delta-wing vortex lift enhancement using oblique channeled ... · vortex breakdown through...

Delta-Wing Vortex Lift Enhancement Using Oblique Channeled Distribution

ME 4335: MECHANICAL ENGINEERING LABORATORY

MEAG MCNARY, RUBEN NUÑEZ III, RYAN PARKER, ADAM EAKER, DREW

WAGGONER

ADVISOR: DR. STEPHEN MCCLAIN

DEPARTMENT OF MECHANCIAL ENGINEERING

BAYLOR UNIVERSITY

2 MAY 2011

FINAL REPORT DELTA-WING VORTEX LIFT ENHANCEMENT USING OBLIQUE CHANNELED DISTRIBUTION

I. ABSTRACT

Flow development across a delta wing is very intricate and depends highly on angle of

attack and delta wing geometry. During reasonable angles of attack, vortical formations

allow for an elevated coefficient of lift. However, at high angles of attack, vortical

breakdown and separation occurs, causing decreased wing performance. In order to diminish

the vortical breakdown phenomena, this experiment helps to quantify the steady flow effects

of obliquely aligned channels interacting with vortical structures attached to a delta wing

micro-unmanned air vehicle. The lift and drag coefficients associated with the delta wing

structure are of particular importance to this project. The experiment determines how a delta

wing is affected by the addition of obliquely aligned channels. Two different models were

tested: a control model with a smooth surface, and a model with obliquely aligned channels.

For each model the lift and drag forces were measured at varying angles of attack, ranging

from zero to forty-five degrees (encompassing stall) in five degree increments in order to

calculated lift and drag coefficients. It was found that the addition of the obliquely aligned

channels did not improve the performance of the delta wing. The smooth wing achieved a CL

of 1.44 and CD of 0.69 while the channeled wing had a CL of 1.34 and CD of 0.66 when tested

at a Reynolds number of 179,260. Recommendations for future tests would be to run the

experiment at higher Reynolds numbers and to test delta wings with various distributions of

obliquely aligned elements.

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II. TABLE OF CONTENTS

I. ABSTRACT ............................................................................................................. 2

II. TABLE OF CONTENTS ......................................................................................... 3

III. LIST OF TABLES AND FIGURES ........................................................................ 4

IV. NOMENCLATURE ................................................................................................. 5

V. INTRODUCTION .................................................................................................... 5

VI. EXPERIMENT METHODS .................................................................................... 9

VII. RESULTS AND DISCUSSION ............................................................................ 17

VIII. CONCLUSIONS AND RECOMMENDATIONS ................................................. 19

IX. ACKNOWLEDGEMENTS ................................................................................... 20

X. REFERENCES ....................................................................................................... 21

XI. APPENDIX ............................................................................................................ 22

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III. LIST OF TABLES AND FIGURES Table 1: Nomenclature 5 Table 2: Equipment and Support 10 Table 3A: Device Uncertainties 14 Table 3B: Smooth Wing Uncertainties 14 Table 3C: Channeled Wing Uncertainties 15 Figure 1: Experimental Setup 11 Figure 2: Initial Schedule Summary 16 Figure 3: Final Schedule Summary 16 Figure 4: Coefficients of Lift and Drag 18 Figure 5: L/D of Smooth and Channeled Wings 19

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IV. NOMENCLATURE

Below is a list of variables that are used in the report. This list is made available for quick

reference.

Table 1: Nomenclature

Lift Coefficient Drag Coefficient

c Chord D Drag L Lift Planform Area

s Span V Velocity of Air Λ Sweep Angle

Density of Fluid

V. INTRODUCTION

The delta wing is a wing in the shape of a triangle. It is named after the Greek uppercase

letter delta, ∆, because it is similar in shape. The concept of the delta wing suggested that

there was no need for a tailplane, which was commonly used for equilibrium and stability

prior to delta wing development. At low speeds, it was difficult to ensure continuous flight of

the delta wing, but at higher speeds, it was more efficient than its other designs. This also

significantly simplified plane structures and proved to be extremely easy to manufacture.

Additional benefits of the emerging delta wing were that it allowed the aircraft to travel at

supersonic speeds and have significantly improved maneuverability. This increased

performance is due to the large sweep angle on the rear, which prevents the wings from

contacting the shock wave boundary which forms at the nose (Benson, [1]). Another benefit

that was realized after an immense amount of research and investigation was that the body of

the plane could be combined with the wings to make for a wholly aerodynamic structure that

minimized losses but also has an increase on drag.

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One benefit of the delta wing design that is of great concern in this research is the wing’s

effectiveness over a high range of attack angles. This is due to the development of vortices

on the wing. Delta wings are used in various applications where performance and

maneuverability are crucial. The constraining mechanism for this effectiveness is governed

by the vortical flow, occurring at the leading edge of the delta wing. At moderate angles of

attack, the vortical flow is robust and promotes a pressure decrease over the wing, creating an

increase in lift (Mitchell and Delery, [2]). At high angles of attack these vortices tend to

break down before reaching the trailing end of the wing. The breakdown location tends to

oscillate from the front of the wing to the rear in an unsteady manner. Thus, these oscillations

cause vibrations and buffeting of the aircraft, resulting in more turbulence, wing fluctuation,

and an increase in drag on the delta wing (Gursul, [3]).

Other than oscillation and the breakdown of vortices, much about vortex behavior is

unpredictable. However, these oblique elements are meant to control the physics of air flow

on micro-air vehicles operating at a low speed and cause complete vortex circulation,

promoting an enhanced overall lift. The research that has already taken place demonstrates

turbulent and transitional flow with increasing Reynolds Numbers, as well as flow

visualization showing vortical substructures and the breakdown that occurs.

The most common justification to instability in vortices credits wave propagation, which

is highly dependent on sweep angle and angle of attack. Lower sweep angles limit this

breakdown, while an increased angle of attack induces vortex breakdown. The best way to

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quantify these characteristics is to measure the lift and drag, and then calculate the lift and

drag coefficients using the equations below.

(1)

(2)

In the past, research has been done to improve the performance of delta wings by delaying

vortex breakdown through mechanical and pneumatic methods. Mechanical methods attempt

to control vortex breakdown by changing the surface of the wing, while pneumatic methods

attempt to introduce perturbations through forced airflow. However, this report is only

concerned with mechanical methods.

Using jet flaps is one such mechanical device that has been researched in the past. These

flaps can be placed at the leading edge or trailing edge and actively control the vortical flow

around a wing by using actuators to adjust the angles of the flaps. Leading edge flaps

typically improve the lift to drag ratio, while trailing edge flaps typically increase the

stability of the delta wing while only slightly increasing the lift (Mitchell and Delery, [2]). A

disadvantage to jet flaps is that they can be difficult to implement due to the complexity of

adding actuators and altering the wing structure.

Piezoelectric strips are another type of mechanical device that have been researched to

combat the effects of vortical breakdown. These strips bond to a wing and actively control

wing oscillations by countering wing flutter. This is done by sensing oscillations and creating

7

forces that negate the motion of the wing (Shrivastava, [4]). The biggest benefit to these

strips is that they are affordable, lightweight, and easy to manufacture.

Obliquely aligned elements in the form of raised elliptical elements have also been

researched because of their ability to improve the performance of a delta wing by

manipulating air flow. The elements are expected to enhance vortex lift by inducing

secondary flows. The increase in complete circulation and lift are accomplished by

promoting a higher lateral flow in the near-wall region to reduce the resistance to an attached

vortex (McClain, [5]). It is expected that obliquely aligned channels will have a similar effect

as the raised elements and will be the focus of this research.

The objective of the experiment is to determine and quantify any difference between a

delta wing with obliquely aligned channeled elements versus a smooth delta wing. Prior

research has been done proving the existence of an induced secondary flow when

directionally aligned surface elements are mounted to a flat surface, and it is desired to see if

the same is true for channeled elements. Complete vortical circulation could occur due to

these channeled elements.

It is theorized that the channels inset in the delta wing will provoke transverse flow in

turbulent boundary layers and reduce surface resistance for vortical reattachment, causing

increased lift with a limited drag increase. Theoretically, the vortices will have more surface

area allowing manipulation of the air on the surface of the wing to cause the vortices to

reattach, resulting in a significant increase in lift.

8

In order to determine how the performances of delta wings are affected by the added inset

elements, two different models were tested. The tested models were comprised of a control

model with a smooth surface, and one model with a predetermined distribution of obliquely

aligned channels. For each model the lift and drag forces were measured at varying angles of

attack, going from zero until 45 degrees, in five degree increments. By determining these

coefficients at each angle of attack and oblique channel placement, the steady flow effects of

the channeled elements on vortical flow are demonstrated and quantified.

VI. EXPERIMENT METHODS

Prior to experimentation, the delta wings as well as a connector piece used to attach the

delta wing to the force balance were machined using a Hass VF-1 Vertical Machining Center

in the Baylor University machine shop. A LabVIEW 7 program was also created, and force

balance calibration was performed. The experiment was conducted within the test section of

Baylor University’s subsonic wind tunnel. One delta wing was connected at the wing’s

center of gravity to the force balance at varying attack angles from 0 to 45 degrees.

Adjusting the attack angle was accomplished by employing a set screw and confirming a five

degree incremental difference by using a digital inclinometer. The inclinometer was placed

on the top centerline of the delta wing to measure the attack angle. The calibrated force

balance was then connected to a computer operating LabVIEW via data acquisition cards. A

pitot - static tube was placed on a traverse above and upstream of the delta wing and

connected to the Omega PCL-2A to transmit pressure differences. The Omega PCL-2A was

then connected to the computer via a data acquisition card to transmit and record this

information. Figure 1displays how the apparatus was placed within the test section of the

wind tunnel. Table 2 lists the required equipment for experimentation.

9

Table 2: Equipment and Support

EQUIPMENT NAME EQUIPMENT MODEL AND SERIAL NUMBER

Wind Tunnel Baylor University Subsonic Wind Tunnel Model 406(B), Serial Number: 41403

Inclinometer 7 in. Multi-Function Digital Torpedo Level Serial Number: 320.48295

Omega PCL-2A PCL-2A Serial Number: 50294 Pitot – Static Tube Pitot - Static Tube Force Balance ELD Force Balance Scale Ohaus Scout Pro SP2001

Serial Number: 7123241518 Barometer Oakton Barometer with Digital Thermometer,

Model Number:03316-72 Cold Junction Omega Cold Junction, Model Number: CJ-T Thermocouple Type T Vertical Machining Center Hass VF-1 VMC

The only apparatus that needed to be calibrated was the force balance. The force balance

was calibrated to the range of 0 to 1.5 pound for drag force and 0 to 1.5 pound for lift force.

This range was accomplished by placing known weights on the force balance, receiving the

voltage output via LabVIEW, and creating a trendline graph that allows for a voltage to

pound-force conversion describing the exact relationship between the two. All of the other

apparatus used was calibrated by the manufacturer and does not need additional calibration.

Below is the specific setup of this experiment.

10

Figure 1: Experimental Setup

The following procedure has been used for this project.

1. Fasten the force balance to the calibration stand.

2. Connect the force balance to the computer using the serial port.

3. Calibrate the force balance from 0 to 1.5 lb. for lift and drag. (vertical and horizontal)

Measure the weight of the cup that will hold the lead pellets using the Ohaus Scout

Pro 2000g.

Take LabVIEW reading of force balance when it is unloaded.

Measure 0.1 lb of lead.

Put the lead in the cup and attach it to the force balance.

LabVIEW will give an output voltage that corresponds to the weight of the tin cup.

Continue adding 0.1 lb increments of lead and take readings for each increment until

the force balance is loaded to 1 lb.

PCL-2A

LabView Program

Pitot – Static Tube

Force Balance

11

Produce a calibration curve for the force balance in Microsoft Excel using the

LabVIEW output.

The lift calibration is now complete. Perform the same procedure for drag calibration

by flipping the force balance mechanism.

4. Prepare the wind tunnel for testing.

Hook up pressure probes in the wind tunnel testing section.

Turn on the Velmex Controller, which will allow the traverse to move.

Adjust the pitot - static tube to the desired position in the wind tunnel using the

Velmex Controller.

Attach the force balance to the bottom plate of the wind tunnel test section.

5. Input required preliminary data to LabVIEW.

Ambient Temperature, T.

Turn on the cold junction compensator (Thermocouples).

Record Temperature

Turn off the cold junction compensator.

Pressure, P, is found using the barometer found on the wall of the lab.

R is the specific gas constant for air.

Calculate the density of air using .

6. Attach the smooth delta wing to the force balance by tightening the connector screw.

7. Secure the base to the wind tunnel.

8. Open the small access window to the wind tunnel.

9. Use the inclinometer to set the delta wing at a zero angle of attack, and carefully tighten

the set screw.

12

10. Close the access window.

11. Take an offset for a 0 degree angle of attack in LabVIEW.

12. Turn the wind tunnel on and set the flow to a velocity of 15 m/s.

13. Wait for the air flow to become steady.

14. Take 5 data points consisting of an average of 10,000 individual points taken over 10

seconds using LabVIEW.

15. Turn the wind tunnel off.

16. Open the access window.

17. Loosen the set screw.

18. Increase the angle of attack of the delta wing by 5 degrees using the inclinometer, and

carefully tighten the set screw.

19. Close the access window.

20. Repeat steps 12 through 19 until a 45 degree angle of attack is tested.

21. Remove the wind tunnel base and remove the smooth delta wing from the force balance.

22. Repeat steps 6 through 20 using the channeled delta wing.

23. Remove the wind tunnel base and remove the channeled delta wing from the force

balance.

The lift and drag forces of each delta wing were experimentally determined in this project,

and from this the lift and drag coefficients were calculated (1). These calculations have

sources of error that come from uncertainties associated with instruments and methods used

in the experiment. The overall uncertainty analysis was done using the Kline-McClintock [6]

in Mathcad 15, and the calculations can be found in Appendix iii.

13

Some of the values used in the analysis were assumed based on preliminary specifications

and typical expectations in order to predict the uncertainty before the experiment was carried

out. The delta wing parameters were initially determined in order to be able to be printed

within a Dimension SST 768 Solid printer, and the expected lift and drag coefficients were

based on the delta wing having lift and drag coefficients similar to that of a vertical plate.

The uncertainties of each contributing instrument can be found in Table 6A. The first

source of error comes from the pressure measurements made by the pitot - static tube

connected to the PCL-2A. The uncertainty of the pitot - static tube was stated to be 0.06% of

the full scale. The small pressure differences that are associated with the low free stream

velocity of 15 m/s contributes to the uncertainty in the pressure readings. The uncertainty of

the lengths produced by the Hass VMC was found to be 0.0002 inches. That uncertainty was

stated by the manufacturer and corresponds to the positioning accuracy and repeatability.

The error of the lift and drag forces also comes from the uncertainty of the force balance,

which is 0.001 lbf. It should be noted that the device which had the biggest contribution to

the uncertainty was the force balance, because only 9.72% of the full range of lift and

22.68% of the drag was used. The resulting uncertainty for the lift was on average 1.17%

for the smooth wing and 1.23% for the channeled wing. The resulting uncertainty for the

drag coefficients was on average 1.18% for the smooth wing and 1.23% for the channeled

wing. A detailed listing of the uncertainties by angle of attack can be found in Table 6B a

smooth wing and Table 6C for a channeled wing.

Table 3A: Device Uncertainties

Pitot Static Tube 0.00002168 psi Haas VMC 0.0002 in Force Balance 0.001 lbf

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Table 3B: Smooth Wing Uncertainties

Uncertainties: Smooth Wing

Attack Angle (degrees)

Lift Coefficient Uncertainty

Drag Coefficient Uncertainty

0 0.39534682 0.00518327 0.05906726 0.00210644

4.9 0.65563342 0.00807623 0.08202781 0.00219825

10.1 0.85811464 0.00856068 0.14412538 0.0024109

15.1 1.08356801 0.01142 0.24158164 0.00319765

20.1 1.22987609 0.01077 0.36603878 0.00371866

25 1.3642587 0.02079 0.51965474 0.00812705

30.1 1.44472537 0.01358 0.68861494 0.00671125

35 1.34143904 0.01946 0.78018633 0.01144

40.5 1.02357147 0.64799467

45.7 0.96679552 0.69848001

Table 3C: Channeled Wing Uncertainties

Uncertainties: Channeled Wing

Attack Angle (degrees)

Lift Coefficient Uncertainty

Drag Coefficient Uncertainty

0 0.410318531 0.00512219 0.060395681 0.0021134

5 0.629921056 0.00714793 0.091825243 0.00222284

10 0.838283826 0.01126 0.150896206 0.0028368

15.1 1.019184535 0.00991963 0.243754295 0.00305657

20 1.220204072 0.01424 0.367174079 0.00467889

24.8 1.328386975 0.01369 0.507141135 0.0054085

30 1.336950184 0.01819 0.657060318 0.00910697

34.9 1.354045736 0.02044 0.743972801 0.01136

39.7 1.09861577 0.645325258

44.8 1.049175114 0.691446995

Upon receiving the research project on the delta wing, a schedule was determined to

project the amount of time that was needed to research the theory behind delta wings and

their development, as well as to begin the testing of prototype delta wings for further analysis

on ways to increase performance. Fig. 2 is the initial timeline that was employed. Fig. 3 is

what actually happened over the course of the semester. Not all of the desired research was

15

accomplished; however, a firm basis for future research was developed as well as results that

will be useful in that research.

Figure 2: Initial Schedule Summary

Figure 3: Final Schedule Summary

6‐Feb 16‐Feb 26‐Feb 8‐Mar 18‐Mar 28‐Mar 7‐Apr 17‐Apr 27‐Apr 7‐May

Preliminary Data Collection

Test Plan Due

Develop Connector Piece

Develop Rotating Mechanism

Printing of Delta Wings

Data Collection

Final Presentation

Final Project Due

6‐Feb 16‐Feb 26‐Feb 8‐Mar 18‐Mar 28‐Mar 7‐Apr 17‐Apr 27‐Apr 7‐May

Preliminary Data Collection

Research

Test Plan Due

Work on Report

Develop Connector Piece

Develop Rotating Mechanism

Manufacturing of Delta Wings

Data Collection

Final Presentation

Final Project Due

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VII. RESULTS AND DISCUSSION

The tests were carried out at an average air velocity of 15.09 m/s resulting in an average

Reynolds Number of 179,000. As can be seen in Fig. 4 the lift and drag coefficients of the

smooth and the channeled delta wings follow the same general trend, but the channeled wing

generally has lower coefficients of lift and drag up to stall. Both wings can be seen to stall at

approximately 35˚ and it is interesting to note that the tests show the channeled wing

achieving a moderately higher lift coefficient after stall. From this test it appears to be

conclusive that the oblique striations did not enhance the lift, and instead moderately reduce

it. Furthermore this suggests that the channels did not enhance vortical reattachment as was

theorized. It is possible that this is due to the elements being machined into the surface rather

than being on top, and thus did not create a secondary flow as was seen in prior research.

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Figure 4: Coefficients of Lift and Drag

Similar to the comparison of lift and drag coefficients, the trend in lift to drag ratio for

both wings is very similar as seen in Fig. 5. Once again the smooth wing generally exhibits a

higher ratio as well as a larger maximum ratio. The maximum difference in lift to drag ratio

is 14.2% at an angle of 5˚. As seen in the trend for lift and drag coefficients, the only time the

channeled wing exhibits a higher ratio is after stall, which occurred at 35˚. This further

supports the conclusion that the channels do not enhance the general performance of the

wing. It is possible that similar structures could be used to enhance performance at angles of

attack greater than stall.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0 10 20 30 40 50

Coefficients of Lift and Drag

Angle of Attack (deg)

Coefficients of Lift and DragRe=179,260 V=15.09m/s

Smooth CL

Smooth CD

Channeled CL

Channeled CD

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Figure 5: L/D of Smooth and Channeled Wings

VIII. CONCLUSIONS AND RECOMMENDATIONS

The results of the testing conclude that the channeled wing design decreases both lift and

drag coefficients from the values seen with the smooth control model testing. Even though

the channeled wing design did not offer general improvement over this control model, the

results indicate that improvements could be possible. Because the channeled design offers

improved lift and drag after stall, the design could be used to increase performance at

extremely high angles of attack.

In order to determine the validity of this assumption, more testing needs to be done with

the channeled model in the wind tunnel. It is suggested that the channeled design be subject

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50

L/D

Angle Of Attack (deg)

L/D: Smooth and Channeled WingsRe=179,260 V= 15.09 m/s

L/D Smooth

L/D Channeled

19

to higher Reynolds numbers in order to see the possible effects of the design. It is possible

that the higher Reynolds numbers will decrease the size of the boundary layer and allow the

same size channels to have a higher impact on improving lift and drag coefficients.

In addition to testing the channeled model at higher Reynolds numbers, a prototype

containing obliquely aligned roughness elements should to be tested. The roughness

elements are theorized to have a greater affect on the breakdown of the vortical structures

associated with the flow across a delta wing aircraft. By delaying or preventing altogether

this breakdown, the oblique roughness elements will increase lift and drag coefficients at

higher angles of attack and prevent other disturbances such as buffeting of the aircraft.

While simply placing the oblique roughness elements on the aircraft should improve the lift

and drag characteristics, multiple arrangements of these elements need to be tested. The

testing of various patterns, sizes, and arrangements of the oblique distributions will determine

the true impact of these structures in regards to its performance. Ideally, the arrangements

could eventually be tailored to specific applications and environments for which the micro-

unmanned aircraft will be used.

IX. ACKNOWLEDGEMENTS

The authors thank Dr. Stephen McClain for his guidance and support in this project. The

authors also thank Ashley Orr, Lance Case, Steven Mart, and Tim Burdett for their help in

making the delta wings, constructing the connector piece for the force balance, setting up the

wind tunnel, and LabVIEW programming.

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X. REFERENCES

[1] Benson, T. Normal Shock Waves. 9 December 2008. National Aeronautics and Space

Administration, Glenn Research Center. 22 April 2011.<http://www.grc.nasa.gov/WWW/K-

12/airplane/normal.html>

[2] Mitchell, A.M., Delery, J., Research into vortex breakdown control, Progress in

Aerospace Sciences, Volume 37, Issue 4, May 2001, Pages 385-418.

[3] Gursul, I., 2003, “Review of Unsteady Vortex Flows over Slender Delta Wings,” AIAA

21st Applied Aerodynamics Conference. Copyright Clearance Center, Inc., Danvers, MA.

Vol. 42, No. 2.

[4] Shrivastava, S., 1998, “Aerolastic Oscillations of a Delta Wing with Bonded Piezolectric

Strips,” Masters of Engineering thesis, McGill University, Montreal, Quebec, Canada.

[5] McClain, S.T., 2010, “Delta Wing Vortex Control and Lift Enhancement Using Active

Arrays of Oblique Elements,” Technical Report, Baylor University, Waco, TX.

[6] Kline, S.J., and F.A. McClintock. Describing Uncertainties in Single-Sample

Experiments. Mechanical Engineering: the journal of the American Society of Mechanical

Engineers. January 1953, pp.3-8.

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XI. APPENDIX

i. Preliminary Sizing Data

ii. Experimental Data

iii. Uncertainty Analysis

iv. Executive Summary

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Appendix ii: Experimental Data

Smooth Wing Angle of Attack Lift(lbf) CL

Lift Uncertainty Std. Dev Drag(lbf) CD Drag

Uncertainty Std. Dev

0 0.2030946 0.40 0.0051833 0.005650 0.03034350 0.06 0.0021064 0.005786 4.9 0.3386498 0.66 0.0080762 0.005653 0.04236931 0.08 0.0021983 0.005626

10.1 0.4416888 0.86 0.0085607 0.005694 0.07418424 0.14 0.0024109 0.005624 15.1 0.5550317 1.08 0.0114200 0.005652 0.12374487 0.24 0.0031977 0.005675 20.1 0.6339781 1.23 0.0107700 0.005686 0.18868736 0.37 0.0037187 0.005779

25 0.7042753 1.36 0.0207900 0.005637 0.26826403 0.52 0.0081271 0.005881 30.1 0.7384211 1.44 0.0135800 0.005676 0.35196268 0.69 0.0067113 0.006677

35 0.6835672 1.34 0.0194600 0.005678 0.39756717 0.78 0.0114400 0.008312 40.5 0.5248721 1.02 0.005712 0.33230145 0.65 0.007926 45.7 0.4939855 0.97 0.005666 0.35688853 0.70 0.006889

Average 0.54 1.05 0.012230 1.169% 0.2166313 0.4227772 0.0049888 1.18%

Channeled Wing Angle of Attack Lift(lbf) CL

Lift Uncertainty Std Dev Drag(lbf) CD Drag

Uncertainty Std. Dev

0 0.2089862 0.41 0.005122 0.005571 0.03076090 0.06 0.002113 0.005722 5 0.3228555 0.63 0.007148 0.005579 0.04706327 0.09 0.002223 0.005724

10 0.4323125 0.84 0.011260 0.005473 0.07781855 0.15 0.002837 0.005562 15.1 0.5220893 1.02 0.009920 0.005475 0.12486636 0.24 0.003057 0.005659

20 0.6286382 1.22 0.014240 0.005497 0.18916378 0.37 0.004679 0.005680 24.8 0.6793303 1.33 0.013690 0.005501 0.25934972 0.51 0.005409 0.005652

30 0.683492 1.34 0.018190 0.005545 0.33591187 0.66 0.009107 0.006319 34.9 0.6897596 1.35 0.020440 0.005543 0.37898809 0.74 0.011360 0.007356 39.7 0.5604469 1.10 0.005536 0.32920541 0.65 0.009086 44.8 0.5376831 1.05 0.005555 0.35435323 0.69 0.007981

Average 0.52 1.02 0.012501 1.23% 0.213 0.416 0.005098 1.226%

28

Lift/ Drag

Angle of Attack Smooth Channeled Percent Difference

0 6.6931838 6.7938899 -1.50% 5 7.9928088 6.8600312 14.17%

10 5.9539438 5.5553917 6.69% 15 4.4852906 4.1811846 6.78% 20 3.3599397 3.3232481 1.09% 25 2.6253065 2.6193602 0.23% 30 2.0980096 2.0347361 3.02% 35 1.7193754 1.8200034 -5.85% 40 1.579506 1.7024231 -7.78% 45 1.3841451 1.5173646 -9.62%

Average 3.7891509 3.6407633 0.72%

y = 125.351578x - 8.437871R² = 0.999910

y = 7.0268863x + 0.0076874R² = 0.9999872

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.00 0.05 0.10 0.15 0.20 0.25

Wei

ght [

lbf]

Voltage [V]

Force Balance Calibration Curve:Voltage vs. Force

Lift

Drag

Linear (Lift)

Linear (Drag)

29

Appendix iii Uncertainty Analysis: Smooth Wing

Kline-McClintock Uncertainty Analysis for Drag and Lift Coefficients on Delta Wing:

Air Properties: From Fluids Textbook:

ν 15.68 106

m

2

s Uν 0

m2

s

ρ 1.18517kg

m3

0.07399lbm

ft3

Uρ 0.0006kg

m3

3.74568 105

lbm

ft3

Flow Proerties:

vmax 15.0855m

s so the wind tunnel pressure reading would be:

GivenΔPtest 0psi

ΔPtest1

2ρ vmax

2=

ΔP Find ΔPtest 0.01956 psi UP 0.06%1

27.68psi

2.16763 105

psi

Velocity Uncertainty:Sensitivity Coef:

SCP2

2ΔP

ρ ρ

0.05593s m

2

kg

Fixed Uncertainty for Velocity:

UR_V SCP UP 8.35918 103

m

s

Uv UR_V

30

Delta Wing Properties:

Λ 50deg UΛ 0.005deg Sweep Angle(Set by McClain)

Sspan 6.75in US 0.0002in

CLmax 1.0 Guess for lift coefficients determined, based on a flat plate at90degCDmax 1.0

cwing .625ft UCNC 0.0002in

v vmax Sspan 6.75 in

Rec

v cwing

ν1.83277 10

5

Reynolds Uncertainty:Sensitivity Coef.:

CDv

cwing

ν1.21492 10

4

s

m

CDcwingv

ν9.62085 10

5

1

m

Total Uncertainty:

CDv Uv 101.55767

CDcwing UCNC 4.88739

UR_Re CDv Uv 2 CDcwing UCNC 2

1

23 305.0256

Planform area (S):

Sarea 0.18215ft2

Planform Area of chosen airfoil

Planform Area Uncertainty:

UA1

2Sspan UCNC

21

2cwing UCNC

2

1

2

7.0071 106

ft2

31

Limits of Force Balance Scale:

Lmax 15lbfUFB 0.001lbf

Dmax 8lbf

Drag and Lift Coef Uncertainty:

AOA 0 deg: Smooth:FIXED:

L0s 0.203095lbf D0s 0.030344lbf ΔP0s0.546023psi

27.680.01973 psi

Sensitivity Coef:Lift:

CLP0s1

ΔP0s2

L0s

Sarea 2.88602 10

3

1

Pa

CLS0s1

Sarea2

L0s

ΔP0s 23.19549

1

m2

CLL0s1

ΔP0s Sarea1.9327

1

lbf

Drag:

CDP0s1

ΔP0s2

D0s

Sarea 1.46019

1

in_Hg

CDS0s1

Sarea2

D0s

ΔP0s 0.32196

1

ft2

CDD0s1

ΔP0s Sarea1.9327

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

32

UA 6.50981 107

m2

UFB 1 103

lbf

CLP0s UP 4.31323 104

CLS0s UA 1.50998 105

CLL0s UFB 1.9327 103

CDP0s UP 6.44431 105

CDS0s UA 2.25603 106

CDD0s UFB 1.9327 103

Total Fixed Uncertainty:

Lift:BR_L0s CLP0s UP 2 CLS0s UA 2 CLL0s UFB 2

1

21.9803 10

3

Drag:BR_D0s CDP0s UP 2 CDS0s UA 2 CDD0s UFB 2

1

21.93377 10

3

RANDOM:

Lift:L0s 0.20309 lbf σL0s 0.00565lbf ntrials 3000 σmL0s

σL0s

ntrials

1

2

Pressure:

ΔP0s 0.01973 psi σP0s .000616psi ntrialsP 30 σmP0s

σP0s

ntrialsP

1

2

Drag:

D0s 0.03034 lbf σD0s 0.005786lbf σmD0s

σD0s

ntrials

1

2

Student T's:

υ 5 1 4 t95 2.132

33

Total Random Uncertainty:

Lift: SR_L0s CLL0s σmL0s 2 CLP0s σmP0s 2

1

22.24675 10

3

Drag:SR_D0s CDD0s σmD0s 2 CDP0s σmP0s 2

1

23.91763 10

4

Total Uncertainty:

Lift: UR_L0s BR_L0s 2 t95 SR_L0s 2

1

25.18327 10

3

UR_L0s

0.41.296 %

Drag:UR_D0s BR_D0s 2 t95 SR_D0s 2

1

22.10644 10

3

UR_D0s

0.063.511 %



27.680.01983 psi


CLP5s1

ΔP5s2

L5s

Sarea 4.76004 10

3

1

Pa

CLS5s1

Sarea2

L5s

ΔP5s 38.46674

1

m2

CLL5s1

ΔP5s Sarea1.92218

1

lbf

34

Drag:

CDP5s1

ΔP5s2

D5s

Sarea 2.01671

1

in_Hg

CDS5s1

Sarea2

D5s

ΔP5s 0.44711

1

ft2

CDD5s1

ΔP5s Sarea1.92218

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 7.0071 106

ft2

UFB 1 103

lbf

CLP5s UP 7.11401 104

CLS5s UA 2.50411 105

CLL5s UFB 1.92218 103

CDP5s UP 8.90045 105

CDS5s UA 3.13293 106

CDD5s UFB 1.92218 103



1

22.04975 10

3


1

21.92424 10

3

RANDOM:

Lift:L5s 0.33865 lbf σL5s 0.005653lbf ntrials 3 10

3 σmL5s

σL5s

ntrials

1

2

35

Pressure:


σP5s

ntrialsP

1

2

Drag:


σD5s

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

23.66407 10

3


1

24.9851 10

4

Total Uncertainty:


1

28.07623 10

3

UR_L5s

0.661.224 %


1

22.19825 10

3

UR_D5s

0.082.748 %



27.680.01988 psi


CLP10s1

ΔP10s2

L10s

Sarea 6.17972 10

3

1

Pa

36

CLS10s1

Sarea2

L10s

ΔP10s 50.05499

1

m2

CLL10s1

ΔP10s Sarea1.91774

1

lbf

Drag:

CDP10s1

ΔP10s2

D10s

Sarea 3.51478

1

in_Hg

CDS10s1

Sarea2

D10s

ΔP10s 0.78104

1

ft2

CDD10s1

ΔP10s Sarea1.91774

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP10s UP 9.23577 104

CLS10s UA 3.25848 105

CLL10s UFB 1.91774 103

CDP10s UP 1.5512 104

CDS10s UA 5.47279 106

CDD10s UFB 1.91774 103



1

22.1288 10

3

37


1

21.92401 10

3

RANDOM:


3 σmL10s

σL10s

ntrials

1

2

Pressure:


σP10s

ntrialsP

1

2

Drag:


σD10s

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

23.8892 10

3


1

26.81424 10

4

Total Uncertainty:


1

28.56068 10

3 UR_L10s

0.860.995 %


1

22.4109 10

3

UR_D10s

0.141.722 %

38



27.680.01967 psi


CLP15s1

ΔP15s2

L15s

Sarea 7.93286 10

3

1

Pa

CLS15s1

Sarea2

L15s

ΔP15s 63.57385

1

m2

CLL15s1

ΔP15s Sarea1.93829

1

lbf

Drag:

CDP15s1

ΔP15s2

D15s

Sarea 5.98929

1

in_Hg

CDS15s1

Sarea2

D15s

ΔP15s 1.31679

1

ft2

CDD15s1

ΔP15s Sarea1.93829

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP15s UP 1.18559 103

CLS15s UA 4.13853 105

CLL15s UFB 1.93829 103

39

CDP15s UP 2.64328 104

CDS15s UA 9.22691 106

CDD15s UFB 1.93829 103



1

22.27251 10

3


1

21.95626 10

3

RANDOM:


3 σmL15s

σL15s

ntrials

1

2

Pressure:


σP15s

ntrialsP

1

2

Drag:


σD15s

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

25.24842 10

3


1

24.41984 10

4

40

Total Uncertainty:


1

20.01142

UR_L15s

1.081.057 %


1

22.17138 10

3

UR_D15s

0.240.905 %

AOA 20 deg: Smooth:

FIXED:


27.680.01979 psi


CLP20s1

ΔP20s2

L20s

Sarea 8.94708 10

3

1

Pa

CLS20s1

Sarea2

L20s

ΔP20s 72.15764

1

m2

CLL20s1

ΔP20s Sarea1.92605

1

lbf

Drag:

CDP20s1

ΔP20s2

D20s

Sarea 9.01747

1

in_Hg

CDS20s1

Sarea2

D20s

ΔP20s 1.99517

1

ft2

CDD20s1

ΔP20s Sarea1.92605

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

41

UA 6.50981 107

m2

UFB 1 103

lbf

CLP20s UP 1.33717 103

CLS20s UA 4.69732 105

CLL20s UFB 1.92605 103

CDP20s UP 3.97973 104

CDS20s UA 1.39804 105

CDD20s UFB 1.92605 103



1

22.34518 10

3


1

21.96678 10

3

RANDOM:


3 σmL20s

σL20s

ntrials

1

2

Pressure:


σP20s

ntrialsP

1

2

Drag:


σD20s

ntrials

1

2

Student T's:

υ 4 t95 2.132

42



1

24.93033 10

3


1

21.48029 10

3

Total Uncertainty:


1

20.01077

UR_L20s

1.230.876 %


1

23.71866 10

3

UR_D20s

0.371.005 %

AOA 25 deg:

Smooth:FIXED:


27.680.01982 psi


CLP25s1

ΔP25s2

L25s

Sarea 9.9103 10

3

1

Pa

CLS25s1

Sarea2

L25s

ΔP25s 80.04219

1

m2

CLL25s1

ΔP25s Sarea1.92325

1

lbf

Drag:

CDP25s1

ΔP25s2

D25s

Sarea 12.78328

1

in_Hg

43

CDS25s1

Sarea2

D25s

ΔP25s 2.83249

1

ft2

CDD25s1

ΔP25s Sarea1.92325

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP25s UP 1.48112 103

CLS25s UA 5.21059 105

CLL25s UFB 1.92325 103

CDP25s UP 5.64171 104

CDS25s UA 1.98476 105

CDD25s UFB 1.92325 103



1

22.42803 10

3


1

22.00439 10

3

RANDOM:


3 σmL25s

σL25s

ntrials

1

2

44

Pressure:


σP25s

ntrialsP

1

2

Drag:


σD25s

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

29.68522 10

3


1

23.69418 10

3

Total Uncertainty:


1

20.02079

UR_L25s

1.361.529 %


1

28.12705 10

3

UR_D25s

0.521.563 %

AOA 30 deg: Smooth:

FIXED:L30s 0.738421lbf D30s 0.351963lbf ΔP30s

0.543264psi

27.680.01963 psi


CLP30s1

ΔP30s2

L30s

Sarea 0.0106

1

Pa

CLS30s1

Sarea2

L30s

ΔP30s 84.76341

1

m2

45

CLL30s1

ΔP30s Sarea1.94251

1

lbf

Drag:

CDP30s1

ΔP30s2

D30s

Sarea 17.10931

1

in_Hg

CDS30s1

Sarea2

D30s

ΔP30s 3.75346

1

ft2

CDD30s1

ΔP30s Sarea1.94251

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP30s UP 1.58419 103

CLS30s UA 5.51793 105

CLL30s UFB 1.94251 103

CDP30s UP 7.55094 104

CDS30s UA 2.63008 105

CDD30s UFB 1.94251 103



1

22.5072 10

3


1

22.08428 10

3

46

RANDOM:


3 σmL30s

σL30s

ntrials

1

2

Pressure:


σP30s

ntrialsP

1

2

Drag:


σD30s

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

26.26123 10

3


1

22.99221 10

3

Total Uncertainty:


1

20.01358

UR_L30s

1.440.943 %


1

26.71125 10

3

UR_D30s

0.690.973 %

47

AOA 35 deg: Smooth:

FIXED:


27.680.01957 psi


CLP35s1

ΔP35s2

L35s

Sarea 9.87179 10

3

1

Pa

CLS35s1

Sarea2

L35s

ΔP35s 78.70332

1

m2

CLL35s1

ΔP35s Sarea1.94837

1

lbf

Drag:

CDP35s1

ΔP35s2

D35s

Sarea 19.44289

1

in_Hg

CDS35s1

Sarea2

D35s

ΔP35s 4.25258

1

ft2

CDD35s1

ΔP35s Sarea1.94837

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP35s UP 1.47537 103

CLS35s UA 5.12343 105

CLL35s UFB 1.94837 103

48

CDP35s UP 8.58083 104

CDS35s UA 2.97982 105

CDD35s UFB 1.94837 103



1

22.44448 10

3


1

22.12916 10

3

RANDOM:


3 σmL35s

σL35s

ntrials

1

2

Pressure:


σP35s

ntrialsP

1

2

Drag:


σD35s

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

29.05631 10

3


1

25.2742 10

3

49

Total Uncertainty:


1

20.01946

UR_L35s

1.341.452 %


1

20.01144

UR_D35s

0.781.467 %

50

Appendix iii Uncertainty Analysis: Channeled Wing

Kline-McClintock Uncertainty Analysis for Drag and Lift Coefficients on Delta Wing:

Air Properties: From Fluids Textbook:

ν 15.68 106

m

2

s Uν 0

m2

s

ρ 1.18517kg

m3

0.07399lbm

ft3

Uρ 0.0006kg

m3

3.74568 105

lbm

ft3

Flow Proerties:

vmax 15.0855m

s so the wind tunnel pressure reading would be:

GivenΔPtest 0psi

ΔPtest1

2ρ vmax

2=

ΔP Find ΔPtest 0.01956 psi UP 0.06%1

27.68psi

2.16763 105

psi

Velocity Uncertainty:Sensitivity Coef:

SCP2

2ΔP

ρ ρ

0.05593s m

2

kg

Fixed Uncertainty for Velocity:

UR_V SCP UP 8.35918 103

m

s

Uv UR_V

51

Delta Wing Properties:

Λ 50deg UΛ 0.005deg Sweep Angle(Set by McClain)

Sspan 6.75in US 0.0002in

cwing .625ft UCNC 0.0002in

v vmax Sspan 6.75 in

Rec

v cwing

ν1.83277 10

5

Reynolds Uncertainty:Sensitivity Coef.:

CDv

cwing

ν1.21492 10

4

s

m

CDcwingv

ν9.62085 10

5

1

m

Total Uncertainty:

CDv Uv 101.55767

CDcwing UCNC 4.88739

UR_Re CDv Uv 2 CDcwing UCNC 2

1

23 305.0256

Planform area (S):

Sarea 0.18215ft2

Planform Area of chosen airfoil

Planform Area Uncertainty:

UA1

2Sspan UCNC

21

2cwing UCNC

2

1

2

7.0071 106

ft2

52

Limits of Force Balance Scale:

Lmax 15lbfUFB 0.001lbf

Dmax 8lbf

Drag and Lift Coef Uncertainty:

AOA 0 deg: Channeled:FIXED:

L0c 0.208986lbf D0c 0.030761lbf ΔP0c0.5413574psi

27.680.01956 psi


CLP0c1

ΔP0c2

L0c

Sarea 3.02114 10

3

1

Pa

CLS0c1

Sarea2

L0c

ΔP0c 24.07401

1

m2

CLL0c1

ΔP0c Sarea1.94935

1

lbf

Drag:

CDP0c1

ΔP0c2

D0c

Sarea 1.50588

1

in_Hg

CDS0c1

Sarea2

D0c

ΔP0c 0.3292

1

ft2

CDD0c1

ΔP0c Sarea1.94935

1

lbf

53

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP0c UP 4.51518 104

CLS0c UA 1.56717 105

CLL0c UFB 1.94935 103

CDP0c UP 6.64596 105

CDS0c UA 2.30675 106

CDD0c UFB 1.94935 103


Lift:BR_L0s CLP0c UP 2 CLS0c UA 2 CLL0c UFB 2

1

22.00102 10

3

Drag:BR_D0s CDP0c UP 2 CDS0c UA 2 CDD0c UFB 2

1

21.95049 10

3

RANDOM:

Lift:L0c 0.20899 lbf σL0c 0.005571lbf ntrials 3000 σmL0c

σL0c

ntrials

1

2

Pressure:

ΔP0c 0.01956 psi σP0c .0005792psi ntrialsP 30 σmP0c

σP0c

ntrialsP

1

2

Drag:

54

D0c 0.03076 lbf σD0c 0.005658lbf σmD0c

σD0c

ntrials

1

2

Student T's:

υ 5 1 4 t95 2.132


Lift: SR_L0c CLL0c σmL0c 2 CLP0c σmP0c 2

1

22.21162 10

3

Drag:SR_D0c CDD0c σmD0c 2 CDP0c σmP0c 2

1

23.81665 10

4

Total Uncertainty:

Lift: UR_L0c BR_L0s 2 t95 SR_L0c 2

1

25.12219 10

3

UR_L0c

0.411.249 %

Drag:UR_D0c BR_D0s 2 t95 SR_D0c 2

1

22.11341 10

3

UR_D0c

0.063.522 %



27.680.01968 psi


CLP5c1

ΔP5c2

L5c

Sarea 4.60898 10

3

1

Pa

55

CLS5c1

Sarea2

L5c

ΔP5c 36.95824

1

m2

CLL5c1

ΔP5c Sarea1.93715

1

lbf

Drag:

CDP5c1

ΔP5c2

D5c

Sarea 2.27518

1

in_Hg

CDS5c1

Sarea2

D5c

ΔP5c 0.50051

1

ft2

CDD5c1

ΔP5c Sarea1.93715

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 7.0071 106

ft2

UFB 1 103

lbf

CLP5c UP 6.88826 104

CLS5c UA 2.40591 105

CLL5c UFB 1.93715 103

CDP5c UP 1.00412 104

CDS5c UA 3.50714 106

CDD5c UFB 1.93715 103


Lift:BR_L5c CLP5c UP 2 CLS5c UA 2 CLL5c UFB 2

1

22.05611 10

3

56

Drag:

BR_D5c CDP5c UP 2 CDS5c UA 2 CDD5c UFB 2

1

21.93975 10

3

RANDOM:

Lift:L5c 0.32286 lbf σL5c 0.005579lbf ntrials 3 10

3 σmL5c

σL5c

ntrials

1

2

Pressure:


σP5c

ntrialsP

1

2

Drag:

D5c 0.04706 lbf σD5c 0.005724lbf σmD5s

σD5c

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

23.21099 10

3

Drag:SR_D5c CDD5c σmD5s 2 CDP5c σmP5c 2

1

25.09163 10

4

Total Uncertainty:

Lift: UR_L5c BR_L5c 2 t95 SR_L5c 2

1

27.14793 10

3

UR_L5c

0.631.135 %

Drag:UR_D5c BR_D5c 2 t95 SR_D5c 2

1

22.22284 10

3

UR_D5c

0.90.247 %

AOA 10 deg:

57

Channeled:FIXED:


27.680.0198 psi


CLP10c1

ΔP10c2

L10c

Sarea 6.09576 10

3

1

Pa

CLS10c1

Sarea2

L10c

ΔP10c 49.18326

1

m2

CLL10c1

ΔP10c Sarea1.92521

1

lbf

Drag:

CDP10c1

ΔP10c2

D10c

Sarea 3.71577

1

in_Hg

CDS10c1

Sarea2

D10c

ΔP10c 0.82249

1

ft2

CDD10c1

ΔP10c Sarea1.92521

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP10c UP 9.11028 104

CLS10c UA 3.20173 105

CLL10c UFB 1.92521 103

58

CDP10c UP 1.6399 104

CDS10c UA 5.76329 106

CDD10c UFB 1.92521 103



1

22.13013 10

3

Drag:BR_D10c CDP10c UP 2 CDS10c UA 2 CDD10c UFB 2

1

21.93219 10

3

RANDOM:


3 σmL10c

σL10c

ntrials

1

2

Pressure:


σP10c

ntrialsP

1

2

Drag:


σD10c

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

25.18463 10

3

59


1

29.52888 10

4

Total Uncertainty:


1

20.01126 UR_L10c

0.841.34 %


1

22.80368 10

3

UR_D10c

0.151.869 %



27.680.01967 psi


CLP15c1

ΔP15c2

L15c

Sarea 7.46102 10

3

1

Pa

CLS15c1

Sarea2

L15c

ΔP15c 59.79655

1

m2

CLL15c1

ΔP15c Sarea1.93816

1

lbf

Drag:

CDP15c1

ΔP15c2

D15c

Sarea 6.04275

1

in_Hg

CDS15c1

Sarea2

D15c

ΔP15c 1.32864

1

ft2

CDD15c1

ΔP15c Sarea1.93816

1

lbf

60

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP15c UP 1.11507 103

CLS15c UA 3.89264 105

CLL15c UFB 1.93816 103

CDP15c UP 2.66688 104

CDS15c UA 9.30989 106

CDD15c UFB 1.93816 103



1

22.23638 10

3


1

21.95645 10

3

RANDOM:


3 σmL15c

σL15c

ntrials

1

2

Pressure:


σP15c

ntrialsP

1

2

Drag:

61


σD15c

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

24.53295 10

3


1

21.1015 10

3

Total Uncertainty:


1

29.91963 10

3

UR_L15c

1.020.973 %


1

23.05657 10

3

UR_D15c

0.241.274 %

AOA 20 deg: Channeled:

FIXED:


27.680.01978 psi


CLP20c1

ΔP20c2

L20c

Sarea 8.88192 10

3

1

Pa

CLS20c1

Sarea2

L20c

ΔP20c 71.59099

1

m2

62

CLL20c1

ΔP20c Sarea1.92716

1

lbf

Drag:

CDP20c1

ΔP20c2

D20c

Sarea 9.05066

1

in_Hg

CDS20c1

Sarea2

D20c

ΔP20c 2.00136

1

ft2

CDD20c1

ΔP20c Sarea1.92716

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP20c UP 1.32743 103

CLS20c UA 4.66043 105

CLL20c UFB 1.92716 103

CDP20c UP 3.99437 104

CDS20c UA 1.40237 105

CDD20c UFB 1.92716 103



1

22.34055 10

3


1

21.96817 10

3

63

RANDOM:


3 σmL20c

σL20c

ntrials

1

2

Pressure:


σP20c

ntrialsP

1

2

Drag:


σD20c

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

26.58598 10

3


1

21.99099 10

3

Total Uncertainty:


1

20.01424

UR_L20c

1.221.167 %


1

24.67889 10

3

UR_D20c

0.371.265 %

AOA 25 deg:

Channeled:

64

FIXED:


27.680.01964 psi


CLP25c1

ΔP25c2

L25c

Sarea 9.74105 10

3

1

Pa

CLS25c1

Sarea2

L25c

ΔP25c 77.93775

1

m2

CLL25c1

ΔP25c Sarea1.94145

1

lbf

Drag:

CDP25c1

ΔP25c2

D25c

Sarea 12.59349

1

in_Hg

CDS25c1

Sarea2

D25c

ΔP25c 2.76428

1

ft2

CDD25c1

ΔP25c Sarea1.94145

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP25c UP 1.45583 103

CLS25c UA 5.0736 105

CLL25c UFB 1.94145 103

CDP25c UP 5.55795 104

65

CDS25c UA 1.93696 105

CDD25c UFB 1.94145 103



1

22.42719 10

3


1

22.01953 10

3

RANDOM:


3 σmL25c

σL25c

ntrials

1

2

Pressure:


σP25c

ntrialsP

1

2

Drag:


σD25c

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

26.32043 10

3


1

22.42012 10

3

Total Uncertainty:

66


1

20.01369

UR_L25c

1.331.029 %


1

25.54085 10

3

UR_D25c

0.511.086 %


FIXED:


27.680.01963 psi


CLP30c1

ΔP30c2

L30c

Sarea 9.80692 10

3

1

Pa

CLS30c1

Sarea2

L30c

ΔP30c 78.44

1

m2

CLL30c1

ΔP30c Sarea1.94206

1

lbf

Drag:

CDP30c1

ΔP30c2

D30c

Sarea 16.32151

1

in_Hg

CDS30c1

Sarea2

D30c

ΔP30c 3.58145

1

ft2

CDD30c1

ΔP30c Sarea1.94206

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

67

UA 6.50981 107

m2

UFB 1 103

lbf

CLP30c UP 1.46567 103

CLS30c UA 5.10629 105

CLL30c UFB 1.94206 103

CDP30c UP 7.20325 104

CDS30c UA 2.50956 105

CDD30c UFB 1.94206 103



1

22.4336 10

3


1

22.0715 10

3

RANDOM:


3 σmL30c

σL30c

ntrials

1

2

Pressure:

ΔP30c 0.01963 psi σP30c 0.0006846psi ntrialsP 30 σmP30c

σP30c

ntrialsP

1

2

Drag:

68


σD30c

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

28.45367 10

3


1

24.15959 10

3

Total Uncertainty:


1

20.01819

UR_L30c

1.341.357 %


1

29.10697 10

3

UR_D30c

0.661.38 %


FIXED:


27.680.01956 psi


CLP35c1

ΔP35c2

L35c

Sarea 9.96785 10

3

1

Pa

CLS35c1

Sarea2

L35c

ΔP35c 79.44274

1

m2

69

CLL35c1

ΔP35c Sarea1.94902

1

lbf

Drag:

CDP35c1

ΔP35c2

D35c

Sarea 18.54663

1

in_Hg

CDS35c1

Sarea2

D35c

ΔP35c 4.0552

1

ft2

CDD35c1

ΔP35c Sarea1.94902

1

lbf

Uncertainty Coeff:

UP 0.14945 Pa

UA 6.50981 107

m2

UFB 1 103

lbf

CLP35c UP 1.48972 103

CLS35c UA 5.17157 105

CLL35c UFB 1.94902 103

CDP35c UP 8.18528 104

CDS35c UA 2.84152 105

CDD35c UFB 1.94902 103



1

22.45369 10

3


1

22.11411 10

3

70

RANDOM:


3 σmL35c

σL35c

ntrials

1

2

Pressure:


σP35c

ntrialsP

1

2

Drag:D35c 0.37899 lbf σD35c 0.007356lbf σmD35c

σD35c

ntrials

1

2

Student T's:

υ 4 t95 2.132



1

29.51562 10

3


1

25.23378 10

3

Total Uncertainty:


1

20.02044

UR_L35c

1.351.514 %


1

20.01136 UR_D35c

0.741.535 %

71

Appendix iv- Executive Summary

Executive Summary It is important to keep in mind that the entirety of the report was collectively done with the entire group. Each member is able to give a full explanation of any part of the Test Plan Report. Below is a breakdown of the Test Plan Report, and who in the Delta Wing group completed the majority of each portion. Abstract- Ruben Nuñez and Ryan Parker Nomenclature- Ryan Parker Introduction- Meag McNary Experimental Methods- Meag McNary Experimental Procedure- Ruben Nuñez Uncertainty- Adam Eaker Results and Discussion- Ryan Parker Conclusion and Recommendations- Drew Waggoner Acknowledgements- Ruben Nuñez References- Ryan Parker and Ruben Nuñez General Formatting- Meag McNary

72

delta-wing vortex lift enhancement using oblique channeled ... · vortex breakdown through...

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