# What are the effective span and lifting properties of a circular wing?

Today I read an article on FlightGlobal about the Bell air taxi demonstrator. It includes some paraphrased quotes from the Bell VP of innovation, Scott Drennan, among which the following stood out:

The ducted fans will provide lift during hover, forward propulsion and lift during forward flight, says Drennan. That forward lift will not come from the fans being tilted slightly down, but from the ducts, which act as aerofoils – "circular" wings, engineers call them.

This sounded odd to me for a variety of reasons. I realize this could be the effect of the journalist miss-hearing or miss-quoting the VP, so I'd like to focus on the aerodynamics at play here.

The Bell Nexus air taxi is a quad tiltrotor design with small engine pylons, so cruise lift must come at least in part from the ducted fans, either via downward thrust vectoring or through "duct lift", and the latter presents a slew of issues.

Therefore, the question: what would be the effective lift achievable by a circular wing, or duct without a fan installed in it, in forward flight? In particular, how close would it come to the performance of a regular slender wing of a span equal to the duct diameter. Let us limit the discussion to low-subsonic flight.

Bonus points: what would be the bonus or malus of having a fan installed in such a duct or circular wing, adding its own component to the circulation around the duct walls?

• The lift coefficient slope of a planar circular wing is 1.79002303 (to 9 sig. figs.) See, for example,: Peter F. Jordan, "Exact Solutions for Lifting Surfaces", AIAA Journal, Vol. 11, No. 8, 1973., pp. 1123-1129. Peter F. Jordan, "On Lifting Wings with Parabolic Tips", ZAMM 54, pp. 463-477, 1974. Apr 30 '19 at 13:43
• @Lysistrata funny you should mention those articles, I printed them out for later reference just yesterday. Apr 30 '19 at 13:44
• I hope that they are useful and that we are talking about the same type of wings. Sometimes "circular wing" means circular planform, sometimes what I would call a "ring wing". May 2 '19 at 3:27