View Full Version : Area Ruling: Nuther question for Eric

06-20-2002, 10:44 AM
Eric, I was just reading in the back of the July Air & Space about Whitcomb and his "area ruling" stuff... interesting to say the least.

Could something like this be retrofitted to existing fuselage design to decrease drag, or would the costs be like much else that we *can* do but for the cubic dollars involved??

Also found it interesting that his wing shape looked an awful lot like the wing cross section for a certain new Sport plane being developed down in the hot country..


06-30-2002, 08:06 AM
The "coke bottle" fuselage (first used on the F-102) is a form of area ruling. Other than that, please disregard anything you've previously heard about it. It is yet another of those wonderful little points of aeronautics that is not intuitive nor easily understood.

First let's look at the concept of the "area rule". This refers to a plot of the cross sectional area of the fuselage along the longitudinal axis. Simply put, slice the airframe cross wise every foot and plot the cross sectional area vs. the datum. If it is an average aircraft, the chart will have a bulge at the wing and tail. Wherever there is a bulge, there is acceleration of the airflow and displacement of compressible flow. Let's look and the first one (the easier one to explain).

Air accelerates when it is displaced, so it accelerates over the fat part of the fuselage, and fat part of a wing. When you combine the two (the wing root) the flow will accelerate to a speed that is the sum of the separate fuselage and wing accelerations. This means that the local flow at the wing root will be faster than out on the span of the wing. This local "supervelocity" area causes drag in 3 ways:

1. The greater acceleration causes higher velocity and local skin friction drag varies with the square of the velocity. So faster local flow causes more drag in that area.

2. Greater acceleration and peak velocity cause more stagnation and separation. The air coming up the supervelocity region has to turn more, accelerate more, lose more pressure, and then recover that higher pressure drop in a shorter distance than the wing was probably designed for. So it is typical to find a region of stagnated airflow forward of a supervelocity region and an area of separation behind it.

Local area ruling is the art of adding a little cross section forward and aft of supervelocity regions to "smooth out" the local flow field and get rid of primarily stagnation and separation. This is an area that I have made a study of for years and it is what we applied to Lee Behel's Venture.

3. Mach displacement drag. When everyone thinks of "area ruling" this is what they think of. When an area of flow goes supersonic, it creates shock waves. Shock "wave drag" is the drag associated with this effect. These shock waves and their drag are proportional in strength to the displacement gradient and the displacement volume. In simpler terms, this is how blunt the aircraft is and how big it is.

A good analogy would be four boats:

A) A rowboat is blunt and displaces a great deal of water at a slow speed. It is however small, so the displacement "wave" is also small. The rowboat is a Navion.

B) A supertanker is blunt and also VERY large. It displaces a great deal of water both because of it's size and shape. (please don't get into the bow tricks they use to get around this) The supertanker is the Goodyear blimp.

C) A rowing shell. Sharp, long, light. The displacement is minimal, the displacement gradient as we go aft on the "fuselage" is very gradual and smooth. "Wave drag" is VERY small. The shell is a supersonic air-to-air missile.

D) An offshore powerboat racer. Sharp, long, heavy. Wave drag is low for it's weight, but higher than the rowing shell / missile.

Aircraft designed to be efficient supersonic cruisers are sharp and gradually streamlined, like the SR-71 and XB-70. Aircraft that have to operate around M.7 to M1.5 (most modern fighters) have to compromise between a broad range of Mach numbers and the ability to maneuver in both direction and energy throughout the envelope. Because of this, we should NOT use fighters as a reference for understanding area ruling. We need something more pure.

Mach displacement waves and the drag associated with them will happen first at any point of supervelocity already on the airframe. Since a prop air racer is a subsonic animal and we want to keep the drag low, we may use local area ruling to manage the supervelocity areas.

If we want to go supersonic and run there, then we need to look at the whole aircraft. This is where Mach area ruling comes in. By smoothing the cross sectional area of the entire aircraft, we can reduce the peak displacement and with it, the Mach wave drag. The largest cross sectional area "bulge" in most aircraft is the wing, so low supersonic aircraft have "coke bottle" fuselages to reduce the displacement of the fuselage at the point of the highest displacement of the wing. Contrary to common understanding, this decelerates the local flow over the wing root and makes the wing LESS efficient.

It is only a good idea to area rule in this fashion if the aircraft design lends itself to doing it in an integrated manner. The F-16A had a beautifully area ruled fuselage, while the F-15A did not. External fuel tanks on either aircraft made them pigs in terms of area rule. The Israelis came up with conformal fuel tanks for the Eagle and (in one of those rare moments when the US actually used an idea someone else invented) they were adopted by McDonnell and sold to the Air Force. They are an integral part of Randy's Strike Eagle.

Use of the area rule by adding bumps and fairings on the aircraft is dangerous and can lead to failures like the Convair 990. Bumps were added to the fore and aft fuselage and trailing edge of the wing in an effort to area rule the airframe. The problem was that the extra wetted area and interference drag of all those bumps outweighed any area ruling benefit! The result was the aircraft was a dog, all orders were cancelled without penalty and Convair ended up getting bought out.

Local area ruling to reduce separation has great promise for air racers. Mach area ruling of the entire aircraft is not applicable until speeds reach true supersonic, and would be harmful to wing efficiency below this speed.