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Sunset Sundial from Scratch. Roger Bailey NASS, Aug 2008 St Louis, Missouri. Algarve Coast, Portugal. November Sunsets. Sunset Sundial from Scratch. Sunset views south west over Atlantic Ocean West facing wall on sundeck Design a sunset sundial, Reverse Italian Hours Limited tools:
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Sunset Sundial from Scratch Roger Bailey NASS, Aug 2008 St Louis, Missouri
Sunset Sundial from Scratch • Sunset views south west over Atlantic Ocean • West facing wall on sundeck • Design a sunset sundial, Reverse Italian Hours • Limited tools: • No texts, files computers, programs, internet • Math: geometry, spherical trigonometry • Navigators Equation: Sine Sine Sine Cos Cos Cos • NASS Calculator: scientific & programmable
Wall (Meridian) Plane: West 90º • Project Equatorial Disc EE’ for time from solar noon • Angle to Horizon = Co-Latitude • Mark 15º segments projected to GxTan t on EE’ • Draw hour lines perpendicular
Navigation Triangle • Latitude, Altitude & Declination Angles from Horizon on Great Circles • Navigation Triangle contains time and azimuth angles
Co-Angles in Navigation Triangle • Navigation Triangle sides are complementary angles (90- x) • Solve for Altitude with Cosine Rule, 2 sides and contained angle known • Solve for Azimuth with Sine Rule
Design Technique for Sunset Sundial • Calculate polar sundial using equatorial disc • Solve for sunset times at solstices Cos t = Tan Lat x Tan Dec • Tabulate t = sunset time – N hours (15º/hour) • Calculate Altitude for t knowing Lat & Dec Sin Alt = Sin Lat x Sin Dec + Cos Lat x Cos Dec x Cos t • Calculate Azimuth for t knowing Altitude • Sin Az = Cos Dec x Sin t / Cos Alt • Project point onto wall knowing declination of wall, altitude and azimuth • Plot the results and join the points for hours to sunset and solstice declination lines
NASS Programmable Scientific Calculator Programs: Workshop at NASS Conference in Chicago 2005 Calculator Functions: Trigonometry: Sine, Cosine, Tangent, Inverse-1 Angles: DEG, DMS, Time Memories: M, K1, K2 Programs: LRN, COMP, HLT, (x) Solar Position: Noon, Sunrise, Sunset Prime Vertical Altitude, Azimuth Declination Lines Great Circle Distance and Direction (Qiblah)
NASS Programmable Scientific Calculator Programs: Sundials Design Programs: Horizontal: Time & Hour Angles Offsets Vertical: Time & Hour Angles, Offsets Vertical Declining: Substyle Distance, Substyle Height, Difference in Longitude Time, Polar & Hour Angles, Offsets Analemmatic: Hour Points, Zodiac Date Line, Seasonal Markers Longitude Correction
NASS Calculator: Sunset Time Latitude and Declination into the K Memories. Latitude: 41.88 2NDX->K1, Declination: 12.78 2NDX ->K2 Sunset Time: Cos t = - Tan (Lat) x Tan (Dec) Program: ON/C K1TAN x K2TAN = +/- 2ND COS-1 This gives you t, the time as an angle from noon. (101.73) Divide by 15 for hours. ÷15 = (6.782) For Sunset* add 12 for noon + 12 = (18.782) Convert to Hours:Minutes:Seconds with 2ND ->DMS Sunset Time is 18:46:56
NASS Calculator: Altitude & Azimuth Sin Alt = Sin Lat x Sin Dec + Cos Lat x Cos Dec x Cos t Program: 2ND LRN MR COS x K1 COS x K2COS + K1SINxK2SIN= 2NDsin-12NDHLT The display shows the Altitude of the sun at 1 pm (58.1064º). Continue for Azimuth using the equation: Sin Az = Cos Dec x Sin t / Cos Alt COS2ND1/X x MR SIN x K2 COS =2NDsin-12NDLRN
NASS Calculator: Sample OutputAltitude & Azimuth TimetºAltitude Azimuth Noon 0 60.90º 0º 1:00pm 15 X->M: ON/C COMP (58.106º) COMP (28.537º) SW 2:00pm 30 X->M: ON/C COMP (50.941º) COMP (50.700º) SW 3:00pm 45 X->M: ON/C COMP (41.384º) COMP (66.793º) SW 4:00pm 60 X->M: ON/C COMP (30.712º) COMP (79.191º) SW 5:00pm 75 X->M: ON/C COMP (19.609º) COMP (89.769º) SW 6:00pm 90 X->M: ON/C COMP ( 8.492º) COMP (80.414º)*NW 7:00pm 105 X->M: ON/C COMP (-2.31º)** COMP (70.520º)*NW 11:00am -15 X->M: ON/C COMP (58.106º) COMP (-28.537º) SE Chicago Latitude (41.88º N), Aug 18 Declination (12.78º)
