Frederick William Lanchester

“ Dines says:—“It had been assumed in the above that the wind pressure varies as the square of the velocity. The experiments have proved this to be the case, for when upon a calm day equilibrium for any plate is once attained, it has been found impossible to disturb it by any alteration of the velocity of rotation, and since the centrifugal force varies as the square of the velocity the wind pressure must do so also. For the smaller planes the maximum velocity of which the machine is capable is about seventy miles per hour.” ”

“ The weights of different planes employed for any given series of experiments are all brought up to the same amount by gumming lead-foil in the region of the centre of gravity, the only difference between the different planes of a series being the position of the centre of gravity, and therefore the position of the centre of pressure, and consequently the angle of equilibrium. ”

“ It may be stated at once that no such provision is necessary, and that a properly designed rigid structure is capable of maintaining its own equilibrium, and possesses complete stability within prearranged limits; and further, that such a rigid structure (or aerodone) may be designed to automatically simulate many of the apparently life-like movements of birds in flight or at will glide steadily at its natural velocity at a constant angle of flight path. ”

“ The condition of equilibrium is that the resultant of the two forces passes through the pivot centre E. It is evident that these two forces, in equilibrium at any one speed, will be in equilibrium for all speeds, for their relative direction undergoes no change, and they are each proportional to the velocity squared and so are proportional to one another. The bob weight D is made adjustable on the arm D and the condition of equilibrium is ascertained by trial. ”

“ The Method of the Ballasted Aeroplane.—The method of the ballasted aeroplane not only permits of the determination of the coefficient of skin-friction but simultaneously provides data from which the constant and the relation between the angle and centre of pressure of the aeroplane may be calculated.
The following examples will serve for the purposes of illustration. A standard form of aeroplane has been employed throughout (Fig. 109) , measuring 8 in. by 2 in., and ballasted by a lead shot presenting a resistance taken as equivalent to .025 sq. in. of normal plane. ”

“ A co-ordinate combination of tension springs is employed to hold the beam radial to the whirling table, and the whole is accurately counterpoised so that the plane is virtually weightless; thus, so long as the apparatus is at rest the pencil point is central or at the co-ordinate zero, but when the whirling table is in motion the total reaction on the plane is measured, both as to direction and magnitude, by the resulting displacement of the pencil point. ”

“ Experiment apart, there is a primâ facie case for the existence of a coefficient skin-friction of some considerable magnitude in the fact that the similar coefficient, as determined by Froude and others, is, in the case of water, a matter of one per cent, or thereabouts, and in the fact that the kinematic viscosity of air is fourteen times as great as that of water. ”

“ The aerodynamic balance, Fig. 153, consists of a horizontal arm or beam pivoted about a vertical axis the amplitude of motion permitted being regulated by the screws which also form electrical contacts.
For the determination of a normal plane is attached to one end of the beam and a friction plane to the other, the areas of the two being adjusted until they exactly balance. The instrument is used either by being exposed to the wind and held stationary, or fitted in front of an automobile vehicle in still air. ”

“ For small angles it is highly probable that Dines' results are not accurate, but when once the motion is frankly discontinuous it is difficult to believe that the form of the back of the planes employed can account for so marked a departure of the curve as that observed. It is therefore most probable that the “kick up” is a real feature in the pressure-velocity curve that has escaped the notice of other experimenters.
Dines concludes from his experiments that the effect of skin friction is negligible ”

“ In the absence of any mechanical launching device, it is quite easy to obtain faulty data if any but straight uniform glides are recorded, and if such data are utilised it is as likely as not the values of the constants deduced will be wide of the mark, even negative values being sometimes obtained. The method is one of which the advantages have only very recently impressed themselves on the author, and time and opportunity have been at present lacking to carry out more than a few rough preliminary experiments. ”

“ It may be said that, notwithstanding the great difference between the character of the media, one being a light and very compressible, and the other a heavy and very incompressible, fluid, these observations have indicated that there is a very considerable analogy between the best form of aerial and of marine propeller. ”

“ Fig. 149 is also a plotting (Fig. 11 of the Memoir) , showing the direct determination of the horizontal component. The small circles represent the actual observations, and the crosses give points calculated on the basis of a simple resolution of forces, assuming the reaction exactly at right angles to the surfaces of the plane—that is to say, neglecting skin-friction. The curve drawn is a so-called corrected curve, the basis of the correction being given in the Memoir, and which we will now proceed to examine. ”

“ Langley's Experiments. Method.—The method of experiment adopted by the late Professor Langley resembles that of Mr. Dines in the employment of a whirling table driven by power, and in the use of independent measuring appliances to determine the resistances or reactions on the body subject to investigation. ”

“ Author's Experiments. Method (continued) .—In addition to the free flight experiments enumerated above, an attempt has been made to effect the direct measurement of by means of a new instrument, which may be appropriately termed an aerodynamic balance. [6]
The magnitude of as determined by the method of free flight suggested that, in spite of the failure of previous experimenters, it should be quite possible to effect a direct measurement of this quantity by the aid of a suitably designed appliance. ”

“ Any and all of the methods described should be capable of giving results of a reasonable degree of accuracy—far more so than at present achieved—and the results so obtained should be in closer accord, one with another, than the author has so far been able to demonstrate. ”

“ Generally speaking, the flight measurements showed greater variation than in the example given; the day of these experiments was exceptionally calm, and the aerodone used (No. 1) made a long series of good straight glides without mishap; a performance which it is not always easy to obtain. Flights of circular or otherwise curved path need to be rejected. ”

“ The method of employment is described as follows: “The wind plane is set at an angle of elevation a disc of paper is placed upon the recording board and oriented so that a line drawn through its centre to serve as a reference line is exactly vertical. The whirling table is then set in motion, and when a uniform velocity has been attained a current is passed through
Fig. ”

“ This is probably due to the fact that this problem forms the basis of prop, xxxiv., Book II., of the “Principia” as touching the Newtonian Medium. It was evidently the aim of the early workers to ascertain the extent to which Newton's results would prove applicable to a real fluid. ”

“ It would appear from the data given that the propeller employed, having a diameter of 30 inches, had an effective pitch of 1 foot approximately, that is to say, its radius was 1 times the pitch.
Referring to our efficiency diagram (Fig. 127) , we see that this denotes the employment of rather more than the whole of the diagram given, so that the efficiency will vary over the length of the blade from 70.4 per cent, to about 40 per cent.; if we take the mean as a rough approximation of the efficiency value to be expected, we have 55 per cent. ”

“ Model No. 2. Series E. (Fig. 156) .—Trials with this model gave the result about .03. This value is probably too high. The weather was unfavourable, and the weight of the model (1.66 grams) proved too great for the method of construction; frequent repairs had to be made in the course of a single series of experiments.
Model No. 3. Series E. (Fig. 152) , Construction.— Aeroplane and fins, varnished cedar. Tail planes, mica plates. Body, cedar, ballasted with lead.
Weight = 46.3 grams = .102 lbs.
Area—
Angle of aeroplane
Preliminary Trial, Aerodone launched by hand, 13 ft. 6 in. altitude. ”

“ The results were drawn from observation; sample diagrams for a square plane at 45 degrees are given, for front and rear aspect, in Fig. 144. It is evident that we have strong evidence here of the centrifugal shedding of the “dead-water,” the influence of which has already been the subject of comment in connection with the theory of the screw propeller.
The quantitative results of Mr. Dines' pressure reaction experiments have been given in most part in Chap. ”