Half-duct wing concept
 
LIFT ANALYSIS OF AN ENCLOSED-FLOW
HALF-DUCT USING BERNOULLI's EQUATION

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PropellerFLOW-ENCLOSED HALF-DUCT WING
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 differential (
Dp) 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.
 

BASIC PHYSICS FOR BERNOULLI'S EQUATION
Subsonic Bernoulli equation

Application of the Bernoulli equation
Bernoulli's equation between upstream (p1) and internal duct (p2) locations

Figure-1
Figure-1: Ohaus scale turned on with half-duct in place and initialized to zero

Figure-2
Figure-2: Half-duct with fan producing lift of 6.2 grams (notice negative sign)

Figure-3
Figure-3: Half-duct with fan producing lift of 6.3 grams and 2500 ft/min exit half-duct velocity

Figure-4
Figure-4: Half-duct with fan producing lift of 5.8 grams and 150 ft/min entrance half-duct velocity

Half-duct wing concept
MathCAD analysis
Figure-5, MathCAD analysis using the Bernoulli equation to approximate half-duct wing lift

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