Temperature of the Air.
—If the air is allowed to become heated by compression, as is the case in practice, we have a new set of conditions. If the air in the tank A is hot,—that is, warmer than the surrounding atmosphere,—it will by radiation cool somewhat before it enters the tube, and it will be still further cooled when it expands in the tube. Again, if its temperature falls below the temperature of the ground in which the tube is laid, it will absorb heat from the ground, and this will tend to keep up its temperature; so in practice we have very complicated relations between the temperature, pressure, and volume of the air. These relations cannot be exactly expressed by mathematical formulæ, and we will make no attempt so to express them, but will be content with saying that in practice we find that the temperature of the air in the tubes is nearly constant after the first few hundred feet, so that we can without appreciable error compute the pressures and velocities as if it were constant. Now, if the air in the tank A is hot, we must raise the pressure a little above ten pounds per square inch to obtain the velocities given on our diagram. When the air cools it contracts in volume, or, if the volume cannot change, being fixed by the limits of the containing vessel, then the pressure is reduced, so by raising the pressure in the tank A a little above ten pounds, we compensate the loss of pressure.
Horse-Power.
—Having shown how the quantity of air can be computed we are now in a position to estimate the horse-power of the air-compressor necessary to operate the tube. I say estimate, because we have to take into consideration the efficiency of the air-compressor, and that is not an absolutely fixed quantity: it varies with different types of machines and with their construction. When working with pressures of less than ten pounds, the friction of the machine is an important factor. The area and construction of the valves in the air-cylinders is another very important factor. If the valves are not large enough or do not open promptly, our cylinders will not be filled with air at each stroke; this will reduce the efficiency of the machine. In practice we go to a manufacturer of air-compressors and tell him how much air must be compressed per minute, and the pressure to which it must be compressed, with other conditions, and then he tells us what size of machine we shall require and the horse-power of the machine approximately. He is supposed to know the efficiency of his own machines. We may endeavor to prove his estimate by computations of our own. To give some idea of the horse-power required to supply the air needed to operate our eight-inch tube one mile long, I will say that the steam-engines of the air-compressor will have to develop in the vicinity of one hundred and twenty-five actual horse-power. From the horse-power of the steam-engine we can easily compute the coal that will be consumed under boilers of the usual type.
Efficiency.
—It will be noted that most of the power is not used primarily in moving the carriers, but to move the air through the tube. Very nearly as much power is used to keep the air flowing in the tube when no carriers are in it as when carriers are being despatched. If we should define the efficiency of a pneumatic tube as the ratio of the power consumed in moving the carriers to the power consumed in moving the carriers and the air, we should find this so-called efficiency to be very low. It is analogous to pulling the carrier with a long rope and dragging the rope on the ground. Much more power would be consumed by the rope than by the carrier. But a business man would define the efficiency of a pneumatic tube as the ratio of the cost of transporting his letters, parcels, etc., to the cost of transporting them with equal speed in any other way. Defined in this practical manner the efficiency of a pneumatic tube is high. We do not care what becomes of the power so long as it accomplishes our purpose.
Pressure and Exhaust Systems.
—We have noticed that pneumatic tubes have not always been operated by compression of the air, but that some of the small tubes used in the telegraph service of European cities have been operated by exhausting the air. The two systems are sometimes distinguished by calling one a pressure system and the other an exhaust system. These terms are very misleading, for an exhaust system is a pressure system. The current of air is kept flowing in a tube by maintaining a difference of pressure at the two ends, and the result is the same whether we raise the pressure at one end above the atmospheric or lower it at the other below the atmospheric. In either case it is pressure that causes the air to flow. It happens that we are living in an atmosphere of about fifteen pounds pressure per square inch, and it is very convenient oftentimes in our computations to take the pressure of the atmosphere as our zero, and reckon all other pressures above and below this. If all our pressure scales read from absolute zero, the pressure of a perfect vacuum, then all this confusion would be avoided. We have not used the absolute zero in our diagram, because all our gauges are graduated with their zero at atmospheric pressure, and it is customary to speak of pressures above and below the atmospheric.
It is very natural to ask the question, why are tubes sometimes operated by compressing the air and at other times by exhausting it? We answer by saying that it is usually a question of simplicity and convenience that determines which system shall be used. Some of the cash systems in the stores use compressed air in the out-going tubes from the cashier’s desk and exhaust the air from the return tubes. Both ends of the tubes are then left open at the counters, no sending or receiving apparatus being required there. The carriers are so light, their velocity so low, and the air-pressure varies so little from the pressure of the atmosphere that the carriers can be allowed to drop out of the tubes on to the counters, and they can be despatched by simply placing them at the open end of the tube into which the air is flowing. The currents of air entering and leaving the tubes are not so strong as to cause any special annoyance. At the cashier’s desk some simple receiving and sending apparatus has to be used, but it is better to concentrate all of the apparatus at one point rather than have it distributed about the store, as would be the case if the double system were not used. In the London pneumatic telegraph both methods of operation have been in use. Double lines were laid, and the engines exhausted the air from one tube and forced it into the other. The exhausted tube was therefore used to despatch in one direction, while the other tube, operated by the compressed air, served for despatching in the opposite direction. So far as I know, both work equally well.