# What is the physical-based/theoretical reason why supersonic area ruling works?

Supersonic area ruling is used to reduce the drag rise that occurs as aircraft pass through the transonic regime. While it has been validated experimentally, what is the theoretical/physics-based reasoning why area ruling reduces the drag?

I know that the following answer suggests that it is simply a "rule," but could someone shed more light into WHY the area ruling technique works? (What is the "area rule"?)

That's because Bernoulli's principle breaks down at and above supersonic velocities.

In the subsonic realm, when an atom is sped up, it doesn't have much time to spend pushing around a fixed place (it passes by that place quickly). In doing so, the static pressure drops as the speed increases. And in doing so, the neighboring atoms, who are also not doing as much repelling, can group together.

In Busemann's and Whitcomb's metaphor, the tube of air gets thinner.

In supersonic flow, much like the reason behind shockwaves, the communication between atoms breaks down. They are moving too fast for the air to carry out the effect of moving fast (pressure disturbances cannot propagate), and thus, the tube of air doesn't get smaller. This results in an increase in the drag versus the calculated one; instead of the tubes getting smaller, they remain both big and fast.

Drag increase is highest when there is a sudden cross sectional change. Consider the face of a box compared to a cone pointy-end first.

Applying that, the supersonic area rule aims at keeping the cross sectional size of the whole vehicle constant without abrupt changes. If thinning the fuselage where the wing meets it is not possible, then gradually thickening it before the wing starts is also an option.

The tubes not getting smaller, and considering the cross section of the vehicle as a whole, were the reasoning behind the area rule.

Reference and further reading: Chapter 5 - The Whitcomb Area Rule - From Engineering Science to Big Science, via NASA.

• Atoms communicating? Would it not make more sense to say air is more like water near Mach, and simply has no where to go (can't get out of the way, builds a drag producing shock wave), so it is best to keep cross sectional area as constant as possible? Last part of your answer is a +. – Robert DiGiovanni Jan 23 '20 at 15:29
• I think Robert brings up a good point. Rather than phrasing the idea as atoms communicating, it makes sense to say that the pressure disturbances cannot propagate and so the streamtube areas stay constant. This means that the shocks will impact a larger area than expected and lead to more drag. So, to reduce the drag, the aircraft is designed to have weaker shocks, which only occur if the changes in area are gradual. – Nick Hill Jan 24 '20 at 15:30