RATING AND GENERAL PROPORTIONS OF STEAM ENGINES
The capacity or power of a steam engine is rated in horsepower, one
horsepower (H. P.) being the equivalent of 33,000 foot-pounds of work
done per minute. The horsepower of a given engine may be computed by the
formula:
_APLN_
H. P. = ------
33,000
in which
_A_ = area of piston, in square inches,
_P_ = mean effective pressure per square inch,
_L_ = length of stroke, in feet,
_N_ = number of strokes per minute = number of revolutions x 2.
The derivation of the above formula is easily explained, as follows: The
area of the piston, in square inches, multiplied by the mean effective
pressure, in pounds per square inch, gives the total force acting on the
piston, in pounds. The length of stroke, in feet, times the number of
strokes per minute gives the distance the piston moves through, in feet
per minute. It has already been shown that the pressure in pounds
multiplied by the distance moved through in feet, gives the foot-pounds
of work done. Hence, _A_ x _P_ x _L_ x _N_ gives the foot-pounds of work
done per minute by a steam engine. If one horsepower is represented by
33,000 foot-pounds per minute, the power or rating of the engine will be
obtained by dividing the total foot-pounds of work done per minute by
33,000. For ease in remembering the formula given, it is commonly
written
_PLAN_
H. P. = ------,
33,000
in which the symbols in the numerator of the second member spell the
word "Plan."
_Example_:--Find the horsepower of the following engine, working under
the conditions stated below:
Diameter of cylinder, 12 inches.
Length of stroke, 18 inches.
Revolutions per minute, 300.
Mean effective pressure (M. E. P.), 40 pounds.
In this problem, then, _A_ = 113 square inches; _P_ = 40 pounds; _L_ =
1.5 feet; and _N_ = 600 strokes.
Substituting in the formula,
40 x 1.5 x 113 x 600
H. P. = -------------------- = 123.
33,000
The mean effective pressure may be found, approximately, for different
conditions by means of the factors in the following table of ratios,
covering ordinary practice. The rule used is as follows: Multiply the
absolute initial pressure by the factor corresponding to the clearance
and cut-off as found from Table II, and subtract the absolute back
pressure from the result, assuming this to be 17 pounds for
non-condensing engines, and 3 pounds for condensing.
_Example 1_:--A non-condensing engine having 3 per cent clearance, cuts
off at 1/3 stroke; the initial pressure is 90 pounds gage. What is the
M. E. P.?
The absolute initial pressure is 90 + 15 = 105 pounds. The factor for 3
per cent clearance and 1/3 cut-off, from Table II, is 0.71. Applying the
rule we have: (105 x 0.71) - 17 = 57.5 pounds per square inch.
_Example 2_:--A condensing engine has a clearance of 5 per cent. It is
supplied with steam at 140 pounds gage pressure, and has a ratio of
expansion of 6. What is the M. E. P.?
The absolute initial pressure is 140 + 15 = 155. The factor for a ratio
of expansion of 6 (1/6 cut-off) and 5 per cent clearance is 0.5, which
gives (155 x 0.5) - 3 = 74.5 pounds per square inch.
The power of an engine computed by the method just explained is called
the indicated horsepower (I. H. P.), and gives the total power
developed, including that required to overcome the friction of the
engine itself. The delivered or brake horsepower (B. H. P.) is that
delivered by the engine after deducting from the indicated horsepower
the power required to operate the moving parts. The brake horsepower
commonly varies from 80 to 90 per cent of the indicated horsepower at
full load, depending upon the type and size of engine.
In proportioning an engine cylinder for any given horsepower, the
designer usually has the following data, either given or assumed, for
the special type of engine under consideration: Initial pressure, back
pressure, clearance, cut-off, and piston speed.
These quantities vary in different types of engines, but in the absence
of more specific data the values in Table III will be found useful. The
back pressure may be taken as 17 pounds per square inch, absolute, for
non-condensing engines, and as 3 pounds for condensing engines as
previously stated.
TABLE II. FACTORS FOR FINDING MEAN EFFECTIVE PRESSURE
+--------------+-----------------------------------------+
| | Point of Cut-off |
| Percentage +------+------+------+------+------+------+
| of Clearance | 1/10 | 1/6 | 1/4 | 1/3 | 1/2 | 3/4 |
+--------------+------+------+------+------+------+------+
| 1.75 | 0.35 | 0.48 | 0.60 | 0.70 | 0.85 | 0.96 |
| 3.00 | 0.37 | 0.49 | 0.61 | 0.71 | 0.85 | 0.96 |
| 5.00 | 0.39 | 0.50 | 0.62 | 0.72 | 0.86 | 0.97 |
| 7.00 | 0.41 | 0.52 | 0.63 | 0.73 | 0.86 | 0.97 |
| 9.00 | 0.43 | 0.54 | 0.64 | 0.73 | 0.86 | 0.97 |
+--------------+------+------+------+------+------+------+
The first step in proportioning the cylinder is to compute the
approximate mean effective pressure from the assumed initial pressure,
clearance, and cut-off, by the method already explained. Next assume the
piston speed for the type of engine to be designed, and determine the
piston area by the following formula:
33,000 H. P.
A = -----------------------.
M. E. P. x piston speed
This formula usually gives the diameter of the piston in inches and
fractions of an inch, while it is desirable to make this dimension an
even number of inches. This may be done by taking as the diameter the
nearest whole number, and changing the piston speed to correspond. This
is done by the use of the following equation.
First piston speed x first piston area
-------------------------------------- = new piston speed.
new piston area
In calculating the effective piston area, the area of the piston rod
upon one side must be allowed for. The effective or average piston area
will then be (2_A_ - _a_)/2, in which _A_ = area of piston, _a_ = area
of piston rod. This latter area must be assumed. After assuming a new
piston diameter of even inches, its effective or average area must be
used in determining the new piston speed. The length of stroke is
commonly proportioned to the diameter of cylinder, and the piston speed
divided by this will give the number of strokes per minute.
_Example_:--Find the diameter of cylinder, length of stroke, and
revolutions per minute for a simple high-speed non-condensing engine of
200 I. H. P., with the following assumptions: Initial pressure, 90
pounds gage; clearance, 7 per cent; cut-off, 1/4; piston speed, 700 feet
per minute; length of stroke, 1.5 times cylinder diameter.
TABLE III. PRESSURE, CLEARANCE, CUT-OFF AND PISTON SPEED OF STEAM
ENGINES
+---------------------+------------+-----------+-------------+------------+
| | Initial | Clearance,| Cut-off, | Piston |
| Type of Engine | Pressure, | Per Cent | Proportion | Speed, Feet|
| | (Gage) | | of Stroke | per Minute |
+---------------------+------------+-----------+-------------+------------+
|Simple high-speed | 80 to 90 |4 to 10 | 1/4 to 1/3 | 600 to 800 |
|Simple medium-speed | 80 to 90 |3 to 8 | 1/4 to 1/3 | 500 to 700 |
|Simple Corliss | 80 to 90 |1.5 to 3.5| 1/4 to 1/3 | 400 to 600 |
|Compound high-speed | 130 to 140 |4 to 10 | 1/10 to 1/8 | 600 to 800 |
|Compound medium-speed| 130 to 140 |3 to 8 | 1/10 to 1/8 | 500 to 700 |
|Compound Corliss | 130 to 140 |1.5 to 3.5| 1/10 to 1/8 | 400 to 600 |
+---------------------+------------+-----------+-------------+------------+
By using the rules and formulas in the foregoing, we have:
M. E. P. = (90 + 15) x 0.63 - 17 = 49 pounds.
33,000 x 200
_A_ = ------------ = 192.4 square inches.
49 x 700
The nearest piston diameter of even inches is 16, which corresponds to
an area of 201 square inches. Assume a piston rod diameter of 2-1/2
inches, corresponding to an area of 4.9 square inches, from which the
average or effective piston area is found to be ((2 x 201) - 4.9)/2 =
198.5 square inches.
Determining now the new piston speed, we have:
700 x 192.4
----------- = 678.5 feet per minute.
198.5
Assuming the length of stroke to be 1.5 times the diameter of the
cylinder, it will be 24 inches, or 2 feet.
This will call for 678.5 / 2 = 340 strokes per minute, approximately, or
340 / 2 = 170 revolutions per minute.