(6) Expansion of the Charge.
When an explosive mixture is ignited in the cylinder with the piston fixed in one position thus making the volume constant, the increase of temperature is accompanied by an increase of pressure. If the piston is now allowed to move forward increasing the volume, the increase of volume decreases the pressure. Since in the operation of the gas engine the piston continuously expands the volume on the working stroke it is evident that there is no point in the stroke where the pressures are equal, and that the pressure is the least at the end of the stroke, it being understood of course that no additional heat is supplied to the medium after the piston begins its stroke.
This distribution of pressure in the cylinder in relation to the piston position is best represented graphically by means of a diagram as shown by Fig. 3, in which K is the cylinder and P the piston. Above the cylinder is shown the diagram HGDE the length of which (HE) is equal to the stroke of the piston shown by (BC). Intersecting the line HI are vertical lines, A, a, b, c, C, which represent certain positions of the piston in its stroke. The height of the diagram H G represents to scale the maximum explosion pressure in pounds per square inch, and the line HG is drawn immediately above the piston position B which is at the inner end of the stroke. To the left of the line HS is drawn a scale of pressures ML divided in pounds per square inch so that the pressures may be read off of the pressure curve GD. The line JI represents atmospheric pressure, and the divisions on ML, of course, begin from this line and increase as we go up the column. As an example in the use of the scale we find that the point F is at 50 pounds pressure above the atmospheric line JI.
We will consider that the clearance space AB is full of mixture at the point B, and that it is moved toward the left to the point C filling the space AC full of mixture at atmospheric pressure. The location of the piston on the diagram is shown by D and E. The opening through which the gas was supplied to the cylinder is now closed, and the piston starts on its compression stroke, moving from C to A. As the volume is reduced from AC to AB, there is an increase of pressure which is shown graphically by the rising line EF. This line rises gradually from the line JI in proportion to the reduction in volume until the piston reaches the end of the compression stroke at B, at which point the compression is at a maximum. The extent of this pressure is shown by the length of HF which on referring to the scale of pressure at the left will be found to be 50 pounds per square inch.
Ignition now occurs and the pressure increases instantly from the compression pressure at F to the maximum pressure at G which on referring to the scale will be found to equal 200 pounds. The actual increase of pressure due to ignition above the compression pressure will be shown by the length of the line FG which is equal to 150 pounds. As the pressure is now established against the piston it will begin to move forward with an increase of volume and a corresponding decrease in pressure, until it reaches the point C. This point at the end of the stroke is indicated on the diagram by D which by reference to the scale will be found equal to 25 pounds above atmosphere. An exhaust valve is now opened allowing the gas to escape to the atmosphere which reduces the pressure instantly from D to E on the atmospheric line. Expansion along the line GD is not complete as the pressure is not decreased to atmospheric pressure in the cylinder which means that there is a considerable loss of heat in the exhaust. In practice the expansion is never complete, but ends considerably above atmospheric pressure as shown.
Fig. F-3. Front Elevation of Curtiss “V” Type Aeronautical Motor. This is the Front View of the Motor Shown in the Frontispiece. See Chapter V for Description of this Type of Motor.
Complete expansion is shown by the dotted line GE which terminates at E on the atmospheric line. By following the vertical lines up from the points a, b, c, and d, the pressures corresponding to these piston positions can be found by measuring the distance of the curve from the atmospheric line, on the given lines a, b, c or d. To find the pressure at the position a, for instance, follow upwards along the line a to the point c on the curve, the length of the line ef from the curve to the atmospheric represents the pressure, which by reference to the scale ML will be found equal to 125 pounds. The pressure at any other point can be found in a like manner. Compression pressures may be found at any point by measuring from the atmospheric line to the compression curve FE along the given line. It will be noted that the combustion is so quick that the pressure rises in a straight line along GH, indicating that combustion was complete before the piston had time to start on the outward stroke. The expansion curves GE and GD are similar to the compression curve FE. With the actual engine the shape of the ideal card as shown by Fig. 3 is sometimes considerably deformed owing to the effects of defective valves, leaks, or improperly timed ignition.
Pressure curves of actual engines are of the greatest value as they show the conditions within the cylinder at a glance and make it possible to detect losses due to leaks, poor valve settings, etc. These curves are traced by means of the INDICATOR which is an instrument consisting of a small cylinder which is connected to the cylinder of the engine, and an oscillating drum that is driven to and fro by the engine piston. The piston in the indicator cylinder is provided with a spring that governs its movements and communicates its motion to a recording pencil through a system of levers. The spring is of such strength that a pressure of so many pounds per square inch in the cylinder causes the pencil to draw a line of a definite length, this line being equivalent to the pressure line GH in Fig. 3. A piece of paper is wrapped about the indicator drum, and the drum is attached to the piston in such a manner that it turns a certain amount for every piston position, the complete stroke of the piston turning the drum through about three-quarters of a revolution. Rotation of the drum traces the horizontal lines of the diagram and the movement of the piston draws the vertical lines, so the combined movements of the drum and piston records the pressures and piston positions as shown by Fig. 3.
Since the movement of the indicator piston represents the pressures in the cylinder to scale it is possible to compute the power developed in the cylinder as the output in mechanical units is equal to the product of the average force acting on the piston multiplied by the speed of the piston in feet per minute. This product of the force and velocity (known as “foot pounds per minute”) divided by 33,000 (one horse-power = 33,000 foot pounds) gives the output of the engine, in horse-power.
As the pressure on the piston fluctuates throughout the stroke, it would be wrong to consider the force, in the calculation for power as being equal to the explosion pressure, and so the effective pressure is taken as being the average of all the pressures from the point of explosion to the exhaust. The average pressure or “mean effective pressure” as it is called is computed from the indicator diagram by dividing it into a number of equal parts along the horizontal line, adding the lengths of the pressure lines such as CH, CF, etc., and dividing the total length by the number of the lines. After the average height of the diagram is thus determined, the average length is multiplied by the scale of the indicator or the pressure that is shown by it per inch.
Fairbanks-Morse Gasoline Pumping Engine. Pump is Gear Driven From the Engine Crank-Shaft at Reduced Speed.
Knowing the mean effective pressure, the total pressure on the piston, or the force is found by multiplying the area of the piston in square inches by the average pressure per square inch. This product is multiplied by the piston speed in feet per minute and is divided by the product of the number of strokes to the explosion and the quantity 33,000. Should there be more than one cylinder the result is multiplied by the number of cylinders, and this is multiplied by 2 in the case of a double acting engine. Stated as a formula this rule becomes:
| A × P × 2R × L × N × O | |
| H.P. = | |
| 33000 × C |
| When | A = | Area of piston in square inches. |
| P = | Average or mean effective pressure per square inch. About 75 pounds for Gasoline Engines. See Table on Page [31]. | |
| R = | Revolutions per minute. | |
| L = | Stroke of piston in feet. | |
| N = | Number of cylinders. | |
| O = | 2 when engine is double acting, that is when explosions occur on both sides of the piston. | |
| C = | Number of strokes per explosion. C = 4 in a four cycle engine, and 2 in a two cycle. |
It should be specially noted that the area of the piston is given in square inches and the stroke of the piston in feet. The number of revolutions per minute, R, is multiplied by two in order to obtain the number of strokes, as there are two strokes per revolution. When the engine governs its speed by dropping explosions to meet varying loads, the quantity C should be omitted and the explosions counted.
Due to the fact that the incoming charge of the mixture is expanded by the heat of the passages, a full charge computed at atmospheric temperature is never obtained in the cylinder and for this reason the gas should be kept as cold as possible before entering the passages in order to obtain the maximum output. Friction due to restricted passages and valve openings also reduces the amount of mixture available. Small exhaust valves and pipes prevent the gases from escaping freely to the atmosphere and produces a back pressure on the piston which cuts down the effective pressures. All of these items are recorded by the indicator and makes it possible to make alterations that will increase the output of the engine.
Because of the reduced atmospheric pressures at high altitudes the output and compression are reduced for every foot of elevation above sea level. As the weight of the atmosphere is reduced, less mixture is drawn into the cylinder. Taking the output of the engine as 100 per cent at sea level, it is reduced to less than 62 per cent at an elevation of 15,000 feet.