MINNESOTA STATE UNIVERSITY, Mankato Aviation Department   Theory of Flight© (AVIA 201)   Project 1 Wind-Tunnel Laboratory (Trafton Science Center E 104)   PROJECT 1 Assignment  WIND-TUNNEL LAB (AVIA 201) Purpose: To introduce aviation/aeronautics/aerospace students to wind tunnel(s) and methods used in experimental identification of various aerodynamic (and stability) coefficients of airfoils (2D), wings (3D) and scale models

Subject:PhysicsPrice:0 Bought3

Share With

MINNESOTA STATE UNIVERSITY, Mankato

Aviation Department

 

Theory of Flight^© (AVIA 201)

 

Project 1 Wind-Tunnel Laboratory (Trafton Science Center E 104)

 

PROJECT 1 Assignment 

WIND-TUNNEL LAB (AVIA 201)

Purpose: To introduce aviation/aeronautics/aerospace students to wind tunnel(s) and methods used in experimental identification of various aerodynamic (and stability) coefficients of airfoils (2D), wings (3D) and scale models. To understand the value and purpose of wind-tunnel and experimental identification (measurement) of lift, drag, sideforce, and aerodynamic moments (pitching, rolling, yawing). To review the basic aerodynamic theory and knowledge of wings and airfoils presented in classroom. To apply and correlate knowledge acquired in the lab to better understanding of fixed- and rotary-wing flight control, stability and performance. To practice unit conversions (from SI to English engineering and vice versa). To perform visualization study of the boundary layer separation and stall patterns at higher AOAs. To visualize wingtip vortices when 3D (finite wing) airfoil is installed.

 

Grade: Wind-Tunnel lab project is required project in AVIA 201 course and brings 10% of the overall grade. Two students conduct one measurement, but all project completion is individual. Measurement report is required with all the graphs constructed. 

 

Project Deliverables, calculations and Graphical presentation: Measure static pressure and temperature in a lab. Calculate dry air density. Calculate dynamic and kinematic viscosity. Set the fan speed to achieve desired air dynamic pressure (p_dyn = q). Typically, in a range of 600-650 Pa. Calculate TAS. From the airfoil geometry (2D or 3D) measure chord length and reference surface area. Calculate the acoustic velocity (speed of sound). Calculate Reynolds and Mach numbers. Measure lift and drag. Evaluate aerodynamic coefficients. Estimate drag polar, parabolic drag model and other useful aerodynamic parameters (endurance polar and range polar). Present the final results in a graphical form for:

 

1. C_L vs AOA
2. C_D vs AOA
3. C_L vs C_D (Polar diagram)
4. C_D vs C_L² (Parabolic drag model C_D ? C_D,0 ? K ?C_L² )
5. ?C_LC_D? vs AOA (Aerodynamic efficiency)

6. 2

   3

   2

   1

   ?C_LC_D? vs AOA (Endurance efficiency)
7. ?C_LC_D? vs AOA (Range efficiency)

 

in a graphical format (diagrams) by using MS Excel^TM, Matlab^TM, Fortran, (Visual) Basic, C++, Maple^TM or any other appropriate calculation/spreadsheet/engineering/mathematical software (hand drawn graphs on millimeter paper is acceptable) and attach to cover page.

 

Workload: 2.5 hours of data collection and experiments. 6-10 hours per student for data processing and plotting/constructing diagrams and results. Overall, this wind-tunnel project should not exceed 13 effective physical hours workload per student.

 

Important Safety Note: Discipline and order during lab work will be enforced. Exercise safety precautions and common sense. Do not touch or come close to the large exhaust fan. Do not touch any electrical connections and cables. Do not wander around touching and moving things during the experimentation. Do not stand at the suction or the exhaust end of the wind tunnel.

Experimental Procedure: Two measurements of lift and drag aerodynamic coefficients will be conducted at two different wind-tunnel uniform speeds (adjusted by the fan). Reynolds and Mach numbers are to be evaluated for each experiment. The experimental procedure is:

 

1. Measure the barometric pressure p and temperature T in the lab. Assume dry air. Convert from ⁰F and inches Hg into Celsius (⁰C), Kelvin (K) and pressure in Pascals (and hPa=mbar). Call MKT ASOS to verify (KMKT elevation is about 1,000 ft).
2. Calculate the air density assuming that dry air mixture obeys ideal-gas law. The air gas constant R? 287.053 J/kgK . The isentropic coefficient of expansion for air is ??1.4 .
3. Calculate the speed of sound: a ? ?? R?T ? 20.05? T ?m/s?.
4. Calculate the dynamic viscosity of dry air ?.
5. Calculate the kinematic viscosity of the air ? ? ??.
6. Chose the airfoil/wing. Measure its chord and span. Calculate its mean chord length (if applicable), aspect ratio (AR), taper ratio (TR), sweep angle ?, planform type. Convert Imperial units into SI as necessary.
7. Set the airfoil/wing in a wind tunnel under desired AOA. Make sure that the Pitot tube is parallel with the longitudinal axis of the wind-tunnel test section, i.e., parallel with the flow. Close and tighten lightly the upper section.
8. Calibrate and re-calibrate the force balance to show about zero in L and D without flow.
9. Set the wind tunnel fan frequency so that the pitot-static system measures desired dynamic pressure (say 575, 600, 625, 650, etc. Pa). Higher dynamic pressure translates into faster speeds. At high AOAs too much dynamic pressure could lead to damage of the airfoil and/or balance. Typical speeds are 60-65 knots (100-110 ft/s or about 32 m/s).
10. Measure the lift and drag force using the dynamic balance. Record lift (L) and drag (D) for each set AOA. Unit for lift and drag is non-SI “kgf” which is about 9.81 N or 2.2 lbf. 
    1. Repeat the same measurement of L and D at different AOAs. Maintain constant measured dynamic pressure (same speed).
    2. Check that dynamic pressure and AOA didn’t change during the  experiment.
11. Calculate the speed (true) from measured dynamic pressure q and air density ?. Convert measured and all calculated speeds in m/s into km/h, ft/s, mph, and knots.
12. Calculate the Mach number M ? u a and the Reynolds number Re ? ??^cv ?u ?.
13. After all the measurements are done measure the temperature and barometric pressure again and find average air mass-density if applicable.
14. Evaluate C_L,C_L²,C_D,?C_L C_D ?,?C_L³² C_D ?,?C_L¹² C_D ? at each AOA from measured L and D and dynamic pressure q and given reference surface area.
15. Construct required diagrams.

 

Note: Environmental air pressure and temperature (possible multiple) in the lab will be measured at the time of experiments and dry air density calculated. Wind tunnel corrections, turbulence, and wall effects are neglected. Use no more than 6 significant digits accuracy when appropriate.

 

Airfoil tested: ___________________________ (e.g., NACA 2412, 4412, 0012, etc.)

 

Finite (3D) wing

Infinite (2D) airfoil/wing                                                                        

Wing/Airfoil Geometric characteristics

 

b [inch/m]	c [inch/m]	S [inch2/m2]	c [inch/m]	AR ?b2 S [-]	TR???ct [-]	cr	? [deg]

 

Static air data I (beginning of experiment)

 

p [inch Hg]	T [0F]	p [Pa]	T [0C/K]	? [kg/m3]	? [Pa s]	? [m2/s]

 

Static air data II (end of experiment if conducted)

 

p [inch Hg]	T [0F]	p [Pa]	T [0C/K]	? [kg/m3]	? [Pa s]	? [m2/s]

 

Average dimensional and non-dimensional air data (if both static measurements performed) 

 

p [Pa]	T [0C/K]	? [kg/m3]	? [-]	? [-]	? [-]	? [-]

 

Dynamic air data I (measured, set, and calculated)

 

 

q

[

Pa]

?

?

S

q

N

[

]

?

q

u

?

?

2

]

m/s

[

T

R

a

?

?

]

m/s

[

a

u

M

?

[

-

]

?

?

u

c

?

?

?

v

Re

[

-

]

 

 

Dynamic air data II (measured, set, and calculated if conducted)

 

 

q

[

Pa]

?

?

S

q

N

[

]

?

q

u

?

?

2

]

m/s

[

T

R

a

?

?

]

m/s

[

a

u

M

?

[

-

]

?

?

u

c

?

?

?

v

Re

[

-

]

 

Calculate Air Density from the ideal gas equation:

 

??  [kg/m3] R? 287?J/kgK (DryAir? ) R T?   Non-dimensional air data	p[Pa]      T[K]
p                  T                   ? ? ?  ??  ? ?  ? ? ???? pSL TSL ?SL pSL ?101,325 Pa TSL ? 288.15 K ?SL ?1.225 kg/m3   8.14807 10?2 T32	aSL ? 340.294 m/s

p

                                                                        ?      ?                        ^?5 Pa?s

Dynamic viscosity: ?? ?_SL?_SL ?1.78936?10

?T ?110.4?

or: ?? ?_SL ??0.76 ?1.78936?10?5 ??? T ?K? ??0.76 ?Pas? ?288.15?

 

                                                  ??          ^0.76         m /s²       ?_? ?_SL ?1.460702 10?                            ^?5 m /s²               

Kinematic viscosity: ??    ?? ?_SL ?    ?_?

                                                                           a          ?RT       ? T ?1/ 2           ^{1/ 2}

Speed of sound: a ? ?RT ?? a_SL ? ?RT ?_??_TSL ?_??       ?^? The “Lift” Equation: L?

??u² ?S?C_L ?q?S?C_L          q?

??u² ? p_dyn The “Drag” Equation: D?

??u² ?S?C_D ?q?S?C_D                                                   

                                                                                                 _{SL       ?}

 

 

 

Aerodynamic coefficients and efficiencies:

 

             L N? ? L?kgf??9.81?N/kgf ?

C_L ? q S N? ?? ? ? q Pa S m? ??      ?_{?         2}?_?     ???

?

             D N? ? D?kgf??9.81?N/kgf ?

CD ? q S N? ?? ? ? q Pa S m? ??       ?_?                                     2_?? ???        

?

E_D ? CL ? L ???      EP ? CL3 2   ???    E_R ? CL12   ???

              CD D                             CD                                         C_D

 

             ? CL ?              EMP ? ?? CL^{3 2} ??

EMD ? ?         ?        ??? ? CD ?max              ? CD ?max

 

? C^L12 ?

???    E_MRC ? ??     ???

? CD ?_max

 

1. Tabular presentation of measured and calculated results (Table I measurement)

1	AOA [deg]	L [kgf]	D [ kgf]	CL  [-]	CD [-]	CL2  [-]	CL CD [-]	CL 2 3  CD   [-]	CL 2 1  CD   [-]
	-4
2	-2
3	0
4	2
5	4
6	6
7	8
8	10
9	12
10	14
11	16
12	18
13	20
14	22
15	24

2. Tabular presentation of measured and calculated results (Table II measurement)

1	AOA [deg]	L [kgf]	D [ kgf]	CL  [-]	CD [-]	CL2  [-]	CL CD [-]	CL 2 3  CD   [-]	CL 2 1  CD   [-]
	-4
2	-2
3	0
4	2
5	4
6	6
7	8
8	10
9	12
10	14
11	16
12	18
13	20
14	22
15	24

3. Tabular presentation of measured and calculated results (Table III measurement)

1	AOA [deg]	L [kgf]	D [ kgf]	CL  [-]	CD [-]	CL2  [-]	CL CD [-]	CL 2 3  CD   [-]	CL 2 1  CD   [-]
	-4
2	-2
3	0
4	2
5	4
6	6
7	8
8	10
9	12
10	14
11	16
12	18
13	20
14	22
15	24

 

Useful equations and definitions:

 

a ? ?? R T ? 20.05? T

 

a

u

M _?           Re _? u ?c _? u ?c ??

 

                                      ?            ?

1 ??SL ? KCAS2 ? 1 ??? KTAS2 _? KTAS _? KCAS _? KCAS 

2                              2                                                    ?        ???SL ?

L ?

 ??? KTAS² ? S ?c_L ? q ? S ?c_L ? S ??p ? S ??p_l ? p_u ?

 

D ?

 ??? KTAS² ? S ?c_D ? q ? S ?c_D

 

 

Useful units, conversions and constants:

 

                       m                N

1 N ?1 kg s₂ 1 Pa ? m2

m

1 kgf ?1 kg?9.80665 s₂ ? 9.81 N ? 2.2 lbf

1 lbf ? 4.448 N ? 4.448 kg m/s?    ² ?1slug 1 ft/s? ² ? 32.174 lbm ft/s       ² 1 slug ?14.59 kg      1kg=2.205 lbm

1 mph ? 5280 ft/3600 s     1 knot ?1NM/h ? 6080 ft/3600 s ?1.689 ft/s

1 km/h ?1000 m/h ?1000 m/3600 s ? 3281 ft/3600 s ? 0.911 ft/s

1 mile ?1.61 km     1 NM ?1.15SM ?1.852 km     

1 m ? 3.2808 ft     1 inch ? 25.4 mm ? 2.54 cm 1 ft ? 0.3048 m

1 inch² ? ?2.54_?² ?10^-4 m² ? 6.452 10?                          ^-4 m²                                                                  1m² ?10.764ft² ?1550inch²

1 ata = 760 mm Hg ? 29.92 inch Hg ?101,325 Pa ?1013.25 hPa ?1013.25 mbar ?14.69 psi 1bar ?14.5 psi 1 inch Hg ? 3386.53  Pa ? 33.865 hPa ? 0.491 psi

^{t[ F]-32o}

t[ C]^o ?     1^oC ?1.8^oF             T[K] ? 273.15? t[ C]^o                  

1.8 g₀ ? 9.80665 m/s² ? 9.81 m/s² ? 32.174 ft/s² ? 32.2 ft/s²

 

 

 

 

References

 

Abbot, Ira H. and von Doenhoff, Albert E., Theory of Wing Section, Dover, New York, 1959.

 

Ackroyd, J. A. D., Axcell, B. P., and Ruban, A. I., Early developments of Modern Aerodynamics, AIAA, Reston, VA. 2001.

 

Anderson, J. D. Jr., Fundamentals of Aerodynamics, 2^nd edition, McGraw-Hill Book Company, New York, 1991.

 

Anderson, J. D. Jr., Aircraft Performance and Design, McGraw-Hill Book Company, New York, 1999.

 

Anderson, J. D. Jr., Introduction to Flight, McGraw-Hill Book Company, New York, 2005.

 

Anon, Principles of Flight, JAA ATPL Training, Edition 2, Book 8  (JAR Ref. 080), Atlantic Flight Training, Ltd., Sanderson Training products, ISBN 0-88487-495-8, Jeppesen GmbH, NeuIsenburg, Germany, 2007.

 

Ashley, H., and Landahl, M., Aerodynamics of Wings and Bodies, Dover, New York, 1965.

 

Ashley, H., Engineering Analysis of Flight vehicles, Dover, New York, 1992.

 

Bertin, J. J., and Cummings, R. M., Aerodynamics for Engineers, 5^th edition, Pearson PrenticeHall, Upper Saddle River, NJ, 2009. 

 

Drela, M., Flight Vehicle Aerodynamics. The MIT Press, Cambridge, MA, 2014.

 

Etkin, B., Dynamics of flight: Stability and control, John Wiley & Sons, New York, 1959. 

 

Etkin, B., Dynamics of atmospheric flight, Dover, Mineola, 2005.  

 

Glauert, H., The Elements of Aerofoil and Airscrew Theory, 2^nd edition, Cambridge University Press, London, 1947. 

             

Hubin, W. N., The Science of Flight: Pilot-oriented Aerodynamics, Iowa State University Press, Ames, 1992 (1995 second printing).

 

Hurt, H. H. Jr., Aerodynamics for Naval Aviators, Revised, reprinted with permission by Aviation Supplies & Academics, Inc., Renton, Washington 98059-3153, 1965.

 

Kolk, R. W., Modern flight dynamics, Prentice-Hall, Englewood Cliffs, 1961.

 

Kuethe, A. M., and Schetzer, J. D., Foundations of Aerodynamics, 2^nd edition, John Wiley and Sons, New York, 1959.

 

Miele, A., Flight Mechanics: Theory of flight paths. Dover, Minneola, 2016.

 

Milne-Thomson, L. M., Theoretical Aerodynamics, Dover, New York, 1973.

 

von Misses, R., Theory of Flight, Dover, New York, 1959.

 

Moran, J., An introduction to theoretical and computational aerodynamics, Dover, Mineola, 2003.

 

Nelson, R. C., Flight stability and automatic control, 2^nd edition, McGraw-Hill, New York, 1998.

 

Phillips, W. F., Mechanics of flight, John Wiley & Sons, New York, 2004.

 

Pope, A., Basic Wing and Airfoil Theory, Dover, Mineola, 2009.

 

Prandtl, L., and Tietjens, O. G., Applied Hydro- and Aeromechanics, (Translation), Dover, New York, 1957.

 

Rae, W. H., and Pope, A., Low-Speed wind tunnel testing, 2^nd edition, John Wiley & Sons, New York, 1984.

 

Shevell, R. S., Fundamentals of Flight, 2^nd edition, Prentice Hall, New Jersey, 1989.

 

Smith, H. C., The illustrated guide to Aerodynamics, 2^nd Edition, ISBN 0-8306-3901-2 (pbk.), McGraw-Hill Book Company, New York, 1992.

 

Stinton, D., The anatomy of the airplane, 2^nd edition, AIAA, Reston, VA. 1998.

 

Swatton, P. J., Principles of Flight for Pilots, John Wiley and Sons, Ltd. Chichester, West Sussex, 2011.