The clock code is a method of mentally computing the sine of an angle between zero and sixty degrees. Pilots sometimes need to do this to estimate the heading correction due to the wind, and sailors may find it useful to do the same thing to allow for the current due to the tides.
The basic assumption is that for angles up to around 60°, it is adequately accurate to assume that sine(A) = A, when A is expressed as a fraction of 60. Thus, the sine of 30° = 30/60 = 1/2 = 0.5.
The clock code is a further method of visualising fractions of 60, since we are very used to expressing fractions of an hour (60 minutes) when telling the time.
The angle is the angle of the wind or tide as it presents itself relative to the ship or aircraft, so if the wind is coming from the left at a relative angle of 30°, we use a sine of 0.5. Once the sine has been estimated, the drift due to wind or tide can be estimated accordingly by resolving the velocity of the wind or tide into a forward component and a sideways component. The sideways component is the wind speed x the sine, and the forward component is (1 - the sine) x wind speed (i.e. the cosine). Naturally we must apply these corrections to our groundspeed in the appropriate direction according to logic - a wind from the left will blow us off course in that direction; a headwind will slow our progress, a tailwind will increase it. Converting this back to a heading correction can be done using the 1 in 60 rule.
For wind angles greater than 60°, it is adequate to assume it's at 90°, i.e. a side wind.
More accurate corrections are done when possible, but in the particular case of a VFR pilot mentally calculating an unexpected diversion, using tables or the E6B slide rule in flight is usually not an option, so the clock code is one method of handling the required calculation without excessive error. In practice the wind strength can only be guessed or based on earlier reports, and the error due to the sine calculation will usually be much less than that due to the wind itself. Fine tuning of the heading can be done en route using the usual methods for doing so.
Sexagesimal, also known as base 60, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates.
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Rangekeepers were electromechanical fire control computers used primarily during the early part of the 20th century. They were sophisticated analog computers whose development reached its zenith following World War II, specifically the Computer Mk 47 in the Mk 68 Gun Fire Control system. During World War II, rangekeepers directed gunfire on land, sea, and in the air. While rangekeepers were widely deployed, the most sophisticated rangekeepers were mounted on warships to direct the fire of long-range guns.
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In trigonometry, a skinny triangle is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to that angle in radians. The solution is particularly simple for skinny triangles that are also isosceles or right triangles: in these cases the need for trigonometric functions or tables can be entirely dispensed with.
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Tree height is the vertical distance between the base of the tree and the tip of the highest branch on the tree, and is difficult to measure accurately. It is not the same as the length of the trunk. If a tree is leaning, the trunk length may be greater than the height of the tree. The base of the tree is where the projection of the pith (center) of the tree intersects the existing supporting surface upon which the tree is growing or where the seed sprouted. If the tree is growing on the side of a cliff, the base of the tree is at the point where the pith would intersect the cliff side. Roots extending down from that point would not add to the height of the tree. On a slope this base point is considered as halfway between the ground level at the upper and lower sides of the tree. Tree height can be measured in a number of ways with varying degrees of accuracy.
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