抄録
When an aeroplane is diving vertically at the zero-lift angle, the aerodynamical coefficients such as cz cx cm etc. being kept constant, the air force and moment on each part of the aeroplane are proportional to the dynamic pressure. The change of the dynamic pressure during nose dive from a height to another may be calculated by solving the following equation of motion, (1)
where P is the total weight of the aeroplane, S is the wing area, and q is the dynamic pressure. Transforming this, we obtain (2)
In the above equations, the air density γ (kg/m3) is a function of the height Z, while cx, the drag coefficient of the complete machine, including that of the propeller, is a function of Z and q (or υ).
For simplification, assuming that cx is constaht and the air density is expressed approximately as (3)
we obtain the solution of The equation (2) as where qT is the "terminal" dynamic pressure at which the total drag of the complete machine becomes equal to the total weight of the aeroplane, and q0 and Z0 are determined by the initial conditions.
As to the values of constants a and b, using Table I (see p. 43), and calculating q step by step every 1, 000m, errors due to the approximation of (3) are practically reduced to zero.
The accurate value of the resistance of the propeller in various conditions may be calculated by the negative thrust corresponding to the aeroplane speed and the number of revolutions which is determined by equilibrium of the negative torque of the propeller and the friction torque of the engine. Thus the drag coefficient of the propeller may be expressed as a function of Z and q as shown, for example, in Fig. 2. Calculating the drag coefficient of the propeller as described above, and putting the results in the equation (2), the equation may be solved step by step. The result of an example, however, showed that the effect of the variation of cx during the dive was negligible. For practical purposes, therefore, we may obtain fairly accurate results, on the assumption that cx remains constant, whose value is taken from the conditions at the end of the dive.
By the above method of calculation, let me revise the load assumptions for C (Nose dive) case in the strength requirements of aeroplanes. It is laid down in the regulations (July 1932) of the Advisory Committee for Aeronautics of Nippon that qc the dynamic pressure in C case should be determined by the relation qc=kqT, where the constant k varied with the categories, for instance, k=0.5 for the category III. The height of drop until qc becomes kqT, however, differs with the characteristics (qT or and cx) of aeroplanes as shown in Fig. 4 and the above assumption means that the finer the aeroplane, the greater is the height of drop, which is unreasonable. The author now proposes that for civil aeroplanes it is quite reasonable to lay down that the height of drop shall be constant for each category, supposing that the aeroplane, though it begins to dive vertically, must be pulled out after falling some distance.
If we take the height of drop for each category as follows, the dynamic pressure attained may be calculated by the formula (4), whose results are shown in Fig. 8. This may be available with satisfactory results, for the calculation of applied loads in C case.
