Time and Temperature
Part 2: Fitting
to Daylight Data
Rather than work with data
sets with 365 elements, we give the data here for sunrise and sunset on
the first day of each month. You will find this data in your worksheet,
with minutes converted to fractions of an hour, and with time measured
in months.
1997 Sunrise and Sunset,
Durham, NC
(all times EST)
| Date |
Sunrise |
Sunset |
| Jan.1 |
07:26 |
17:13 |
| Feb. 1 |
07:16 |
17:43 |
| Mar. 1 |
06:46 |
18:11 |
| Apr. 1 |
06:02 |
18:38 |
| May 1 |
05:23 |
19:03 |
| Jun. 1 |
05:00 |
19:27 |
| Jul. 1 |
05:03 |
19:36 |
| Aug. 1 |
05:23 |
19:20 |
| Sep. 1 |
05:47 |
18:43 |
| Oct. 1 |
06:11 |
17:59 |
| Nov. 1 |
06:38 |
17:20 |
| Dec. 1 |
07:08 |
17:02 |
- Compute the number of hours
of daylight for the first day of each month. Make a scatter plot of this
data.
- From Part 1, you have estimates
of the coefficients A, B, C, and t0
of a function of the form
h(t) = A + B sin [ C (t - t0)]
that should fit this data. Refine these estimates if necessary -- now
that you know some of the numbers -- and plot your sinusoidal function
on the data. How good is the fit? Adjust the coefficients as necessary
to make the fit as good as you can.
- Choose either the sunrise
or sunset data, and find a sinusoidal approximation to the data. How good
can you make the fit? Does this confirm or contradict your answer in Part
1 about which curves looked sinusoidal?
Send comments to the
authors <modules at math.duke.edu>
Last modified: October 28,
1997
