Aspect ratio used in induced drag and lift calculations

[MaxKang]

Hello everyone,

I am working on a 3.2 meter wing span electric aircraft with another group of 30 engineering students. In calculating the induced drag and lift for preliminary calcs I am a little confused as to whether I need to include the width of the fuselage in the wing span(b) for induced drag calculation(CL^2/(pi*AR*e) and the area used for the lift calculation. e is assumed to be 0.99 due to taper. Or do I ignore the fuselage contribution and just use the wing area?

thank you!

 

[FactChecker]

Unless the fuselage is such an integrated part of the wing (like a "flying wing" plane), it's form is too different to be lumped in with the wing. Even then, the two wings are not considered as one. The calculations are done for each wing separately because a rolling motion or crosswind has different effects on each. In a rough analysis, the wings and the fuselage are usually considered separately. In a detailed analysis, the airflow is calculated at a much finer resolution.

 

[MaxKang]

Unless the fuselage is such an integrated part of the wing (like a "flying wing" plane), it's form is too different to be lumped in with the wing. Even then, the two wings are not considered as one. The calculations are done for each wing separately because a rolling motion or crosswind has different effects on each. In a rough analysis, the wings and the fuselage are usually considered separately. In a detailed analysis, the airflow is calculated at a much finer resolution.

Thank you so much!

 

[David Lewis]

The fuselage between the wing roots considered part of the total wing area, so you would include the shaded area shown in the diagram.

 

[FactChecker]

I stand corrected. If the wings are considered separately, the term "semi-span" would be appropriate (see https://www.grc.nasa.gov/WWW/k-12/VirtualAero/BottleRocket/airplane/area.html).
The term "span" refers to the total tip-to-tip distance, including the center line fuselage (see https://www.grc.nasa.gov/www/k-12/airplane/geom.html ) and the term "wing area" includes the entire tip-to-tip wing area.
I don't know if everyone (even NASA) strictly adheres to these definitions. I think that, in practice, the aerodynamic calculations are done in a much more detailed way.

 

[David Lewis]

Here is a diagram of how the lift is imagined to be distributed.
When designing a model airplane the induced drag formula doesn't account for a sharp rise in wing section drag coefficient that usually accompanies a decrease in Reynolds number (Re is proportional to wing chord). Also for a given span, cube loading is inversely proportional to the 1.5 power of the wing chord.

 

[David Lewis]

For the performance calculations you mentioned, the lift distribution diagram in post #6 is adequate. To calculate wing bending moment, however, a more conservative load distribution is assumed; the fuselage has a lower lift coefficient than the wing. (Note the area under the curve equals the maximum gross weight multiplied by the load factor.)