City-Data Forum How to calculate midday sun angle at the December and June solstices (plus values for certain U.S. cities)
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Today, 01:26 PM
 Status: "Subtropical climates don't necessarily have 12 warm months." (set 3 days ago) Location: Putnam County, TN 623 posts, read 140,973 times Reputation: 423

Step 1: Find your city's latitude. Round however much you prefer, although best to the nearest tenth of a degree.

Step 2: Subtract your latitude from 90. Follow steps a for summer and b for winter.

Step 3a: Add the current tilt of the Earth's axis to 90 - L to get your summer solstice midday sun angle. The tilt is currently 23.5 degrees, but it varies between 22.1 and 24.5 degrees over time. This will be December in the southern hemisphere and June in the northern.

Step 3b: Subtract the current tilt of the Earth's axis (23.5) from 90 - L to get your winter solstice midday sun angle. This will be December in the northern hemisphere and June in the southern.

Step 4a: If the resulting value is over 90 degrees for the summer solstice, then you have to subtract the excess. The tropics don't experience maximum insolation at their summer solstice, instead occurring at two points between the equinoxes and the solstice with a relative minimum at the solstice.

Step 4b: If the resulting value is a negative number for the winter solstice, then that means that's how far below the horizon the sun is at noon at the solstice. This means you live in a polar region with a perpetual night for some time; the reverse (midnight sun) happens for an equal length surrounding that region's summer solstice.

June/December values for 50 largest U.S. cities (italicized), largest city in every U.S. state/territory (bolded) and a few special entries with the current 23.5-degree tilt, rounded to the nearest tenth...
Spoiler
New York, New York: 72.8/25.8

Los Angeles, California: 79.4/32.4

Chicago, Illinois: 71.6/24.6

Houston, Texas: 83.7/36.7

Phoenix, Arizona: 80.1/33.1

San Antonio, Texas: 84.1/37.1

San Diego, California: 80.8/33.8

Dallas, Texas: 80.7/33.7

San Jose, California: 76.2/29.2

Austin, Texas: 83.2/36.2

Jacksonville, Florida: 83.2/36.2

Fort Worth, Texas: 80.7/33.7

Columbus, Ohio: 73.5/26.5

San Francisco, California: 75.7/28.7

Charlotte, North Carolina: 78.3/31.3

Indianapolis, Indiana: 73.7/26.7

Seattle, Washington: 65.9/18.9

Washington, District of Columbia: 74.6/27.6

Boston, Massachusetts: 71.1/24.1

El Paso, Texas: 81.7/34.7

Detroit, Michigan: 71.2/24.2

Nashville, Tennessee: 77.3/30.3

Portland, Oregon: 68.0/21.0

Memphis, Tennessee: 78.3/31.3

Oklahoma City, Oklahoma: 78.0/31.0

Louisville, Kentucky: 75.2/28.2

Baltimore, Maryland: 74.2/27.2

Milwaukee, Wisconsin: 70.5/23.5

Albuquerque, New Mexico: 78.4/31.4

Tucson, Arizona: 81.3/34.3

Fresno, California: 76.8/29.8

Mesa, Arizona: 80.1/33.1

Sacramento, California: 74.9/27.9

Atlanta, Georgia: 79.8/32.8

Kansas City, Missouri: 74.4/27.4

Miami, Florida: 87.7/40.7

Raleigh, North Carolina: 77.7/30.7

Long Beach, California: 79.7/32.7

Virginia Beach, Virginia: 76.6/29.6

Oakland, California: 75.7/28.7

Minneapolis, Minnesota: 68.5/21.5

Tulsa, Oklahoma: 77.3/30.3

Arlington, Texas: 80.8/33.8

Tampa, Florida: 85.5/38.5

New Orleans, Louisiana: 83.5/36.5

Wichita, Kansas: 75.8/28.8

Honolulu, Hawaii: 87.8/45.2 (tropical location yields a June value of 92.2, thus June sun appears in the southern sky)

San Juan, Puerto Rico: 85.0/48.0 (tropical location yields a June value of 95.0, thus June sun appears in the southern sky)

Newark, New Jersey: 72.8/25.8

Boise, Idaho: 69.9/22.9

Des Moines, Iowa: 71.9/24.9

Birmingham, Alabama: 80.0/33.0

Salt Lake City, Utah: 72.7/25.7

Little Rock, Arkansas: 78.8/31.8

Brownsville, Texas: 87.6/40.6

Sioux Falls, South Dakota: 70.0/23.0

Providence, Rhode Island: 71.7/24.7

Jackson, Mississippi: 81.2/34.2

Bridgeport, Connecticut: 72.3/25.3

Charleston, South Carolina: 80.7/33.7

Fargo, North Dakota: 66.6/19.6

Manchester, New Hampshire: 70.5/23.5

Billings, Montana: 67.7/20.7

Wilmington, Delaware: 73.8/26.8

Portland, Maine: 69.8/22.8

Cheyenne, Wyoming: 72.4/25.4

Saipan, Northern Mariana Islands: 81.7/51.3 (tropical location yields a June value of 98.3, thus June sun appears in the southern sky)

Charleston, West Virginia: 75.1/28.1

Dededo, Guam: 80.0/53.0 (tropical location yields a June value of 100.0, thus June sun appears in the southern sky)

Burlington, Vermont: 69.0/22.0

Key West, Florida: 88.9/41.9

Charlotte Amalie, U.S. Virgin Islands: 84.8/48.2 (tropical location yields a June value of 95.2, thus June sun appears in the southern sky)

Tafuna, American Samoa: 52.2/80.8 (summer/winter solstices reversed due to southern latitude; tropical location yields a December value of 99.2, thus December sun appears in the northern sky)

Blaine, Washington: 64.5/17.5

Utqiagvik, Alaska: 42.2/-4.8 (Arctic location means the sun is never less than 4.8 degrees below the horizon on the December Solstice)

Hawaiian Ocean View, Hawaii: 85.6/47.4 (tropical location yields a June value of 94.4, thus June sun appears in the southern sky)

Angle Inlet, Minnesota: 64.2/17.2

Last but not least, I also have ideas for where the equatorial, extreme polar, subtropical and subpolar latitudes should be defined.

You know how the tropics of Cancer and Capricorn occur at 23.5 degrees north and south, respectively? And the Arctic and Antarctic circles at 66.5 north and south? Well, I believe the Extreme Arctic Circle and Extreme Antarctic Circle should be at 83.5 deg. N/S, Subarctic/Subantarctic Circle at 53.5 N/S, Subtropic of Cancer/Capricorn at 36.5 N/S and Subequator of Cancer/Capricorn at 6.5 N/S. Why?

The extreme polar latitudes would then be the places the sun angle never gets 30+ degrees, the subpolar latitudes the places never 60+ degrees, the subtropical latitudes the places never below 30 degrees and the subequatorial latitudes never below 60 degrees.

This would be adjusted, as the tropics and polar circles would be, as the tilt precesses between 24.5 and 22.1 degrees over time. Here's the values they'd all be at a tilt of 24.5 degrees (including the normal, already-official tropics and polar circles)...
Spoiler
Extreme Arctic Circle: 84.5 N

Arctic Circle: 65.5 N

Subarctic Circle: 54.5 N

Subtropic of Cancer: 35.5 N

Tropic of Cancer: 24.5 N

Subequator of Cancer: 5.5 N

Subequator of Capricorn: 5.5 S

Tropic of Capricorn: 24.5 S

Subtropic of Capricorn: 35.5 S

Subantarctic Circle: 54.5 S

Antarctic Circle: 65.5 S

Extreme Antarctic Circle: 84.5 S

...and at a tilt of 22.1 degrees...
Spoiler
Extreme Arctic Circle: 82.1 N

Arctic Circle: 67.9 N

Subarctic Circle: 52.1 N

Subtropic of Cancer: 37.9 N

Tropic of Cancer: 22.1 N

Subequator of Cancer: 7.9 N

Subequator of Capricorn: 7.9 S

Tropic of Capricorn: 22.1 S

Subtropic of Capricorn: 37.9 S

Subantarctic Circle: 52.1 S

Antarctic Circle: 67.9 S

Extreme Antarctic Circle: 82.1 S

And why do 30 and 60 degree sun angles have any significance? Because if we're to divide evenly, 0-30 degrees is a low sun angle, 30-60 degrees is a moderate sun angle, and 60-90 degrees is a high sun angle.