Line 223: Line 223:
;Yearly
;Yearly
*Sundial season lines may need to be repainted depending on rate of degradation.
*Sundial season lines may need to be repainted depending on rate of degradation.
|}


==Team Members==
==Team Members==

Revision as of 22:03, 30 April 2017

Template:ENGR215inprogress

Final Design of Analemmatic Sundial.

Background

Catherine Zane Middle School in Eureka, California has partnered with the Engineering Design course at Humboldt State University in order to provide an opportunity for students to exercise their skills in sustainable engineering design. Our project team is called Division by Zero. Team members include Hannah Gidanian, Caitlin Gundert, Rick Thomas, and Alex Watson. The front of Zane Middle School features a large rectangle filled with bark mulch, 10 feet wide and over 100 feet long. This empty space receives a large amount of uninterrupted sun throughout the day. Zane wanted to improve this underutilized space and decided that a series of projects would be conducted by the Engineering Design class of Spring 2017.

Problem Statement and Criteria

Students at Zane Middle School currently do not have an interactive and tangible way to learn about the abstract idea of how the sun relates to the earth and the concept of time as a derivation of this relationship. There is a large, vacant section of the front of the school at Zane that has not been serving any purpose over the past several years. As a result, the bark mulch gets trampled across, leaving debris all over the pavement in front of the school.

Criteria Importance Constraints
Durability 10 Withstands abuse from students and elements while lasting at least 20 years
Safety 9 Must follow all safety regulations designated by the school.
Educational Value 8 Must be able to be used as a teaching tool for the teachers
Multiple Time Components 7.5 Can tell the month along with the time
Cost 6.5 Total budget of $400
Accuracy 6 Correct time and months
Interactivity 6 Gets the child engaged and interacting with the sundial
Aesthetics 5 Visually pleasing
Sustainability 4 Constructed of environmentally friendly materials
Precision 3 Recognizable time values

The Solution: Description of Final Project

A group of four Engineering Design students, by the team name of "Division by Zero" have partnered up with Trevor Hammonds and Kristopher Buihner at Zane Middle School in order to implement an interactive and aesthetically pleasing addition to the school front, directly in the center of the previously barren rectangle filled with bark mulch. The analemmatic sundial is stamped in a 9'x10' platform of cement on which middle school children serve as the gnomon. The student's shadow will tell the solar time. This sundial will serve to provide middle school students with an educational activity to emphasize the concept of solar time and the interaction between the sun and the earth in its orbital path.

Costs

Materials Quantity Cost Per Quantity $ Our Cost $
Table Cloth 1 17.99 17.99
Canvas 1 29.99 29.99
Dowels 2 0.69 1.38
Wood Letters 6 3.99 23.94
1x2 Furr Trim 1 30.99 30.99
1/4 in Plywood 1 Donated Donated
Wood Glue 1 4.99 4.99
Sand Paper 4 0.79 3.16
Total Costs 112.44

Design Hours

Amount of hours the team members spent. Total Hours:227

Calculations

Step Description Picture
1 First find the dimensions of the space where the sundial will be placed. Then find the latitude and longitude of the location. After this is done the ellipse of the sundial needs be created. Use the length of the space available to find the major axis of the ellipse. The minor axis can be based off the average height of human that will be using the sundial. To find the length of the minor axis, the length of a person's shadow at 12:00 needs to be calculated. The equation to do this is
                                                                      m=Msin(phi) 
                                                                 Where:  m= Minor axis
                                                                         M= Major Axis
                                                                         phi= latitude of location in degrees

After the minor and major axis are found plug them into the ellipse equation:

              (x^2/M^2)+(y^2/m^2)=1
               Where the x and y are the xy coordinates.

Each number on the sundial is 15 degrees from the positive x axis and the xy vaules of the numbers for the time were found using ellipse equation. Calculations were done with a latitude of 40.7892

[[File:|frame|1px|center]]
2 The place where a person stands (the scale of dates) is based off the Analemma which is the path of the sun in the sky over the year. To find the distance for where to stand for each month use the equation:
    Z=Mtan(d)*Cos(theta). 
    Z is the distance from the the origin
    M is the horizontal radius of the ellipse
    d is the declination for each month
    theta is the latitude in degrees
[[File:|frame|20px|center]]
3 Each of the season lines which are plotted into the cement are based upon the shadow length at each hour of the day, throughout the year. The shadow length was calculated from taking the tangent of the angle of elevation of the sun at each hour of the day on the equinoxes as well as the solstices. Using right triangle trigonometry, it was determined that the shadow length equates to the height of the pole (24") divided by the tangent of the mentioned angle.
Season Line Calculations.jpg

Construction

Step Description
1 Cut out outlined Roman Numerals from 1/2" Plywood.
2 Cut out square base of stamp from the same size plywood.
3 Attach Roman Numerals to the backing using 3/4" wood screws.
4 Cut and attach 1" x 2" pieces of wood to make a frame for the standing locations.
5 Glue two pieces of pre-made wood lettering together (to make them thicker). Glue the letters to a pieces of wood. Remember to reverse the letters
6 Soak stamps in vegetable oil.
7 After concrete has been poured and smoothed out allow the concrete to cure for 30 to 45 minutes.
8 Using string line, measure and mark the locations of Roman Numerals.
9 Submerge the stamps into the concrete.
10 Pull the stamps back out. If the impression left is not acceptable, submerge the stamp again and repeat.

How to Use it

Step Description Picture
1 To find the current solar time, stand in the box with the current and corresponding month. Depending on what date it is within the month you may need to alter where you stand within the box. If it is early in the month, stand on the bottom line of the box, if it's the middle of the month stand in the middle of the box, and if it's the end of the month stand on the top line of the box.
Monthlines.JPG
2 Face forward and stand up straight then determine the time from the location of your shadow. Remember if daylight savings time is in affect the sundial will appear to be an hour behind.
IMG 2728.JPG
3 To determine the present season, place the gnomon on the marker at the bottom of the sundial. Notice the three seasonal lines and locate the tip of the gnomon shadow.
IMG 2731.JPG
4 Measure the shadow length on two consecutive days at the same time. If the shadow length appears to be shrinking and falls between the equinox line and summer solstice line the present season is Spring. If the length appears to be growing and is in the same location it is Summer. If the shadow location is between the winter solstice and equinox line and appears to be growing the present season is Fall and if the shadow is shrinking the season is Winter.

Maintenance

Monthly
  • Rinse the imprint of the numbers with water to keep the sundial clean and the numbers visible.
Yearly
  • Sundial season lines may need to be repainted depending on rate of degradation.

|}

Team Members

References

See Help:Footnotes for more. Template:Reflist https://www.sunearthtools.com/dp/tools/pos_sun.php

Alexander R. Pruss. (2011)."Analemmatic Sundial PDF Generator" http://analemmatic.sourceforge.net/cgi-bin/sundial.pl

Chris Sangwin. (2010). "Analemmatic sundials: How to build one and why they work" https://plus.maths.org/content/analemmatic-sundials-how-build-one-and-why-they-work

https://en.wikipedia.org/wiki/Analemmatic_sundial

Chris Sangwin. (2010). "Analemmatic sundials: How to build one and why they work"

Cookies help us deliver our services. By using our services, you agree to our use of cookies.