In the beginning of the 19th century, sailors were describing wind forces instead of wind speeds, yet they lacks a uniform scale to estimate these forces.
His scale as well as the more precise wind speeds in Knots or sometimes in meters per second are now widely used.

Beaufort scale

Specification and speeds Equivalent speed at 10 m above sea level   Mean Limits Description in forecasts State of sea Probable height of waves* metres Force Description Specification for use at sea* knots metres per second knots metres per second * These columns are a guide to show roughly what may be expected in the open sea, remote from land. Figures in brackets indicate the probable maximum height of waves. In enclosed waters, or when near land with an offshore wind, wave heights will be smaller and the waves steeper.

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Wind chill forecast

The term wind chill goes back to the Antarctic explorer Paul A. Siple, who coined it in a study: “Adaptation of the Explorer to the Climate of Antarctica“.
In 1940 Siple and Charles F. Passel conducted experiments on the time needed to freeze 250 grams of water in a plastic cylinder that was exposed to the elements. The three parameters involved are:

• the initial temperature of the water;
• the outside temperature;
• and the wind speed.

The wind chill factor or equivalent temperature uses a neutral skin temperature of 33 °C as a baseline value, so only two parameters remain. Definition: Wind chill accounts for loss of heat when warm air around a body is replaced with colder air. The factor is an indication of the effect of the combination of air temperature and wind speed on human comfort and safety.

• The ability to forecast wind chill is especially important to yachtsmen since:

• offshore weather forecasts rarely include a wind chill factor;
• both the wind speed and the apparent wind speed are likely to differ from the forecast true wind speed;
• the nature of sailing implies that the duration of exposure to wind chill can not be predicted;
• the threat of hypothermia can be anticipated by using the factor.

Indeed, the wind chill factor is a highly underrated tool to prevent hypothermia and frostbite on board!

Learn to sail: RYA and ASA sailing schools and yacht charters in Greece and Turkey

This table provides equivalent temperatures and is based on the Steadman equation below, though many other variations exist:

ET = 0.045(7.1766 x √KNOTS + 10.45 - 0.5145 x KNOTS)(Celsius - 33.0) + 33.0

• Forecasts made with these equations are reasonably sufficient, though work is being done at this very moment to obtain a better index or factor.

Current inadequacies include:

• the Siple and Passel experiment did not take into account that the water was stored in a container with properties of its own;
• there’s no heat being generated in a water filled object, whereas the human body is constantly generating heat.
• the original experiment uses wind speed at 10 metres above ground.
• the current wind chill index also ignores other environmental factors such as sun shine, air humidity or precipitation;
• the equations are not valid above 40 knots and below 5 knots!

Conclusion: For your safety - even when sailing in the warmer waters of Greece or Turkey: anticipate and use the equivalent temperature to adequately forecast wind chill.

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This is an advanced online course on marine navigation, providing you with the “conditio sine qua non” of offshore sailing. Nowadays most sailors tend to rely on modern equipment like differential GPS or Radar to navigate them through hazardous waters. Not only is such reliance unwanted and possibly dangerous, also the act of navigating by yourself is actually a lot of fun, especially when sailing in Greece or Turkey, which are the perfect to learn how to sail.

What is navigation?

“Navigare necesse est, vivere non est necesse” is latin for: to sail is vital, to live is not. This phrase tells us that both sailing and the “conditio” of positioning are highly intertwined. Indeed, the art of navigation enables you to set a course and sail to your destination by using only nautical charts, a compass and your common sense. The aim of this course is to teach you how to navigate safely while using the minimum of resources: methods that have been in use since the Middle Ages, and are still applied by the professionals. This course greatly extends on - for instance - the ASA courses and gives you the insight and feel of a seasoned navigator.

Enjoy!

This is chapter 0: Use the moving anchor logo on the right of this page to navigate through the course. Alternatively, click on the links below to study the chapters.
Chapter 1 - Positions
Chapter 2 - Nautical chart
Chapter 3 - Compass
Chapter 4 - Plotting
Chapter 5 - Piloting
Chapter 6 - Tides
Chapter 7 - Tide prediction
Chapter 8 - Currents
Chapter 9 - Navigation aids

Math - Running fixes
Math - Distance of horizon
Math - Vertical sextant angles

Compass deviation table
Lunation, phases of the moon

The wind chill forecast
Beaufort wind scale

UK based sailing schools

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Vertical sextant angle

The triangle OBL (see fig. below) can be described in terms of H, α and Distance: Distance = H/tan(α)
The angle in rad. (0-2π) and both height and distance in metres.

• From rad. to degrees: α = A * π/180, ‘A’ being the same angle in degrees.
• To describe angle A in minutes total, then A*60 = a, thus α = (a/60) * (π/180). So, α = a/3438, ‘a’ being the angle in arc minutes.
• FACTUM: tan(x) = x, if angle x is small.

Resulting in (with π = 3.14): Distance (m)= H * 3438/a

• Furthermore, distance in nm. = distance in meters/1852.

Voilà, la very practical equation:

Distance = 1.856 * H/a

It contains just two approximations, both of neglitible influence. First, we left out the tan function and second we used 3.14 for π.
Please realize that a smaller angle improves the approximation of the tan. Yet, as an opposing effect the instrument error of a smaller sextant angle increases. All in all, the factor 1.856 is not a typo, and just by chance near to the nautical mile: 1.852 kilometres. If you are still reading, you are very brave person and might perhaps agree that it originates from: (60 * 180)/(π * 1852).

So far we considered a perfect triangle (OBL) and forgot that life isn’t always perfect. Height h is usually quite small, but distance SB sometimes is not. This leads to an extra premise, which is seldom mentioned by other navigation textbooks:
Angle OLS should be bigger than 15°.

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