窗戶反射 Reflections from windows

山谷對面別墅折光很亮。 The mansion across the valley reflects sunlight brightly.

窗戶反射 (放大)Sun reflected from windows (zoomed) 窗戶反射 Sun reflected from windows

谷歌地球載入此 KML 得見: Loading this KML into Google Earth shows:

KML 模擬 modeling 別墅折光 Rays reflected from the mansion

說明 Explanation

山谷對面, 離我兩多公里, 有座大別墅。 24 米寬前面有許多窗戶。 一年有幾天夕陽由窗戶折射過來我方向。 如圖壯觀。 我們來預測何時發生。

Across the valley a couple of km. there is a big mansion. Its 24 meter wide front has many windows, which on certain days of the year reflect the setting Sun my direction. As in the photos it's quite impressive. Let's calculate when this will happen.

我們約每八天取樣。 冬至後線路迴轉, 也正好在去程之各半。 亦即圖被「牆」分成四日寬塊。

Here we sample about once every eight days. As the path starts coming back after the Winter Solstice, the "walls" happen to fall halfway between the other walls. So we have four-days slots created between walls.

每道「扇片/牆」觸地之線就是折光觸地點當日慢慢爬坡之軌跡。 日越落, 點越升。

So each fan blade / wall's intersection with the earth's surface makes a line, that is the the path of the reflection, as it slowly climbs up the hill on that day. As the Sun goes down, the point climbs up.

(觸地點之地本身不特別亮, 但站在那兒看別墅, 別墅像著火樣!)

(No, the spot where it hits the ground is bright enough to light up the ground. But standing at the spot you see the mansion as if it was on fire!)

如果太陽直直下, 那麼圖片中逐「扇片」也能垂直畫, 也可於 KML 棄面取線, 直接掛一條線在地表面上。

If the Sun set straight downwards, then each "fan blade" in our image would be vertical, and in our KML we could not bother with planes, and instead just draw simple lines draped on the earth surface.

但當然, 緯度越高, 夕陽越斜落。

But as one knows, the more north one's latitude is, the less vertical the Sun sets.

觀看該 KML, 得知每年 2/23, 及 10/23 開始, 維持幾天, 日落前數分鐘, 有幾分鐘該折光會照著我。

OK, viewing the KML I note that every year, for a few days starting Feb. 14th and Oct. 23rd, I should expect the rays to hit me, for a few minutes, several minutes before sunset.

圖中日期旁之 "←"、 "→" 只是引導眼睛尋找下一道「牆」。 末牆註句點 (".")。

The "←", and "→" next to the dates on the map are simply to help the eye find the next "wall." On the final wall the date ends with a period (".").

反射點之寬度也是上述 24 米。 試算幾次發現, 人站著不動, 現象維持三分鐘就結束。

We note that the reflection's width is the same aforementioned 24 meters. Also from plugging different numbers in, we find standing at the same spot, the phenomenon will last about three minutes.

(換算時順便)發現, 在咱特定點, 日落前 18 至 20 分鐘, (視季節而變) 太陽仍離地平線 3.66° 時, 光點就到我們位置了。

(While tinkering with the Moon we also found to) note to expect the Sun's reflection to hit our particular location 18 to 20 minutes (depending on the season) before sunset, when it is still elevation 3.66° above the horizon.

位置 Location

相信每公里都有別墅, 每別墅有窗戶, 故本臺中市東勢區慶福里 13 鄰大坪角例子沒什麼稀奇。

There is probably a mansion a kilometer in the countryside, and all mansions have windows, so this Taichung City Dongshi District Qingfu Village Neighborhood 13 Dapingjiao example isn't anything special.

該座視野分析, 得知太陽若超過方位角 280° 就遭山擋, 不會折射。 但其窗戶方向本身是 321° 加上本山谷細長… 反正站在同一個位置, 本現象能觀測一年兩次, 每次幾天, 每天幾分鐘。 下週若欲繼續觀測, 須搬移幾十公尺。

Checking that mansion's viewshed analysis, we note that after the Sun reaches azimuth 280° it will start getting blocked by mountains, and thus no more reflections for us... But the windows are aligned at 321°, plus the valley's narrow alignment... Anyway standing at the same spot we can see the phenomenon twice a year. Each time for a few days. Each day for a few minutes. If the next week we want to watch it over again, we must relocate our observation point a few tens of meters.


原始碼 Source code.

A 字型屋反射 Reflections from an A-frame.

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積丹尼 Dan Jacobson

Last modified: 2021-05-07 14:43:00 +0800