Holooly Plus Logo
Holooly Plus Logo

Question 7.5: Solar Time to Local Time. Find Eastern Daylight Time for sol......

Solar Time to Local Time. Find Eastern Daylight Time for solar noon in Boston (longitude 71.1 ºW) on July 1^{st}.

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

From Table 7.1, July 1 is day number n = 182. Using (7.12) to (7.14) to adjust for local time, we obtain

E \ = \ 9.87 \ \sin \ 2B \ − \ 7.53 \ \cos B \ − \ 1.5 \ \sin B \quad \left(\text{minutes}\right) (7.12)
\begin{matrix} \text{Solar Time} \ \left(ST\right) & = \ \text{Clock Time} \ \left(CT\right) \ + \ \frac{4 \ \text{min}}{\text{degree}} \ ( \text{Local Time Meridian} & \\ & – \ \text{Local longitude} )º \ + \ E \left(\text{min}\right) \quad \quad \quad \quad \quad \quad \quad & \left(7.14\right) \end{matrix}
\begin{matrix} B & = \ \frac{360}{364} \ \left(n \ – \ 81\right) \ = \ \frac{360}{364} \ \left(182 \ – \ 81\right) \ = \ 99.89º \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ \ \\ E & = \ 9.87 \ \sin \ 2B \ – \ 7.53 \ \cos \ B \ – \ 1.5 \ \sin \ B \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ \ \ \\ & = \ 9.87 \ \sin \left[2 \ \cdot \ \left(99.89\right)\right] \ – \ 7.53 \ \cos \left(99.89\right) \ – \ 1.5 \ \sin \left(99.89\right) \ = \ −3.5 \ \text{min} \end{matrix}

For Boston at longitude 71.7º in the Eastern Time Zone with local time meridian 75º

\begin{matrix} CT & = \ ST \ − \ 4\left(\text{min} \ /º\right) \left(\text{Local time meridian} \ – \ \text{Local longitude}\right) \ – \ E \left(\text{min}\right) \\ CT & = \ 12:00 \ − \ 4\left(75 \ − \ 71.1\right) \ − \ \left(−3.5\right) \ = \ 12:00 \ − \ 12.1 \ \text{min} \quad \quad \quad \quad \ \ \ \ \\ & = \ 11:47.9 \ \text{A.M. EST} \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \ \end{matrix}

To adjust for Daylight Savings Time add 1 h, so solar noon will be at about 12:48 P.M. EDT.

TABLE 7.1 Day Numbers for the First Day of Each
Month
January n = 1 July n = 182
February n = 32 August n = 213
March n = 60 September n = 244
April n = 91 October n = 274
May n = 121 November n = 305
June n = 152 December n = 335

Related Answered Questions

Question: 7.13

Average Monthly Insolation on a Tilted Collector. Average horizontal insolation in Oakland, California (latitude 37.73ºN) in July is 7.32 kWh/m²-day. Estimate the insolation on a south-facing collector at a tilt angle of 30º with respect to the horizontal. Assume ground reflectivity of 0.2. ...

Verified Answer:

Begin by finding mid-month declination and sunrise...
Question: 7.12

One-Axis and Two-Axis Tracker Insolation. Compare the 40º latitude, clear-sky insolation on a collector at solar noon on the summer solstice for a two-axis tracking mount versus a single-axis polar mount. Ignore ground reflectance. ...

Verified Answer:

1. Two-Axis Tracker: To find the beam insolation f...
Question: 7.11

Reflected Radiation Onto a Collector. Continue Examples 7.9 and 7.10 and find the reflected radiation on the panel if the reflectance of the surfaces in front of the panel is 0.2. Recall that it is solar noon in Atlanta on May 21, the altitude angle of the sun β is 76.4º, the collector faces 20º ...

Verified Answer:

From (7.31), the clear-sky reflected insolation on...
Question: 7.10

Diffuse Radiation on a Collector. Continue Example 7.9 and find the diffuse radiation on the panel. Recall that it is solar noon in Atlanta on May 21 (n = 141), and the collector faces 20º toward the southeast and is tipped up at a 52º angle. The clear-sky beam insolation was found to be 902 W/m². ...

Verified Answer:

Start with (7.28) to find the diffuse sky factor, ...
Question: 7.9

Beam Insolation on a Collector. In Example 7.8, at solar noon in Atlanta (latitude 33.7º) on May 21 the altitude angle of the sun was found to be 76.4º and the clear-sky beam insolation was found to be 902 W/m². Find the beam insolation at that time on a collector that faces 20º toward the ...

Verified Answer:

Using (7.26), the cosine of the incidence angle is...
Question: 7.8

Direct Beam Radiation at the Surface of the Earth. Find the direct beam solar radiation normal to the sun’s rays at solar noon on a clear day in Atlanta (latitude 33.7º) on May 21. Use (7.22) and (7.23) to see how closely they approximate Table 7.6. ...

Verified Answer:

Using Table 7.1 to help, May 21 is day number 141....
Question: 7.7

Where in the World Are You? With your watch set for Pacific Standard Time (PST), you travel somewhere and when you arrive you note that the upper limb sunrise is at 1:11 A.M. (by your watch) and sunset is at 4:25 P.M. It is July 1^st (δ = 23.1º, E = −3.5 min). Where are you? ...

Verified Answer:

Between 1:11 am and 4:25 P.M. there are 15 h and 1...
Question: 7.6

Sunrise in Boston. Find the time at which sunrise (geometric and conventional) will occur in Boston (latitude 42.3º) on July 1 (n = 182). Also find conventional sunset. ...

Verified Answer:

From (7.6), the solar declination is \delta...
Question: 7.4

Estimate the insolation available on a clear day in January on a south-facing collector with a fixed, 30º tilt angle at the site having the sun path and obstructions diagram shown in Fig. 7.15. ...

Verified Answer:

With no obstructions, Table 7.3 indicates that the...
Question: 7.2

Tilt Angle of a PV Module. Find the optimum tilt angle for a south-facing photovoltaic module in Tucson (latitude 32.1º) at solar noon on March 1. ...

Verified Answer:

From Table 7.1, March 1 is the sixtieth day of the...