List of Grain-Laden Vessels from United States Ports Abandoned and Missing from 1st September, 1878, to 11th June, 1879. APPARENT AND TRUE DIRECTION OF THE WIND UESTIONS relating to the apparent and true direction of the wind under different velocities of ship and wind, and under different relations of the one to the other, are often referred to us; we trust that the following explanation and Table will be useful for the purpose intended, and sufficiently illustrate the subject. The question appertains to the composition and resolution of forces. In a dead calm, the forward progression of a steamer will appear to make a wind coming from right ahead equal to her rate through the water; hence, if she is steaming 10 knots an hour, there will appear, to a person on board, a head wind blowing 10 miles per hour in a direction opposite to the course. With the wind right aft, the problem presents itself under three forms (1) The velocity of the wind may considerably and palpably exceed the rate of the vessel's progression; hence, if a vessel is making eight knots per hour, and the apparent velocity of the wind is 20 miles, then (the velocity plus the rate) 20+8=28 miles, which is the true velocity of the wind per hour; this case appertains to a sailing ship no less than to a steamer. (2) A steamer's speed may outstrip the wind's velocity, and there may appear to be a head wind; in this case, the steaming rate (say 12 knots) less the apparent velocity of wind (say 3 miles) as a head wind gives (9 miles) the true velocity of the wind in the direction of the course. (3) The steamer's rate and the wind's velocity may be equal, say each ten miles, then there will be neither lagging nor outstriping, but an apparent calm on board. Probably none of these conditions is ever exactly fulfilled. With the wind right ahead, as it may be in the case of a steamer, the apparent exceeds the true velocity of the wind by the steaming rate; hence, if the apparent velocity of wind be 25 miles per hour, and the steaming rate 9 miles, the true velocity of wind is only 25-9-16 miles per hour. For the solution of the problem as to the true direction and velocity of the wind, we have r the ship's rate or speed through the water, and the apparent velocity of the wind. We have also the angle that the apparent direction of the wind makes to the course of the ship reckoned from aft, forward; thus, with the wind apparently abeam, the apparent direction of the wind to the course will be 90°; with the wind apparently 20° before the beam its apparent direction to the course will be 110°; and with the wind four points on the quarter it will make an angle of 45° to the course. Knowing the angle that the apparent direction of the wind makes to the ship's course, we also know the sum of the angles V and R, which are respectively opposite to the sides v and r; the angle V will be the true direction of the wind to the course, and the angle R will be the divergence of the apparent from the true direction. APPARENT AND TRUE DIRECTION OF THE WIND WHEN SAILING. 299 Now, the sum of the two sides of a triangle is to their difference, as the tangent of half the sum of their opposite angles is to the tangent of half their difference. VR the sum of the angles opposite to v and r must be the apparent direction of the wind to the course reckoned from aft; and hence, generally, (V (V – R); R), the sum v + r : v − r : : tan (V + R) : tan knowing (V + R), and having determined of the half sum and half difference gives the angle V, as the true direction of the wind to the course; and the difference of the half sum and half difference gives R the divergence of the apparent and true winds, that is the angle by which the apparent is more forward than the true wind. This is when the wind velocity is greater than the ship's rate; should it be otherwise, we have r+v: r v : : tan (R + V) : tan ¦ (R V) On the basis of these formulæ the annexed table has been computed. The true velocity of the wind may also be ascertained, since the sides of a triangle are to one another as the sines of the opposite angles; hence, tv sin T: sin V; or tr:: sin T: sin R : in which the angle T (opposite to t) is known, since V and R are known; and the solution gives t, the wind's true velocity. On constructing a figure, or referring to the Table, it will be seen that— 1. When the true direction and velocity of the wind remain unchanged, and the ship's course is also unchanged, then the apparent direction of the wind will vary as the ship sails faster or slower. The divergence of the apparent from the true direction increases as the ship's rate increases, and decreases as the rate decreases. 2. When the ship maintains the same rate under winds of different velocities, but inclined at the same angle to the course, the divergence of the apparent from the true direction of the wind will be greater as the wind is slower, and less as it is faster. The Table sufficiently explains itself. |