The Transonic Area Rule
In the early 1950s, a few years after Chuck Yeager broke the ‘Sound Barrier’ using the rocket powered Bell X-1, American aerospace manufacturers were already looking to build the next generation of aircrafts capable of sustained supersonic flight, that would be powered by a turbojet.
During the development and testing, there was a ‘strange’ and ‘unexpected’ increase in drag the planes encountered as they inched closer to Mach 1. No existing mathematical theory or formulation existed that could explain this sharp increase in drag that was simply too much for the engines of the time to overcome at transonic speeds of Mach 0.75 - 1.2. This also meant that the Americans would lose the capability to intercept the large fleet of reliable Soviet long - range heavy bombers, such as the Tupolev Tu - 4.
The solution to this problem came from the genius of Richard Whitcomb, a young researcher at NASA, Langley who was studying the nature of transonic flow in the “8-foot High Speed Tunnel”. His solution came to be popularly known as the ‘Whitcomb Area Rule’ or simply the ‘Transonic Area Rule’. This was a single, non - mathematical solution that has dictated the design of most transonic and supersonic aircraft till date. Whitcomb’ s genius also saved Convair’s F-102 Delta Dart project and heavily influenced the design of a similar delta, the F-106 Delta Dagger. In recognition for its far reaching impact, Whitcomb’s area rule was awarded the 1954 Collier Trophy.
So, what exactly was the problem?
During the design and development of the Convair F-102, engineers observed that the maximum speed of the fighter during level flight was limited to Mach 0.98, much lesser than the intended Mach 1.2, despite featuring the delta wing design that has very low drag at transonic and supersonic speeds.
This extra drag was attributed to come from wing-fuselage interference, due to the high sweep of the delta wing, the incoming air split up into two components, one of the components gets directed towards the fuselage that tries to straighten the flow, thus due to the energetic nature of flow at high speeds and the fuselage counteracting this inward flow creating a propagating pressure gradient along the wing-fuselage interface causing stronger and dangerous shocks and therefore the extra wave drag.
Solution..
To put this simply, just take out that part of the fuselage that interferes with the flow on the wing, this was exactly what was done. The fuselage at the root was tapered (Coke bottle shaped) so as to allow the inward component of the flow to least interfere with the fuselage. Whitcomb originally presented this idea as a ‘rule of thumb’ method of design and hence the name.
But how much taper/indentation should there be?
It is here where Whitcomb’s real stroke of genius can be seen, based on ‘intuitive testing’ and experimentation on existing models in the modified ‘slotted throat’ 8 foot High Speed Tunnel, he observed that indenting the fuselage decreased the wave drag by more than 60%, which is a massive reduction in aeronautical terms and allowed the planes to fly 25% faster with the same available thrust.
A simple yet elaborate geometric statement of the area rule is:
“If a wing/body combination(including the external stores) is so designed that the axial distribution of the cross sectional area normal to the airflow is the same as that of a minimum drag body, then the wing/body combination will have minimum drag.”
What does this even mean?
Practically, it means that the distribution of the cross sectional area of an object along its length should resemble that of a semi circle in order to have minimum wave drag. The rate of shape of change of a body dictates the creation of drag i.e wave drag is proportional to 2nd derivative of volume distribution.
Why don’t we see much applications of area ruling today?
Actually we do, the “hump “of the Boeing 747, Rockwell B-1 Lancer and Lockheed C-5 Galaxy is present so as to satisfy this rule. Moreover, engines of a commercial jet liner and cargo lifters are placed slightly forward of the wing, this is not just to counteract the torsional loads acting on the wings but also as a clever nod to the area rule. Area rule played a key role in design of aircrafts like the legendary F-16 and the Anglo-French Concorde.
The area rule is not prominent in modern 5th generation platforms as they are not limited by thrust, which was not the case in the 1950s. Modern combat platforms emphasize more on stealth and network centric warfare and hence are not deigned to be perfect from an aerodynamicist’s point of view.
