Engineering
41 Laboratory Exercise 3
“Winglab”
25 October 2004
Alexis Reedy, Zach Pezzementi,
Aron Dobos
Introduction
and Theory
External flow
occurs when a solid object moves with respect to a fluid in which it is
immersed. Usually the net force acting on the object is divided into lift and drag, lift corresponding to the vertical component of the
total force and drag to the horizontal component. For an airplane in flight, to
maintain altitude, the lift resulting from the Bernoulli pressure differential
between the bottom and the curved top of the wing equals the downward force of
gravity. This pressure differential results from the fact that a streamline
along the top of the wing travels a longer distance than along the bottom of
the wing, and thus travels at a larger velocity. See the attached handout for
more detail.
In the figure on the cover page, a stall situation is illustrated, which occurs when the streamline over the top of the wing breaks away from the surface of the wing, leaving a separation region of turbulence between the streamline and the upper surface of the wing. This turbulence was observed by moving a string across the surface of the wing and through the streamline. In the areas of smooth flow, the string lay flat along the wing surface, but in the stagnation area, the string fluttered irregularly.
Procedure
See attached handout.
The procedure was as described in the handout, but with the following modifications:
The angles and wind velocities measured were -4, 0, 10, 19 degrees at 10, 15, 20 m/s in tunnel.
Anemometer readings were taken for all angles, all velocities, not just 0 and 10 degrees.
Strain gauge values were recorded for all angles and all wind velocities.
Results
Pressure
Distribution
Three methods were used to measure the lift and drag forces. The method that yielded the most consistent results was based on obtaining the pressure distribution around the wing from a series of ports. A modified version of the MATLAB script liftdrag.m was used to integrate the pressure measurements over the surface of the wing at various angles of attack to arrive at the lift and drag forces. The values (Table 1) and pressure distribution plots (Figure 1-12) are included below.
Table
1. Calculated Lift and Drag
from Pressure Distribution
|
Lift (N) |
-4 |
0 |
10 |
19 |
|
10 m/s |
0.13777 |
0.14832 |
0.49447 |
0.64772 |
|
15 m/s |
0.38018 |
0.54156 |
1.1839 |
1.5222 |
|
20 m/s |
0.44763 |
1.0382 |
2.2135 |
2.8776 |
|
Drag (N) |
|
|
|
|
|
10 m/s |
0.056833 |
0.074481 |
0.084999 |
0.099201 |
|
15 m/s |
0.15508 |
0.14416 |
0.16388 |
0.17444 |
|
20 m/s |
0.26489 |
0.23328 |
0.28236 |
0.32886 |
Strain gauge
We used a modification of calibration equations for a cylindrical tube to convert the voltage readings taken from the strain gauges to lift and drag forces. Given that
Drag = -0.51 + 2.210*Ch 2 mV – 3.572*Ch 4 mV
Lift = 110.32 – 25.45*Ch 1 mV – 8.80*Ch 3 mV,
these equations were re-zeroed for the airfoil such that the lift and drag equations went to zero in still air conditions at zero degrees. Using the same channel coefficients in each equation, the constant term was solved for, giving
Drag = -0.3611 + 2.210*Ch 2 mV – 3.572*Ch 4 mV
Lift = 130.94 – 25.45*Ch 1 mV – 8.80*Ch 3 mV.
These equations were then used to calculate lift and drag for each angle and velocity.
Table
2. Calculated Lift and Drag
from Strain Guages
|
Lift |
-4 |
0 |
10 |
19 |
|
10 m/s |
129.6929 |
135.7265 |
134.67 |
135.5297 |
|
15 m/s |
131.7334 |
135.2605 |
136.7596 |
147.1929 |
|
20 m/s |
131.7608 |
138.6513 |
154.5587 |
162.499 |
|
Drag |
|
|
|
|
|
10 m/s |
-0.23736 |
-0.04315 |
0.071137 |
-0.19498 |
|
15 m/s |
-0.0068 |
-0.04263 |
0.106321 |
-0.52675 |
|
20 m/s |
-0.18223 |
-0.27065 |
-0.42319 |
-1.61577 |
Velocity profiles
Anemometer voltages were converted
to velocities by the calibration equation V = 2.12321 + 0.26722*X +
-1.70959*X^2-0.0443017*X^3 + 0.326697*X^4, where X is the anemometer voltage
reading. Drag estimates were then calculated from these velocities by the equation 
, where Vr is the reference velocity and Va
is the velocity measured by the anemometer. Since our readings were discrete,
we used 
, where ρ = 1.23 kg/m3, L = 17.25cm and
Y=2mm.
Table
3. Calculated Drag from
Velocity Profiles
|
Drag |
-4 |
0 |
10 |
19 |
|
10m/s |
-0.02217 |
0.003603 |
-0.07634 |
-0.00756 |
|
15m/s |
-0.01925 |
0.03261 |
-0.16821 |
-0.35503 |
|
20m/s |
0.091598 |
-0.08261 |
-0.36823 |
-0.51866 |
Angle comparisons at different wind velocities
Velocity comparisons at different angles
Discussion and Conclusions
The anemometer readings did not correspond to the velocities at which the air in the wind tunnel was supposed to be running. The velocities returned by the anemometer were usually about 3/5 of the setting of the wind tunnel. This discrepancy could result from error in the calibration of the anemometer or in that of the wind tunnel. The anemometer readings were largely self-consistent though. As angle of attack increased, the height at which stall occurred moved downwards. At each angle of attack, the shape of the profile did not vary much at different velocities, although they were translated in velocity. As angle of attack increases, both lift and drag increase. From Table 3, one can see that on the whole, the drag increases with velocity and with angle of attack.
Similar trends are apparent from the strain gauge data, although the absolute values are entirely incomparable to those returned by the other measurement methods (see Table 2). Since the strain gauges take into account friction drag as well as form drag, whereas the other measurement methods do not, the difference between the drag they measure and the drag measured by the other methods should correspond to the friction drag. Since the values are incomparable, however, it is not possible to evaluate the friction drag.
The same trends hold for the pressure port measurements, as seen in Table 1. The values for this data seem more reasonable and consistent than those of the other measurement methods.
These data have implications for aircraft flight and inter-aircraft relationships under close proximity conditions upon arrival and takeoff at airports. The wake effect of streamlines coming off airfoils imposes restrictions on how close to each other successive landings or takeoffs can be performed, since the air in the wake would have turbulent characteristics that would cause difficulties in achieving sufficient control of the aircraft for safe travel.