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Aviation History
1917
1917 - 1081.PDF
OCTOBER 18, 191 j. of the note that he hears. Thus we have three variables, namely, wave-length, amplitude and wave-form. It is obvious that when both the wave-length and the amplitude are the same, that there is still a considerable latitude remaining for the alteration of wave-form. The wave- length, as we have already seen, determines the frequency or pitch of the note heard; the amplitude determines the loudness of the note ; while the third variable wave-form determines the quality of the note. Fig. 3 shows the displacement diagrams for a note of equal wave-length and amplitude produced by three different sources— (a) being produced by the piano. (b) being produced by an open organ pipe. (c) being produced by a violin string. Now the velocity with which a wave-form travels relatively to the air when it has once been produced will be unaffected whether the source that produced it, or the observer that hears it, is stationary or moving, or whether the air in which it has been produced is stationary or moving. Suppose now that the aeroplane engine is producing a note of frequency n. Let V feet per second be the velocity with which these waves travel relatively to the air, and let the component of the velocity of the aeroplane in the direction of the observer be vs, which of course may be either positive or negative according as to whether the aeroplane is moving towards or away from the observer. At the end of xjn seconds, when the engine is about to emit its second wave the first wave must have travelled V/w ft. while the aeroplane will have travelled vsfn ft. towards the observer. Hence the first wave in the direction of the observer has a start over the second wave of (V — vs)/n ft. This, therefore, must be the length of the waves travelling in the direction of the observer. Hence, when vs is positive, that is when the aeroplane is approaching the observer, the frequency of the note heard must rise, and when vs is negative, that is when the aeroplane is receding from the observer, the frequency of the note heard must fall. Again, to consider the effect of the wind in addition, and also movement on the part of the observer. Let S and O in Fig. 4 represent the positions of the aeroplane and observer. Let SA = OB = V. After 1 second the wave from S will have reached C, but the aeroplane tneanwhile Will have travelled to D, while if the component of the velocity of the wind in the direction of motion towards the observer is v-u,, then the wave-form will move in addition from A to Cr due to the influence of the wind. Hence the w waves per second emitted must be contained in the distance CD, and from Fig. 4 CD - SC - SD. = SA + AC - SD. = V + V-u, — Vs.Next, considering the observer, we have «he waves in the length FE as the length received per second by the observer, and FE =. OE - OF. = OB + BE - OF. -= V + Vu. - Vo-The n waves emitted per second by the source are contained in the distance CD and are received in the distance FE. Then the number contained in the distance FE, will be n x _—, which by substitution equals—- -— > and this is the frequency of the note heard by the observer. This last equation is the complete mathematical expression for Doppler's Principle, and will enable us at once to state whether the pitch or frequency of the note emitted will rise or fall as heard by an observer, when we know the velocities concerned. We can at once see that if both source and observer are moving with the same velocity then the pitch is unaltered. Again, the effect of the wind is to lessen the change of pitch When blowing in the same direction as the aeroplane is travelling, and to increase the change in pitch when blowing in the opposite direction. All possible conditions can be investigated from this equation, but as the velocity of sound in air is roughly 1,100 ft. per second, or say 750 m.p.h., it would be unpractical to consider what the effect would be if vs, the velocity of the aeroplane, were greater than V, although any reader sufficiently curious can easily do so. It may be of interest to mention that Doppler's Principle, outlined above with reference to the change in the pitch of the note emitted by an approaching and receding aero- plane, has been applied by Sir William Huggins to solve the problem of ascertaining the motion of the fixed stars to and from the earth, and of our motion relatively to them in the line of sight ; a problem which had previously been declared to be insoluble for all time. CORRESPONDENCE Parachute Velocity. [1950] Being interested in the question of air resistance, I should like to offer the following comments on an article on " The determination of parachute velocity " appearing in the current issue (No 455) of " FLIGHT." There are a few errors which it is necessary to point out, viz. :— The total pressure (whereby is apparently intended the total force resisting motion) is given by ZpV*A + PA, not ~? + P as stated in the text and shown on Fig. 2.g The downward acceleration is obviously given by g - ZtV»A, not by g - Z-?V*A. rrb gThere is no increase in velocity when the resistance is equal to the weight, that is when mg = ZpV*A, so that the the maximum velocity =l;-^-JJ- The article omits m. It is necessary to attach much importance to these errors, as slips of this nature are easily made, and the careful reader will doubtless have noted them for himself. The article is based on the assumption that " for prac- tical purposes " the pressure on a curved surface is the same as the pressure on a plane surface having an area equal to the " projected " area of the curved surface. This is assum- ing that a parachute of umbrella form is no more efficient than a flat disk would be, and presumably, also, than a curved parachute falling convex side first would be, provided that the projected areas are the same in the three cases. Is this assumption really justified by practice ? If so, why does the ordinary anemometer having hemispherical cups trouble to rotate ? The article proceeds to show that the velocity of fall is given by V2 = K2 11 — e 2&x\ and states that " for practical purposes when the parachute reaches the ground its velocity is given by K." This is only true when e ~ ??* = o, i.e., When x — oe or K = o. The latter condition is ruled out as indicating that the parachute is not falling at all. Thus it is assumed that for practical purposes the parachute may be considered to have fallen so far that not only does it reach the ground with maximum velocity, but it may, without appreciable error, be taken to have fallen with- this velocity all the way. If this assumption be justified in prac- • rice, is it really necessary to use a differential equation to show that 5£ ^ ZpAJ V m zel that the velocity of a body moving with uniform velocity a distance h in time * is -? J statement immediately below Fig. 2 should appar- ently read " This formula holds only when the height from which the parachute falls is very large." The article concludes by stating that the calculated value of V should be " corrected " by adding .0002 V. It is not clear why this " correcting factor " is needed, nor how it is arrived at, but why use a correction of this order, seeing that it makes the difference between the calculated and corrected velocities merely equivalent to the difference between the velocities attained by a mass falling freely from, say, a height of ido inches and a height of 100.04 inches ? |A. E. WATSON.™ To Readers—One and'All. THE Editor of " FLIGHT " will at all times be pleased to consider original articles (illustrated or otherwise) on subjects directly or indirectly allied with aviation. All articles accepted will be paid for ; a high literary standard of writing is not essential; it is the facts Which matter. Practical explanatory articles are most acceptable. Diagrams and similar illustrations need only be rough sketches if necessary. IO8l
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