Lesson 12

Vertical sextant angles (VSA)

The distance off a charted object of known height can be obtained by measuring, with a sextant, the vertical angle subtended by the object above the sea level.  Lighthouses are most commonly used and the measurement should be made from the centre of the lantern, not the top of the tower.  The distance off can be calculated by solving the following plane right-angles triangle, but it is more practical to extract the value from the appropriate table given in Norie's or Burton's Tables.

0              =              VSA observed (corrected for index error if any)

h        =                   charted height of Lt Ho giving distance off 'd'

H       =                   actual height of Lt Ho above tide level at time of                                                      observation giving actual distance off 'D'

The above diagram illustrates the normal Chartwork practice of using the charted height of an object to obtain the distance off by VSA, thus ignoring the state of the tide.

As the actual tide level will invariably be below MHWS on most occasions, the ship's actual distance off the object will be slightly greater than that obtained.  Hence, the practice of ignoring the height of tide for VSA questions is said to incur an Error on the Safe Side as the ship is really further from the danger (marked by the lighthouse) than anticipated.  Obviously extreme care must be taken when an island, reef or other danger lies to seaward of the ship as she will then be closer to this danger than anticipated.

Example:              Charted height of Lt Ho 75 metres, VSA 1°10'

From Vertical Angle Table - distance off is 2.0 miles.

If, however, the actual tide level is 4 metres below MHWS, the actual distance off is 2.1 miles, a difference of 1 cable.

Calculation Method

We can see from the diagram above that the following trigonometric formula will apply

TAN Θ  =  h / d   where h is the charted height of the light in meters.

Likewise by rearranging the formula we have

d   =   h / Tan Θ 

Note: d will be in meters, therefore to convert to nautical miles we must divide d by 1852. The formula now becomes

d  =  h / (Tan Θ x 1852)

In the example above

D  =  75 / (Tan 1o 10’ x 1852)

    =  75 / (0.0203…. x 1852)

    =  75 / 37.7

    =  1.99 nm

This agrees very well with the value obtained from tables.

In general, Chartwork questions ignore the height of tide for VSA observations.  Finding the actual height of an object above the tide level is only required for certain examination tide questions when Admiralty Tide Tables are used.

A further minor error is incurred due to disregarding the observer's height of eye above sea level.

A useful coasting practice when rounding an exposed lighthouse and requiring to maintain a minimum safe distance off is to set the required vertical angle (then referred to as a Vertical Danger Angle) on the sextant, then observe and alter course accordingly.  In strong tidal conditions it is possible to quickly detect if ship is being set in towards the lighthouse as the angle would be observed to increase.

Lesson 12.doc              Vertical Sextant Angles              DGR1999

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