The following subsonic
half-duct wing analysis was
envisioned and developed by John Cipolla as an
undergraduate mechanical engineering design study. Conceptually,
a half-duct wing encloses high
velocity fan-accelerated air that according to Bernoulli's equation
will provide wing lift augmentation.
Initially, the digital Ohaus scale is calibrated to read
zero grams when loaded by the half-duct with the
electric motor turned off. This
step is simple when using the Ohaus digital scale
because the zeroing operation is automatic when the
applied mass is present at start-up. When operating at
full power the measured mass on the scale is reduced by
6.2 grams from an initial mass of approximately 24
grams. The total mass of the half-duct system includes
half-duct wing, electric motor, propeller, electric power cable and strain relief bend in the cable
as illustrated in Figure-1. For the operational
half-duct wing, Figure-2 clearly displays a mass reading of
- 6.2 grams which is a significant Bernoulli lift
effect generated by high velocity air in the half-duct.
While a half-duct wing will not levitate by itself the
added lift of the enclosed flow will allow the designer to
employ smaller and stubbier wings having reduced aspect
ratio (AR) thus reducing total drag.
The subsonic Bernoulli equation illustrated below is used to
approximate lift (L) generated by the half-duct wing.
Using Bernoulli's equation to determine pressure
for a half-duct wing requires that average air
velocity be determined within the half-duct. For the
purpose of determining half-duct air velocity the
pitot tube and velocity meter from the
AeroRocket subsonic wind tunnel was used with great success. The pitot tube was used to measure air velocity at the exit
of the half-duct as illustrated in Figure-3 and then at
the entrance to the half-duct as illustrated in
Figure-4. Half-duct exit air velocity was measured to be
2500 ft/min and entrance half-duct air velocity was
measured to be approximately 0.0 ft/min. The
average root mean squared air velocity in the half-duct
was computed to be approximately 883 feet per minute or
approximately 4.5 meters per second in the half-duct.
Using the measured approximation for half-duct air
velocity the lift generated by the Bernoulli effect is
computed in the MathCAD analysis in Figure-5 as approximately 5.9 grams. The Bernoulli analysis
result of 5.9 grams of lift compares favorably to
experimental lift results that range between 5.8 grams
and 6.3 grams depending on battery pack freshness.