Physical Description of Lift
A jet engine and a propeller produce thrust by blowing air back. A
helicopter’s rotor produces lift by blowing air down, as can be seen in
Figure 1.1, where the downwash of a helicopter hovering over the
water is clearly visible. In the same way, a wing produces lift by diverting
air down. A jet engine, a propeller, a helicopter’s rotor, and a wing
all work by the same physics: Air is accelerated in the direction opposite
the desired force.
This chapter introduces a physical description of lift. It is based
primarily on Newton’s three laws. This description is useful for understanding
intuitively many phenomena associated with flight that one
is not able to understand with other descriptions. This approach
allows one to understand in a very clear way how lift changes with
such variables as speed, density, load, angle of attack, and wing area.
It is valid in low-speed flight as well as supersonic flight. This physical
description of lift is also of great use to the
pilot who desires an intuitive understanding of
the behavior and limitations of his or her airplane.
With the knowledge provided in this
book, it will be easy to understand why the
angle of attack must increase with decreasing
Its modern name comes from the Greek word for "star". The curve had a variety of names, including tetracuspid (still used), cubocycloid, and paracycle. It is nearly identical in form to the evolute of an ellipse.
A circle of radius 1/4 rolls around inside a circle of radius 1 and a point on its circumference traces an astroid. A line segment of length 1 slides with one end on the x-axis and the other on the y-axis, so that it is tangent to the astroid (which is therefore an envelope). Thepolar equation is
The astroid is therefore of degree six, and has four cusp singularities in the real plane, the points on the star. It has two more complex cusp singularities at infinity, and four complex double points, for a total of ten singularities.
The formative period of aviation and airports:
The birth of civil aviation: 1903–1913
December 17, 1903, the day Orville and Wilbur Wright succeeded in achieving
flight with a fixed-wing, heavier-than-air vehicle at Kitty Hawk, North
Carolina, has gone down in history as being the “birth of aviation.” Their first
airplane flight occurred on a large field, with sufficient room for the aircraft
to take off and land. There were no paved runways, gates, fuel facilities,
lights, or air traffic control. There was no terminal building and there was no
automobile-parking garage. There were no rules and regulations governing
the flight. That field in Kitty Hawk was, however, the first airport.
In the 10 years following the Wright brothers’ first flight, the aviation world
evolved in a very slow and hesitant manner, with most of the advances
focusing on improving aircraft technology, and much of the efforts trying to
promote the technology. Little, if any, consideration was focused on creating
facilities for aircraft to take off and land.
As a result, by 1912, there were only 20 recognized landing facilities in the country,
all of which were privately owned and operated. The earliest operational
airfields date as far back as 1909, although they were generally indistinguishable
from, and often also functioned as, local athletic fields, parks, and golf courses.
Construction and maintenance of early airfields were, in general, considered local
responsibility, and with limited municipal funds, and the very low level of
aviation activity, priorities to build “airports” were understandably low.
World War I: 1914–1918
The outbreak of World War I in 1914 opened up initial opportunities for fixedwing
aircraft to serve in a military capacity. The effort to use aviation as a military
force in World War I resulted in the production of thousands of aircraft
(most of which were produced and served in France, Germany, and England),
and hundreds of military pilots, to first fly reconnaissance and later fighting
missions. As a result, the U.S. military built 67 airports for the war effort. These
predominantly grass fields provided facilities to base, fuel, and maintain aircraft,
as well as provide sufficient room for takeoff and landing—but required
little other infrastructure. After the war, 25 of these military airfields remained
operational, and the rest were decommissioned.