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Unformatted text preview: Making Measurements of the Earth, e.g.,
Locating points
Calculating distances
Determining elevation A systematic referencing scheme is needed
systematic
(a coordinate system). A fundamental
question becomes what is the shape and
size of the earth.
size Babylonian map 2500 BP Stick chart from Micronesia depicting waves
and currents around islands, which are represented by shells. Early
cartographers
had little in the
way of good
information
about the
absolute location
of places, the
size of the earth
or its real shape
(13th century).
In Robinson et al. (1995) http://en.wikipedia.org/wiki/Early_world_maps#Kangnido_wor
ld_map_.281402.29 The Flatout Truth: Earth
Orbits? Moon Landings? A
Fraud!
Copyright 1980 Robert J.
Schadewald
Reprinted from Science
Digest, July 1980
The facts are simple," says
Charles K. Johnson, president
of the International Flat Earth
Research Society. "The earth
The
is flat."
is The earth is not flat. Pythagoras (6th century B.C) taught that humans must live on a body with “perfect
shape”– a sphere. Aristotle (4th century B.C.) based idea of
spherical earth on observing ships as they
disappeared hullfirst, mastlast. It was difficult to figure out size, however… Eratosthenes was an early
pioneer in earth
measurement. Eratosthenes estimated the circumference of the
earth.
Eratosthenes’ assumptions:
Syene is on the Tropic of Cancer and the Sun (23.5oN) went
straight down a well at Syene at solstice.
Due north at Alexandria (the same meridian), shadows were at
7degrees, 12 minutes.
7°12’ is 1/50 of a circle.
He thought the distance from SyeneAlexandria was 500 mi.
500*50 = 25,000 miles
vs.
24,900 actual! Dent (1996) Bolstad (2002)
Bolstad Eratosthenes was lucky! Cities (Syene and Alexandria) were not due north (i.e. not on the same meridian). Syene is not on the Tropic of Cancer. “Actual” distance between cities is 453
miles, not 500. Multiple sources of error partially
compensated for each other. Earth is not a sphere … Early convention held earth as spherical. Newton proposed that a consequence of gravitation would be equatorial bulging
due to centrifugal force generated by
rotation. In this view the “correct shape” would be
an oblate ellipsoid (note that this is not
quite right either). Bolstad (2002) Satellite measurements are used to define World
Satellite
Geodetic System 84 (WGS 84) ellipsoid.
Geodetic According to WGS 84: polar flattening is 1/298.257
According But the earth is
not perfectly
ellipsoidal
either.
either.
Geoid deviates
Geoid
from the ellipsoid
in an irregular
manner.
manner.
Mass is not constant everywhere, therefore, the effect of gravity and rotation
would not be constant (the equatorial bulge due to centrifugal force). Dent (1996) http://en.wikipedia.org/wiki/Geoid Geoid The Datum
• A combination of an ellipsoid, which
specifies the size and shape of the earth, and a
base point from which the latitude and
longitude, of all other points are referenced.
• Examples are NAD27 and NAD83.
• The geoid is a figure that adjusts the best
ellipsoid and the variation of gravity locally. How are these shapes
used? Maps for large areas can be based on a spheroid to simplify mathematics of map production (e.g.,
projections). More detailed maps may use ellipsoid. GPS
receivers computer latitude, longitude and
elevation using WGS 84 ellipsoid. Geoid used for geodetic surveys when very high
accuracy is needed. GPSderived elevations can
be adjusted to the geoid by subtracting difference
between it and WGS 84. OK, we have a good idea of what the
shape and size of the earth is how do we
used this knowledge to construct a
used
systematic referencing scheme?
systematic Location on the sphere or
ellipsoid Latitude and Longitude Early motivation navigation Axis of rotation provides a starting point to develop
concepts of location on the sphere.
concepts
Equator is a plane orthogonal (at a right angle) to
the axis of rotation (perpendicular bisector). Dent (1996) Determining latitude (north
south reference) is a matter of
figuring out how far from the
equator you are.
One way of doing this has been
know for centuries.. estimate the
angle between your location and
Polaris (North Star).
Polaris
If this is done systematically,
If
then we have the beginning
of the graticule. Each latitude
observation defines a plane
that is parallel to the equator,
thus the term, parallels of
Dent (1996)
latitude.
latitude. Longitude (east/west reference) is
more difficult than latitude.
First, need a fixed point of reference, but
there is no logical starting pointlike the
equator for latitude.
equator
The difficulty of calculating longitude
The
caused huge losses of life at sea.
caused
The solution relied on a combination of
The
science, technology and politics.
science, Dent (1996) One solutionOne
We know that the earth rotates 360° in
in
24 hours – or 15°/hr (360/24 ).
24
Keep track of time difference between
Keep
fixed point and local time and you can
compute the difference in degrees of
longitude between that point and your
location.
location. Determining longitude can be
reduced to a “time problem”.
Dent (1996) Longitude Calculation
Basics 360°/24 hrs = 15°/hr If it’s noon where you are and it is 3pm at a standard fix location (e.g., Greenwich Mean
Time (GMT) the time at the prime meridian),
Therefore you are at 45° West longitude (3
hrs*15°) Chronometers kept accurate time so differentials could be computed. Now radio and atomic clocks are used. Early Problem Pendulum clocks at the time they were trying to work this out (early 1700s) didn’t
work well on moving (pitching, yawing)
ships. The regular swings are disrupted and time
is gained or lost in an unpredictable way. Dead Reckoning in the 1600s…
Dead
Throw overboard a “log” attached to a rope with knots at regular
Throw
intervals (51 ft) and using an hourglass count the number of
hourglass
knots in 30 seconds. Three people needed to perform an
approximate task.
approximate Jupiter? Jupiter is kind of difficult to see during the day and through clouds. Other “astronomical” solutions relied on
observing Venus and the Moon. The astronomers had great political clout
as well. Clocks were viewed as too mechanical for
“real science.” Three delineations of the coast of France. Shaded version is presentThree
day. Fine line is from 1679; heavy line is from 1693 when longitude
day.
was improved by observations of Jupiter’s satellites.
was The amount of EW stretching in this early
map is caused, in part, by an inability to
accurately specify longitude.
accurately October 1707, 21
ships returning to
England after a raid
hit fog. The flagship
sank in 4 minutes
after hitting rocks,
drowning 650
sailors. Three other
ships sank with total
loss at 1,647.
loss This got the
This
attention of the
British Parliament.
British Longitude The British were active in exploration and conquest. They needed to know where their ships
were. A contest with a large prize was begun to
solve the longitude problem. The Longitude Act Parliament passed the Longitude Act (1714) which promised £20,000 to the
person who could solve the longitude
problem to an accuracy of half a degree of
a great circle. This is approximately 34 miles.
34 Had to be “practicable and useful”. John Harrison devised a solution. An escapement connects the wheels
which transmit power and indicate time, and the oscillator which
dictates the speed of the clock. With each swing of the pendulum, the
escapement allows one tooth to escape and transmit power to maintain
pendulum’s motion. This is Harrison’s “grasshopper escapement”.
pendulum’s Harrison’s H1.
Harrison’s
It is 2 feet tall, took five
It
years to make and weighs
75 pounds.
75
Harrison could have
Harrison
won the prize but he
was a perfectionist. A
sea trial turned up
some flaws that he
“knew” he could fix
(please note that this
might be “an urban
myth.”
myth.” This is H4 which
was accurate
enough to win
Harrison the prize.
It was 5 inches in
diameter and weighed
only three pounds.
It was the culmination
of three decades of
work.
work. In a test it lost only
In
five seconds after
81 days at sea.
81 John Harrison won his
sought after £20,000, but
20,000,
only after much effort to
overcome the political
machinations of his
enemies who were
committed to
astronomical methods. Prime Meridian Lines of longitude are called meridians. Because the Britain ruled the seas at the time and because they were active in geodetic
studies the socalled “Prime Meridian” was
established to run through the Royal
Observatory at Greenwich. Convention dictates. Other countries had their own “primes”
however. France’s ran through Paris and
Russia’s through Moscow. Iowa City
41° 39' 40" N , 91° 31' 48" W
41° 39' 40" N , 91° 31' 48“
(Actually we would want to convert to decimal degrees) A graticule Horizontal and Vertical
Control U.S. is covered by over 200,000 points of precisely known latitude and longitude. Points are roughly 3 to 8 kilometers apart
in urban areas and 6 to 25 km apart in
rural areas. Location denoted by a survey monument Horizontal Control
Networks Triangulation used: if you know one side (base line) and the two adjacent angles
you can compute the remaining angle (Σ =
180°) and the two other sides (which
define a point at the vertex). Network is built triangle by triangle; each
new triangle adds a vertex point to the
network. http://www.ngs.noaa.gov/ The triangulation gets “densified” as additional
legs and angles are added…
legs The Wisconsin horizontal control network.
The position of each
point with respect to
neighbors is known to
an accuracy of at least
1:100,000 which
amounts to approx 1
ft in 19 miles.
ft
Most are on hill tops
Most
since clear lineofsince
sight is needed by
sight
optical equipment...
optical Basic idea of Vertical Control is to make
precise relative measurements
precise This
bench
mark is
for a
vertical
control
point.
point. First U.S. base line established near
NYCT border in 1833.
NYCT
This network grew and
This
was densified, and
others grew as well.
others
In 1927 these networks
In
were “adjusted” and
integrated into a single
national network with
origin at Meades Ranch,
KS.
KS.
North American Datum
North
of 1927
of NAD 83 The North American Datum of 1983 is an adjustment of NAD 27 that reflects higher
accuracy in geodetic surveying. NAD 83 is tied into WGS 84 The “adjustment” from NAD 27 to NAD 83
causes some displacement in locations ...
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 Fall '11
 DavidBennett

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