Wetted Aspect Ratio and You!

Wetted Aspect Ratio and You!

This article discusses Wetted Aspect Ratio and its utility in plane design.

Wetted Aspect Ratio

Wetted aspect ratio is an excellent shorthand tool for aircraft evaluation. It compares wingspan with exposed surface area (wetted area) of the plane, a simple combination of the induced drag due to lift and skin friction drag over the whole airplane.

b = wingspan

S = wing planform area

S_wetted = total wetted area

AspectRatio = b^2/S  

AspectRatiowetted=b^2/S_wetted

Comparison

I’ll compare two planes to demonstrate Wetted Aspect Area: the FT Arrow, and the Zipper (a plane I designed). The Arrow is a flying wing, while the zipper is a conventional tractor-type.

Figure 1. FT Arrow (Photo Credit to Flite Test)

Figure 2. Zipper

Table 1. FT Arrow compared to Zipper

By sheer coincidence, these two designs have about the same wetted aspect ratio despite being wildly different configurations. Given that they have the same wetted aspect ratio, we can draw some interesting conclusions about the two aircraft! (Another example of this coincidence in action is when comparing the B-47 and Avro Vulcan)

First, the similar wetted aspect ratio means they have about the same lift to drag ratio (while the Zipper’s higher wing loading means it comes in hotter, L/D is actually independent of wing loading).

Second, it demonstrates the “budgeting” of each design. The Arrow, by removing the fuselage and tail, is able to invest in the wing, decreasing wing loading. This keeps around the same L/D as the conventional Zipper, but gives it much less stall speed than if it were made conventionally (see below).

A conventional arrow?

I thought a more direct comparison would be useful. I’ve “converted” the Arrow to a conventional configuration, basing it on the Zipper’s design. Its key parameters are listed below, keeping the Arrow’s wetted aspect ratio and weight, but matching the Zipper’s ratio of wetted area to planform area.

Table 2. FT Arrow vs. “Conventional Arrow”

Table 2 shows the estimated effects of changing the Arrow’s configuration. To keep the same wetted aspect ratio and thus the same L/D, you’d have to sacrifice 32% of the wing area to make a fuselage and empennage possible. Wing loading would increase by 48%, increasing stall speed.

Conventional wisdom says a flying wing reduces drag, but the Arrow instead uses that configuration to expand its flight envelope with a generous wing area that improves low-speed flight and overall maneuverability for the same L/D.

So: constraining wetted aspect ratio, you can see how two different configurations can serve the same purpose, and look a little further down the line at secondary performance effects!

Conclusions

Next time you’re designing an airplane, think about its wetted aspect ratio! You could incorporate it into your design process by solving for it and comparing to other designs, or by constraining it and seeing how other design parameters affect each other. Maybe you have a high performance design where you’re splitting hairs, or maybe you want to guide your early design choices. Remember, it’s not a be-all/end-all but it can be a powerful tool.

Photo Credit to Boeing for its X-48 Blended Wing Body subscale model in the thumbnail