brief of aerodynamic loads_moments prediction for micro-mutt wind tunnel model (1)

Brief of Aerodynamic Loads/Moments Prediction for Micro-Mutt Wind

Tunnel Model

Adria Serra Moral 6/9/2015

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Contents Preface: ..................................................................................................................................................... - 2 -

Micro-Mutt Geometry and Aerodynamic Predictions: ............................................................................. - 2 -

Analysis Process Flowchart: ...................................................................................................................... - 5 -

Results: ...................................................................................................................................................... - 5 -

Lift vs. Angle of Attack ...................................................................................................................... - 5 -

Drag vs. Angle of Attack .................................................................................................................... - 7 -

Pitch vs. Angle of Attack .................................................................................................................... - 8 -

Pitch Moment Produced by Maximum Control Surface Defection ................................................ - 10 -

Roll Moment Produced by Maximum Control Surface Defection .................................................. - 11 -

Lift vs. Angle of Attack Result from Previous Experiment ...................................................................... - 13 -

Error Propagation.................................................................................................................................... - 14 -

Future Work ............................................................................................................................................ - 15 -

Appendix ................................................................................................................................................. - 16 -

Lift vs. Angle of Attack .................................................................................................................... - 16 -

Drag vs. Angle of Attack .................................................................................................................. - 18 -

Pitching Moment vs. Angle of Attack .............................................................................................. - 20 -



Normal Force and Axial Force vs. Angle of Attack .......................................................................... - 26 -

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Brief of Aerodynamic Loads/Moments Prediction for Micro-Mutt Wind Tunnel Model

Preface: This brief does not capture all the details of the analysis, but it is a short summary of the

important results, the conclusions made, and the possible plan moving forward. In this brief, the Mutt

Aerodynamic coefficient predictions and the Micro-Mutt wind tunnel model geometry have been used

to calculate some of the loads/moments that the Micro-Mutt should produce if run in the wind tunnel at

different speeds and angles of attack. Then, the uncertainty results obtained—and explained in the Brief

of Wind Tunnel Uncertainty Results—are used to predict potential error bars that should be expected at

each condition. NOTE: this document only includes the analysis for the sting uncertainty; true and more

complete error bars would have to include other sources of uncertainty such as free stream airspeed,

angle of attack, model dimensions uncertainty, etc.

Micro-Mutt Geometry and Aerodynamic Predictions: To visualize the magnitude of the results and possibilities moving forward, it is important to

know the geometry of the model. The important parameters of the model, such as wing span or mean

aerodynamic chord, are included in Table 1; a graphical representation of the model is attached in

Figure 1. Also, it is important to point out that the Micro-Mutt model is scaled to 1/3rd of the Mutt-

aircraft.

Table 1: Micro-Mutt Important Geometry Values

Meters Inches

Wing Span (b) 1.016 40

Mean Aerodynamic Chord (�̅�) 0.107 4.213

Wing Area (S) [Length2] 0.117 180.8

Aspect Ratio (AR) [non-dimensional]

8.85

CG Location from Nose (rCG) [ x, y, z ]

[ 0.1972, 0, 0 ] [ 7.764, 0, 0 ]

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Figure 1: Micro-Mutt Wind Tunnel Model

Also, Figure 2 includes a close-up display of the Micro-Mutt wing and its control surfaces. It is

important to emphasize that the Micro-Mutt has 9 control surfaces in each wing instead of the 4 control

surfaces that the Mutt has; control surfaces 2, 3, and 4 are separated into smaller control surfaces

making a total of 9. For the purpose of this analysis and to use the control effectiveness coefficients of

Table 2, the Micro-Mutt model is assumed to deflect the required controlled surfaces together to have

the same effect as one Mutt surface deflection.

Figure 2: Micro-Mutt Control Surfaces

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Table 2: Predicted Aerodynamic and Control Coefficients Used in Test

Lift

CLα [1/rad] CLo CLδ1 [1/rad] CLδ2 [1/rad] CLδ3 [1/rad] CLδ4 [1/rad]

4.5598

0 (assumed exactly symmetric airfoil

shape)

0.3731 0.3497 0.3124 0.2457

Drag

CDα [1/rad] CDo** CDδ1 [1/rad] CDδ1 [1/rad] CDδ1 [1/rad] CDδ1 [1/rad]

0.129 0.01 0.0012 0.0015 0.0018 0.0012

Pitch

Cmα [1/rad] Cmo Cmδ1 [1/rad] Cmδ2 [1/rad] Cmδ3 [1/rad] Cmδ4 [1/rad]

-0.3299 0 -8.7e-04 -0.0329 -0.1301 -0.187

Roll

--- Clδ1 [1/rad] Clδ2 [1/rad] Clδ3 [1/rad] Clδ4 [1/rad]

0.02 0.055 0.0853 0.0924

**-The value of CDo was not obtained from the Rigid Mutt Values, but it was assumed by me to construct

a “more realistic” Drag Polar ( CD = CDo + K*CL2 ).

Also, other values or parameters that are important to emphasize for the purpose of the

experiment are shown in Table 3.

Table 3: Other Important Parameters Used Throughout Analysis

Wing Oswald Coefficient ( e )**

Air Density ( ρ ) [ kg / m3 ]

Airspeed Array [m/s]

Angle of Attack Array ( α )

[ deg. ]

0.8 1.185 [ 5, 10, 15, 20, 25, 30] -10 to 12 in 1 deg.

increments

**- The value of e was not obtained from the Rigid Mutt Values, but it was assumed by me to

construct a “more realistic” Drag Polar ( CD = CDo + K*CL2 ).

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Analysis Process Flowchart: In order to keep it as brief and as complete as possible and to simplify the explanation of the

steps taken throughout the analysis, the flowchart of all the steps taken is displayed in Figure 3.

Figure 3: Analysis Flowchart

As it can be observed in Figure 3, the predicted coefficients were used to obtain the predicted

loads that the sting should observe in the sting axes, and the uncertainty predictions were used to

obtain the predicted error bars that the aerodynamic loads would display if we propagated such

uncertainties from the sting back to the vehicle.

Results: The loads/moments that were able to analyze in a possible wind tunnel experiment using the

obtained data were: Lift vs Angle of Attack, Drag vs. Angle of Attack, Pitching Moment vs. Angle of

Attack, Pitching Moment Produced by maximum control surface deflection, Rolling Moment Produced

by maximum control surface deflection.

Lift vs. Angle of Attack

To discuss the results in this section, only the cases for airspeed equal to 5 m/s and 25 m/s were

included. The plots containing the rest of the results will be attached in the Appendix section.

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Figure 4: Lift vs. Angle of Attack Plot at 5m/s

As it can be observed in Figure 4, the error bars at smaller angles of attack are quite large as the

values of lift are very small—the normal force and axial force that produced such lift are smaller than

the minimum measurable forces. It is important to point out that to construct the error bars for forces

that are smaller than the minimum measurable forces; the percentage error at such forces was assumed

to be 30%.

Figure 5: Lift vs. Angle of Attack Plot at 25m/s

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As it can be observed in Figure 5, the error bars at all angles of attack are small as all the

expected loads are high enough—the normal and axial forces that produce such lift are greater than the

minimum measurable forces; so, the percentage of error is bounded at 2%. Hence, it can be concluded

that setting experiments at higher speeds produce better and more accurate results.

Drag vs. Angle of Attack



Figure 6: Drag vs. Angle of Attack Plot at 5m/s

As it can be observed in Figure 6, the drag loads at 5 m/s cannot be measured at all. The drag

loads are so small—all quite smaller than the minimum measurable loads.

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Figure 7: Drag vs. Angle of Attack Plot at 25m/s

In Figure 7, it can be observed that at higher speeds the magnitude of the error bars decreased,

especially at higher angles of attack. A reason for that could be that, at higher angles of attack, the

magnitudes of the loads are larger and the magnitude of the normal force has a greater contribution. On

the other hand, at smaller angles of attack, the magnitudes of the loads are smaller and are obtained

mostly by the magnitude of the axial force—which has a larger minimum measurable load than the

normal force. Nonetheless, knowing the expected shape of the drag polar, some weights and constraints

could be enforced at smaller angles of attack to predict the value of the minimum drag.

Pitch vs. Angle of Attack



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Figure 8: Pitching Moment vs. Angle of Attack Plot at 5m/s

In Figure 8, the conclusions are the same as for the drag. The magnitudes of the pitching

moment are too small to be measured accurately.

Figure 9: Pitching Moment vs. Angle of Attack Plot at 25m/s

On the other hand, it can be observed in Figure 9 that at larger speeds—hence, larger loads—the

magnitudes of the pitching moment could be measured accurately enough. The increasing error bars are

a result of the propagation of the 2% percentage error bound.

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Pitch Moment Produced by Maximum Control Surface Defection


included. The plots containing the rest of the results will be attached in the Appendix section. The

maximum control surface deflection was assumed to be 30 degrees.

Figure 10: Pitching Moment Produced by Maximum Control Surface Deflection at 5m/s

Similarly, at lower speeds the pitching moment produced by deflecting the control surfaces

would be so small that it would not be recorded accurately.

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Figure 11: Pitching Moment Produced by Maximum Control Surface Deflection at 25m/s

On the other hand, at high speeds, the magnitude of the produced pitching moment would

increase, making it possible to be observed and recorded by the sting. Again, it is important to

emphasize that we are only considering 4 control surfaces that would be obtained by deflecting various

Micro-Mutt control surfaces together—as shown in Figure 2. However, it is also important to note that

due to the model design and air gaps between surfaces, it is very possible to have quite smaller and

different results that the ones predicted theoretically.

Roll Moment Produced by Maximum Control Surface Defection


included. The plots containing the rest of the results will be attached in the Appendix section. The

maximum control surface deflection was assumed to be 30 degrees.

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Figure 12: Rolling Moment Produced by Maximum Control Surface Deflection at 5m/s

Figure 13: Rolling Moment Produced by Maximum Control Surface Deflection at 5m/s

Surprisingly enough, the moment arm of the control surfaces is large enough that the

magnitude of the load produced by their deflection would create a large enough rolling moment that

could be observed at most speeds. However, again, it is important to emphasize that the air gap

between surfaces and other effects/uncertainties could make these moments smaller and have more

error than expected.

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Lift vs. Angle of Attack Result from Previous Experiment To check the predicted results, we compared them to the loads recorded from the Micro-Mutt

wind tunnel test performed in the past. The results are shown in Figure 14 or in a more zoomed-in

vision in Figure 15.

Figure 14: Lift vs. Angle of Attack of Predicted and Measured Values at 25 m/s (55 Hz)

Figure 15: Lift vs. Angle of Attack of Predicted and Measured Values at 25 m/s (55 Hz) Zommed

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As it can be observed from both Figure 13 and Figure 14, the predicted values are not too

different from the recorded values. It is important to show that the predicted lift is obtained assuming a

linear relationship with the predicted CLα; hence, it does not account for the non-linear stall that can be

observed close to 10 degrees. Also, while the error bars are small, it is important to emphasize again

that all error bars are obtained by propagating the sting uncertainty only, and the measured

experimental results could differ due to other sources of uncertainty such as angle of attack, airspeed,

etc. Also, another reason why values could be different than the predicted is because the experimental

results were obtained by taking only 4-5 measurements instead of 100 that could average out some

noise.

Error Propagation In order to have a better understanding on how each uncertainty affects the overall result, it is

good to include this short summary of the error propagation equations used. Note, this error

propagation only includes the uncertainty of the sting.

𝐿𝑖𝑓𝑡 = 𝑁𝐹 ∗ 𝑐𝑜𝑠(𝛼) − 𝐴𝐹 ∗ 𝑠𝑖𝑛(𝛼); ∆𝐿𝑖𝑓𝑡 = √(∆𝑁𝐹 ∗ cos(𝛼))2 + (Δ𝐴𝐹 ∗ sin(𝛼))2

𝐷𝑟𝑎𝑔 = 𝑁𝐹 ∗ 𝑠𝑖𝑛(𝛼) + 𝐴𝐹 ∗ 𝑐𝑜𝑠(𝛼); ∆𝐷𝑟𝑎𝑔 = √(∆𝑁𝐹 ∗ sin(𝛼))2 + (Δ𝐴𝐹 ∗ cos(𝛼))2

𝑃𝑖𝑡𝑐ℎ = 𝑇𝑀 + (𝑟𝐶𝐺𝑆𝑡𝑖𝑛𝑔⁄

× �⃗�) = 𝑇𝑀 − (𝑟𝑎𝑥𝑖𝑎𝑙 ∗ 𝑁𝐹); Δ𝑃𝑖𝑡𝑐ℎ = √(Δ𝑇𝑀)2 + (𝑟𝑎𝑥𝑖𝑎𝑙 ∗ Δ𝑁𝐹)^2

as rnormal = 0; Note: if rnormal was not exactly zero but was very small, this uncertainty would be included

and multiplied with the magnitude of the Axial Force. But since both would be small, the overall result

would not change too much.

𝑅𝑜𝑙𝑙 = − (𝐴𝑀 + (𝑟𝐶𝐺𝑆𝑡𝑖𝑛𝑔⁄

× �⃗�)) = −𝐴𝑀; ∆𝑅𝑜𝑙𝑙 = |Δ𝐴𝑀|

as rnormal and rtransverse are both = 0; Note: if both rnormal and rtransverse were not exactly zero but had a small

uncertainty, this uncertainty would be propagated and multiplied by the magnitudes of the Transverse

and Normal forces respectively. While the transverse force would be expected to be small enough that

its result would not affect much, the magnitude of the Normal force could be large enough that its result

could impact the overall Roll uncertainty.

The uncertainty of an aerodynamic coefficient would look like:

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Δ𝐶𝐿 = |𝐶𝐿| ∗ √(Δ𝐿𝑖𝑓𝑡

𝐿𝑖𝑓𝑡⁄ )

2

+ (Δ𝑞

𝑞⁄ )2

+ (Δ𝑆𝑆⁄ )

2

Where

∆𝐿𝑖𝑓𝑡 = √(∆𝑁𝐹 ∗ cos(𝛼))2 + (𝑁𝐹 ∗ sin(𝛼) ∗ Δ𝛼)2 + (Δ𝐴𝐹 ∗ sin(𝛼))2 + (𝐴𝐹 ∗ cos(𝛼) ∗ Δα)2

Δ𝑞 = 𝑞 ∗ √(Δ𝜌

𝜌⁄ )2

+ 2 ∗ (Δ𝑉𝑉⁄ )

2 and Δ𝑆 = 𝑆 ∗ √(Δ𝑐̅

𝑐̅⁄ )2

+ (Δ𝑏𝑏⁄ )

2 which is probably negligible

Future Work Now that we have a better knowledge of what to expect from the sting in a complete wind

tunnel experiment using the current Micro-Mutt model, it would be useful to run some tests at angle of

attacks and speeds where most loads/moments could be predicted more accurately to check their

validity.

Also, it would be very useful to assume some uncertainties for other parameters (such as ∆α =

±0.5 deg.) and propagate those extra uncertainties to see how the error bars of the aerodynamic

loads/moments change.

Another thing to consider is, as the uncertainty for the normal and axial loads was initially

computed and propagated, we do have what is the contribution of each sting force to the total

uncertainty of the vehicle aerodynamic load. Hence, it could be good to consider whether to use the

axial force reading to calculate the lift and drag in conditions where the uncertainty of such axial force is

as large. Example plots of Normal and Axial forces uncertainty have been included in the Appendix

section.

Also, if necessary, simple tools could be used to try to predict what would the control

effectiveness coefficients be for all 9 Micro-Mutt control surfaces individually and run the same analysis

using the 9 control surfaces as opposed to the 4 used.

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Appendix

Lift vs. Angle of Attack

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Drag vs. Angle of Attack

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Pitching Moment vs. Angle of Attack

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Normal Force and Axial Force vs. Angle of Attack

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brief of aerodynamic loads_moments prediction for micro-mutt wind tunnel model (1)

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