<p>In most sundials, the gnomon is aligned with the Earth's polar axis so that the shadow indicates the Sun's <a href="https://en.wikipedia.org/wiki/Hour_angle" rel="nofollow noreferrer">hour angle</a>.
A vertical tower instead casts a shadow indicating the Sun's <a href="https://en.wikipedia.org/wiki/Azimuth" rel="nofollow noreferrer">azimuth</a>.
The time of day can be computed from this, but simple hour marks won't quite do it.</p>

<p>Let's try it with your photo.
The <a href="https://en.wikipedia.org/wiki/Tokyo_Skytree" rel="nofollow noreferrer">Skytree</a> is at 35.7&deg;N, 139.8&deg;E, and the antenna tip is 634 m above ground.
The buildings near the shadow tip appear to match the satellite image about 830m away and 1&deg; west of due north.
So the Sun's azimuth at that time is 179&deg; and its altitude is atan(634/830) = 37&deg;.
Assuming a date of 2019-11-12, and jiggling the inputs of the <a href="https://www.esrl.noaa.gov/gmd/grad/solcalc/" rel="nofollow noreferrer">NOAA Solar Calculator</a>, I find a matching azimuth at 11:22 AM JST (UTC+9).</p>

<p>Alternatively we can solve the <a href="https://en.wikipedia.org/wiki/Celestial_coordinate_system#Equatorial_%E2%86%94_horizontal" rel="nofollow noreferrer">coordinate conversion</a> formulas for hour angle:</p>

<pre><code>ha = atan2(-sin(az), -cos(az) * sin(lat) + tan(alt) * cos(lat))
</code></pre>

<p>which works out to -0.8&deg; or about 11:57 apparent <a href="https://en.wikipedia.org/wiki/Solar_time" rel="nofollow noreferrer">solar time</a>.
Subtracting 19 minutes for Tokyo's longitude east of the JST central meridian, and 16 minutes for the <a href="https://en.wikipedia.org/wiki/Equation_of_time" rel="nofollow noreferrer">equation of time</a> on Nov 12, we also get 11:22 AM.</p>

CC BY-SA 4.0
2019-11-14T16:12:29.397Z
It's a lot easier to just check the time of year and the sun's position in the sky. Once you get NSEW sorted, and make a habit of looking, you can get within half an hour easily; no shadows involved.
Wayfaring Stranger
CC BY-SA 4.0
2019-11-12T21:51:07.163Z
2019-11-13T03:54:12.367Z
2019-11-13T03:54:12.367Z
Mike G
<p>Anything which casts a shadow can become a sundial, as JH's comment points out.</p>

<p>The other thing you need to know is the latitude of the building, as that affects the change in shadow direction per hour of elapsed time.  Worse, due to the eccentricity of Earth's orbit (and rotation axis), there's an offset between clock time and sundial time which varies over the year.  You can get most of the formulas at the <a href="https://en.wikipedia.org/wiki/Sundial" rel="nofollow noreferrer">Wikipedia page</a> .</p>

<p>There's a handy calculator at <a href="https://www.blocklayer.com/sundial.aspx" rel="nofollow noreferrer">blocklayer.com</a></p>

CC BY-SA 4.0
2019-11-12T18:56:14.960Z
2019-11-12T18:56:14.960Z
Carl Witthoft
<p>After my observation today at the <a href="https://en.wikipedia.org/wiki/Tokyo_Skytree" rel="nofollow noreferrer">Skytree in Tokyo</a>, I am wondering if this building could be used as a giant sundial? </p>

<p>As an aside, it would be interesting to consider how the Skytree might be used to <em>display</em> the time.</p>

<p><a href="https://i.sstatic.net/0pRC9.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/0pRC9.jpg" alt="Tokyo Skytree"></a></p>

CC BY-SA 4.0
2019-11-12T15:10:23.250Z
Anything that casts a shadow could be used as a sundial. Just paint big numbers (10, 11, 12, etc) on the roofs of the buildings to know the time. :-)
JohnHoltz
<the-sun><time><clock>
Can I use the Tokyo Skytree as clock?
FrankStein
# Can I use the Tokyo Skytree as clock?

(Asked by: username_0 on 2019-11-12)

After my observation today at the [Skytree in Tokyo](https://en.wikipedia.org/wiki/Tokyo_Skytree), I am wondering if this building could be used as a giant sundial?

As an aside, it would be interesting to consider how the Skytree might be used to *display* the time.

[![Tokyo Skytree](https://i.sstatic.net/0pRC9.jpg)](https://i.sstatic.net/0pRC9.jpg)

**Tags:** the-sun, time, clock

> **Comments:**
> **username_1**: Anything that casts a shadow could be used as a sundial. Just paint big numbers (10, 11, 12, etc) on the roofs of the buildings to know the time. :-)  

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## 2 answers

### Answer by username_2 on 2019-11-12. Score: 1 | Accepted answer

In most sundials, the gnomon is aligned with the Earth's polar axis so that the shadow indicates the Sun's hour angle.
A vertical tower instead casts a shadow indicating the Sun's azimuth.
The time of day can be computed from this, but simple hour marks won't quite do it.
Let's try it with your photo.
The Skytree is at 35.7°N, 139.8°E, and the antenna tip is 634 m above ground.
The buildings near the shadow tip appear to match the satellite image about 830m away and 1° west of due north.
So the Sun's azimuth at that time is 179° and its altitude is atan(634/830) = 37°.
Assuming a date of 2019-11-12, and jiggling the inputs of the NOAA Solar Calculator, I find a matching azimuth at 11:22 AM JST (UTC+9).
Alternatively we can solve the coordinate conversion formulas for hour angle:
ha = atan2(-sin(az), -cos(az) * sin(lat) + tan(alt) * cos(lat))

which works out to -0.8° or about 11:57 apparent solar time.
Subtracting 19 minutes for Tokyo's longitude east of the JST central meridian, and 16 minutes for the equation of time on Nov 12, we also get 11:22 AM.

> **Comments:**
> **username_3**: It's a lot easier to just check the time of year and the sun's position in the sky. Once you get NSEW sorted, and make a habit of looking, you can get within half an hour easily; no shadows involved.  

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### Answer by username_4 on 2019-11-12. Score: 1

Anything which casts a shadow can become a sundial, as JH's comment points out.

The other thing you need to know is the latitude of the building, as that affects the change in shadow direction per hour of elapsed time. Worse, due to the eccentricity of Earth's orbit (and rotation axis), there's an offset between clock time and sundial time which varies over the year. You can get most of the formulas at the [Wikipedia page](https://en.wikipedia.org/wiki/Sundial) .

There's a handy calculator at [blocklayer.com](https://www.blocklayer.com/sundial.aspx)


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