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5ECEA
Lapus, Aja LorenzoLlanera, Ian Carlo
Lopez, John GregoryMagsino, Chermaine
Manrique, Dianne StephanieMateo, Ma. Khristina
Matira, EmersonNarciso, Ma. Kristina
AN INTRODUCTION AND A PEEK AN INTRODUCTION AND A PEEK ON ITS HISTORY...ON ITS HISTORY...
INTRODUCTION
CELESTIAL NAVIGATION - the art of finding one's way with reference to the Sun, the Moon and the stars.
celestial bodies obey certain behavior and the cycles repeat over a period of time.
HISTORY
in the late 15th century the Portuguese and the Castillians (Spanish) started their voyages of discovery their instruments of navigation were: Chip log and hour glass to determine speed and
dead reckoning Sounding lead to determine depth and nature of
bottom Magnetic needles floating on bit of cork to
determine orientation Astrolabe to measure the height of a celestial
body above the horizon (H).
HISTORY
Astrolabe - used to determine latitude by a sight of Polaris or the meridian passage of the Sun. invented by the Arabs.
cross staff – an “improvement” of the astrolabe. had to be aligned simultaneously (and therefore view simultaneously) one end of the cross-staff with the horizon and the other with the Sun or other celestial body. Highly impractical.
HISTORY
backstaff – invented in 1590 by davis(also called Davis' octant)
The observer, with his back to the Sun, aligns the shadow of the Sun with the horizon therefore maintaining one single line of sight.
Sextant – invented around 1750. it allowed a more precise measurement of H and
has remained basically unchanged to these days.
telescope and subsequent astronomical research allowed accurate prediction of the position of celestial bodies
in the latter part of the 18th century the British Royal Observatory started publishing the Nautical Almanac.
The first systems devised to determine GMT were by observing celestial movements which were quite fast and predicted in the almanac.
Lunar distance method○ By measuring the angular distance between the
moon and a star near the ecliptic, one determines the Moon's SHA and, with that, GMT.
Another method of determining GMT was by observing the fast movement of the four planets of Jupiter in their orbits and their eclipses.
John Harrison coupled the pendulum with an escapement of his invention and produced the first useful chronometers during the 18th century. The first one weighed 65 pounds.
In 1837 Capt. Sumner – invented the line of position (LOP).
19th century, Capt. Marcq St. Hilaire invented the intercept method
Around 1930, Ageton, then a student at the Naval Academy in Annapolis, invented the method that bears his name and which has later been known under other names such as HO211 and Bayless
This method uses a short table of logarithmic functions and is still useful today. It truly simplified the intercept method. Later, other similar methods have been proposed and one of them known as the Compact or Davies method is included in the Nautical Almanac
This system and tables evolved in the 50s into HO249 for air navigators and later HO229 for marine navigators. Both are essentially the same but HO229 give more precision, are bulkier and a bit slower to use.
CELESTIAL COORDINATE SYSTEM... position of an object uses a sphere (celestial sphere) as its
reference body use of the fact that there are 360
degrees in a circle coordinates are usually written in
degrees, minutes, and seconds
CELESTIAL COORDINATE SYSTEM...
1. Equatorial Coordinate System 2. Horizon Coordinate System
CELESTIAL SPHERE...
a huge, transparent imaginary rotating sphere of "gigantic radius", concentric and coaxial with the Earth
all objects in the sky can be thought of as lying upon the sphere
Projected from their corresponding geographic equivalents are the celestial equator and the celestial poles.
CELESTIAL SPHERE...
contains any number of large circles called great circles
any great circle intersecting the celestial poles is called an hour circlecelestial sphere is divided by hour circles
into 24 sectionsdistance between each hour circle is 15
degrees.
CELESTIAL SPHERE...
CELESTIAL SPHERE... divided by projecting the equator into
space; north celestial hemisphere and the south celestial hemisphere
ecliptic - a great circle on the plane of the earth’s orbit
celestial equator - the great circle where the plane of the equator intersects the celestial sphere. It is inclined by 23.5 degrees to the ecliptic
celestial poles - the points where the line making up the axis of the earth meets the sphere
CELESTIAL SPHERE...
CELESTIAL SPHERE... Zenith - point where a line extending from the
center of the earth through the point and out into space meets the celestial sphere
Nadir - the opposite side of the earth (in reference to zenith) where a line extending from the center of the earth through the point and out into space meets the celestial sphere
Zenith-Nadir axis - line connecting the zenith to the nadir
astronomical horizon - a great circle on the celestial sphere which is perpendicular to the zenith-nadir axis
CELESTIAL SPHERE... celestial meridian - a great circle which
intersects the zenith, the nadir, and the celestial poles
cardinal points - four points in the astronomical horizon which correspond to the directions of a compass
North (N) and South (S) points - two points which lie on the intersection of the celestial meridian
East (E) and West (W) points – two points which lie at the intersections of the horizon and the celestial equator
CELESTIAL SPHERE...
Zenith – Nadir axis
Astronomical horizon(Celestial horizon)
CELESTIAL SPHERE...
CELESTIAL SPHERE...
All parts of the celestial sphere: The horizon, zenith, nadir, celestial meridian, celestial poles, celestial equator, and cardinal points.
EQUATORIAL COORDINATE SYSTEM alternatively known as the 'RA/Dec coordinate
system' uses the celestial equator, the hour lines, and the
vernal equinox to describe the position of stars Vernal equinox - point where the Sun crosses from the
south to the north of the celestial equator. It occurs around March 21 every year.
independent of the observer's location and the time of the observation only one set of coordinates is required for each object same coordinates can be used by observers in different
locations and at different times
EQUATORIAL COORDINATE SYSTEM origin: vernal equinox (zero point for the hour
circles)also known as the First Point of Aries, since about
2,000 years ago, the intersection point on the celestial sphere where the ecliptic and celestial equator
the time at which the apparent longitude of the Sun is 0°.
primary reference circle: the celestial equator secondary reference circles: hour circles two coordinates: the right ascension (RA)
point and declination (DEC) point
EQUATORIAL COORDINATE SYSTEM
EQUATORIAL COORDINATE SYSTEM Declination (Dec) point, δ
analogous to the latitude coordinate on Earth angular distance above or below the celestial
equatormeasured in degrees, minutes, and seconds
from -90 to +90 degrees with ZERO (0) being on the celestial equator○ Note:
negative degrees - point is south of the celestial equator; positive degrees – point north of the celestial equator
stars on the celestial equator : Dec=0o
stars at the south celestial pole : Dec= -90o
stars at the north celestial pole : Dec=+90o.
EQUATORIAL COORDINATE SYSTEM
EQUATORIAL COORDINATE SYSTEM
An object's position is given by its RA (measured east from the vernal equinox) and Dec (measured north or south of the celestial equator).
REMINDERS:
The equatorial coordinate system is tied to the orientation of the Earth in space
Earth’s orientation changes over a period of 26,000 years due to the precession of the Earth's axis. Precession - refers to the movement of the
rotational axis of a body, such as a planet
consider EPOCH!!!
REMINDERS:
Epoch a moment in time used as a reference for the
orbital elements of a celestial bodyeither the moment an observation was made or
the moment for which a prediction was calculated
Julian years - a year of exactly 365.25 days○ Ex. J2000.0 coordinates
Besselian years - beginning of a Besselian year to be the moment at which the mean longitude of the Sun is exactly 280 degrees○ Ex. B1900.0 coordinates, B1950.0 coordinates
EQUATORIAL COORDINATE SYSTEM
Example: Star = Einstein CrossRA = 22h 37m Dec = +03o05' (according to B1950.0 coordinates)RA = 22h 37m Dec = +03o 21' (according to J2000.0 coordinates)
NAUTICAL ALMANAC...
a publication describing the positions and movements of celestial bodies for the purpose of enabling navigators to use celestial navigation to determine the position of their ship while at sea including the sun, moon, planets, and 57 stars chosen for their ease of identification and wide spacing.
specifies for each whole hour of the year the position on the Earth's surface at which each body is directly overhead.
CELESTIAL COORDINATE SYSTEM... 1. Equatorial Coordinate System
2. Horizon Coordinate System
HORIZON COORDINATE SYSTEM Also called as horizontal coordinate system Measured in relation to the zenith Time and date dependent uses the zenith, the horizon, and the
cardinal points to describe the position of the stars
Primary reference circle: horizon Secondary reference circle: vertical circles
Vertical circles – perpendicular to the horizon and intersect the zenith
HORIZON COORDINATE SYSTEM Coordinates: the altitude and the
azimuth of a point Altitude – angular distance above or
below the horizon Zenith distance – angular distance
between the zenith and the point Azimuth – angular distance between the
north point and the vertical circle which intersects the point
HORIZON COORDINATE SYSTEM
TRANSFORMATION OF COORDINATES
Horizon to Equatorial Coordinates
D. α = GST – H (if negative, add 24)Where: α = right ascension (a) aka RA
δ = declination (d) aka Decφ = observer's geographic latitudeA = azimutha = latitudeH = hour angle
A.
B.
C.
TRANSFORMATION OF COORDINATES Example:
Horizon to equatorial transformation. Convert horizon coordinates azimuth= 283°16'16" and latitude = 19°20'04" to equatorial coordinates.
The observer is at the Greenwich meridian, 52° N, and GST (Greenwich Sidereal Time) is 0h24m05s.
TRANSFORMATION OF COORDINATES Answer:
Steps:To find δ (Dec):1. convert azimuth and altitude to decimal degrees2. find δ using eqn .A3. convert δ in degrees, minutes, and seconds formTo find α (RA):1. find H using eqn.B (answer is in degree hours)2. convert degree hours H to decimal hours 3. convert GST to decimal hours4. find α using eqn.D (answer in decimal hours)5. convert decimal hour to hours, minutes, seconds
form
TRANSFORMATION OF COORDINATES
Equatorial to Horizon Coordinates
Where: α = right ascension (a) aka RAδ = declination (d) aka Decφ = observer's geographic latitudeA = azimutha = latitudeH = hour angle
A.
B.
C.
TRANSFORMATION OF COORDINATES Answer:
Steps:
1.Convert H to decimal hours. 2.Convert H to degrees. 3.Convert δ to decimal degrees. 4.Find sin α. 5.Find sin-1 to find α. 6.Find cos A. 7.Find cos-1 to find A'. 8.Find sin H (if positive, A = 360 – A', else A = A'). 9.Convert a and A to hour angle form.
THE CELESTIAL (ASTRONOMICAL) TRIANGLE
The terrestrial, celestial, and horizon coordinate systems are combined on the celestial sphere to form the astronomical or celestial triangle.
COORDINATE SYSTEM COMPARISON
COMPASS
Compass was first used in China in the 400 BC in Feng Shui (geomancy). The first Compass was a simple piece of lodestone floating on water that pointed South.
COMPASS
The magnetic field of Earth is not uniform and varies at different latitudes of the planet. The Compass needle is attracted by magnetic force and therefore, it is fluctuating too. When the needle reads North, it is actually the direction of the magnetic North Pole. There is a slight deviation from true North and this phenomenon is called declination
QUADRANT
The Quadrant was the first altitude-measuring instrument developed for use in celestial navigation, dating back to the 15th century. Its first recorded use at sea was by Diego Gomes in 1461.
QUADRANT
The Quadrant does not require the view of the horizon to find altitude unlike most other instruments used to find altitude.
CROSS STAFF
Cross-staff is restricted from around 20° to 60°. therefore it is impossible to use the Cross-staff in low latitude regions.
ASTROLABE
The Mariner's Astrolabe (left) is the adapted version of the Astrolabe used solely for navigation
MARINER’S ASTROLABE
It is a much simpler device compared to the typical Astrolabe, consisting of a heavy ring suspended from a thumb ring. The circumference of the ring is marked in degrees and the alidade is pivoted in the center of the ring with pointers against the scale for measuring celestial altitudes.
Using the thumb ring, the astrolabe is held above eye level. The alidade is then rotated until the Sun or star is visible and the altitude is then read off the scale
SEXTANT
SEXTANT PARTS
Sextant: a navigation instrument that is used to establish position by measuring the height of stars from the horizon.Index mirror: large polished plate that reflects light.Telescope: optical instrument made of lens that magnifies objects.Telescope clamp: reinforcing circle.Eyepiece: lens the user looks through.Telescope printing: lens adjustment.Frame: structure that serves as the base for the different parts of the sextant.Graduated arc: graduated edge of the arc.Locking device: apparatus that holds the sextant in place.Drum: graduated button used to take measurements.Index arm: type of ruler that determines direction or measures an angle.Screw to regulate small mirror: piece of metal used to adjust the horizon mirror.Glass filter: colored transparent substance.Horizon mirror: small polished glass plate that reflects light.Glass filter: colored transparent substance.
SEXTANT
BACK-STAFF : ORIGIN
Circa 1594 Intention: Improvement over
Mariners’ QuadrantsAstrolabesCross-staves
BACK-STAFF : CONSTRUCTION graduated staff a half-cross in the shape of an arc of a
circle on the radius of the staff with a fixed vane
a brass horizon vane with a slit in it at the fore-end of the staff.
BACK-STAFF : USAGE
The observer places the staff on his shoulder and stand with his back to the sun.
With the horizon vane lined up with the horizon, he slides the half-cross back and forth until the shadow of its vane falls across the slit in the bottom vane while the horizon remains visible through the slit.
BACK-STAFF : ILLUSTRATION
BACK-STAFF : REMARKS
The observer is able to sight both the sun and the horizon while his back is towards the sun.Eliminated problems from Cross-staff
○ Ocular parallax○ Eye damage from looking directly at the Sun
Can only be used to measure the altitude of the Sun and not other celestial bodies.
OCTANT : ORIGIN
Around late 1600s and early 1700s Shifted to optical systems based on
mirrors and prisms Independent & almost simultaneous
developmentJohn Hadley, an EnglishmanThomas Godfrey, a Philadelphia glazierAbout 1731
OCTANT : CONSTRUCTION
a frame (one eighth of a circle) an index arm two mirrors an eyepiece
Illustration:
OCTANT : USAGE
index arm is pivoted at the circle’s center and moving over the graduation on the arc
the index glass, fully reflecting, is placed on the index arm exactly above the pivot
the horizon mirror, half-silvered, is placed on one radius of the octant
the eyepiece is placed upon the other radius, opposite to the horizon mirror
OCTANT : USAGE
Horizon is viewed through the horizon mirror
Index glass reflects light from celestial body, then by the horizon mirror to the eyepiece
Navigator must align the horizon to the reflection of light and the scale would follow
The angle measured is transferred to the lunar table whereby the longitude of the observer will be known
OCTANT : BASIS
Law of reflection of lightthe angle of incidence is equal to the angle
of reflection for a plane mirrorIt follows that if the mirror is moved so that
the angle of incidence is altered, the angle at which the emergent ray is reflected will be altered by an angle twice that through which the mirror has been moved.
OCTANT : COMPARISON
To the Sextant:Same operation/usageReduction in radius helps reduce weight
OCTANT : REMARKS
One of the first instruments that could measure angle with sufficient accuracy
The observer need only to look at one place while adjusting the instrument Prevents ocular parallax
Reading is not affected by the rolling and pitching of the ship
Glare from the sunlight is reduced when observing the Sun using the Octant (compared to the Quadrant or the Cross-staff)
OCTANT : REMARKS
Difficult to use at nightHorizon is invisiblePeople tried to make use of artificial horizon
○ Bubble Sextant (spirit level)
More complex construction
SUNDIAL : ORIGIN
More than 3500 years agoUsed the Sun to tell the timeStarted to construct sundials
SUNDIAL : USAGE
Set in direct sunlightMagnetic compass needed
Set in cloudless nightLine up with Polaris
SUNDIAL : ILLUSTRATION
SUNDIAL : REMARKS
very simple to make and to use no longer accurate after a month
obliquity of Earth causes the 'path' of the Sun to change over the months
The same Sundial cannot be used in two different placesThe Sun has different 'paths' for two
different places
NOCTURNAL : ORIGIN
AKA Nocturlabe 1272 Calculates the time at night
NOCTURNAL : BASIS
works on the principle that stars close to the Celestial Poles are circumpolar
Circumpolar, adj. Denoting a star that from a given observer's latitude does not go below the horizon.
NOCTURNAL : CONSTRUCTION several pieces of metal or wood
attached at the center so they can rotate relative to one another
at the axis of rotation is a hole
NOCTURNAL : USAGE
Held upright by the handle until the Polaris can be sighted through the hole
The long arm of the device is then turned until it lies along the line made by the two brightest stars in the constellation Ursa Major.The bright star in the Ursa Minor can be
used in the same way.
NOCTURNAL : USAGE
If Ursa Minor is used, the inner dial would be turned so that the pointer marked "LB" would lie against the date on which the observation is being made.
If the Ursa Major is chosen as a reference, the procedure is the same, except that the small pointer marked "GB" is set against the date
By doing this, the correction from sidereal time to solar time is automatically corrected.
NOCTURNAL : REMARKS
Could only be used in the northern hemisphere because it requires the user to be able to see Ursa Major or Ursa Minor, which lie near the North Celestial Pole
CHRONOMETER : ORIGIN
Idea: circa 13th century Invention: 18th century English clock-maker, John Harrison Brothers John and James made two
clocks that lost no more than a second per monthRemarkable at the year 1726
AKA sea-clock
CHRONOMETER : H1
Harrison Number 1 1735 Balance ring with two 5-pound weights
connected by brass arcs replace the pendulumWeights balances the spring during tilts and
turns by the sea Total weight: 72 pounds
CHRONOMETER : H1
CHRONOMETER : H2
Harrison Number 2 1739 Tall and heavier, but took up less space Innovation: The remontoire mechanism
ensures that the force on the escapement is constant, thus improving the accuracy of the clock
CHRONOMETER : H2
CHRONOMETER : H3
Harrison Number 3 1741 Similar to H2, but smaller, lighter, had
circular balances instead of dumbbell shapes
A bi-metallic curb was used to allow for variations in temperature
Impossible to adjust without dismantling and re-assembling
CHRONOMETER : H3
CHRONOMETER : H4
Harrison Number 4 Breakthrough: 5.25 inches Oil was used as lubricants
to minimize the problems of ageing oil, Harrison used wheels and pinions with a great number of teeth that increased the efficiency of the clock
lost 5 seconds in 2 monthscorresponded to an error in longitude of only
1.25 minutes
CHRONOMETER : H4
CHRONOMETER : H5
Harrison Number 5 1772 Harrison’s final longitude time-keeper Mechanically very similar to H4.
INERTIAL NAVIGATION SYSTEM
A self-contained navigation technique in which measurements provided by accelerometers and gyroscopes are used to track the position and orientation of an object relative to a known starting point, orientation and velocity
Inertial navigation is used in a wide range of applications including the navigation of aircraft, tactical and strategic missiles, spacecraft, submarines and ships
1
2
Inertial measurement units (IMUs)
Contain three orthogonal rate-gyroscopes and three orthogonal accelerometers, measuring angular velocity and linear acceleration
By processing signals from these devices it is possible to track the position and orientation of a device
and...
INERTIAL NAVIGATION SYSTEM
INERTIAL SYSTEM CONFIGURATION
INERTIAL SYSTEM CONFIGURATION
Stable Platform Systems
INERTIAL SYSTEM CONFIGURATION
- the inertial sensors are mounted on a platform which is isolated from any external rotational motion. In other words the platform is held in alignment with the global frame
Stable Platform Systems
INERTIAL SYSTEM CONFIGURATION
INERTIAL SYSTEM CONFIGURATION
- this is achieved by mounting the platform using gimbals (frames) which allow the platform freedom in all three axes
Stable Platform Systems
INERTIAL SYSTEM CONFIGURATION
INERTIAL SYSTEM CONFIGURATION
- the platform mounted gyroscopes detect any platform rotations. These signals are fed back to torque motors which rotate the gimbals in order to cancel out such rotations, hence keeping the platform aligned with the global frame
Stable Platform Systems
INERTIAL SYSTEM CONFIGURATION
INERTIAL SYSTEM CONFIGURATION
- to track the orientation of the device the angles between adjacent gimbals can be read using angle pick-offs. To calculate the position of the device the signals from the platform mounted accelerometers are double integrated
Stable Platform Systems
INERTIAL SYSTEM CONFIGURATION
INERTIAL SYSTEM CONFIGURATION
Strapdown Systems
- the inertial sensors are mounted rigidly onto the device, and therefore output quantities measured in the body frame rather than the global frame
INERTIAL SYSTEM CONFIGURATION
Strapdown Systems
INERTIAL SYSTEM CONFIGURATION
- to keep track of orientation the signals from the rate gyroscopes are ’integrated’. To track position the three accelerometer signals are resolved into global coordinates using the known orientation, as determined by the integration of the gyro signals. The global acceleration signals are then integrated as in the stable platform algorithm.
Strapdown Systems
INERTIAL SYSTEM CONFIGURATION
Stable platform and strapdown systems are both based on the same underlying principles. Strapdown systems have reduced mechanical complexity and tend to be physically smaller than stable platform systems. These benefits are achieved at the cost of increased computational complexity. As the cost of computation has decreased strapdown systems have become the dominant type of INS.
INERTIAL SYSTEM CONFIGURATION
GYROSCOPE
device for measuring or maintaining orientation based on the
principles of angular momentum
defy gravity
GYROSCOPE: HISTORY
1817 it simply called the "Machine.“ by Johann Bohnenberger
Recommended the machine for use as teaching aid
by French mathematician Pierre-Simon Laplace
In 1852, it was used for an experiment involving the rotation of the Earth by Foucault, he was also the one who gave
the device its modern name (Greek skopeein, to see) the Earth's rotation
(Greek gyros, circle or rotation)
GYROSCOPE: HISTORY
1860s, electric motors made the concept feasible, leading to the first prototype gyrocompasses
the first functional marine gyrocompass was developed between 1905 and 1908 by German inventor Hermann Anschütz-Kaempfe
The American Elmer Sperry followed with his own design in 1910, and other nations soon realized the military importance of the invention
The Sperry Gyroscope Company quickly expanded to provide aircraft and naval stabilizers as well, and other gyroscope developers followed suit.
GYROSCOPE: HISTORY
In 1917, the Chandler Company created the "Chandler gyroscope," a toy gyroscope with a pull string and pedestal
MEMS (Micro Electro-Mechanical System)idea of the Foucault produce by Systron Donner Inertial (SDI).
GYROSCOPE: HISTORY
GYROSCOPE
GYROSCOPE
GYROSCOPE
GYROSCOPE
ACCELEROMETER
a device that measures non-gravitational accelerations non-gravitational acceleration is produced
by forces other than gravity or inertial/fictitious forces
simple mechanical forces, these are transmitted to the accelerometer device through mechanical stress on its mounting.
ACCELEROMETER
expressed in SI units (m/s2) or popularly in terms of g-force
does not measure the "acceleration" due to gravity
in free fall in a gravity field, even though being accelerated, will read "zero" uses in an earth orbiting spaceship.
ACCELEROMETER: HISTORY
micro electro-mechanical systems (MEMS)
consisting of little more than a cantilever beam with a proof mass (also known as seismic mass).
ACCELEROMETER
ACCELEROMETER