1. Dulles Airport

        Dulles Airport, designed by Eero Saarinen, is in the
shape of a hyperbolic paraboloid. The hyperbolic paraboloid is a three-dimensional
curve that is a hyperbola in one cross-section, and a parabola in another cross section.





2. Lampshade

        A household lamp casts hyperbolic shadows on a wall.





3. Gear transmission

        Two hyperboloids of revolution can provide gear transmission between two skew axes.
The cogs of each gear are a set of generating straight lines.





4. Sonic Boom

        In 1953, a pilot flew over an Air Force Base
flying faster than the speed of sound. He damaged every building on the base.

As the plane moves faster than the speed of sound, you get a cone-like wave.
Where the cone intersects the ground, it is an hyperbola.

The sonic boom hits every point on that curve at the same time. No sound is
heard outside the curve. The hyperbola is known as the "Sonic Boom Curve."
In the picture below, the sonic boom is "visible" due to the humidity.

The photo below was taken by Ensign John Gay, U.S. Navy from the aircraft
carrier Constellation.   Sports Illustrated and Life both ran the photo.



Details about the Photo

 

Comparing Speeds in Miles per Hour

Human Walking 3 mph
Human Running 34.3 mph
Race Horse 44.9 mph
Cheetah Running 65 mph
Car on Interstate Highway in Colorado 75 mph
Fastest Train 250 mph
Passenger Jetliner
(McDonald Douglas DC-9)
575 mph
Speed of Sound
(At sea level, 59 degrees)
761 mph
Concorde 1,450 mph
Fastest Jet Fighter 4,500 mph
Space Shuttle in Orbit 17,000 mph



5. Cooling Towers of Nuclear Reactors

        The hyperboloid is the design standard for all nuclear
cooling towers.   It is structurally sound and can be built with straight steel beams.

When designing these cooling towers, engineers are faced with two problems:
(1) the structutre must be able to withstand high winds and
(2) they should be built with as little material as possible.
The hyperbolic form solves both of these problems.   For a given diameter
and height of a tower and a given strength, this shape requires less material
than any other form.   A 500 foot tower can be made of a reinforced concrete
shell only six or eight inches wide.   See the pictures below (this nuclear power
plant is located in Indiana).







6. Hyperbolas from 3-dimensional shapes






7. Stones in a Lake

        When two stones are thrown simultaneously into
a pool of still water, ripples move outward in concentric circles.
These circles intersect in points which form a curve known as the hyperbola.