Your research should incorporate following points * History of sundial * Types of sundial( discuss the construction of any one in detail) * Working of sundial * Famous sundials * Modern use

Introduction
A sundial is a device that tells the time of day by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style onto a surface marked with lines indicating the hours of the day. The style is the time-telling edge of the gnomon, often a thin rod or a sharp, straight edge. As the sun moves across the sky, the shadow-edge aligns with different hour-lines. All sundials must be aligned with their styles parallel to the axis of the Earth's rotation to tell the correct time throughout the year. The style's angle from the horizontal will thus equal the sundial's geographical latitude.
History

The earliest sundials known from the archaeological record are the obelisks (3500 BC) and shadow clocks (1500 BC) from ancient Egyptian astronomy and Babylonian astronomy. Presumably, humans were telling time from shadow-lengths at an even earlier date, but this is hard to verify. In roughly 700 BC, the Old Testament describes a sundial — the "dial of Ahaz" mentioned in Isaiah 38:8 and II Kings 20:9. The Roman writer Vitruvius lists dials and shadow clocks known at that time. Italian astronomer Giovanni Padovani published a treatise on the sundial in 1570, in which he included instructions for the manufacture and laying out of mural (vertical) and horizontal sundials. Giuseppe Biancani ' s Constructio instrumenti ad horologia solaria (ca. 1620) discusses how to make a perfect sundial. how it works
In general, sundials indicate the time by casting a shadow or throwing light onto a surface known as a dial face or dial plate. Although usually a flat plane, the dial face may also be the inner or outer surface of a sphere, cylinder, cone, helix, and various other shapes.[citation needed]
The time is indicated where a shadow or light falls on the dial face, which is usually inscribed with hour lines. Although usually straight, these hour lines may also be curved, depending on the design of the sundial (see below). In some designs, it is possible to determine the date of the year, or it may be required to know the date to find the correct time. In such cases, there may be multiple sets of hour lines for different months, or there may be mechanisms for setting/calculating the month. In addition to the hour lines, the dial face may offer other data—such as the horizon, the equator and the tropics—which are referred to collectively as the dial furniture.
The entire object that casts a shadow or light onto the dial face is known as the sundial's gnomon.[2] However, it is usually only an edge of the gnomon (or another linear feature) that casts the shadow used to determine the time; this linear feature is known as the sundial's style. The style is usually aligned parallel to the axis of the celestial sphere, and therefore is aligned with the local geographical meridian. In some sundial designs, only a point-like feature, such as the tip of the style, is used to determine the time and date; this point-like feature is known as the sundial'snodus.[2][a] Some sundials use both a style and a nodus to determine the time and date.
Types of sundials
Sundials are classified into a number of different types, mainly by the plane in which the dial lies, as follows: * horizontal dials * vertical dials * equatorial dials * polar dials * analemmatic dials * reflected ceiling dials * portable dials * Horizontal * This is the type found commonly on pedestals in gardens. The dial plate is horizontal. The gnomon (which casts the shadow) makes an angle equal to the latitude of the location * Vertical * This is the type found on the walls of churches and other buildings. Vertical sundials may bedirect south dials if they face due south (in which case the gnomon will be at an angle equal to the co-latitude of the place, and the hour lines, if delineated for local time at the place, will be symmetrical about the vertical noon line).

* Equatorial dials * have the dial plate fixed in the plane of the equator. The gnomon is perpendicular to the dial plate. The hour lines are spaced equally at 15 degree intervals.. * Polar dials * have the dial plate fixed parallel with the earths axis. The gnomon is parallel to the dial plate, typically the edge of a rectangular plate fixed to the dial plate. The hour lines are parallel to the gnomon and thus to each other. * Analemmatic dials * . They are unusual because the gnomon is vertical, and the hours are marked not by lines but by points falling on the circumference of an ellipse. The gnomon has to be moved depending on the time of year, so that the shadow falls on the correct point. Analemmatic Reflected ceiling dials * . They are a special form of horizontal sundial, in which a mirror laid on a south-facing windowsill reflects the sun onto the ceiling. The hour lines are drawn on the ceiling. * Portable dials * come in many varieties, such as the shepherd's dial, the tablet dial, the ring dial and others. They are not strictly a separate type of dial, but can be of the types listed above.

Vertical sundial!!
Instructions
Draw a horizontal line and a vertical line passing through the horizontal line. Name the intersecting point as O. Name a point on the vertical line (above O) as C. C will be the point from which the hour lines radiate, and this is the center of the vertical sundial. Draw a line, CD, passing through the horizontal line in such a way that the angle made by the lines CO and CD is equal to (90-latitude). This value, (90-latitude), is known as co-latitude. Draw a perpendicular line OB to CD, which means the angle B should be 90 degrees. * 2
Draw an arc with center as O and passing through the perpendicular line below O. Name the intersecting point of the arc and perpendicular line as E. Draw a circle with center E and radius OE. Draw a horizontal line passing through E inside the circle. Inside the upper half of the circle, draw lines spaced at 15 degrees. These are the lines for full hours between 6 a.m. and 6 p.m. * 3
Extend all the lines in the circle to the horizontal line passing through O. Draw lines from C to the points on the horizontal line. Draw a horizontal line passing through C. Mark 6 West on the left side of C and 6 East on the right side of C. In the counter clockwise direction, mark 7, 8, and so on. You will mark 12 on the vertical line. Again start from 1 to reach 6 on the right hand side. * 4
Remove all the extra lines that are all the lines below the horizontal line passing through O (including the horizontal line). The gnomon is to be made separate. The gnomon is the part of sundial that acts as the indicator. The triangle COB is the gnomon in this case, with angle C with co-latitude and angle B with 90 degrees.

famous sundials

* London (England) The bell tower of the church Saint Margaret (next to Westminster Abbey) has four sundials, one on each face. Next to it, you can see an analemmatic sundial. The four sundials on St Margaret's were designed Christopher St.J. Daniel. The analemmatic sundial was designed by Frank King for the Golden Jubilee of HM the Queen.
At the Greenwich Royal Observatory, you can stand on the prime meridian, in front of a big equatorial sundial.
Griffith observatory, in Los Angeles

* The Samrat Yantra, Jaipur, India
Made of marble and stone, this sundial may not have the latest technology but it is so accurate there is just a 2-second margin of error – day or night. jantar Mantar Sundial * The Janta Mantar Sundial in Delhi, India. * The Sundial Bridge in Redding, California claims to be the world’s tallest sundial. * Taipei 101 is a massive skyscraper located in China.
The park which serves as a sundial, using the shadow of the Taipei 101 skyscraper.
Since the gnomon of Taipei 101′s sundial is the 1671 foot tower, this makes it the largest sundial we could identify through research! * The sundial dubbed the most valuable in the world is the Yanggu’s gold sundial which has an estimated value of $800,690,000
Modern use of sundial
If a horizontal-plate sundial is portable and is made for the latitude in which it is being used, and if the user has a watch and the necessary information to calculate the local sundial time from its reading, the sundial can be used to find the directions of True North, South, etc. The sundial should be placed on a horizontal surface, and rotated about a vertical axis until it shows the correct time. The gnomon will then be pointing to the North, in the northern hemisphere, or to the South in the southern hemisphere. This method is much more accurate than using the watch as a compass (see watch) and can be used in places where the magnetic declination is large, making a magnetic compass unreliable

How does a sundial work
A sundial is in essence simply any form of stick - known as a style or gnomon - which casts a shadow. The position of the shadow can then be used to determine the current solar time.

A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the Sun casts a shadow from the gnomon, which is a thin rod straight edge, onto a flat surface marked with lines indicating the hours of the day. The shadow cast by the end of the gnomon is the solar time at all times. As the Sun moves across the sky, the shadow of the gnomon's edge progressively aligns with different hour-lines on the plate. Such designs rely on the gnomon that is aligned with the Earth's rotation axis. Hence, if such a sundial is to tell the correct time, the gnomon must point towards the true North and the gnomon's angle with the horizontal plane must be equal to the geographical latitude where the sundial is placed.

The installation of many dials requires knowing the local latitude, the precise vertical direction (e.g., by a level or plumb-bob), and the direction to true North.

During the day people saw that the shadow cast by a tree, a rock, or even their own body was long early in the morning and grew shorter and shorter until it almost disappeared when the Sun was in the middle of the day. They also would have noticed that the shadow grew longer again, on the other side of the tree, as night came.

The shadow stick is the earliest form of sundial. People judged the time of day by the length and position of the stick's shadow.

As the Earth turns on its axis, the Sun appears to move across the sky. The shadows the Sun casts move in a clockwise direction for objects in the northern hemisphere. If the Sun rose and set at the same time and spot on the horizon each day, sticks would have been accurate clocks. However, the Earth is always spinning like a top. It spins around an imaginary line called its axis. The axis runs through the center of the Earth from the North Pole to the South Pole. The Earth's axis is always tilted at the same angle.

Every 24 hours the Earth makes one complete turn, or rotation. The Earth rotates on its axis from west to east. The Earth's rotation causes day and night.

On the Earth's yearly trip around the Sun the North Pole is tilted toward the Sun for six months and away from the Sun for six months. This means the shadows cast by the Sun change from day to day.

Because the Earth is almost spherical, the ground at the base of a shadow stick will not be at the same angle to the Sun's rays as at the equator. Because of this, the shadow stick will not move at a uniform rate during the day.