To assess the fundamental efficiency of a vehicle, it makes sense to compare the ‘total energy consumed’ with the momentum obtained (speed times weight). Clear back in 1950, Gabrielli and von Karman published “What Price Speed?”, a sweeping look at this topic for various forms of transportation.
Unfortunately, what it revealed is still true: the economics of flight are only reasonable when we fly big, heavy airplanes very, very fast… or when we fly very slowly with lots of wingspan. Airplanes in the middle miss the achievable efficiency target… by a factor of six!
To ask why until real answers emerge is to discover one of the largest opportunities in the modern world.
Two reasons especially stand out. One, airframe drag under power has always been assumed to be essentially the same or higher than the drag when towed or gliding. That isn’t true, nor should it be. A source of power can be used to cut drag by huge amounts, especially in the largely unexplored domain in question, if used to promote free circulation.
This can be illustrated by understanding there is a ‘static condition’ implicitly assumed in the math of lift and drag. If, for example, one drags a streamlined hull down a canal with a team of horses, the ‘horsepower’ it takes at a certain speed can be measured in the rope tension. However, long ago it was learned that if one puts a motor of roughly half that power on board, with proper propulsive design it can essentially achieve the same speed. Boat propulsion is acting, not upon a fixed, immovable stream bank, but upon the fluid medium directly, which can be naturally circulated in a way that recovers much of the initial resistance.
Second, the basic equations of drag and lift embed this fixed, static assumption, rather than a dynamic circulation, which can only be directly computed with a completed design. It turns out that this assumption in the simplified math doesn’t approximate the physics of airflow in the unconstrained atmosphere equally in every domain, which can be seen by the changing coefficients required to make it work out at different speeds. Yet virtually every tool available early in the design process, or to a casual reviewer, relies entirely upon these proven equations.
The track record of GA inefficiency makes it obvious that something deeply hidden must be wrong in our standard practice, just as in the days when a different aspect of this same topic held center stage in the debate between ‘mathematically certain’ Cambridge physicists and technically competent German engineers. It took decades for Britain to catch on and accede to the obvious experimental results of Germany’s mastery of the circulation theory of lift.
Ludwig Prandtl and his student Blasius resolved a paradox that had been central to this puzzle for close to two centuries, by giving us the ironically named ‘dynamic pressure’ concept; the ‘1/2 density times velocity squared’ portion of the basic lift and drag equation. The irony is that the required condition to allow our cavalier acceptance of the kinetic energy equation is that there is…there MUST be…a non-dynamic, ‘static condition’ in the system somewhere, wherein fluid movement is simply not allowed.
What can be said now, as the physics of circulation are finally reapplied to the topic of drag, is that the static condition assumption is only approximately useful for the flow regimes where either viscosity or inertia have the upper hand. In those ‘fast’ or ‘slow’ domains, this assumption is reasonably true, and consequently in those domains we’ve done quite well.
In the flight regime in question, actual boundary layer behaviors differ, sometimes dramatically, from the assumptions of this century-old mathematical model. Even today this fact has remained largely invisible, although experimenters found it strongly implied for at least half that time. The natural application of circulation to drag reduction using power has thereby been a sometimes controversial and always poorly-understood topic. For example, the result shown here is ‘news’ known to some (and applied successfully) for forty years.
The basic architecture of most aircraft now reflects the pervasive influence of these underlying 2-D mathematical assumptions from a century ago, rather than the 4-D physics that was, until recently, impossible to analyze accurately. That architecture is often fundamentally at odds with circulation methods, and therefore hardly benefits when used to evaluate concepts that require the body length and fineness ratio to be appropriate for the Reynolds number involved.