A Catechism of the Steam Engine Part 18

341. _Q._--What is Boulton and Watt's rule for fly wheels?

_A._--Their rule is one which under any given circ.u.mstances fixes the sectional area of the fly wheel rim, and it is as follows:--multiply 44,000 times the square of the diameter of the cylinder in inches by the length of the stroke in feet, and divide this product by the product of the square of the number of revolutions of the fly wheel per minute, multiplied by the cube of its diameter in feet. The quotient is the area of section of the fly wheel rim in square inches.

STRENGTHS OF LAND ENGINES.

342. _Q._--Can you give a rule for telling the proper thickness of the cylinders of steam engines?

_A._--In low pressure engines the thickness of metal of the cylinder, in engines of a medium size, should be about 1/40th of the diameter of the cylinder, which, with a pressure of steam of 20 lbs. above the atmosphere, will occasion a strain of only 400 Lbs. per square inch of section of the metal; the thickness of the metal of the trunnion bearings of oscillating engines should be 1/32d of the diameter of the cylinder, and the breadth of the bearing should be about half its diameter. In high pressure engines the thickness of the cylinder should be about 1/16th its diameter, which, with a pressure of steam of 80 lbs. upon the square inch, will occasion a strain of 640 lbs. upon the square inch of section of the metal; and the thickness of the metal of the trunnion bearings of high pressure oscillating engines should be 1/13th of the diameter of the cylinder. The strength, however, is not the sole consideration in proportioning cylinders, for they must be made of a certain thickness, however small the pressure is within them, that they may not be too fragile, and will stand boring. While, also, an engine of 40 inches diameter would be about one inch thick, the thickness would not be quite two inches in an 80 inch cylinder. In fact there will be a small constant added to the thickness for all diameters, which will be relatively larger the smaller the cylinders become. In the cylinders of Penn's 12 horse power engines, the diameter of cylinder being 21-1/2 inches, the thickness of the metal is 9/16ths: in Penn's 40 inch cylinders, the thickness is 1 inch, and in the engines of the Ripon, Pottinger, and Indus, by Messrs. Miller, Ravenhill and Co., with cylinders 76 inches diameter, the thickness of the metal is 1-11/16. These are all oscillating engines.

343. _Q._--What is the proportion of the piston rod?

_A._--The diameter of the piston rod is usually made 1/10th of the diameter of the cylinder, or the sectional area of the piston rod is 1/100th of the area of the cylinder. This proportion, however, is not applicable to locomotive, or even fast moving marine engines. In locomotive engines the piston rod is made 1/7th of the diameter of the cylinder, and it is obvious that where the pressure on the piston is great, the piston rod must be larger than when the pressure on the piston is small.

344. _Q._--What are the proper dimensions of the main links of a land beam engine?

_A._--The sectional area of the main links in land beam engines is 1/113th of the area of the cylinder, and the length of the main links is usually half the length of the stroke.

345. _Q._--What are the dimensions of the connecting rod of a land engine?

_A._--In land engines the connecting rod is usually of cast iron with a cruciform section: the breadth across the arms of the cross is about 1/20th of the length of the rod, the sectional area at the centre 1/28th of the area of the cylinder, and at the ends 1/35th of the area of the cylinder: the length of the rod is usually 3-1/2 times the length of the stroke. It is preferable, however, to make the connecting rod of malleable iron, and then the dimensions will be those proper for marine engines.

346. _Q._--What was Mr. Watt's rule for the connecting rod?

_A._--Some of his connecting rods were of iron and some of wood. To determine the thickness when of wood, multiply the square of the diameter of the cylinder in inches by the length of the stroke in feet, and divide the product by 24. Extract the fourth root of the quotient, which is the thickness in inches. For iron the rule is the same, only the divisor was 57.6 instead of 24.

347. _Q._--What are the dimensions of the end studs of a land engine beam?

_A._--In low pressure engines the diameter of the end studs of the engine beam are usually made 1/9th of the diameter of the cylinder when of cast iron, and 1/10th when of wrought iron, which gives a load with low steam of about 500 lbs. per circular inch of transverse section; but a larger size is preferable, as with large bearings the bra.s.ses do not wear so rapidly and the straps are not so likely to be burst by the bearings becoming oval.

These sizes, as also those which immediately follow, suppose the pressure on the piston to be 18 lbs. per circular inch.

348. _Q._--How is the strength of a cast iron gudgeon computed?

_A._--To find the proper size of a cast iron gudgeon adapted to sustain any given weight:--multiply the weight in lbs. by the intended length of bearing expressed in terms of the diameter; divide the product by 500, and extract the square root of the quotient, which is the diameter in inches.

349. _Q._--What was Mr. Watt's rule for the strength of gudgeons?

_A._--Supposing the gudgeon to be square, then, to ascertain the thickness, multiply the weight resting on the gudgeon by the distance between the trunnions, and divide the product by 333. Extract the cube root of the quotient, which is the thickness in inches.

350. _Q._--How do you find the proper strength for the cast iron beam of a land engine?

_A._--If the force acting at the end of an engine beam be taken at 18 lbs.

per circular inch of the piston, then the force acting at the middle will be 36 lbs. per circular inch of the piston, and the proper strength of the beam at the centre will be found by the following rule:--divide the weight in lbs. acting at the centre by 250, and multiply the quotient by the distance between the extreme centres. To find the depth, the breadth being given:--divide this product by the breadth in inches, and extract the square root of the quotient, which is the depth. The depth of a land engine beam at the ends is usually made one third of the depth at the centre (the depth at the centre being equal to the diameter of the cylinder in the case of low pressure engines), while the length is made equal to three times the length of the stroke, and the mean thickness 1/108th of the length--the width of the edge bead being about three times the thickness of the web. In many modern engines the force acting at the end of the beam is more than 18 lbs. per circular inch of the piston, but the above rules are still applicable by taking an imaginary cylinder with an area larger in the proportion of the larger pressure.

351. _Q._--What was Mr. Watt's rule for the main beams of his engines?

_A._--Some of those beams were of wood and some of cast iron. The wood beams were so proportioned that the thickness was 1/58th of the circ.u.mference, and the depth 1/375. The side of the beam, supposing it square, was found by multiplying the diameter of the cylinder by the length of the stroke, and extracting the cube root of the quotient, which will be the depth or thickness of the beam. This rule allows a beam 16 feet long to bend 1/8th of an inch, and a beam 32 feet long to bend 1/4 of an inch. For cast iron beams the square of the diameter of the cylinder, multiplied by the length between the centres, is equal to the square of the depth, multiplied by the thickness.

352. _Q._--What law does the strength of beams and shafts follow?

_A._--In the case of beams subjected to a breaking force, the strength with any given cohesion of the material will be proportional to the breadth, multiplied by the square of the depth; and in the case of revolving shafts exposed to a twisting strain, the strength with any given cohesive power of the material will be as the cube of the diameter.

353. _Q._--How is the strength of a cast iron shaft to resist torsion determined?

_A._--Experiments upon the force requisite to twist off cast iron necks show that if the cube of the diameter of neck in inches be multiplied by 880, the product will be the force of torsion which will twist them off when acting at 6 inches radius; on this fact the following rule is founded: To find the diameter of a cast iron fly wheel shaft:--multiply the square of the diameter of the cylinder in inches, by the length of the crank in inches, and extract the cube root of the product, which multiply by 0.3025, and the result will be the proper diameter of the shaft in inches at the smallest part, when of cast iron.

354. _Q._--What was Mr. Watt's rule for the necks of his crank shafts?

_A._--Taking the pressure on the piston at 12 lbs. pressure on the square inch, and supposing this force to be applied at one foot radius, divide the total pressure of the piston reduced to 1 foot of radius by 31.4, and extract the cube root of the quotient, which is the diameter of the shaft: or extract the cube root of 13.7 times the number of cubic feet of steam required to make one revolution, which is also the diameter of the shaft.

355. _Q._--Can you give any rule for the strength of the teeth of wheels?

_A._--To find the proper dimensions for the teeth of a cast iron wheel:-- multiply the diameter of the pitch circle in feet by the number of revolutions to be made per minute, and reserve the product for a divisor; multiply the number of _actual_ horses power to be transmitted by 240, and divide the product by the above divisor, which will give the strength. If the pitch be given to find the breadth, divide the above strength by the square of the pitch in inches; or if the breadth be given, then to find the pitch divide the strength by the breadth in inches, and extract the square root of the quotient, which is the proper pitch in inches. The length of the teeth is usually about 5/8ths of the pitch. Pinions to work satisfactorily should not have less than 30 or 40 teeth, and where the speed exceeds 220 feet in the minute, the teeth of the larger wheel should be of wood, made a little thicker, to keep the strength unimpaired.

356. _Q._--What was Mr. Watt's rule for the pitch of wheels?

_A._--Multiply five times the diameter of the larger wheel by the diameter of the smaller, and extract the fourth root of the product, which is the pitch.

STRENGTH OF MARINE AND LOCOMOTIVE ENGINES.

357. _Q._--Cannot you give some rules of strength which will be applicable whatever pressure may be employed?

_A._--In the rules already given, the effective pressure may be reckoned at from 18 to 20 lbs. upon every square inch of the piston, as is usual in land engines; and if the pressure upon every square inch of the piston be made twice greater, the dimensions must just be those proper for an engine of twice the area of piston. It will not be difficult, however, to introduce the pressure into the rules as an element of the computation, whereby the result will be applicable both to high and low pressure engines.

358. _Q._--Will you apply this mode of computation to a marine engine, and first find the diameter of the piston rod?

_A._--The diameter of the piston rod may be found by multiplying the diameter of the cylinder in inches, by the square root of the pressure on the piston in lbs. per square inch, and dividing by 50, which makes the strain 1/7th of the elastic force.

359. _Q._--What will be the rule for the connecting rod, supposing it to be of malleable iron?

_A._--The diameter of the connecting rod at the ends, may be found by multiplying 0.019 times the square root of the pressure on the piston in lbs. per square inch by the diameter of the cylinder in inches; and the diameter of the connecting rod in the middle may be found by the following rule:--to 0.0035 times the length of the connecting rod in inches, add 1, and multiply the sum by 0.019 times the square root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches. The strain is equal to 1/6th of the elastic force.

360. _Q._--How will you find the diameter of the cylinder side rods of a marine engine?

_A._--The diameter of the cylinder side rods at the ends may be found by multiplying 0.0129 times the square root of the pressure on the piston in lbs. per square inch by the diameter of the cylinder; and the diameter of the cylinder side rods at the middle is found by the following rule:--to 0.0035 times the length of the rod in inches, add 1, and multiply the sum by 0.0129 times the square root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches; the product is the diameter of each side rod at the centre in inches. The strain upon the side rods is by these rules equal to 1/6th of the elastic force.

361. _Q._--How do you determine the dimensions of the crank?

_A._--To find the exterior diameter of the large eye of the crank when of malleable iron:--to 1.561 times the pressure of the steam upon the piston in lbs. per square inch, multiplied by the square of the length of the crank in inches, add 0.00494 times the square of the diameter of the cylinder in inches, multiplied by the square of the number of lbs. pressure per square inch on the piston; extract the square root of this quant.i.ty; divide the result by 75.59 times the square root of the length of the crank in inches, and multiply the quotient by the diameter of the cylinder in inches; square the product and extract the cube root of the square, to which add the diameter of the hole for the reception of the shaft, and the result will be the exterior diameter of the large eye of the crank when of malleable iron. The diameter of the small eye of the crank may be found by adding to the diameter of the crank pin 0.02521 times the square root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder in inches.

362. _Q._--What will be the thickness of the crank web?

_A._--The thickness of the web of the crank, supposing it to be continued to the centre of the shaft, would at that point be represented by the following rule:--to 1.561 times the square of the length of the crank in inches, add 0.00494 times the square of the diameter of the cylinder in inches, multiplied by the pressure on the piston in lbs. per square inch; extract the square root of the sum, which multiply by the diameter of the cylinder squared in inches, and by the pressure on the piston in lbs. per square inch; divide the product by 9,000, and extract the cube root of the quotient, which will be the proper thickness of the web of the crank when of malleable iron, supposing the web to be continued to the centre of the shaft. The thickness of the web at the crank pin centre, supposing it to be continued thither, would be 0.022 times the square root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder. The breadth of the web of the crank at the shaft centre should be twice the thickness, and at the pin centre 1-1/2 times the thickness of the web; the length of the large eye of the crank would be equal to the diameter of the shaft, and of the small eye 0.0375 times the square root of the pressure on the piston in lbs. per square inch, multiplied by the diameter of the cylinder.

363. _Q._--Will you apply the same method of computation to find the dimensions of a malleable iron paddle shaft?