Greenwood press

104
RATIO

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water. But when the plane hits the speed of sound, the airwaves can’t move out
of the way of the plane. The build up at the front of the plane causes a shock
wave that creates stress on the plane and is often audible to people on the ground
as a “sonic boom.” The speed of sound varies according to temperature and other
factors. It is about 762 miles per hour at sea level, and about 664 miles per hour
at 35,000 feet. A jet traveling at 1,400 miles per hour 35,000 feet above sea level
would be traveling at 1400/664 
≈ Mach 2.1. A jet-propelled wheeled vehicle
achieved Mach 1.02 on the Bonneville Salt Flats on a day when the speed of
sound was 748 mph. Its speed was 763 miles per hour. 
Astronomers measure solar-system distances with a ratio measure called an
astronomical unit (AU). An AU of 1 represents the average distance of the earth
to the sun, about 14,960,000,000 kilometers. For even larger distances than the
solar system (which is about 80 AU in diameter), astronomers use ratio measures
based on light years. One light year is the distance traveled by light in one year
(about
9.46 × 10
17
cm). Our galaxy is about 100,000 light years in diameter. Par-
secs (3.26 light years), kiloparsecs (1,000 parsecs), and megaparsecs (1 million
parsec) are used to measure distances across many galaxies.
Trigonometric ratios are used to find unusual or inaccessible heights and
lengths. By measuring angles and shorter distances, an engineer can calculate the
height of skyscrapers by creating diagrams with right triangles and using these
ratios. (See Triangle Trigonometry for an explanation.)
Scale models use ratios to indicate how the lengths of an object compare to
corresponding measures in the model. A 1:29 scale-model train would be large
enough for children to ride outdoors on top of the cars. It would be 1/29th of the
size of a real train. An HO-gauge tabletop train is at a scale of about 1:87. An
8.64-inch model of an 18-foot-long automobile (216 inches) would be at the
scale of 1:25. Scale models can also help provide information to calculate
unknown information, such as the mass of a dinosaur. (See Similarity.) Although
the design of buildings, cars, toasters, and furniture may involve drawings and
models that are smaller than the final version, scale models that are larger than
real life are important in many fields. Manufacturers of computer chips make
scale drawings much larger than the actual chip to show the packed circuitry.
Medical researchers make large-scale models of viruses and cell structures to
determine how shapes affect resistance to disease. 
The fundamental law of similarity uses scaling to indicate how surface area
and volume of the model relate to the actual object. If 
k is the ratio of a length in
the object to the corresponding length in the model, 
k
2
is the ratio of surface
areas, and 
k
3
is the ratio of volumes. This law explains the limits on human and
animal growth. If a six-foot-tall, 180-pound human were to double in size so that
his relative proportions were maintained, he would be twelve feet tall, but his
volume, and hence his weight, would be eight times as much. The giant’s weight
would be 1,440 pounds—which couldn’t be supported by human bone structures.
(See Proportions for an alternate explanation.)