# What would be the Sref i.e. Reference Wing Area for Drag Build Up Calculation in case of a box wing design?

Would Sref be sum of areas of both, the front and the back wing? or just one wing? Assuming both the wings have equal areas (image below)

Details - So, I am calculating drag using the component drag build up method and using the below equation for the following parts of my box wing design.

1. Front Wing
2. Aft Wing
3. Fuselage
4. Tail

as you can see in the equation below, Swet for all different parts are divided by "Sref". For example assuming that both wings have area of 10m^2 and therefore wetted area of roughly about 20m^2 each.

for Cd0 calculation what should use as my Sref? total lift generating area of the aircraft, as in 10+10=20? or just the area of any one wing, 10?

If I use 20, for example, and apply the below formula for the front wing, my (Swet/Sref = 1) whereas it's = 2 if I use, Sref as 10m^2?

Basically, my total CD0 values changes drastically as I change my Sref according to the below equation, why is that?

• Related: How is wing area defined? Note that the specifics of the method used is irrelevant for the purpose: This wing area serves as the reference area of most aerodynamic coefficients and either method is good enough for the purpose. Consistency is more important than precision here.
– user14897
Apr 23, 2021 at 16:45

You could argue for one or for both, but ultimately, it doesn't matter - as long as you are consistent and use the same reference area throughout your calculation/analysis.

If I personally were to choose, I would go for both, on the basis of total lifting area.

EDIT for details ------

Well yet again, it doesn't matter. You will get some value for your $$C_{Dmin}$$. Then later for other calculations you will use the same $$S_{ref}$$ and you will get comparable drag coefficients. Finally, when you use $$D_{total} \text{ [N]} = C_{D} \cdot 0.5 \cdot \rho \cdot v^2 \cdot S_{ref}$$ you will input same $$S_{ref}$$ and you will get the same Newtons regardless of chosen $$S_{ref}$$.

What matters is that you're consistent, i.e. if you use $$S_{ref} = 10 \text{ m}^2$$, use that for everything. If you use $$S_{ref} = 20 \text{ m}^2$$, use that for everything.

Additionally, do recheck the wetted area argument. $$S_{wet} \neq S_{ref}$$, because $$S_{wet}$$ includes both upper and lower surface of each wing, whereas $$S_{ref}$$ includes only the planform surface.

• Hi Thanks, yes I agree! I have been using that assuming Sref means the total lift generating area! However, my drag significantly decreases, which looks too good to be true, and if I halve that Sref, total drag increases.
– Leo
Apr 23, 2021 at 11:48
• @Leo Your total drag in N should be independent of the reference value you choose. Can you elaborate more how you calculate the drag, and how the value of Sref is used in it? Apr 23, 2021 at 13:15
• Something's not right there. $S_{ref}$ serves to calculate lift and drag coefficients, so it should not affect your lift and drag forces [N]. Maybe you could add more details so we would be able to point you better.
– Mat
Apr 24, 2021 at 20:40
• Hi, thank you, I have added the details above
– Leo
Apr 25, 2021 at 22:02