scholarly journals Note on the trajectories of rifled projectiles with various shapes of head

1908 ◽  
Vol 80 (541) ◽  
pp. 519-529
Keyword(s):  
Approximate Formula ◽  
Air Resistance

In two previous papers I gave an approximate formula for the determination of the range and elevation of a pointed rifle projectile, of which the head was an ogive with a radius of two diameters. This approximation agreed so closely with the results obtained in practice that it seemed worth while to ascertain whether the same type of formula would not apply equally well to other shapes of head. For this purpose I have made the experiments which will be presently described. In order to explain clearly what the exact points to be decided were, I will briefly restate the origin of the formulæ given in the former papers. The results of all the experiments made on air resistance at high velocities agree in giving a curve of retardation in terms of velocity of the form shown in Diagram I.

scholarly journals ЗОВНІШНЯ БАЛІСТИКА СНАРЯДУ БМ1 ВИПУЩЕНОГО З Т-12 (МТ-12)

World Science ◽  
2020 ◽  
Vol 1 (1(53)) ◽  
pp. 23-29
Author(s):  
Величко Лев Дмитрович ◽  
Горчинський Ігор Володимирович ◽  
Сорокатий Микола Іванович
Keyword(s):  
Atmospheric Pressure ◽  
Sound Speed ◽  
Functional Dependence ◽  
Resistance Force ◽  
Kinematic Parameters ◽  
Muzzle Velocity ◽  
Velocity Magnitude ◽  
Air Resistance ◽  
The Mathematical Model

The magnitudes of the kinematic parameters of projectiles motion in the air depends on deterministic (form of projectile, its mass, temperature of air and charge, atmospheric pressure, derivation) and nondeterministic (muzzle velocity, magnitude and direction of wind velocity) values. During the projectile movement, its weight and frontal air resistance force have a determining influence on its dynamics. In the article it is investigated proposed by authors the mathematical model of determination of the functional dependence of the magnitude of the frontal air resistance force of the projectile’s motion on its velocity, mass and caliber, geometric characteristics, temperature and density of air, atmospheric pressure, sound speed in air. Since the trajectory of movement of the BM1 projectile released from the T-12 (MT-12) is canopy, it is assumed that during the projectile’s flight the air temperature and atmospheric pressure are unchanged and equal to their value at the point of the gun.

scholarly journals An Approximate Formula for the Length of an Arc of a Suspended Rope

1917 ◽  
Vol 36 ◽  
pp. 94-95
Author(s):  
E. M. Horsburgh
Keyword(s):  
Approximate Formula ◽  
Transcendental Equation ◽  
Central Angle ◽  
Circular Arc

The length of an arc of a flexible rope or chain suspended in the catenary y = c cosh x/c is s = c sinh x/c when measured from the vertex, but the practical determination of s is troublesome, owing to the difficulty in finding the parameter c from the transcendental equation when the coordinates of the point of suspension are given. The importance of a formula such as Huygens' approximation to the length of a circular arc s = 2B+⅓(2B−A), where A is the chord of the arc and B that of half the arc, is due to the fact that one can scale directly these lengths by rectilinear measurements without requiring to find the central angle or to make any subsidiary calculations. Formulae of this nature applicable to the parabola, or to curves whose arcs might be replaced by parabolic arcs, would be useful in the design of structural works dealing with ropes or chains. In such cases, as the dip is frequently less than one-eighth of the space, the catenary may be replaced by a parabola.

scholarly journals MODIFICATION OF WIND TUNNELS IN THE AUTOMOTIVE INDUSTRY AND THE RESULTS OF DETERMINATION OF COMPONENT AIR RESISTANCE

2018 ◽  
Vol 3 (11) ◽  
pp. 114-121
Author(s):  
Исмаил Мустафаев ◽  
Ismail Mustafaev ◽  
Елена Чубенко ◽  
Elena Chubenko
Keyword(s):  
Automotive Industry ◽  
Wind Tunnels ◽  
Air Resistance

scholarly journals Determination of Inductance of Vehicle Electromagnet in Magnetic Levitation Transprort System

2017 ◽  
Vol 3 (4) ◽  
pp. 75-88
Author(s):  
Gennady E Sereda ◽  
Vladimir M Strepetov
Keyword(s):  
Approximate Formula ◽  
Magnetic Levitation ◽  
Practical Importance ◽  
Skin Layer ◽  
Minimum Size ◽  
Geometrical Parameters ◽  
Elementary Functions ◽  
Cross Sectional ◽  
Analytic Expressions

Objective. Of the work consists in receiving new analytic expressions for determination of inductance of vehicular electromagnets of transport levitation systems. Methods. The key feature of calculation model of onboard coils in accordance with their inductance on the example of squared electromagnets lies an assumption about a smallness of the size «heights» in comparison with its other geometrical sizes. There is also an assumption that thickness of a skin layer of the conductor significantly surpasses cross sectional size of the wire making the coil. The single-turn coil is considered, inductance of an actual electromagnet is accepted proportional to a square of the number of turns. When calculating inductance the dimensionless quantities are used. As an absolute, a quarter of perimeter of the coil on the centerline is chosen. The condition of obtaining the approximate formula for calculation of inductance of the flat rectangular coil is the small thickness of a winding in comparison with the geometrical sizes of the coil. Results. Accurate analytical expression for inductance of a «thin» source of squareshaped magnetic field as the algebraic sum of elementary functions has been received. Results of a numerical analysis show dependence of the relative inductance of the square-shaped flat coil on thickness relation to its minimum size. Influence of «elongation» of the coil (relation of length to width) is investigated. It is noted that inductance decreases with decrease of «elongation», and also with increase in the relation of thickness to the minimum size. Practical importance. The approximate formula for calculation of value of inductance has been obtained. Its uncertainty does not exceed 14 % in the areas of changes of all geometrical parameters of an electromagnet is output. Borders of practical application of the received analytic expressions at the accepted assumptions have been set. The received expressions are fairly simple structurally and are easily programmed

A new absolute determination of the acceleration due to gravity at the National Physical Laboratory, England

1967 ◽  
Vol 261 (1120) ◽  
pp. 211-252 ◽  
Keyword(s):  
National Physical Laboratory ◽  
Atomic Unit ◽  
Time Intervals ◽  
Gravity Station ◽  
Absolute Determination ◽  
Physical Laboratory ◽  
Air Resistance ◽  
Definition Of ◽  
First Time

A new absolute determination of the acceleration due to gravity at the National Physical Laboratory has been made by timing the symmetrical free motion of a body moving under the attraction of gravity; it is the first time this method has been used. The moving body was a glass ball and it was timed at its passage across two horizontal planes by the flashes of light that it produced when it passed between two horizontal slits which served to define each plane optically, the ball focusing light from one of the slits, which was illuminated, upon the other slit which had a photomultiplier placed behind it. The separation of the two planes defined by the pairs of slits was measured interferometrically and referred directly to the international wavelength definition of the metre, while the time intervals were measured in terms of the atomic unit of time scale A l. The value of gravity as reduced to the British Fundamental Gravity Station in the N. P. L. is 981 181.75 mgal, s.d. 0.13 mgal (1 mgal = 10 -5 m/s 2 ). Systematic errors, are believed to be very small; this is particularly true of the error due to air resistance. The main contribution to the observed scatter of the results comes from microseismic disturbances. The new result is 1.4 mgal less than that obtained at the fundamental station by J. S. Clark (1939) using a reversible pendulum . It is very close to the mean of a number of recent absolute determinations by other methods, but this may not be very significant because the uncertainties of those determinations and of the comparisons between the sites at which they were made and the present site are not less than 5 times the standard deviation of the new result.

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