naca 4412 yapılmış analiz

Aero 307-02 - Lab 2Survey of a NACA-4412 Airfoil

Chris D. Rasmussen and Mathew L. ThomasCalifornia Polytechnic State University, San Luis Obispo, CA, 93410

February 10, 2010

1American Institute of Aeronautics and Astronautics

The objective of this report is to present the results from a wind tunnel test of a NACA-4412 airfoil. The goal of the experiment is to measure Cp, Cd, and Cl. To do this a model of the NACA-4412 airfoil with a 10" chord is placed along the width of Cal Poly's 3ft x 4ft low speed wind tunnel. At a speed of 20m/s, Cp values were taken at angles of attack of 0, 8, 16, and 25 degrees. Then Cd and Cl values were calculated based on that data.

Nomenclature

Cd = drag coefficient per unit span, d

q∞ c

Cl = lift coefficient per unit span, l

q∞ c

Cp = pressure coefficient, p−p∞

q∞

c = airfoil chord d = drag per unit span di = drag at panel i l = lift per unit span li = length of panel i P = pressure P∞ = free stream static pressure Pi = pressure at panel i

q∞ = free stream dynamic pressure 12

ρ∞ u∞2

Re = Reynolds number, ρ∞ u∞ c

μ∞Si = panel length U∞ = free stream velocity θi = angle between pressure and lift vector of panel i

I. Introduction


The purpose of this report is to find Cp, Cd, and Cl of a NACA-4412 airfoil. To do this a scale model with a 10"

chord is mounted across the test section of the wind tunnel with a rake of 20 pitot tubes positioned behind the airfoil. These measure the velocity distribution of the wake flow behind the airfoil. In addition, 20 pressure ports mounted on the center plane of the airfoil measure the pressure distribution on the upper and lower surfaces.

The 4412 in the airfoil name represents the airfoil shape. The first 4 is the max camber in (1/100)*c, the second 4 is the location of max camber in (1/10)*c and the 12 is the max thickness in (1/100)*c. So, the airfoil has 0.04c max camber at 0.4c, with a max thickness of 0.12c.

The reason for doing this test was to find the lift and drag, including the pressure and profile drag. Lift and drag values were found at angles of attack of 0, 8, 16, and 25 degrees. The results show no separation occurs at 0 and 8 degrees, some separation at 16 degrees, and complete separation along the upper surface at 25 degrees. This trend can be seen in the images below.

Figure 1: Water tunnel flow visualization

The airfoil lift below stall is primarily dependent on surface pressure, which in turn depends on airfoil shape, angle of attack, and Reynolds number. The airfoil lift produced by skin friction is negligible.

To do the analysis on the airfoil, a panel method is used. The Cp is applied to the panel method to find the lift coefficient and pressure drag coefficient. Also, the momentum method is used to find the total drag coefficient and the skin friction coefficient. In the panel method, the airfoil surface is conceptually replaced by panels. Then vortices, sources, or sinks on the panels are adjusted until the airfoil surface becomes a streamline and the Kutta conditions are satisfied. Then, you have the surface Cp and this in turn gives you lift and pressure drag.

II. Analysis

In order to calculate the drag and lift of the airfoil due to pressure forces using the panel method, the pressure coefficients from the wind tunnel data are used. The formula used to calculate drag on the airfoil from the pressure coefficient data is:

Cd=∑i

±(Pi−P∞

q∞)

si

csinθ i

Where Cd is the drag coefficient, Pi is the pressure on panel i, P∞ is the free stream static pressure, q∞ is the free stream dynamic pressure, si is the length of panel I, c is the chord length, and θi is the angle from the normal to the airfoil surface to the lift vector of the airfoil. The lift vector of the airfoil is perpendicular to the free stream velocity vector pointing in the upward direction.

In order to calculate the lift coefficient of the airfoil, the pressure coefficients from the wind tunnel test are used along with the following formula:

C l=∑i

±(Pi−P∞

q∞)s i

ccosθ i

The lift coefficient equation used is very similar to the drag calculation except that the cosine of the angle between the lift vector and surface normal is taken.

However, the equation can be simplified by noticing that


P i−P∞

q∞=C p ,i.

Then Cp can be used to simplify the drag and lift coefficient calculations.

Cd=∑i

± (C p ,i )s i

csin θi Cl=∑

i±(Cp ,i)

s i

ccosθi

In order to calculate the total drag on the airfoil, the rake data is used along with the momentum method. The momentum method drag calculation will include both the pressure drag and viscous drag of the airfoil. In order to calculate the drag on the airfoil conservation of momentum is used as follows:

Cd=∑i=1

20

2(√ qi

q∞

¿−qi

q∞) ∆ y

c¿

Where qi is the dynamic pressure at port i, q∞ is the free stream dynamic pressure, ∆y is the distance between rake pressure sensors, and c is the chord length of the airfoil.

The panel construction figure used is shown on the next page. The normal to the airfoil surface at panel 1 is labeled P1. The angle is taken from the normal to the chord and then we used θ i = (90o – the measured angle) to find the angle between the surface normal and the lift vector for an angle of attack of 0. When the angle of attack was not zero, the angle of attack was added to θi.


III. Apparatus and Procedures

The procedure for this experiment starts with documenting and checking all of the test equipment. Once the equipment has been checked, the wind tunnel is set to a speed of 20 m/s. This is done with a speed controller made by Square D(model #altivar) and an incline manometer made by Meriam(model #40HE35). The least significant reading (LSR) for the manometer was 1mm and the tare reading is zero. The next step is to level the airfoil and then rotate it until the leading edge pressure port is at the stagnation point. Once the stagnation point is found, the airfoil is set to zero angle of attack. Also, a rake of pitot tubes is mounted roughly in the center of the wake flow. For zero angle of attack, pressure values are recorded for both the airfoil and the rake. Then the airfoil is adjusted to angles of 8, 16, and 25 degrees and surface pressure around the airfoil, and the pressure readings for the rake are recorded.

IV. Results and Discussion

Figure 2 below shows the pressure coefficient distribution along the wing at an angle of attack of 0 degrees from our wind tunnel test data. The top line is the pressure coefficient distribution on the top of the wing. The bottom curve is the pressure coefficient distribution along the bottom of the wing.

Figure 2: Pressure coefficient distribution at 0 degree angle of attack

The Cp axes on Figure 2 have the negative values on the upper portion so that the upper curve will represent the upper surface of the wing. We can see that there are not any flat areas on the graph, which indicates that there is no separation of the boundary layer.

Figure 3 below shows the pressure coefficient distribution for an angle of attack of 0 degrees from the CFD (Computational Fluid Dynamics) data.


Figure 3: Pressure coefficient distribution from CFD data

From Figure 3 the graph is a similar shape, and the trends are the same. The stagnation point is still at the leading edge of the airfoil and the pressure coefficient at the trailing edge is 0.2. There are no signs of stagnation because there are no regions of flat Cp.

Figure 4 below is a picture taken of the water tunnel flow visualization at an angle of attack of 0 degrees.

Figure 4: Water tunnel flow visualization at 0 degrees angle of attack

Figure 4 clearly shows that there is no boundary layer separation because the red dye follows the surface smoothly over the entire wing. Comparing this with the pressure coefficient plots leads us to conclude that there is no boundary layer separation at an angle of attack of 0 degrees.

Figure 5 below shows the CFD velocity distribution in the flow around the airfoil.


Figure 5: Velocity distribution around airfoil at 0 degrees angle of attack from CFD data

It can clearly be seen in Figure 5 that the velocity is higher along the upper surface of the wing, represented by the redder colors. Also there is a velocity defect area directly behind the airfoil represented by the green and blue colors coming off the trailing edge. The velocity defect region is small.

Figure 6 below shows the pressure coefficient distribution from our wind tunnel test data at an angle of attack of 8 degrees. Again, the top curve corresponds to the top surface of the wing, and the bottom curve corresponds to the bottom surface of the wing.

Figure 6: Pressure coefficient distribution at angle of attack of 8 degrees

Figure 6 indicates that there is no boundary layer separation due to the fact that there are no flat areas of pressure coefficient that would indicate separation. Also the top surface of the wing has much more negative pressure coefficients than at 0 degrees angle of attack, which leads us to believe that more lift is being produced


because there is a larger pressure difference between the top and bottom of the wing. We can also see that the stagnation point is very near the leading edge, if possibly a bit back on the lower surface of the wing.

Figure 7 below shows the pressure coefficient distribution along the wing at an angle of attack of 8 degrees from the CFD data.

Figure 7: Pressure coefficient distribution at 8 degrees angle of attack from CFD data

From Figure 7 we can see that the stagnation point is indeed on the underside of the wing very near the

front, at xc=0.01. There are no flat areas of Cp which indicates that there is no boundary layer separation.

Figure 8 below shows the water tunnel flow visualization at 8 degrees angle of attack.

Figure 8: Water tunnel flow visualization at angle of attack of 8 degrees

In Figure 8 the flow is clearly turbulent. However the flow does not separate from the surface of the wing leading to the conclusion that the boundary layer stays attached over the entire wing.

Figure 9 below shows the velocity distribution around the airfoil from CFD data at 8 degrees angle of attack.


Figure 9: Velocity distribution around airfoil at 8 degrees angle of attack from CFD Data

Along the upper surface of the wing, especially near the leading edge, the velocity is higher which leads to a lower pressure due to Bernoulli’s principle. Also there is again a velocity defect area directly behind the trailing edge of the airfoil represented by the blue region. This velocity defect area is also rather small.

Figure10 below shows √ qq∞

for the wake flow data taken by the rake.

0 5 10 15 20 250.8

0.85

0.9

0.95

1

1.05

AoA 8 degrees

Pitot tube

sqrt(q/q_inf)

Figure 10: Wake flow velocity profile from experimental data at 8 degrees angle of attack

Figure 10 clearly shows that there is a velocity defect region behind the airfoil centered at the 14th pitot tube in the wake array. This velocity defect area indicates that the airfoil is producing drag.

Figure 11 below shows the pressure coefficient distribution at an angle of attack of 16 degrees from our wind tunnel test data.


Figure 11: Pressure coefficient distribution at angle of attack of 16 degrees

The stagnation point has moved from the front to slightly back and on the underside of the wing and is slightly further back than where it was at 8 degree angle of attack. Also there is a clear area of flat Cp starting at

about xc=0.5 and continuing to the trailing edge. Clearly the boundary layer has separated and we have a stagnant

region near the trailing edge of the wing.Figure 12 below shows the pressure coefficient distribution at an angle of attack of 16 degrees from the

CFD data.

Figure 12: Pressure coefficient at 16 degree angle of attack from CFD data

Clearly there is a region of flat pressure coefficient which means that there is stagnation and boundary layer separation. This region starts at around x/c = 0.5 and continues until the trailing edge. At the leading edge the

boundary layer is still attached. Also the stagnation point has moved back to xc=0.03.

Figure 13 below shows the water tunnel flow visualization at an angle of attack of 16 degrees.


Figure 13: Water tunnel flow visualization at 16 degree angle of attack

Figure 13 clearly shows that there is boundary layer separation which seems to occur around the midpoint of the airfoil. The transition to turbulent flow has also moved further towards the leading edge.

Figure 14 below shows the velocity distribution around the airfoil at 16 degrees angle of attack.


Figure 14 shows that there is once again higher velocities along the upper surface, although they are now concentrated along the leading edge of the airfoil. The separated region is clearly visible due to the low velocity of the stagnant flow which is shown by the blue region on the back of the upper surface of the airfoil. Also the velocity


defect area following the trailing edge is significantly larger than at either 0 or 8 degrees angle of attack, leading to the conclusion that there is more drag on the airfoil at 16 degrees angle of attack because more momentum is being lost.

Figure 15 below shows the pressure coefficient distribution at 25 degree angle of attack from our wind tunnel test data.

Figure 15: Pressure coefficient distribution at 25 degree angle of attack

Figure 15 clearly shows that there is leading edge boundary layer separation because the entire wing has a flat Cp distribution which indicates a stagnation region.

Figure 16 below shows the pressure coefficient distribution at 25 degree angle of attack from the CFD data.

Figure 16: Pressure coefficient distribution at 25 degree angle of attack from CFD data

Figure 16 is not nearly as smooth as our wind tunnel test data. The reason could be that the iteration scheme did not converge to a value for either lift or drag and the algorithm could be having trouble with the flow field from leading edge separation.

Figure 17 below shows the water tunnel flow visualization at 25 degree angle of attack.


Figure 17: Water tunnel flow visualization at 25 degree angle of attack

Figure 17 clearly shows that there is leading edge boundary layer separation and that some of the flow from the lower surface is being sucked onto the upper surface.

Figure 18 below shows the velocity distribution around the airfoil at 25 degrees angle of attack.


Figure 18 clearly shows that there is leading edge separation when the angle of attack is 25 degrees. The velocity defect region coming off the trailing edge is also much larger than the 16 degree angle of attack airfoil meaning that even more drag is produced. Also there is a lot of slow moving flow along the upper surface of the airfoil which means that not much lift is being produced compared to the lower angles of attack.


At 8 degrees angle of attack, the lift coefficient was C l=1.304 and the pressure drag (form drag) coefficient was Cd , p=0.173 the profile drag coefficient from the rake data calculations was Cd=0.059 these results indicate that the airfoil has not stalled. The momentum data is not needed for the lift coefficient because lift is negligibly affected by viscous forces. The difference between the profile drag coefficient and the form drag coefficient is the viscous drag coefficient or skin friction drag.

At 25 degrees angle of attack the lift coefficient was C l=0.539 and the pressure drag coefficient was Cd , p=0.506. It is clear that at 25 degrees angle of attack the airfoil is in post stall because the lift coefficient has dropped dramatically because the flow has separated. Also the drag coefficient has increased dramatically due to the large separated region.

However, there is a fair amount of experimental uncertainty in our calculations due to the number of pressure ports on the wing and in the wake region. Also the readings from the pressure ports and pitot tubes are not perfect so the experimental uncertainty must be accounted for. The calculated experimental error for the pressure coefficient was 0.38% and the calculated experimental uncertainty for the lift coefficient was 2.56 ×10−5 at 8 degrees angle of attack and 2.35 ×10−4 for 25 degrees angle of attack.

V. Conclusion

A 10 inch NACA 4412 airfoil was surveyed in the Cal Poly low speed wind tunnel. Pressure ports on the airfoil surfaced were connected to a scanivalve apparatus to record the pressure at 20 different locations along the airfoil. Also a rake of pitot tubes was placed behind the airfoil to measure the wake flow properties to allow for the calculation of the profile drag of the airfoil. When the airfoil was at low angles of attack, there was no boundary layer separation along the wing and the velocity defect area behind the wing was small. At an angle of attack of 16

degrees, there was boundary layer separation at xc=0.5 which led to a stagnation area on the back half of the wing

and a significantly larger velocity defect area in the wake. At the final angle of attack of 25 degrees, there is leading edge separation and a stagnation area along the entire airfoil. There is also a large velocity defect area in the wake. From the data gathered from the surface pressure ports and the wake rake the lift and drag coefficients of the airfoil can be calculated. At 8 degrees angle of attack, the lift coefficient is high and the drag coefficient is low compared to the airfoil at 25 degrees angle of attack which has a much smaller lift coefficient and a much larger drag coefficient. These differences indicate that at 25 degrees the airfoil is post stall while the airfoil at 8 degrees has not stalled.

References

1Tso, Jin. Experimental Aerodynamics. San Luis Obispo: Aerospace Engineering Department, Cal Poly, 2009. Print.

2Tso, Jin. "Lab 2: Survey of a NACA-4412 Airfoil" Aero 307 Class Lecture. San Luis Obispo. 1 Feb. 2010. Lecture


Appendix

0 degrees angle of attack 8 degrees angle of attack 16 degrees angle of attackPort_Num p_avg p_std Cp

1 -0.01024 0.010058 0.9605412 -0.01566 0.009316 0.8069783 -0.02604 0.00866 0.5125274 -0.04355 0.00763 0.0161195 -0.05029 0.007107 -0.174926 -0.05897 0.006146 -0.421027 -0.06725 0.003447 -0.655778 -0.07307 0.002248 -0.820739 -0.07331 0.00163 -0.82755

10 -0.06878 0.00112 -0.6989411 -0.06388 0.000881 -0.560212 -0.04841 0.000553 -0.1214613 -0.04016 0.000262 0.11241914 -0.04236 0.000482 0.04987615 -0.04238 0.001044 0.04940916 -0.04908 0.001583 -0.1405217 -0.05455 0.002881 -0.2957418 -0.05759 0.003834 -0.3816919 -0.05317 0.005811 -0.2565420 -0.04616 0.00735 -0.0578621 -0.00857 0.001014 1.00780822 -0.00954 0.001062 0.98024723 -0.01122 0.000945 0.93285824 -0.01324 0.000791 0.87543125 -0.01434 0.000834 0.8443426 -0.01389 0.000965 0.85714127 -0.01165 0.000974 0.92067428 -0.00929 0.000782 0.98758729 -0.00818 0.000693 1.01900630 -0.00812 0.000675 1.0204931 -0.00807 0.000672 1.02212532 -0.00809 0.000645 1.02146933 -0.00776 0.0006 1.03079234 -0.00818 0.000553 1.01881435 -0.00793 0.000513 1.02599436 -0.00775 0.000446 1.03106237 -0.008 0.000387 1.02393638 -0.00785 0.000332 1.02820239 -0.00793 0.000263 1.02609240 -0.00783 0.000215 1.02897341 -0.00885 0.000123 0.96054142 -0.04412 0.00013

Port_Num p_avg p_std Cp1 -0.09356 0.000339 -1.49482 -0.13019 0.000487 -2.575743 -0.13931 0.000326 -2.845134 -0.15063 0.000298 -3.1795 -0.14383 0.00027 -2.978396 -0.12597 0.000191 -2.451357 -0.11439 0.000134 -2.10978 -0.10463 0.00011 -1.821669 -0.09517 0.000111 -1.54228

10 -0.08129 8.04E-05 -1.1326211 -0.06984 7.70E-05 -0.7949912 -0.04753 6.55E-05 -0.1364413 -0.03916 4.72E-05 0.11050114 -0.03594 5.51E-05 0.20573115 -0.033 5.83E-05 0.29247716 -0.03121 7.40E-05 0.345117 -0.02637 6.96E-05 0.48812118 -0.01927 8.20E-05 0.69743219 -0.00876 5.84E-05 1.00759920 -0.00965 3.67E-05 0.98155521 -0.00796 3.92E-05 1.03122722 -0.00804 4.01E-05 1.02892123 -0.00814 3.77E-05 1.02600724 -0.00813 4.12E-05 1.02635825 -0.00791 4.57E-05 1.0328526 -0.00803 4.55E-05 1.02916127 -0.00811 4.22E-05 1.02691128 -0.00869 5.17E-05 1.00973929 -0.00989 5.37E-05 0.9743830 -0.01212 6.74E-05 0.90847731 -0.01466 7.86E-05 0.83366532 -0.01657 8.59E-05 0.77716933 -0.01663 6.46E-05 0.7754934 -0.0158 7.33E-05 0.80000335 -0.01278 7.99E-05 0.88894436 -0.01027 8.37E-05 0.96309237 -0.00891 6.72E-05 1.00326538 -0.00802 5.44E-05 1.02965939 -0.00785 4.96E-05 1.03449240 -0.00785 5.74E-05 1.03447341 -0.00902 6.52E-05 -1.494842 -0.04291 7.10E-05

Port_Num p_avg p_std Cp1 -0.21809 0.000589 -5.235422 -0.23258 0.00065 -5.667123 -0.22163 0.000713 -5.34084 -0.20147 0.000737 -4.739865 -0.19705 0.00046 -4.608076 -0.19351 0.000552 -4.502727 -0.12417 0.000498 -2.43588 -0.09985 0.000763 -1.711049 -0.08711 0.00042 -1.33139

10 -0.06495 0.000308 -0.6706911 -0.06233 0.000119 -0.5927612 -0.06232 0.000126 -0.5925613 -0.04618 7.22E-05 -0.1114914 -0.03561 5.42E-05 0.20366515 -0.02995 5.40E-05 0.37230916 -0.02424 4.85E-05 0.54251917 -0.01663 4.57E-05 0.76934118 -0.01001 4.56E-05 0.96682219 -0.01149 7.76E-05 0.92250520 -0.03257 0.000178 0.29440521 -0.01819 0.001085 0.72293722 -0.01909 0.001092 0.69611223 -0.01994 0.001062 0.67081424 -0.02065 0.001043 0.64963325 -0.0212 0.00101 0.63322126 -0.02202 0.000924 0.60874427 -0.02249 0.000852 0.59482828 -0.02285 0.00074 0.58404229 -0.02294 0.000639 0.5812130 -0.02285 0.00053 0.58385631 -0.02259 0.000409 0.59166132 -0.02211 0.000405 0.60609833 -0.021 0.000458 0.63927634 -0.02056 0.000492 0.65227935 -0.01906 0.0006 0.69689436 -0.01794 0.000603 0.73042637 -0.01703 0.000648 0.75754938 -0.01557 0.000659 0.80102839 -0.01419 0.000631 0.84223440 -0.01309 0.00064 0.87477941 -0.00889 9.35E-05 -5.2354242 -0.04244 9.26E-05


25 degrees angle of attackPort_Num p_avg p_std Cp

1 -0.0901 0.000234 -1.477092 -0.08122 0.000262 -1.207283 -0.07753 0.00023 -1.095074 -0.07736 0.000227 -1.089755 -0.07779 0.000206 -1.102866 -0.07761 0.000222 -1.097397 -0.07717 0.000225 -1.084168 -0.07669 0.000229 -1.069599 -0.07681 0.000216 -1.07328

10 -0.07715 0.000232 -1.0835911 -0.07742 0.000236 -1.0915912 -0.07705 0.000207 -1.0805313 -0.0548 8.48E-05 -0.4038314 -0.03932 6.69E-05 0.06654315 -0.03181 8.02E-05 0.29489116 -0.02514 7.03E-05 0.4978917 -0.01784 7.42E-05 0.71973918 -0.01143 7.35E-05 0.91477619 -0.00805 6.01E-05 1.0175220 -0.01572 6.27E-05 0.78415621 -0.07375 0.000643 -0.9802222 -0.07358 0.000645 -0.9750223 -0.07374 0.000646 -0.9798224 -0.07381 0.000683 -0.9819325 -0.07347 0.0007 -0.9714826 -0.07338 0.000752 -0.9688627 -0.07325 0.000784 -0.96528 -0.0725 0.000844 -0.9419929 -0.07177 0.000874 -0.9198330 -0.07077 0.000907 -0.8895631 -0.06946 0.000944 -0.8495832 -0.06775 0.000986 -0.7978233 -0.06562 0.000966 -0.7329334 -0.06355 0.001021 -0.6699835 -0.06034 0.001124 -0.5722936 -0.0579 0.001028 -0.4982237 -0.0551 0.000994 -0.4129438 -0.05198 0.000922 -0.3183439 -0.04837 0.000885 -0.2083440 -0.04485 0.000895 -0.1014241 -0.00862 0.000149 -1.4770942 -0.04151 8.05E-05


8 degrees angle of attack processed data

theta(measured) theta(total) panel mid panel length Cl Cd Cl/Cd signs port/c Cl_total 1.30391415 1.44862328 0.001 0.0005 -9.10853E-05 0.000742 0 Cd_total 0.17312337 1.06465084 0.0035 0.0025 -0.00312186 0.005632 0.00243 0.95993109 0.009 0.0055 -0.008975437 0.012818 0.00553 0.78539816 0.017 0.008 -0.017983114 0.017983 0.01358 0.6981317 0.034 0.017 -0.038786846 0.032546 0.02164 0.59341195 0.0735 0.0395 -0.080274291 0.054146 0.04777 0.36651914 0.15 0.0765 -0.150672216 0.057838 0.186 0.20943951 0.25 0.1 -0.178185531 0.037875 0.292 0.10471976 0.375 0.125 -0.191728908 0.020152 0.396 0.03490659 0.525 0.15 -0.169789747 0.005929 0.45

101 -0.0523599 0.75 0.225 -0.178627618 0.009361 0.6106 -0.1396263 0.9 0.15 -0.020266505 0.002848 0.9

89 0.15707963 0.75 0.15 0.016371052 0.002593 0.989 0.15707963 0.5 0.25 0.050799567 0.008046 0.688 0.17453293 0.3 0.2 0.05760671 0.010158 0.489 0.15707963 0.15 0.15 0.051127668 0.008098 0.292 0.10471976 0.076 0.074 0.035923053 0.003776 0.198 0 0.036 0.04 0.027897277 0 0.052

127 -0.5061455 0.015 0.021 0.018506589 0.010258 0.02141 -0.7504916 0.005 0.01 0.00717864 0.006694 0.01

q q_inf rake span Cd_i0.0349465 0.03388494 0.1336842 0.004875154 15 23

0.034868375 0.006034734 37 450.034769625 0.007498563 43 51

0.0347815 0.007322645 53 610.0350015 0.004058025 58 660.0348765 0.005914199 64 72

0.03480025 0.007044816 77 850.034218375 0.015631092 86 94

0.03302025 0.03307265 92 1000.030787125 0.064671424 96 1040.028252125 0.098963447 101 109

0.02633775 0.123614673 106 1140.026280875 0.12432929 89 81

0.0271115 0.113788796 89 810.03012525 0.073794503 88 800.03263775 0.038571106 89 81

0.033999 0.018848885 92 840.034893375 0.005663811 98 900.035057125 0.003230951 127 119

0.0350565 0.003240248 141 133

total 0.059201621


25 degrees angle of attack processed data

theta(measured) theta(total) panel mid panel length Cl Cd Cl/Cd signs port/c Cl 0.53902715 40 0.001 0.0005 0.000475 -0.00057 0 Cd 0.50568337 62 0.0035 0.0025 0.002665 -0.00142 0.00243 68 0.009 0.0055 0.005584 -0.00226 0.00553 78 0.017 0.008 0.008527 -0.00181 0.01358 83 0.034 0.017 0.018609 -0.00228 0.02164 89 0.0735 0.0395 0.04334 -0.00076 0.04777 102 0.15 0.0765 0.081126 0.017244 0.186 111 0.25 0.1 0.099855 0.038331 0.292 117 0.375 0.125 0.119537 0.060907 0.396 121 0.525 0.15 0.139323 0.083714 0.45

101 126 0.75 0.225 0.198702 0.144365 0.6106 131 0.9 0.15 0.122323 0.106334 0.9

89 64 0.75 0.15 0.054444 -0.02655 0.989 64 0.5 0.25 0.014952 0.007293 0.688 63 0.3 0.2 0.05255 0.026776 0.489 64 0.15 0.15 0.067125 0.032739 0.292 67 0.076 0.074 0.049027 0.020811 0.198 73 0.036 0.04 0.034992 0.010698 0.052

127 102 0.015 0.021 0.020901 -0.00444 0.02141 116 0.005 0.01 0.007048 -0.00344 0.01


naca 4412 yapılmış analiz

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