2. Page 1 of 21
Micro-Mutt Wind Tunnel Results
Contents
Micro-Mutt Geometry ..................................................................................................................................1
Wind Tunnel Test Settings ............................................................................................................................3
Comparison with Predicted Results as in miniMUTT_rigid_config.m...........................................................3
Comparison with Predicted Results as in STI_FDM_mAEWing1.3.pdf.........................................................7
Uncertainty Propagation...............................................................................................................................8
Appendix .....................................................................................................................................................10
Graphical Comparison FDM-STI-WT .......................................................................................................10
Rest of Wind Tunnel Results and Plots with Error Bars:.............................................................................16
Micro-Mutt Geometry
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.
3. Page 2 of 21
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
predicted in miniMUTT_rigid_config.m, the Micro-Mutt model is assumed to deflect the required
controlled surfaces together—as shown in Figure 2—to add up to the same surface, and thus, have the
same effect as one Mutt surface deflection.
4. Page 3 of 21
Wind Tunnel Test Settings
All the experiments were performed at a constant propeller frequency input of 57 Hz, giving an
airspeed magnitude of more or less 25 m/s. Also, it is important to know that the angle of attack range
was from -6 to 10 degrees in 2 degrees increments. Also, the variables measured by the Data
Acquisition Software that were recorded were:
[ 𝜌, 𝑉, 𝑁𝐹, 𝑇𝐹, 𝐴𝐹, 𝑁𝑀, 𝑇𝑀, 𝐴𝑀, 𝛼 ]
Finally, it is important to know that the Data Acquisition software gathered 100 data points for
the Force and Moment readings while it only measured density, airspeed, and angle of attack once; the
control surface effectiveness experiments were performed by deflecting only one control surface of one
wing at a time, and each control surface was tested for both positive and negative 25 degrees –see
Figure 3 below.
Figure 3: Example of a Positive 25 deg. Deflection for Control Surface # 4
Comparison with Predicted Results as in miniMUTT_rigid_config.m
Before comparing the results, it is important to know that the values of slopes were obtained by
using a total weighted linear least-squares code that computes the linear regression mean and
uncertainty range taking into account the uncertainty of each individual data point in both x and y
directions. The theory behind the code is explained in D. York, N. Evensen, M. Martinez, J. Delgado
"Unified equations for the slope, intercept, and standard errors of the best straight line" Am. J. Phys. 72
(3) March 2004.
25o
5. Page 4 of 21
Table 2: Lift Results
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CLα 4.5598 4.385 ± 0.1529 4.538 4.232 3.91
CLo 0 0.071 ± 0.0059 0.077 0.065 --
CLδ1 0.3731 0.221 ± 0.0244 0.245 0.196 51.2
CLδ2 0.3497 0.204 ± 0.0222 0.226 0.182 52.6
CLδ3 0.3124 0.175 ± 0.0219 0.196 0.153 56.4
CLδ4 0.2457 0.118 ± 0.0169 0.135 0.101 70.2
As it can be observed in Table 2, the predicted value of the lift-curve slope is a little bit off the
range of possible values obtained from the wind tunnel experiment; but the percentage difference from
the predicted value and the wind tunnel average is still small. Also, it is important to notice that the
percentage difference from the predicted control surface effectiveness values and the obtained ones are
at least 50% or greater; so, it is necessary to check whether the steps followed to obtain the predicted
values accounted for 1 or 2 control surfaces (1 for each wing) as some textbooks do. Included below in
Table 3 are the control surface results if we multiply all the obtained wind tunnel results by a constant 2.
Table 3: Control Surface Lift Results Scaled by 2
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CLδ1 0.3731 0.442 ± 0.0488 0.49 0.392 16.9
CLδ2 0.3497 0.408 ± 0.0408 0.452 0.364 15.4
CLδ3 0.3124 0.35 ± 0.0438 0.392 0.306 11.4
CLδ4 0.2457 0.236 ± 0.0338 0.27 0.202 4.0
Now, we can see that if that was to be the case, the obtained values would indeed be more
similar to the predicted ones.
Table 4: Drag Results
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CDα 0.129 0.102 ± 0.0601 0.162 0.041 23.4
CDo 0 0.036 ± 0.0112 0.047 0.025 --
CDδ1 0.0012 0.021 ± 0.0448 0.066 -0.024 178.4
CDδ2 0.0015 0.017 ± 0.0445 0.062 -0.027 167.6
CDδ3 0.0018 0.014 ± 0.0445 0.059 -0.03 154.4
CDδ4 0.0012 0.011 ± 0.0443 0.055 -0.034 160.7
6. Page 5 of 21
As it can be observed in Table 4, the obtained CD data was observed to be slightly different from
the predicted values, which could be expected as Drag magnitudes are small and are hard to accurately
obtain from wind tunnel experiments—which can also be observed by large uncertainty bounds. Here, it
is important to emphasize that the value of CDα was obtained by using the Linear Weighted Least
Squares code, so it fits the results to a linear relationship even if the relationship between CD and angle
of attack is expected to be quadratic. Also, a quadratic fit was calculated and the value of the linear
coefficient CDα was obtained to be -0.09403 ± 0.1856; which—if ignoring the negative values as do not
make sense—give a range from [0 : 0.09403]. Also, to be consistent, Table 5 was included below which
scales the control surface values by a factor of 2.
Table 5: Control Surface Drag Results Scaled by 2
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CDδ1 0.0012 0.042 ± 0.0896 0.132 -0.048 188.9
CDδ2 0.0015 0.034 ± 0.089 0.124 -0.054 183.1
CDδ3 0.0018 0.028 ± 0.089 0.118 -0.06 175.8
CDδ4 0.0012 0.022 ± 0.0886 0.11 -0.068 179.3
Now, we can see that if that was to be the case, the obtained values would still be quite
different, but it also make sense to obtain big percentage difference results as we are dealing with very
small magnitudes. Also, another possible explanation for higher drag values could be due to larger
amount of air bleeding in the control surface deflection since each control surface deflection is obtained
by deflecting smaller control surfaces.
Table 6: Pitching Moment Results
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CMα -0.3299 -0.334 ± 0.0724 -0.262 -0.406 1.2
CMo 0 0.01 ± 0.0037 0.013 0.006 --
CMδ1 -8.70E-04 -0.003 ± 0.0087 0.005 -0.012 110.1
CMδ2 -0.0329 -0.027 ± 0.0087 -0.018 -0.035 19.7
CMδ3 -0.1301 -0.073 ± 0.0128 -0.06 -0.086 56.2
CMδ4 -0.187 -0.098 ± 0.0138 -0.084 -0.111 62.5
As it can be observed above, the pitching moment values are very similar to the predicted ones.
Again, the scaled control surface values obtained from the wind tunnel experiment are included below
in Table 7.
7. Page 6 of 21
Table7: Control Surface Pitching Moment Results Scaled by 2
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CMδ1 -8.70E-04 -0.006 ± 0.0174 0.01 -0.024 149.3
CMδ2 -0.0329 -0.054 ± 0.0174 -0.036 -0.07 48.6
CMδ3 -0.1301 -0.146 ± 0.0256 -0.12 -0.172 11.5
CMδ4 -0.187 -0.196 ± 0.0276 -0.168 -0.222 4.7
Now, we can see that if that was to be the case, the obtained values would indeed be more
similar to the predicted ones; except for control surface #1, but a large percentage difference value is to
be expected as the magnitude of the predicted value is very small.
Table 8: Rolling Moment Results
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CLδ1 0.02 0.012 ± 0.0014 0.014 0.011 50.0
CLδ2 0.055 0.023 ± 0.0028 0.026 0.02 82.1
CLδ3 0.0853 0.035 ± 0.0038 0.038 0.031 83.6
CLδ4 0.0924 0.037 ± 0.004 0.041 0.033 85.6
Again, the scaled wind tunnel results are included below in Table 9.
Table 9: Control Surface Rolling Moment Results Scaled by 2
miniMUTT_rigid_config.m
(Current Predictions)
Wind Tunnel
Result
Wind Tunnel Possible Range % Difference
(w.r.t mean)Max. Min
CLδ1 0.02 0.024 ± 0.0028 0.028 0.022 18.2
CLδ2 0.055 0.046 ± 0.0056 0.052 0.04 17.8
CLδ3 0.0853 0.07 ± 0.0076 0.076 0.062 19.7
CLδ4 0.0924 0.074 ± 0.008 0.082 0.066 22.1
Now, we can see that if that was to be the case, the obtained values would indeed be more
similar to the predicted ones. For more information on how the uncertainties of each data point were
obtained, check the Uncertainty Propagation section below.
8. Page 7 of 21
Comparison with Predicted Results as in STI_FDM_mAEWing1.3.pdf
In this section, the longitudinal wind tunnel results above were compared to both the Flight
Dynamics Model (FDM) developed by Dr. David Schmidt, and the STI model. Before comparing the
results, it is important to emphasize that both FDM and STI models use the FEM model developed by
Virginia Tech; such model has an aft CG location which—in the 1/3rd
scaled micro-Mutt model—would
be located at
𝑟𝑐𝑔 = [ 0.2113, 0, 0 ]
Hence, the different values of the wind tunnel pitching moment coefficient and pitching moment control
surface effectiveness.
Also, it is important to emphasize that the STI model coefficients were extracted after
residualizing the unsteady aerodynamic states as well as some structural modal states; hence, the final
rigid body coefficients do not represent a “true” un-deformed rigid body aircraft. As a result, the
coefficients were expected to be slightly different while keeping the same sign and order of magnitude.
Table 10: Comparison of Longitudinal Coefficients
FDM STI Wind Tunnel
% Difference
FDM-STI
% Difference
FDM-WT
% Difference
STI-WT
CLα 4.59 3.05 4.385 ± 0.1529 40.3 4.52 36.0
CLδ1 0.794 0.546 0.442 ± 0.0488 37.0 58.2 22.4
CLδ2 0.603 0.746 0.408 ± 0.0408 21.2 38.6 58.6
CLδ3 0.506 0.633 0.35 ± 0.0438 22.3 36.4 57.6
CLδ4 0.416 0.664 0.236 ± 0.0338 45.9 55.2 95.1
CDα 0.077 0.07 0.118 ± 0.054 9.52 42.1 51.1
CMα 0.208 -0.016 0.259 ± 0.0679 171 21.8 177
CMδ1 0.085 0.046 0.054 ± 0.0178 59.5 44.6 16.0
CMδ2 -0.001 -0.022 0.0 ± 0.0154 (--) (--) (--)
CMδ3 -0.162 -0.16 -0.102 ± 0.0246 1.24 45.5 44.3
CMδ4 -0.27 -0.37 -0.166 ± 0.0312 31.3 47.7 76.1
In Table 10, it was observed that most of the wind tunnel results agreed with both the FDM and
STI models—in the same order of magnitude, as the percentages difference were more or less
consistent. Also, to better compare the different results, graphical representations of their comparisons
were included in the Appendix section.
9. Page 8 of 21
Uncertainty Propagation
In order to have a better understanding on how the uncertainty bounds were obtained, it is
important to describe the uncertainty propagation equations that were used as well as the uncertainty
magnitudes that were assumed for certain parameters. To illustrate the procedure, an example of the
uncertainty propagation for the Lift coefficient and the Pitching moment coefficient were included.
𝐶𝐿 =
𝐿𝑖𝑓𝑡
𝑞 ∙ 𝑆
∴ Δ𝐶𝐿 = |𝐶𝐿| ∙ √(Δ𝐿𝑖𝑓𝑡
𝐿𝑖𝑓𝑡⁄ )
2
+ (
Δ𝑞
𝑞⁄ )
2
+ (Δ𝑆
𝑆⁄ )
2
Where,
𝐿𝑖𝑓𝑡 = 𝑁𝐹 ∙ 𝑐𝑜𝑠(𝛼) − 𝐴𝐹 ∙ 𝑠𝑖𝑛(𝛼)
𝑞 =
1
2
𝜌𝑉2
𝑆 = 𝑐̅ ∙ 𝑏
Therefore,
∆𝐿𝑖𝑓𝑡 = |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 ∙ (Δ𝑉
𝑉⁄ )
2
Δ𝑆 = 𝑆 ∙ √(Δ𝑐̅
𝑐̅⁄ )
2
+ (Δ𝑏
𝑏⁄ )
2
Similarly,
𝐶 𝑀 =
𝑃𝑖𝑡𝑐ℎ
𝑞 ∙ 𝑆 ∙ 𝑐̅
∴ Δ𝐶 𝑀 = |𝐶 𝑀| ∙ √(Δ𝑃𝑖𝑡𝑐ℎ
𝑃𝑖𝑡𝑐ℎ⁄ )
2
+ (
Δ𝑞
𝑞⁄ )
2
+ (Δ𝑆
𝑆⁄ )
2
+ (Δ𝑐̅
𝑐̅⁄ )
2
Where,
𝑃𝑖𝑡𝑐ℎ = 𝑇𝑀 + (𝑟⃗ 𝐶𝐺
𝑆𝑡𝑖𝑛𝑔⁄
× 𝐹⃗) = 𝑇𝑀 − (𝑟𝑎𝑥𝑖𝑎𝑙 ∙ 𝑁𝐹) + (𝑟𝑛𝑜𝑟𝑚𝑎𝑙 ∙ 𝐴𝐹)
10. Page 9 of 21
Therefore,
Δ𝑃𝑖𝑡𝑐ℎ = |𝑃𝑖𝑡𝑐ℎ|
∙ √(Δ𝑇𝑀)2 + (𝑟𝑎𝑥𝑖𝑎𝑙 ∙ Δ𝑁𝐹)2 + (∆𝑟𝑎𝑥𝑖𝑎𝑙 ∙ 𝑁𝐹)2 + (𝑟𝑛𝑜𝑟𝑚𝑎𝑙 ∙ Δ𝐴𝐹)2 + (∆𝑟𝑛𝑜𝑟𝑚𝑎𝑙 ∙ 𝐴𝐹)2
Hence, the values used throughout the uncertainty propagation were obtained or assumed as
shown in Table 11 below.
Table 11: Uncertainty Parameters
Uncertainty Parameter(s) Value Assumed / Obtained
ΔNF, ΔAF, ΔTF
Obtained from sting inherent 2% uncertainty and
standard deviation of the 100 recorded data points
ΔNM, ΔAM, ΔTM
Obtained from sting inherent 2% uncertainty and
standard deviation of the 100 recorded data points
Δα Assumed ±0.5 Deg.
Δρ Assumed ±0.09 kg/m3
ΔV Assumed ±0.2 m/s
Δb Assumed ±0.005 m
Δc̅ Assumed ±0.002 m
ΔδCS Assumed ±5 Deg.
Δrnormal, Δraxial, Δrtransverse All assumed ±0.00254 m (or ±0.1 inches)
11. Page 10 of 21
Appendix
Graphical Comparison FDM-STI-WT
