User:Eas4200c.f08/HW report table/The best of HW4

 Under construction; not final (but close to being stable after a couple of weeks). The intention here is to document the best features in any HW report for the readers (including you); if you see excellent features in any HW report (including your team's) that I may have missed noticing, don't hesitate to let me know. (I don't have time to read all HW reports in detail.) Eml4500.f08 13:46, 28 October 2008 (UTC)


 * classnotes graded over 100%
 * idealized single-cell airfoil (semi-circular leading edge, straight-line body), find $$\displaystyle J$$; need to complete the solution to find the numerical value of $$\displaystyle J$$. Some team went well beyond expectation and solved this problem by coding it up with matlab; see Team Aero6.
 * analytical result: $$\displaystyle J = 0.100 m^4$$ Team Aero, $$\displaystyle J = 0.1001 m^4$$ Team VQCrew
 * numerical result: $$\displaystyle J = 0.125 m^4$$ Team Aero6; the error compared to the analytical result was large; perhaps there was not enough accuracy in the quadrature.
 * idealized 2-cell airfoil (rectangular body), find $$\displaystyle J$$; need to complete the solution to find the numerical value of $$\displaystyle J$$ Some team went well beyond expectation and solved this problem by coding it up with matlab; see Team Aero6.
 * analytical result: $$\displaystyle J = 0.855 \times 10^{-4} m^4$$ Team VQCrew
 * numerical result: $$\displaystyle J = 0.855 \times 10^{+4} cm^4 = 0.855 \times 10^{-4} m^4$$ Team Aero6
 * engineering (ad-hoc) derivation of expression for $$\displaystyle \theta$$ in terms of $$\displaystyle (G, \bar{A}, q, t)$$. Best explanation: Team VQCrew
 * figure for the derivation. The figure in Team VQCrew is not exactly correct since the line $$\displaystyle \overline{PP^{\prime\prime}}$$ is not distinguishable from the tangent to the contour; see the more correct figure in Exam 2.
 * 3 ad-hoc aspects of engineering derivation. Best description: Team VQCrew
 * torsional analysis by elasticity theory (cont'd)
 * kinematic assumption (review from previous lecture)
 * 4 zero strain components for torsion problem
 * strain-stress relation for isotropic elasticity
 * inversion for stress-strain relation for isotropic elasticity
 * 4 zero stress components for torsion problem


 * matlab problem graded over 100%
 * problem description (a repeat of my wiki page Airfoil with figure describing the various variables defining the NACA airfoil). Best description: Team ZYX had matlab figure of the NACA airfoil with all of its geometric quantities presented.
 * figure showing various points on the NACA airfoil and method of area integration by triangles for each cell. Best figure: Team Aero_(Eelman) Team Aero
 * those who did not finish their matlab problem in HW3 should finish it in HW4:
 * computation of centroid coordinates and area $$\displaystyle \bar{A}$$ for single-cell airfoil
 * validate their code with circular airfoil with convergence plot(s)
 * validate their code with various observer points $$\displaystyle P_0$$
 * plot of circular airfoil
 * apply their code to NACA 2415 airfoil with $$\displaystyle c=0.5m$$ to find centroid location and area $$\displaystyle \bar{A}$$ with convergence plot(s)
 * plot of NACA airfoil and centroid at crosshair
 * develop matlab code to find torsional constant $$\displaystyle J$$ of NACA airfoil
 * single-cell NACA 2415 airfoil, compute $$\displaystyle J$$
 * 3-cell NACA 2415 airfoil, compute $$\displaystyle J$$
 * quadrature by triangles at different points in the 3-cell NACA airfoil.
 * compute the area $$\displaystyle \bar{A}_i$$ for cell $$\displaystyle C_i$$, and sum them up to get total area $$\displaystyle \bar{A}$$; error must be within 1% of the area $$\displaystyle \bar{A}$$ for the single-cell NACA airfoil.
 * compare the numerical values of $$\displaystyle J$$ and draw some conclusion
 * best solution: Team Aero Team Aero_(Eelman) Team Aero6, figure showing the quadrature by triangles and selection of observer points $$\displaystyle P_0$$ in each cell; computed $$\displaystyle J_{1C}$$ for the single-cell NACA 2415 airfoil, and $$\displaystyle J_{3C}$$ for the 3-cell NACA 2415 airfoil, showing that $$\displaystyle J_{3C} \approx J_{1C}$$ (as noted in the textbook) even though they did not make this remark; Team VQCrew did make this remark, but they initially obtained $$\displaystyle J_{3C} \approx 2 J_{1C}$$, clearly not consistent with the remark; later, they updated their work to provide the correct result; see Team VQCrew Updated. See also Team ZYX, which did not have a figure to describe the quadrature by triangles and observer points $$\displaystyle P_0$$, but had a section describing the NACA airfoil geometry.
 * Team Aero: $$\displaystyle J_{1C} = 5.129 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.6884 \times 10^{-6} m^{4}$$
 * Team Aero_(Eelman): $$\displaystyle J_{1C} = 5.1163 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.5358 \times 10^{-6} m^{4}$$, relative difference $$\displaystyle 7\%$$.
 * Team Aero6: $$\displaystyle J_{1C} = 4.9978 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.4653 \times 10^{-6} m^{4}$$
 * Team ZYX: $$\displaystyle J_{1C} = 4.970 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 5.276 \times 10^{-6} m^{4}$$
 * Team VQCrew: $$\displaystyle J_{1C} = 4.7543 \times 10^{-6} m^{4}$$, $$\displaystyle J_{3C} = 8.6086 \times 10^{-6} m^{4}$$, later corrected to $$\displaystyle J_{3C} = 5.250 \times 10^{-6} m^{4}$$ in Team VQCrew Updated.
 * the above 5 teams agreed more or less with the result for $$\displaystyle J_{1C}$$ and for $$\displaystyle J_{3C}$$, except for the value of $$\displaystyle J_{3C}$$ from Team VQCrew; as a result, it is likely that the value of $$\displaystyle J_{3C}$$ from Teams Aero, Aero_(Eelman), Aero6, ZYX is the correct one. After Team VQCrew updated their work, all 5 teams agreed on both $$\displaystyle J_{1C}$$ and $$\displaystyle J_{3C}$$.


 * matlab-code certification: some students signed this section, after having claimed not knowing how to code with matlab but did not report their matlab tutorial work.

EML 4500, The best of HW4
 * contributing team members