# Physics

## Density of V4A (AISI 316/316L)

According to theworldmaterial.com the density of V4A stainless steel is approximately 8000 kg/m³ or 8.0 g/cm³

Posted by Uli Köhler in Physics

## How to compute & plot sun path diagram using skyfield in Python

In this example, we’ll show how to generate a sun path diagram for any given day for a preselected location. By using the skyfield library, we can obtain extremely accurate predictions of the sun’s position in the sky, and in contrast to many other libraries, we can use the same method to predict the position of other celestial bodies. #!/usr/bin/env python3
from skyfield import api
from skyfield import almanac
from datetime import datetime
from datetime import timedelta
from matplotlib import pyplot as plt
import pytz
import dateutil.parser
from collections import namedtuple
from UliEngineering.Utils.Date import *
import matplotlib.ticker as mtick

# Matplotlib formatter
def format_degrees(value, pos=None):
return f'{value:.0f} °'

sun = ephem["Sun"]
earth = ephem["Earth"]

# Data types
AltAz = namedtuple("AltAz", ["altitude", "azimuth", "distance"])
TimeAltAz = namedtuple("TimeAltAz", ["time", "altitude", "azimuth", "distance"])

def sun_altaz(planet_at_location, ts):
# Compute the sun position as seen from the observer at <location>
sun_pos = planet_at_location.at(ts).observe(sun).apparent()
# Compute apparent altitude & azimuth for the sun's position
altitude, azimuth, distance = sun_pos.altaz()
return AltAz(altitude, azimuth, distance)

def sun_altaz_for_day(location, year, month, day, tz):
earth_at_location = (earth + location)

minutes = list(yield_minutes_on_day(year=year, month=month, day=day, tz=tz))
skyfield_minutes = ts.from_datetimes(minutes)

minutely_altaz = [sun_altaz(earth_at_location, ts) for ts in skyfield_minutes]
# Extract components for plotting
minutely_alt = [altaz.altitude.degrees for altaz in minutely_altaz]
minutely_az = [altaz.azimuth.degrees for altaz in minutely_altaz]
minutely_distance = [altaz.distance for altaz in minutely_altaz]

return TimeAltAz(minutes, minutely_alt, minutely_az, minutely_distance)

# Random location near Munich
location = api.Topos('48.324777 N', '11.405610 E', elevation_m=519)
# Compute Alt/Az for two different days
jun = sun_altaz_for_day(location, 2022, 6, 15, pytz.timezone("Europe/Berlin"))
dec = sun_altaz_for_day(location, 2022, 12, 15, pytz.timezone("Europe/Berlin"))

# Plot!
plt.gca().yaxis.set_major_formatter(mtick.FuncFormatter(format_degrees))
plt.gca().xaxis.set_major_formatter(mtick.FuncFormatter(format_degrees))

plt.plot(jun.azimuth, jun.altitude, label="15th of June")
plt.plot(dec.azimuth, dec.altitude, label="15th of December")
plt.ylim([0, None]) # Do not show sun angles below the horizon
plt.ylabel("Sun altitude")
plt.xlabel("Sun azimuth")
plt.title("Apparent sun position at our office")
plt.grid()
plt.gca().legend()
plt.gcf().set_size_inches(10,5)

plt.savefig("Sun path.svg")

Posted by Uli Köhler in Physics, Python, skyfield

## How to compute position of sun in the sky in Python using skyfield

The following code computes the position of the sun (in azimuth/altitude coordinates) in the sky using the skyfield library. Note that you need to download de421.bsp .

from skyfield import api
from skyfield import almanac
from datetime import datetime
from datetime import timedelta
import dateutil.parser
from calendar import monthrange

sun = ephem["Sun"]
earth = ephem["Earth"]

# Compute sunrise & sunset for random location near Munich
location = api.Topos('48.324777 N', '11.405610 E', elevation_m=519)
# Compute the sun position as seen from the observer at <location>
sun_pos = (earth + location).at(ts.now()).observe(sun).apparent()
# Compute apparent altitude & azimuth for the sun's position
altitude, azimuth, distance = sun_pos.altaz()

# Print results (example)
print(f"Altitude: {altitude.degrees:.4f} °")
print(f"Azimuth: {azimuth.degrees:.4f} °")

### Example output

Altitude: -3.3121 °
Azimuth: 48.4141 °

### Factors influencing the accuracy of the calculation

This way of calculating the position takes into account:

• The slight shift in position caused by light speed
• The very very slight shift in position caused by earth’s gravity

But it does not take into account:

• Atmospheric distortions shifting the sun’s position
• The extent of the sun’s disk causing the sun to emanate not from a point but apparently from an area
Posted by Uli Köhler in Physics, Python, skyfield

## How to compute sunrise & sunset in Python using skyfield

The following code will compute the sunrise & sunset at a specific location & elevation using the skyfield library. Note that you need to download de413.bsp .

from skyfield import api
from skyfield import almanac
from datetime import datetime
from datetime import timedelta
import dateutil.parser
from calendar import monthrange

def compute_sunrise_sunset(location, year=2019, month=1, day=1):
t0 = ts.utc(year, month, day, 0)
# t1 = t0 plus one day
t1 = ts.utc(t0.utc_datetime() + timedelta(days=1))
t, y = almanac.find_discrete(t0, t1, almanac.sunrise_sunset(ephem, location))
sunrise = None
for time, is_sunrise in zip(t, y):
if is_sunrise:
sunrise = dateutil.parser.parse(time.utc_iso())
else:
sunset = dateutil.parser.parse(time.utc_iso())
return sunrise, sunset

# Compute sunrise & sunset for random location near Munich
location = api.Topos('48.324777 N', '11.405610 E', elevation_m=519)
now = datetime.now()
sunrise, sunset = compute_sunrise_sunset(location, now.year, now.month, now.day)

# Print result (example)
print(f'Sunrise today: {sunrise}')
print(f'Sunset today: {sunset}')

#### Definition of sunrise & sunset in this context

According to the skyfield documentation:

Skyfield uses the same definition as the United States Naval Observatory: the Sun is up when its center is 0.8333 degrees below the horizon, which accounts for both its apparent radius of around 16 arcminutes and also for the 34 arcminutes by which atmospheric refraction on average lifts the image of the Sun.

#### Other caveats

• Note that obstructions like mountains are not taken into account for this model
• Note that the resulting timestamps are UTC, if you want local time, you’ll have to convert them appropriately

#### Example output:

Sunrise today: 2022-06-19 03:12:56+00:00
Sunset today: 2022-06-19 19:18:38+00:00

Posted by Uli Köhler in Physics, Python, skyfield

## FR4 PCB thermal expansion online calculator

Calculate the thermal expansion in millimeters (mm) of a FR4 PCB in X/Y direction. A typical temperature difference default is 65°C, the difference between 20°C room temperature and the max temperature rating of 85°C parts. The default 13ppm/°C thermal expansion coefficient is from this website.

TechOverflow calculators:
You can enter values with SI suffixes like 12.2m (equivalent to 0.012) or 14k (14000) or 32u (0.000032).
The results are calculated while you type and shown directly below the calculator, so there is no need to press return or click on a Calculate button. Just make sure that all inputs are green by entering valid values.

mm

°C

ppm/°C

Posted by Uli Köhler in Calculators, Electronics, Physics

## Lumen to Candela online calculator & Python code

TechOverflow calculators:
You can enter values with SI suffixes like 12.2m (equivalent to 0.012) or 14k (14000) or 32u (0.000032).
The results are calculated while you type and shown directly below the calculator, so there is no need to press return or click on a Calculate button. Just make sure that all inputs are green by entering valid values.

lm

°

#### Formula

$$\Omega_{sr} = 2\cdot\pi\cdot(1-\cos(\frac{\theta}{2}))$$
$$I_{v} = \frac{\Phi_v}{\Omega_{sr}}$$

where:

• $\theta$ is the apex angle in radians
• $\Omega_{sr}$ is the solid angle in Steradians
• $\Phi_v$ is the luminous flux in lux (lx).
• $I_{v}$ is the luminous intensity in candela (cd).

#### Python code

You can use the UliEngineering library like this:

from UliEngineering.Physics.Light import lumen_to_candela_by_apex_angle
from UliEngineering.EngineerIO import auto_format, auto_print

# These are equivalent:
intensity = lumen_to_candela_by_apex_angle("25 lm", "120°") # intensity = 7.9577 (cd)
intensity = lumen_to_candela_by_apex_angle(25.0, 120.0) # intensity = 7.9577 (cd)

# ... or get out a human-readable value:
intensity_str = auto_format(lumen_to_candela_by_apex_angle, "25 lm", "120°") # "7.96 cd"
# ... or print directly
auto_print(lumen_to_candela_by_apex_angle, "25 lm", "120°") # prints "7.96 cd"


In case you can’t use UliEngineering, use this Python function:

import math

def lumen_to_candela_by_apex_angle(flux, angle):
"""
Compute the luminous intensity from the luminous flux,
assuming that the flux of <flux> is distributed equally around
a cone with apex angle <angle>.

Keyword parameters
------------------
flux : value, engineer string or NumPy array
The luminous flux in Lux.
angle : value, engineer string or NumPy array
The apex angle of the emission cone, in degrees
For many LEDs, this is

>>> lumen_to_candela_by_apex_angle(25., 120.)
7.957747154594769
"""
solid_angle = 2*math.pi*(1.-math.cos((angle*math.pi/180.)/2.0))
return flux / solid_angle

# Usage example
print(lumen_to_candela_by_apex_angle(25., 120.)) # Prints 7.957747154594769 (cd)

Posted by Uli Köhler in Calculators, Physics