrix}
a_{11} & 0 & 0
\\
0 & a_{22} & 0 \\
0 & 0
& a_{33}
\end{bmatrix}
%
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
%
=
%
0
a22
0



0  1 0 0 a11
 

 




0  0 1 0 
= 0
 

 

a33
0 0 1
0
0
a22
0

0 


0 



a33
(2.2)
4
\begin{bmatrix}
a_{11} & 0 & 0
\\
0 & a_{22} & 0 \\
0 & 0
& a_{33}
\end{bmatrix}
\end{equation}
ẋ0 = U · cos Θ cos Ψ + V · (sin Φ sin Θ cos Ψ − cos Φ sin Ψ) + W · (cos Φ sin Θ cos Ψ + sin Φ sin Ψ)
ẏ 0 = U · cos Θ sin Ψ + V · (sin Φ sin Θ sin Ψ + cos Φ sin Ψ) + W · (cos Φ sin Θ sin Ψ − sin Φ cos Ψ)
(2.3)
ż 0 = −U · sin Θ + V · sin Φ cos Θ + W · cos Φ cos Θ
\begin{equation}
\begin{split}
\dot{x}’&=U\cdot \cos{\Theta}\cos{\Psi}+V \cdot\left(\sin{\Phi}\sin{\Theta}
\cos{\Psi} -\cos{\Phi}\sin{\Psi}\right)+W \cdot \left(\cos{\Phi}\sin{\Theta}
\cos{\Psi}+\sin{\Phi}\sin{\Psi}\right) \\
%
\dot{y}’&=U\cdot \cos{\Theta}\sin{\Psi}+V \cdot\left(\sin{\Phi}\sin{\Theta}
\sin{\Psi} +\cos{\Phi}\sin{\Psi}\right)+W \cdot \left(\cos{\Phi}\sin{\Theta}
\sin{\Psi}-\sin{\Phi}\cos{\Psi}\right) \\
%
\dot{z}’&=-U \cdot \sin{\Theta} + V\cdot \sin{\Phi}\cos{\Theta}+W \cdot
\cos{\Phi}\cos{\Theta}
\end{split}
\end{equation}
5
CHAPTER 3
RESULT
Tabulations, data sheets, plots, graphs and discussion of the results. The discussion should always
include sources of errors, and estimate of their magnitudes. If you compared to books/articles or tables,
please do cite them in here (i.e., according to Anderson) Use section only if you have more than 1
section. Always remember to label your equations/figures/tables. Should NOT have toooooooooooooo
many tables in here. Put them in the appendix. Initial conditions and parameters regarding each test
case should be tabulated.
6
CHAPTER 4
CONCLUSION
A conclusion is the place where you got tired of thinking.... According to Section 2.2 of Chapter 2 on
page 2 .... For more details, please refer to Figure A.1 on the following page in Appendix A, According
to J. J. Bertin [1], stuff stuff stuff...
4.1
Referencing
A conclusion is the place where you got tired of thinking....
According to Section~\ref{sec:bc} of Chapter~\vref{ch:theo} ....
For more details, please refer to Figure~\vref{fig:scale} in Appendix~\ref{ap:xyz},
According to J. J. Bertin \cite{bertin}, stuff stuff stuff...
7
APPENDIX A
Importing figures into Latex
0.5
0.4
0.3
0.2
Y
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.2
0
0.2
0.4
0.6
0.8
X
Figure A.1 Importing an eps figure created in tecplot and scaling it.
\begin{figure}[h!bt] \centering
\includegraphics[angle=0,scale=.3]{figures/af}
%\setlength{\captionwidth}{2.5 in} % to set the width of caption = to figure width
%captions should be descriptive!! It may be longer than 1 line.
\isucaption{B-2 Spirit Stealth Bomber breaking sound barrier}
\label{fig:scale}
\end{figure}
8
0.5
0.4
0.3
0.2
0.8
Y
0.1
0
0.6
1
-0.
0.4
X
2
-0.
0.2
3
-0.
0
4
-0.
2
-0.
Figure A.2 Importing an eps figure created in tecplot and scaling+rotating it
\begin{figure}[h!bt] \centering
\includegraphics[angle=30,scale=.3]{figures/af}
%\setlength{\captionwidth}{2.5 in} % to set the width of caption = to figure width
%captions should be descriptive!! It may be longer than 1 line.
\isucaption{Importing an eps figure created in tecplot and scaling$+$rotating it}
\label{fig:rotate}
\end{figure}
9
APPENDIX B
11
c
12
13
14
15
SAMPLE CODE
SUBROUTINE gaussj(a,n,np,b,m,mp)
INTEGER m,mp,n,np,NMAX
REAL*8 a(np,np),b(np,mp)
PARAMETER (NMAX=50)
INTEGER i,icol,irow,j,k,l,ll,indxc(NMAX),indxr(NMAX),ipiv(NMAX)
REAL*8 big,dum,pivinv
do 11 j=1,n
ipiv(j)=0
continue
do 22 i=1,n
big=0.
do 13 j=1,n
if(ipiv(j).ne.1)then
do 12 k=1,n
if (ipiv(k).eq.0) then
if (abs(a(j,k)).ge.big)then
big=abs(a(j,k))
irow=j
icol=k
endif
else if (ipiv(k).gt.1) then
pause ’singular matrix in gaussj’
endif
continue
endif
continue
ipiv(icol)=ipiv(icol)+1
if (irow.ne.icol) then
do 14 l=1,n
dum=a(irow,l)
a(irow,l)=a(icol,l)
a(icol,l)=dum
continue
do 15 l=1,m
dum=b(irow,l)
b(irow,l)=b(icol,l)
b(icol,l)=dum
continue
endif
indxr(i)=irow
10
c
16
17
18
19
21
22
23
24
indxc(i)=icol
if (a(icol,icol).eq.0.) pause ’singular matrix in gaussj’
pivinv=1./a(icol,icol)
a(icol,icol)=1.
do 16 l=1,n
a(icol,l)=a(icol,l)*pivinv
continue
do 17 l=1,m
b(icol,l)=b(icol,l)*pivinv
continue
do 21 ll=1,n
if(ll.ne.icol)then
dum=a(ll,icol)
a(ll,icol)=0.
do 18 l=1,n
a(ll,l)=a(ll,l)-a(icol,l)*dum
continue
do 19 l=1,m
b(ll,l)=b(ll,l)-b(icol,l)*dum
continue
endif
continue
continue
do 24 l=n,1,-1
if(indxr(l).ne.indxc(l))then
do 23 k=1,n
dum=a(k,indxr(l))
a(k,indxr(l))=a(k,indxc(l))
a(k,indxc(l))=dum
continue
endif
continue
return
END
11
BIBLIOGRAPHY
[1] Bertin, J. J. and M. L. Smith, Aerodynamics for Engineers, 3rd edition, Englewood Cliffs, New
Jersey: Prentice Hall, 1998.
[2] Knacke, T. W., Parachute Recovery Systems Design Manual, Santa Barbara, California: Para
Publishing, 1992.
[3] Lissman, P. B. S., and G. J. Brown, “Apparent Mass Effects on Parafoil Dynamics,” AIAA-93-1236,
1993, pp. 233-239.
[4] Lu, P., Course Notes of AerE 531, “Automatic Control of Flight Vehicles,” Iowa State University,
Spring 1997.
[5] Lu, P., Course Notes of AerE 556, “Guidance and Navigation of Aerospace Vehicles,” Iowa State
University, Spring 1998.
[6] Melbourne, F. L., “Pioneer Aerospace Advances High Glide Recovery System,” Aviation Week and
Space Technology, Vol. 132, April 16, 1990, p. 61.
[7] Murtaugh, S. A., and H. E. Criel, “Fundamental of Proportional Navigation,” IEEE Spectrum,
Vol. 3, Dec. 1966, pp. 75-85.