Velocity ratio

“ This definition of velocity enables us to understand why velocity except in reference to matter is meaningless, whereas acceleration and rotation have a meaning. The philosophical argument, that velocity through space is meaningless, ceases to apply as soon as we admit any kind of structure or aether in empty regions; consequently the problem is by no means so simple as is often supposed. But our definition of velocity is dynamical, not kinematical. Velocity is the ratio of certain components of , and only exists when is not zero. ”

“ Whence since the weight of a globe of water, in the time in which the globe with a velocity uniformly continued describes a length of 30,556 inches, will generate all that velocity in the falling globe; it is manifest that the force of resistance uniformly continued in the same time will take away a velocity, which will be less than the other in the ratio of 1 to 3761/50, that is, the 1/3761/50 part of the whole velocity. ”

“ If a body is resisted in the duplicate ratio of its velocity, and moves by its innate force only through a similar medium; and the times be taken in a geometrical progression, proceeding from less to greater terms: I say that the velocities at the beginning of each of the times are in the same geometrical progression inversely; and that the spaces are equal, which are described in each of the times.
For since the resistance of the medium is proportional to the square of the velocity, and the decrement of the velocity is proportional to the resistance ”

“ Sir Hiram Maxim found, however, as the result of his experiments that the thrust with a propeller travelling through the air at a velocity of 40 miles an hour was the same as when stationary, the r.p.m. remaining constant throughout. The explanation is that when travelling the propeller is continually advancing on to "undisturbed" air, the "slip" velocity is reduced, but the undisturbed air is equivalent to acting upon a greater mass of air.
§ 8. Pitch Coefficient or Pitch Ratio.—If we divide the pitch of a screw by its diameter we obtain what is known as pitch coefficient or ratio. ”

“ The expression becomes more simple when the velocity is expressed with reference to the energy involved. If we set the probability that lies between any given limits is expressed by Here is the ratio of the component velocity to that which would give the energy ; in other words, is the quotient of the energy due to the component velocity divided by . The distribution with respect to the partial energies due to the component velocities is therefore the same for all the component velocities. ”

“ Now in the attaining of a peripheral velocity of nearly 100 m. per second, this being the necessary velocity for a sure appreciation of a displacement in the fringes, two principal mechanical difficulties are found: the enormous centrifugal force, and the very great resistance of air. To diminish the first, it is convenient to enlarge as much as possible the diameter of the trajectory and lessen the number per second of the revolutions. It is known that the centrifugal velocity increases as the square of that number, and the velocity of displacement grows as the first power. ”

“ The slowness with which powders subside, depends partly on the specific gravity of the substance, and partly on the magnitude of the particles themselves. Bodies, in falling through a resisting medium, after a certain time acquire a uniform velocity, which is called their terminal velocity, with which they continue to descend: when the particles are very small, and the medium dense, as water, this terminal velocity is soon arrived at. ”

“ The velocity necessary to just sustain the load at a given angle of inclination is called the critical or soaring velocity. For a given machine, there is an angle of inclination (about half a right angle) at which the minimum speed is necessary. This speed is called the “least soaring velocity.” If the velocity is now increased, the angle of inclination may be reduced and the planes will soar through the air almost edgewise, apparently with diminished resistance and power consumption. ”

“ There are, of course, an infinite number of different movements possible, for there is every degree of velocity and difference of direction to be considered. On the other hand there is only one type of rest, or absolute quiescence, and it would be just as likely that a body should possess any stated velocity, say ten miles, ten yards, and three quarters of an inch per second, as that it should possess that particular characteristic implied in the absence of all movement whatsoever. ”

“ To take the velocity into account, we must take into consideration the number of revolutions made in a given time by the driver. Suppose, for example, that the driver being 3 inches in diameter makes one revolution in a minute, then it will move in that minute a length of belt equal to its circumference, so that the circumference of the driver, multiplied by the number of its revolutions per minute, gives its velocity per minute. Thus, if a pulley has a circumference of 50 inches, and makes 120 revolutions per minute, then its velocity will be 6,000 inches per minute, because 50 × 120 = 6,000. ”

“ A physical conception of velocity potential under these circumstances is somewhat difficult, but if we revert to the dynamical hypothesis and regard the velocity potential system as the pressure system by which the motion is generated, we encounter at once the same difficulty in another form. Before we are able to interfere either to start or to stop the fluid in cyclic motion, we must introduce some imaginary barrier in its path. ”

“ We may in the first place construct a concrete standard for velocity, as, for example, by stretching a string between two pegs on a board with a fixed weight. If we strike the string, a disturbance travels along the string which we can follow with the eye, and we define unit velocity as the velocity of this disturbance. An object has greater than unit velocity if it outruns the disturbance, and less if it lags behind. ”

“ The uncorrected velocities, however, are in all cases too large, and by greater and greater amounts the higher the velocity. At 60 miles per hour the observed velocities are about 12 miles per hour too high, and for an indicated velocity of 90 miles the experiments show that the actual velocity is but a fraction over 69 miles per hour. ”

“ The kinetic energy in the field of flow round a body in motion is imparted to the fluid when the body is started from rest, and is given up when the motion is arrested. The effect of the fluid motion is thus to add to the apparent inertia of the body, so that a given force requires to act through a greater distance to impart a given velocity than for the same body in vacuo. Not only has a force to act for a greater distance, but also for a longer time, which means that the body possesses in effect a greater store of momentum for a given velocity. ”

“ The standard from which all computations are made of the distances passed through in given times by bodies whose motion is uniformly accelerated, and from which the velocity acquired is computed when the accelerating force is known, and the force is found when the velocity acquired or the rate of acceleration is known, is the velocity of a body falling to the earth. It has been established by experiment, that in this latitude near the level of the sea, a falling body in one second falls through a distance of 16.083 feet, and acquires a velocity of 32.166 feet per second ”

“ It is not permissible to say that no velocity can exceed 299,796 kilometres per second. For example, imagine a search-light capable of sending an accurately parallel beam as far as Neptune. If the search-light is made to revolve once a minute, Neptune’s end of the beam will move round a circle with velocity far greater than the above limit. ”

“ In reality, however, such increase of momentum is only apparent; the momentum of the body and fluid system combined is actually less than that of the body at the same velocity in vacuo by the amount due to its fluid displacement. That is to say, if the body be of the same specific gravity as the fluid the total dynamic system possesses no momentum at all, whatever the velocity. ”

“ For when, of two such units, one moving at velocity 4 strikes another at rest, the striking unit must have its velocity 4 instantaneously reduced to velocity 2; must pass from velocity 4 to velocity 2 without any lapse of time, and without passing through intermediate velocities; must be moving with velocities 4 and 2 at the same instant, which is impossible. ”

“ We see at once that, where u=0, the velocity has its “normal” value, while where u is positive the velocity is in excess, and where u is negative the velocity is in defect of the normal value. If, then, a (fig. 10) represents the displacement curve of a train of waves, b will represent the pressure excess and particle velocity, and from (11) we see that while the nodal conditions of b, with ῶ=0 and u=0, travel with velocity √ (E/ρ) , the crests exceed that velocity by 1/4 (γ + 1) u. ”

“ Thus, if the curve be plotted for a one foot diameter circular plane and one foot per second velocity is represented by one inch, then for a two foot circular plane a one foot per second velocity will be represented by two inches, that is to say, a given pressure will be developed at one-half the velocity. ”

“ In a moment, Leonard; then I want you and Jim to ask me any questions you like. All this that I have said, is prefatory. The question is one solely of velocity. The rest is automatic. The natural laws governing the attributes of matter in relation to its velocity are these:
“First: A substance whose velocity is increased loses density proportionately. For instance, our vehicle, I consider it as a whole, you understand. ”

“ Why does the velocity of its "violent" motion decrease as it rises, while that of its "natural" fall increases as it descends. If we mark closely the relation between these two facts, the problem will solve itself. We shall see, as Galileo did, that the decrease of velocity in rising and the increase of velocity in falling are one and the same phenomenon, viz., an increase of velocity towards the earth. Accordingly, it is not a place that is assigned to the body, but an increase of velocity towards the earth. ”

“ But in reference to an observer [Pg 135] in a balloon, or who passes in another train, the velocity has not the same value, and it may cease to be a uniform velocity. We know only relative movements, or, to be quite accurate, movements relative to some material object or other. According to our choice of this object, this standard of comparison, the same velocity may be uniform or accelerated. In the long run, it is clear, we should have to have recourse to Newton’s hypothesis of absolute space to be able to say whether a given velocity is really uniform or accelerated. ”

“ Now we want to investigate whether this definition is not in sharp contrast to the ordinary illustration of velocities. The distances proportional to the relevant velocities are used in ordinary mechanics as representing the velocities of uniform motions. Formula (2) leads to the same result at the limits of our ordinary experience. Only at velocities nearly comparable to the velocity of light, a notable difference occurs that quickly leads to infinite distortion. ”

“ When estimated straight across from surface to surface, that is, in the direction of the liveliest change of pressure, it is the maximum pressure gradient. Along this normal direction the air tends to flow with an acceleration proportional to the gradient. The velocity thus acquired by any portion of air in being pushed along the line of falling pressure, combined with its velocity due to other causes, gives its true velocity. ”

“ Hot Rod's pull on a taut cable would be to the south.
No. Lab One could be re-oriented to trail the thrusting balloon. But the lab's servos should have prevented that re-orientation unless the thrust were really heavy.
"What is our velocity?" he asked. Temporarily he was baffled by the placid Cow's literal translation of his request as one for any actual velocity, since she had replied with a figure very close to their original orbital speed. "What is our velocity at right angles to original course?" ”