# What aerodynamic characteristics arise from trailing edge sweep angle?

I drew 3 wing planforms, each with the same leading edge sweep. But they have different trailing edge sweep.

Let's just assume for the moment that all those wings have the same surface area, so that they all have the same total lift. What would be the different aerodynamic characteristics due to the trailing edge sweep angle?

Note: let's leave out considerations of control surfaces. Obviously the first wing would have the easiest implementation of control surfaces, but I want to focus on what the static wings do.

I looked into this and that related question. IMHO they're not quite the same thing as what I'm asking here.

• Mechanical strength is a important factor. If you need more than 45 degree of sweep angle it's pretty hard to do with a simple parallel sweep (at least to make it strong and light), which contributes to why high speed aircraft prefers delta wings. But to reduce induced drag (for reasons to improve fuel efficiency) you want a high aspect ratio. For the same wing area, a high aspect ratio would translate a wide wingspan with parallel edges. – user3528438 Aug 31 '17 at 19:06
• could you add some more details on what you keep constant and what not? How did you plan to keep the area constant, by increasing the chord length? – rul30 Sep 1 '17 at 5:45
• @rul30 The reason I mentioned constant area is so that each wing produces the same total lift. I want to compare sets of wings that have the same lift but different shape. I didn't have any specific way in mind to achieve that. I guess increasing chord length is the most straightforward. – DrZ214 Sep 1 '17 at 6:17

One aerodynamic behavior appears at high angle of attack : dihedral or anhedral wake, which affects (in some weird mixture) both roll and yaw stability. Forward swept trailing edge is much more stable than backward swept trailing edge.

Some jet fighters (let's say F-22) and most aerobatic airplanes (let's say SU-31) adopted forward swept trailing edges in order to increase stability at high AoA.

Usually, the sweep angle is defined at the quarter chord line, and trailing edge sweep then follows from:

• Wing area. Larger wing area means lower wing loading and associated structural weight, higher profile drag.
• Aspect ratio. Higher aspect ratio results in longer span, higher structural weight, and lower induced drag.
• Taper ratio. Higher taper ratio implies lower tip loading.
• Quarter chord sweep angle. Higher sweep has beneficial effects on postponing transsonic shock waves, but detremental ones on stall behaviour and structural weight due to torque.

Seen in this perspective, trailing edge sweep is just a by-product of the four planform-defining entities. It may be desirable to have a straight trailing edge sweep for secondary purposes such as stowing the landing gear, and this may make the design team reconsider the combination of the four main parameters.

The three wing planforms drawn in the OP differ in all four defining parameters. Wing area and taper ratio decrease from up to down, aspect ratio and quarter chord sweep increase.

This article describes the aerodynamic design considerations for transsonic wings, and compares wings with varying sweep and thickness, same area and taper. The middle wing has a trailing edge sweep angle of close to zero, following more or less by coincidence from the definition of the main parameters.

• maybe you could rephrase your answer. The constrains by DrZ214 might be arguable, but in his question the area and the projected span did not change (the chord is not scaled properly). – rul30 Sep 1 '17 at 5:43
• @rul30 They are drawn that way though, that's why I've included the NASA article drawing. – Koyovis Sep 1 '17 at 6:13
• I can't understand everything in the graphs. What is on the y-axis of the 2nd graph? What does t/c mean? Why is the left graph labeled (a) Lambda = 47 degrees even tho it has 3 lines (which I'm assuming correspond to the 3 wings you drew, each of which have different Lambda)? I found this graph in your link but could not find these answers in the surrounding paragraphs. – DrZ214 Sep 1 '17 at 9:53
• @DrZ214 Y-axis of 2nd graph is $C_{Dmin}$ as well. t/c is wing thickness as a fraction of local wing chord: the article is on critical Mach and the two ways of delaying that are reduction of wing profile thickness, or increase of wing sweep. Graph (a) is three different thickness ratios at constant sweep, graph (b) is three different sweep angles at constant thickness. All is to illustrate that the considerations are with wing sweep measured at quarter chord: middle drawing quarter chord sweep $\Lambda$ = 35°, the trailing edge sweep is close to zero as a coincidence, not as a design goal. – Koyovis Sep 1 '17 at 10:18