The thrust of the propeller depends on the power of the motor, and on the diameter and pitch of the propeller. If the required thrust to a certain machine is known, the calculation for the horse-power of the motor should be an easy matter.
The required thrust is the sum of three different “resistances.” The first is the “drift” (dynamical head resistance of the aerofoils), i.e., tan α × lift (L), lift being equal to the total weight of machine (W) for horizontal flight and α equal to the angle of incidence. Certainly we must take the tan α at the maximum Ky value for minimum speed, as then the drift is the greatest (Fig. 1, A).
Another method for finding the drift is D = K × AV2, when we take the drift again so as to be greatest.
The second “resistance” is the total head resistance of the machine, at its maximum velocity. And the third is the thrust for climbing. The horse-power for climbing can be found out in two different ways. I first propose to deal with the method, where we find out the actual horse-power wanted for a certain climbing speed to our machine, where
| H.P. = | climbing speed/sec. × W |
| 550 |
In this case we know already the horse-power for climbing, and we can proceed with our calculation.
With the other method we shall find out the “thrust” in pounds or kilograms wanted for climbing and add it to drift and total head resistance, and we shall have the total “thrust” of our machine and we shall denote it with T, while thrust for climbing shall be Tc.
The following calculation is at our service to find out this thrust for climbing
| Vc × W | = H.P., |
| 550 |
thence
| Vc = | H.P. × 550 | (1) |
| W |
| H.P. = | Tc × V | , |
| 550 |
then from (1)
|
Tc × V | |||||
| Vc = | = | , | ||||
| W | W |
thence,
| Tc = | Vc × W | . |
| V |
Whether T means drifts, head resistance and thrust for climbing, or drift and head resistance only, the following calculation is the same, only in the latter case, of course, we must add the horse-power required for climbing to the result to obtain the total horse-power.
Now, when we know the total thrust, we shall find the horse-power in the following manner:
We know that the
| H.P. = | P r 2π R |
| 75 × 60 |
in kilograms, or in English measure,
| H.P. = | P r 2π R | (Fig. 1, B) |
| 33,000 |
where
| P | = | pressure in klgs. or lbs. |
| r | = | radius on which P is acting. |
| R | = | Revolution/min. |
When P × r = M, then
| H.P. = | M.R.2π | , |
| 4,500 |
thence,
| M = | H.P. × 4,500 | = | 716.2 H.P. | in meter kilograms, |
| R2π | R |
or in English system
| M = | H.P. 33,000 | = | 5253.1 H.P. | in foot pounds. |
| R2π | R |
Now the power on the circumference of the propeller will be reduced by its radius, so it will be M/r = p. A part of p will be used for counteracting the air and bearing friction, so that the total power on the circumference of the propeller will be (M/r) × η = p where η is the mechanical efficiency of the propeller. Now η/tan α = T, where α is taken on the tip of the propeller.
I take α at the tip, but it can be taken, of course, at any point, but then in equation p = M/r, r must be taken only up to this point, and not the whole radius; but it is more comfortable to take it at the tip, as tan α = Pitch/r2π (Fig. 1, C).
Now we can write up the equation of the thrust:
| T = | 716.2 H.P. η | , or in English measure | 5253.1 H.P. η | , |
| R r tan α | R r tan α |
thence
| H.P. = | T × R × r tan α | , or in English measure | T × R × r tan α | . |
| 716.2 η | 5253.1 η |
The computations and formulæ given are of most value to the student engineer rather than matters of general interest, but are given so that a general idea may be secured of how airplane design influences power needed to secure sustained flight. It will be apparent that the resistance of an airplane depends upon numerous considerations of design which require considerable research in aerodynamics to determine accurately. It is obvious that the more resistance there is, the more power needed to fly at a given speed. Light monoplanes have been flown with as little as 15 horse-power for short distances, but most planes now built use engines of 100 horse-power or more. Giant airplanes have been constructed having 2,000 horse-power distributed in four power units. The amount of power provided for an airplane of given design varies widely as many conditions govern this, but it will range from approximately one horse-power to each 8 pounds weight in the case of very light, fast machines to one horse-power to 15 or 18 pounds of the total weight in the case of medium speed machines. The development in airplane and power plant design is so rapid, however, that the figures given can be considered only in the light of general averages rather than being typical of current practice.
WHY EXPLOSIVE MOTORS ARE BEST
Internal combustion engines are best for airplanes and all types of aircraft for the same reasons that they are universally used as a source of power for automobiles. The gasoline engine is the lightest known form of prime mover and a more efficient one than a steam engine, especially in the small powers used for airplane propulsion. It has been stated that by very careful designing a steam plant an engine could be made that would be practical for airplane propulsion, but even with the latest development it is doubtful if steam power can be utilized in aircraft to as good advantage as modern gasoline-engines are. While the steam-engine is considered very much simpler than a gas-motor, the latter is much more easily mastered by the non-technical aviator and certainly requires less attention. A weight of 10 pounds per horse-power is possible in a condensing steam plant but this figure is nearly double or triple what is easily secured with a gas-motor which may weigh but 5 pounds per horse-power in the water cooled forms and but 2 or 3 pounds in the air-cooled types. The fuel consumption is twice as great in a steam-power plant (owing to heat losses) as would be the case in a gasoline engine of equal power and much less weight.
The internal-combustion engine has come seemingly like an avalanche of a decade; but it has come to stay, to take its well-deserved position among the powers for aiding labor. Its ready adaptation to road, aerial and marine service has made it a wonder of the age in the development of speed not before dreamed of as a possibility; yet in so short a time, its power for speed has taken rank on the common road against the locomotive on the rail with its century’s progress. It has made aerial navigation possible and practical, it furnishes power for all marine craft from the light canoe to the transatlantic liner. It operates the machine tools of the mechanic, tills the soil for the farmer and provides healthful recreation for thousands by furnishing an economical means of transport by land and sea. It has been a universal mechanical education for the masses, and in its present forms represents the great refinement and development made possible by the concentration of the world’s master minds on the problems incidental to internal combustion engineering.
HISTORICAL
Although the ideal principle of explosive power was conceived some two hundred years ago, at which time experiments were made with gunpowder as the explosive element, it was not until the last years of the eighteenth century that the idea took a patentable shape, and not until about 1826 (Brown’s gas-vacuum engine) that a further progress was made in England by condensing the products of combustion by a jet of water, thus creating a partial vacuum.
Brown’s was probably the first explosive engine that did real work. It was clumsy and unwieldy and was soon relegated to its place among the failures of previous experiments. No approach to active explosive effect in a cylinder was reached in practice, although many ingenious designs were described, until about 1838 and the following years. Barnett’s engine in England was the first attempt to compress the charge before exploding. From this time on to about 1860 many patents were issued in Europe and a few in the United States for gas-engines, but the progress was slow, and its practical introduction for power came with spasmodic effect and low efficiency. From 1860 on, practical improvement seems to have been made, and the Lenoir motor was produced in France and brought to the United States. It failed to meet expectations, and was soon followed by further improvements in the Hugon motor in France (1862), followed by Beau de Rocha’s four-cycle idea, which has been slowly developed through a long series of experimental trials by different inventors. In the hands of Otto and Langdon a further progress was made, and numerous patents were issued in England, France, and Germany, and followed up by an increasing interest in the United States, with a few patents.
From 1870 improvements seem to have advanced at a steady rate, and largely in the valve-gear and precision of governing for variable load. The early idea of the necessity of slow combustion was a great drawback in the advancement of efficiency, and the suggestion of de Rocha in 1862 did not take root as a prophetic truth until many failures and years of experience had taught the fundamental axiom that rapidity of action in both combustion and expansion was the basis of success in explosive motors.
With this truth and the demand for small and safe prime movers, the manufacture of gas-engines increased in Europe and America at a more rapid rate, and improvements in perfecting the details of this cheap and efficient prime mover have finally raised it to the dignity of a standard motor and a dangerous rival of the steam-engine for small and intermediate powers, with a prospect of largely increasing its individual units to many hundred, if not to the thousand horse-power in a single cylinder. The unit size in a single cylinder has now reached to about 700 horse-power and by combining cylinders in the same machine, powers of from 1,500 to 2,000 horse-power are now available for large power-plants.
MAIN TYPES OF INTERNAL-COMBUSTION ENGINES
This form of prime mover has been built in so many different types, all of which have operated with some degree of success that the diversity in form will not be generally appreciated unless some attempt is made to classify the various designs that have received practical application. Obviously the same type of engine is not universally applicable, because each class of work has individual peculiarities which can best be met by an engine designed with the peculiar conditions present in view. The following tabular synopsis will enable the reader to judge the extent of the development of what is now the most popular prime mover for all purposes.
CLASSIFICATION BY CYLINDER ARRANGEMENT
Fig. 2.—Plate Showing Heavy, Slow Speed Internal Combustion Engines Used Only for Stationary Power in Large Installations Giving Weight to Horse-Power Ratio.
Fig. 3.—Various Forms of Internal Combustion Engines Showing Decrease in Weight to Horse-Power Ratio with Augmenting Speed of Rotation.
Fig. 4.—Internal Combustion Engine Types of Extremely Fine Construction and Refined Design, Showing Great Power Outputs for Very Small Weight, a Feature Very Much Desired in Airplane Power Plants.
Of all the types enumerated above engines having less than eight cylinders are the most popular in everything but aircraft work. The four-cylinder vertical is without doubt the most widely used of all types owing to the large number employed as automobile power plants. Stationary engines in small and medium powers are invariably of the single or double form. Three-cylinder engines are seldom used at the present time, except in marine work and in some stationary forms. Eight- and twelve-cylinder motors have received but limited application and practically always in automobiles, racing motor boats or in aircraft. The only example of a fourteen-cylinder motor to be used to any extent is incorporated in aeroplane construction. This is also true of the sixteen- and eighteen-cylinder forms and of twenty-four-cylinder engines now in process of development.
The duty an engine is designed for determines the weight per horse-power. High powered engines intended for steady service are always of the slow speed type and consequently are of very massive construction. Various forms of heavy duty type stationary engines are shown at Fig. 2. Some of these engines may weigh as much as 600 pounds per horse-power. A further study is possible by consulting data given on Figs. 3 and 4. As the crank-shaft speed increases and cylinders are multiplied the engines become lighter. While the big stationary power plants may run for years without attention, airplane engines require rebuilding after about 60 to 80 hours air service for the fixed cylinder types and 40 hours or less for the rotary cylinder air-cooled forms. There is evidently a decrease in durability and reliability as the weight is lessened. These illustrations also permit of obtaining a good idea of the variety of forms internal combustion engines are made in.
CHAPTER II
Operating Principles of Two- and Four-Stroke Engines—Four-cycle Action—Two-cycle Action—Comparing Two- and Four-cycle Types—Theory of Gas and Gasoline Engine—Early Gas-Engine Forms—Isothermal Law—Adiabatic Law—Temperature Computations—Heat and Its Work—Conversion of Heat to Power—Requisites for Best Power Effect.
OPERATING PRINCIPLES OF TWO- AND FOUR-STROKE CYCLE ENGINES
Before discussing the construction of the various forms of internal combustion engines it may be well to describe the operating cycle of the types most generally used. The two-cycle engine is the simplest because there are no valves in connection with the cylinder, as the gas is introduced into that member and expelled from it through ports cored into the cylinder walls. These are covered by the piston at a certain portion of its travel and uncovered at other parts of its stroke. In the four-cycle engine the explosive gas is admitted to the cylinder through a port at the head end closed by a valve, while the exhaust gas is expelled through another port controlled in a similar manner. These valves are operated by mechanism distinct from the piston.
The action of the four-cycle type may be easily understood if one refers to illustrations at Figs. 5 and 6. It is called the “four-stroke engine” because the piston must make four strokes in the cylinder for each explosion or power impulse obtained. The principle of the gas-engine of the internal combustion type is similar to that of a gun, i.e., power is obtained by the rapid combustion of some explosive or other quick burning substance. The bullet is driven out of the gun barrel by the pressure of the gas evolved when the charge of powder is ignited. The piston or movable element of the gas-engine is driven from the closed or head end to the crank end of the cylinder by a similar expansion of gases resulting from combustion. The first operation in firing a gun or securing an explosion in the cylinder of the gas-engine is to fill the combustion space with combustible material. This is done by a down stroke of the piston during which time the inlet valve opens to admit the gaseous charge to the cylinder interior. This operation is shown at Fig. 5, A. The second operation is to compress this gas which is done by an upward stroke of the piston as shown at Fig. 5, B. When the top of the compression stroke is reached, the gas is ignited and the piston is driven down toward the open end of the cylinder, as indicated at Fig. 6, C. The fourth operation or exhaust stroke is performed by the return upward movement of the piston as shown at Fig. 6, D during which time the exhaust valve is opened to permit the burnt gases to leave the cylinder. As soon as the piston reaches the top of its exhaust stroke, the energy stored in the fly-wheel rim during the power stroke causes that member to continue revolving and as the piston again travels on its down stroke the inlet valve opens and admits a charge of fresh gas and the cycle of operations is repeated.
Fig. 7.—Sectional View of L Head Gasoline Engine Cylinder Showing Piston Movements During Four-Stroke Cycle.
The illustrations at Fig. 7 show how the various cycle functions take place in an L head type water cooled cylinder engine. The sections at A and C are taken through the inlet valve, those at B and D are taken through the exhaust valve.
The two-cycle engine works on a different principle, as while only the combustion chamber end of the piston is employed to do useful work in the four-cycle engine, both upper and lower portions are called upon to perform the functions necessary to two-cycle engine operation. Instead of the gas being admitted into the cylinder as is the case with the four-stroke engine, it is first drawn into the engine base where it receives a preliminary compression prior to its transfer to the working end of the cylinder. The views at Fig. 8 should indicate clearly the operation of the two-port two-cycle engine. At A the piston is seen reaching the top of its stroke and the gas above the piston is being compressed ready for ignition, while the suction in the engine base causes the automatic valve to open and admits mixture from the carburetor to the crank case. When the piston reaches the top of its stroke, the compressed gas is ignited and the piston is driven down on the power stroke, compressing the gas in the engine base.
When the top of the piston uncovers the exhaust port the flaming gas escapes because of its pressure. A downward movement of the piston uncovers the inlet port opposite the exhaust and permits the fresh gas to bypass through the transfer passage from the engine base to the cylinder. The conditions with the intake and exhaust port fully opened are clearly shown at Fig. 8, C. The deflector plate on the top of the piston directs the entering fresh gas to the top of the cylinder and prevents the main portion of the gas stream from flowing out through the open exhaust port. On the next upstroke of the piston the gas in the cylinder is compressed and the inlet valve opened, as shown at A to permit a fresh charge to enter the engine base.
The operating principle of the three-port, two-cycle engine is practically the same as that previously described with the exception that the gas is admitted to the crank-case through a third port in the cylinder wall, which is uncovered by the piston when that member reaches the end of its upstroke. The action of the three-port form can be readily ascertained by studying the diagrams given at Fig. 9. Combination two- and three-port engines have been evolved and other modifications made to improve the action.
THE TWO-CYCLE AND FOUR-CYCLE TYPES
In the earlier years of explosive-motor progress was evolved the two types of motors in regard to the cycles of their operation. The early attempts to perfect the two-cycle principle were for many years held in abeyance from the pressure of interests in the four-cycle type, until its simplicity and power possibilities were demonstrated by Mr. Dugald Clerk in England, who gave the principles of the two-cycle motor a broad bearing leading to immediate improvements in design, which has made further progress in the United States, until at the present time it has an equal standard value as a motor-power in some applications as its ancient rival the four-cycle or Otto type, as demonstrated by Beau de Rocha in 1862.
Thermodynamically, the methods of the two types are equal as far as combustion is concerned, and compression may favor in a small degree the four-cycle type as well as the purity of the charge. The cylinder volume of the two-cycle motor is much smaller per unit of power, and the enveloping cylinder surface is therefore greater per unit of volume. Hence more heat is carried off by the jacket water during compression, and the higher compression available from this tends to increase the economy during compression which is lost during expansion.
From the above considerations it may be safely stated that a lower temperature and higher pressure of charge at the beginning of compression is obtained in the two-cycle motor, greater weight of charge and greater specific power of higher compression resulting in higher thermal efficiency. The smaller cylinder for the same power of the two-cycle motor gives less friction surface per impulse than of the other type; although the crank-chamber pressure may, in a measure, balance the friction of the four-cycle type. Probably the strongest points in favor of the two-cycle type are the lighter fly-wheel and the absence of valves and valve gear, making this type the most simple in construction and the lightest in weight for its developed power. Yet, for the larger power units, the four-cycle type will no doubt always maintain the standard for efficiency and durability of action.
The distribution of the charge and its degree of mixture with the remains of the previous explosion in the clearance space, has been a matter of discussion for both types of explosive motors, with doubtful results. In Fig. 10, A we illustrate what theory suggests as to the distribution of the fresh charge in a two-cycle motor, and in Fig. 10, B what is the probable distribution of the mixture when the piston starts on its compressive stroke. The arrows show the probable direction of flow of the fresh charge and burnt gases at the crucial moment.
In Fig. 10, C is shown the complete out-sweep of the products of combustion for the full extent of the piston stroke of a four-cycle motor, leaving only the volume of the clearance to mix with the new charge and at D the manner by which the new charge sweeps by the ignition device, keeping it cool and avoiding possibilities of pre-ignition by undue heating of the terminals of the sparking device. Thus, by enveloping the sparking device with the pure mixture, ignition spreads through the charge with its greatest possible velocity, a most desirable condition in high-speed motors with side-valve chambers and igniters within the valve chamber.
THEORY OF THE GAS AND GASOLINE ENGINE
The laws controlling the elements that create a power by their expansion by heat due to combustion, when properly understood, become a matter of computation in regard to their value as an agent for generating power in the various kinds of explosive engines. The method of heating the elements of power in explosive engines greatly widens the limits of temperature as available in other types of heat-engines. It disposes of many of the practical troubles of hot-air, and even of steam-engines, in the simplicity and directness of application of the elements of power. In the explosive engine the difficulty of conveying heat for producing expansive effect by convection is displaced by the generation of the required heat within the expansive element and at the instant of its useful work. The low conductivity of heat to and from air has been the great obstacle in the practical development of the hot-air engine; while, on the contrary, it has become the source of economy and practicability in the development of the internal-combustion engine.
The action of air, gas, and the vapors of gasoline and petroleum oil, whether singly or mixed, is affected by changes of temperature practically in nearly the same ratio; but when the elements that produce combustion are interchanged in confined spaces, there is a marked difference of effect. The oxygen of the air, the hydrogen and carbon of a gas, or vapor of gasoline or petroleum oil are the elements that by combustion produce heat to expand the nitrogen of the air and the watery vapor produced by the union of the oxygen in the air and the hydrogen in the gas, as well as also the monoxide and carbonic-acid gas that may be formed by the union of the carbon of gas or vapor with part of the oxygen of the air. The various mixtures as between air and gas, or air and vapor, with the proportion of the products of combustion left in the cylinder from a previous combustion, form the elements to be considered in estimating the amount of pressure that may be obtained by their combustion and expansive force.
EARLY GAS ENGINE FORMS
The working process of the explosive motor may be divided into three principal types: 1. Motors with charges igniting at constant volume without compression, such as the Lenoir, Hugon, and other similar types now abandoned as wasteful in fuel and effect. 2. Motors with charges igniting at constant pressure with compression, in which a receiver is charged by a pump and the gases burned while being admitted to the motor cylinder, such as types of the Simon and Brayton engine. 3. Motors with charges igniting at constant volume with variable compression, such as the later two- and four-cycle motors with compression of the indrawn charge; limited in the two-cycle type and variable in the four-cycle type with the ratios of the clearance space in the cylinder. This principle produces the explosive motor of greatest efficiency.
The phenomena of the brilliant light and its accompanying heat at the moment of explosion have been witnessed in the experiments of Dugald Clerk in England, the illumination lasting throughout the stroke; but in regard to time in a four-cycle engine, the incandescent state exists only one-quarter of the running time. Thus the time interval, together with the non-conductibility of the gases, makes the phenomena of a high-temperature combustion within the comparatively cool walls of a cylinder a practical possibility.
THE ISOTHERMAL LAW
The natural laws, long since promulgated by Boyle, Gay Lussac, and others, on the subject of the expansion and compression of gases by force and by heat, and their variable pressures and temperatures when confined, are conceded to be practically true and applicable to all gases, whether single, mixed, or combined.
The law formulated by Boyle only relates to the compression and expansion of gases without a change of temperature, and is stated in these words:
If the temperature of a gas be kept constant, its pressure or elastic force will vary inversely as the volume it occupies.
It is expressed in the formula P × V = C, or pressure × volume = constant. Hence, C/P = V and C/V = P.
Thus the curve formed by increments of pressure during the expansion or compression of a given volume of gas without change of temperature is designated as the isothermal curve in which the volume multiplied by the pressure is a constant value in expansion, and inversely the pressure divided by the volume is a constant value in compressing a gas.
But as compression and expansion of gases require force for their accomplishment mechanically, or by the application or abstraction of heat chemically, or by convection, a second condition becomes involved, which was formulated into a law of thermodynamics by Gay Lussac under the following conditions: A given volume of gas under a free piston expands by heat and contracts by the loss of heat, its volume causing a proportional movement of a free piston equal to 1⁄273 part of the cylinder volume for each degree Centigrade difference in temperature, or 1⁄492 part of its volume for each degree Fahrenheit. With a fixed piston (constant volume), the pressure is increased or decreased by an increase or decrease of heat in the same proportion of 1⁄273 part of its pressure for each degree Centigrade, or 1⁄492 part of its pressure for each degree Fahrenheit change in temperature. This is the natural sequence of the law of mechanical equivalent, which is a necessary deduction from the principle that nothing in nature can be lost or wasted, for all the heat that is imparted to or abstracted from a gaseous body must be accounted for, either as heat or its equivalent transformed into some other form of energy. In the case of a piston moving in a cylinder by the expansive force of heat in a gaseous body, all the heat expended in expansion of the gas is turned into work; the balance must be accounted for in absorption by the cylinder or radiation.
THE ADIABATIC LAW
This theory is equally applicable to the cooling of gases by abstraction of heat or by cooling due to expansion by the motion of a piston. The denominators of these heat fractions of expansion or contraction represent the absolute zero of cold below the freezing-point of water, and read -273° C. or -492.66° = -460.66° F. below zero; and these are the starting-points of reference in computing the heat expansion in gas-engines. According to Boyle’s law, called the first law of gases, there are but two characteristics of a gas and their variations to be considered, viz., volume and pressure: while by the law of Gay Lussac, called the second law of gases, a third is added, consisting of the value of the absolute temperature, counting from absolute zero to the temperatures at which the operations take place. This is the Adiabatic law.
The ratio of the variation of the three conditions—volume, pressure, and heat—from the absolute zero temperature has a certain rate, in which the volume multiplied by the pressure and the product divided by the absolute temperature equals the ratio of expansion for each degree. If a volume of air is contained in a cylinder having a piston and fitted with an indicator, the piston, if moved to and fro slowly, will alternately compress and expand the air, and the indicator pencil will trace a line or lines upon the card, which lines register the change of pressure and volume occurring in the cylinder. If the piston is perfectly free from leakage, and it be supposed that the temperature of the air is kept quite constant, then the line so traced is called an Isothermal line, and the pressure at any point when multiplied by the volume is a constant, according to Boyle’s law,
pv = a constant.
If, however, the piston is moved very rapidly, the air will not remain at constant temperature, but the temperature will increase because work has been done upon the air, and the heat has no time to escape by conduction. If no heat whatever is lost by any cause, the line will be traced over and over again by the indicator pencil, the cooling by expansion doing work precisely equalling the heating by compression. This is the line of no transmission of heat, therefore known as Adiabatic.