Wind Tunnel Balances Page: 32 of 51
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WIND TUNNEL BALANCES.
The equivalent force balanced by hanging weights on the drag arm is equal to MD divided
by 7, or
N
FD=X cos - Y sin # +N
Angle of attack. 50 12
I --------------- ---- .-------- ---.-------.-- - .... j. ,, 8074.4 12 3.0
F- 2)-- ..------------------- -- -------- ----- -- 59-5 76.3 123.0
F --)-....------------------------------------ - - j 50.9 75.6 124.0
It appears that an angle of yaw of -20 may lead to errors of from 1 per cent to 3 per cent
in the measurement of the drag, and that, in order to keep the error within the desired maximum
of I per cent, the angle of yaw must not exceed 0?2. This ideal is perfectly possible to realize
mechanically, but the spindle itself deflects at small angles so that the slope at its tip in the
plane of the wing chords is slightly more than 0?2 when tests are run at 50 meters per second.
The error in lift measurement due to the model being set up at angle of yaw must be found
in the same way. The total moment about an axis passing through the balance pivot and
parallel to the tunnel axis is
ML =Zh + M sin #-- L cos #
and the equivalent force is
M sin 1 -L cosP -
The true and apparent values of Z may be tabulated as for X.
Angle of attack. 0* 12
S----+2 ....--------- ------------------------- ....... 207 611 89
& 4- -20 )- .............................. -.........- .- 204 611 893
F,.(--204 611 893
The error in lift is obviously much smaller than that in drag, and it is the accuracy desired
in the latter measurement that controls the degree of precision necessary in alignment.
To complete the analysis the effect of yaw on the moments about a vertical axis must be
discussed. The equation for the total moment is
My =-Mcos # + L sin t
Angle of attack. 0 60 12*
M .v(*. .0... ..................... ......--------- ..... .. +6.3 0.0 0.0
2)....--------------------- -----..--~- -1.7 +4.0
These differences between the true and the apparent moments correspond to errors of 0.030,
0.027, and 0.004 cm., respectively, in the location of the vector of resultant force. These errors
are negligible, the largest being less than j per cent of the wing chord.
In short, then, it appears that the accurate alignment of the model in yaw is of importance
primarily as regards drag and that its importance there is considerable. If the data for a single
aerofoil, instead of for a complete model, are taken the importance of accurate alignment is
lessened, as Y and N, which cause most of the difficulty, both arise largely from the body and
tail surfaces. For bodies and other streamline forms, on the other hand, the relative importance
of accurate alignment is greater than for models of complete airplanes.
The analysis of the modifications in the measurements when the model is tilted in roll
instead of in yaw is much simpler, since the axis of the tunnel remains parallel to the plane of
symmetry of the model, which merely rotates about it. There are, therefore, no rolling or25
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Warner, Edward P. & Norton, F. H. Wind Tunnel Balances, report, 1920; (https://digital.library.unt.edu/ark:/67531/metadc65722/m1/32/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.