SOME PRINCIPLES 
 
 OF 
 
 SAFETY VALVE DESIGN 
 
 WITH SPECIAL CONSIDERATION OF VALVE SPRINGS 
 FOR LOCOMOTIVE POP SAFETY VALVES 
 
 BY 
 
 ALFRED B. CARHART, E. E. 
 
 MEM. AM. SOC. M. E. 
 
 Reprinted from papers presented before The American Society of 
 Mechanical Engineers 
 
 CROSBY STEAM GAGE & VALVE COMPANY 
 
 F. 887-B. P.-4-09 
 
 19 0 9 
 
C\3so 
 
 Safety Valve Springs* 
 
 T HE spring is the heart of the modern pop safety valve; it is 
 the essential element, to which all other details of design are 
 subordinate. If the spring is not properly proportioned for its 
 purpose, the satisfactory performance, discharge capacity and durability 
 of the valve can not be secured. The operations of a poorly designed 
 valve may be greatly assisted and improved by a suitable spring; and a 
 valve with an excellent arrangement and relation of the other working 
 parts and discharge passages may be seriously handicapped by an 
 improperly designed spring or even transformed from a safety device to 
 a source of danger. 
 
 The history of safety valve making indicates that the spring has 
 been regarded as a relatively unimportant detail, made up without 
 exact knowledge or study, following any general custom or usage that 
 had seemed satisfactory in the past, and doing as well as might be 
 within the dimensions conveniently available in valves designed prima¬ 
 rily with regard to economy of material, pleasing proportions and uni¬ 
 form gradations of size, thus forcing all sizes of springs for wide ranges 
 of pressure to go into the same body or casing. 
 
 A suitable and efficient spring must be the first consideration. A 
 safety valve should be designed by calculating the total spring-load 
 required to be exerted upon the disc when the valve is closed, then 
 the amount of further compression needed for the pre-determined 
 vertical lift of the disc when the valve opens, with a reasonable allowance 
 for a reserve of further possible free movement of the spring in com¬ 
 pression, and thereupon determining the dimensions of the spring that 
 will carry this load at its point of greatest efficiency, with due regard 
 for flexibility, sensitiveness with accurate adjustment, and durability 
 in service. 
 
 There are several variable dimensions and factors that may be to 
 some degree modified, in proper relation to each other, in designing 
 springs to meet any given requirements, and several different springs 
 may be laid out that will accomplish much the same result^ with but 
 slight differences in allowance for the several factors that must be 
 assumed; but there is a certain minimum limit beyond which it is 
 impossible to go, and where the available space has been by custom or 
 commercial considerations absolutely fixed, the obvious procedure is 
 
 ♦Presented at the Meeting of The American Society of Mechanical Engineers 
 held in New York on February 23, 1909. 
 
4 
 
 SAFETY VALVE SPRINGS 
 
 not to let it all go as a difficult problem having no rational solution, but 
 to make the spring of a steel that permits greater fibre stress, to design 
 an arrangement of valve parts which shall have the least throttling or 
 retarding effect upon the steam which the spring does permit to escape, 
 and to utilize all means to reduce the required total spring-load to the 
 least amount without restricting the valve outlet diameter or area. 
 Details of mechanical construction are thus important, but secondary, 
 for the efficiency of the spring in its functions will after all determine 
 the satisfactory performance of the valve. Modifications in valve 
 design may help but can not cure a viciously ineffective spring. On 
 the other hand, it is not always possible, within the limits imposed, to 
 design a spring to overcome or counteract defects of valve design. 
 
 Some of the characteristics of helical springs are commonly known, 
 but it may be well to review briefly the principles involved. The 
 accepted foundation of the mathmetical theory of elastic solids is 
 Hooke’s Law, “Ut tensio sic vis,” or, as the strain is So is the stress, and 
 this is true of the spring, that within the limits of elasticity, the de¬ 
 formation or compression is proportional to the force or pressure which 
 produces it; and in a spring of given dimensions, equal increments of 
 force or pressure applied will produce equal amounts of compression. 
 For example, if it requires a total load of 2000 pounds to compress a 
 given spring having a total possible compression of one inch so that its 
 coils are solid, with no further deflection possible, then a load of 1000 
 pounds would have caused this spring to shorten just one half of that 
 amount or one-half inch, and each 100 pounds load more or less would 
 cause a shortening or lengthening of 1-20 or .05 inch. The total amount 
 of compression or shortening of a spring under load is divided equally 
 among its free or effective coils, and as the amount of deflection under 
 a given load is determinable by formula or by experiment for every 
 combination of size of steel, mandrel diameter and pitch, the total 
 compression of a spring is found by multiplying the deflection of each coil 
 by the number of effective coils; and for any fixed proportions of 
 diameter and pitch, the compression of a spring at any given load is 
 proportional to the number of coils; therefore it is generally said that 
 the long springs have greater compression than short springs and that 
 the simplest way to increase the total compression or movement is to 
 lengthen the spring. But of course an increased compression for a 
 given load can be accomplished by changing other proportions without 
 increasing the total free length. 
 
 This increase of compression of a spring in proportion to the 
 
SAFETY YALYE SPRINGS 
 
 5 
 
 increasing number of its coils is independent of the total load which 
 the spring will carry and does not affect that question. The strength 
 of a spring, or the load which it will carry or sustain at any given pro¬ 
 portionate amount of its total possible compression, is determined by 
 the characteristics of the metal, the size or cross-section of the rod or 
 wire and the diameter of mandrel on which it is wound; for example, 
 if a load of 1000 pounds will compress a spring of certain diameter- 
 dimensions one-half of its total possible compression or one-half inch 
 then a spring of the same diameters but twice as long and having double 
 the number of coils would be compressed by the same load one-half of 
 its total movement or one inch; a load of 1500 pounds would compress 
 either spring three-quarters of its total possible movement, and likewise 
 either spring would be compressed solid under a load of 2000 pounds; 
 the strength or carrying capacity of the two springs would be the same, 
 although of different lengths, and the amount of deflection of each coil 
 in either spring would be the same; although the total amount of move¬ 
 ment would be different, a spring four inches long would be just as strong 
 or would sustain the same load as a spring eight inches long; there would 
 be no difference in their capacity or load strength. But the action of 
 the two springs in safety valve service would be very different; for 
 the longer spring would have its power exerted through a greater 
 distance, with greater amplitude of movement or flexibility, and the 
 oscillations set up by any sudden force would affect the behavior of 
 the valve. 
 
 If all other dimensions remain unchanged, enlarging the cross 
 sectional area of the rod or wire of which the spring is wound will make 
 the spring stiffer or stronger or carry a heavier load for the same amount 
 of compression; and of course square rod will make a spring slightly 
 stiffer than round steel of the same diameter. There are some condi¬ 
 tions which may be better met and special results that can be more 
 readily obtained by using round section rather than square, and vice 
 versa; and generally the controlling consideration is not merely the 
 greater area or volume of the steel, but rather a slightly different 
 characteristic reaction and activity, which can be considerably modified 
 by slight alteration of other elements of the design. Reducing the 
 mandrel diameter will also make the spring stiffer or stronger and thus 
 admit less compression for the same load; while increasing the inside 
 diameter or mandrel upon which the spring is wound will make the 
 spring weaker or more flexible, and will decrease the amount of the 
 load which it will sustain or carry for a given compression or will increase 
 
6 
 
 SAFETY VALVE SPRINGS 
 
 the deflection of each coil and likewise the total compression which 
 carries or balances a given pressure load. 
 
 Therefore the total amount of compression of a spring for a given 
 load may be increased by increasing the number of coils of the same 
 diameters and pitch and thus increasing the total free length; by reduc¬ 
 ing the cross-section area of the rod; by enlarging the mandrel and 
 consequently also the over-all diameter; or by any or all of these modifi¬ 
 cations at the same time. 
 
 In making a safety valve spring, there are certain practical limita¬ 
 tions which must be taken into account. Steel of very large diameter 
 cannot be satisfactorily wound upon a small mandrel, and the flexural 
 or bending strain becomes too great, so that a fracture or transverse 
 set is developed. A spring excessively long in proportion to its diameter 
 and pitch may bend or buckle instead of compressing in a straight 
 thrust axially; and if the number of coils be too great, the reaction of 
 the spring will set up an oscillation which not only permits but ag¬ 
 gravates the undesirable and destructive chattering of the valve. 
 The valve disc must not, in effect, be suspended at the end of a flexible 
 spring, but must have behind it at all times a positive force capable of 
 controlling its action when lifted by the escaping steam. If the spring 
 be too short, not only will the reaction be too sudden, but the active 
 free coils will form a smaller proportion of the total length; it is not then 
 possible to distribute the pressure at the ends of the spring so evenly 
 upon the coils, and the spring compression will be greater on one side 
 than on the other, transmitting an undesirable side thrust to the disc 
 guides. If the pitch is too steep or the coils wound too far apart, there 
 will be room for considerable free movement and apparently a large 
 possible deflection of each coil, so that it might seem as though only a 
 few coils would give the total compression desired; but if this be at¬ 
 tempted, the fibre stress upon the steel is enormously increased, the 
 flexural strain becomes the larger factor, the rod is fractured or the 
 elastic limit of the steel is soon passed and a permanent set takes place, 
 destroying the essential properties of the spring before the required 
 deflection of each coil can be attained. If too many coils are put into 
 a given fixed length of spring the theoretical deflection required of each 
 coil will be within safe limits, but there will not be sufficient free space 
 between the coils to permit even the small necessary movement or 
 compression, and when the pitch is thus too flat, the spring will have 
 insufficient reactive power or force, because of the inadequate strain 
 and fibre stress put upon the steel. The spring must thus have sufficient 
 
SAFETY YALYE SPRINGS 
 
 7 
 
 force to make the valve open and close promptly and positively and 
 keep the seat tight, not only to give prompt relief but to prevent the 
 constant simmering and leaking which cuts and destroys the seats and 
 permits the deposit of boiler-scale upon any exposed threads. The 
 requirements of positive control and extreme lift are thus to a large 
 degree contradictory. 
 
 The character in action and performance required of the spring 
 in a pop safety valve is different from that expected of car springs or 
 similar buffers. In carrying the load of a car or wagon, any unevenness 
 of the road causes a jolting or bouncing, and the momentum of the mov¬ 
 ing car adds temporarily to the effect of its dead weight to increase the 
 violent action of the spring. Under severe conditions such springs are 
 often compressed to their limit, until the coils are in solid contact, and 
 a severe bump or jar is felt in the car itself; but the reaction of the spring, 
 when the unevenness is past, sets the car back to its proper position, and 
 on the rebound it may be that the car has risen above its normal place 
 so that the spring is drawn out in tension; after a while these waves 
 of oscillation subside, and the car rides normally. For such service, 
 car springs are generally designed so that when the car is loaded in 
 ordinary mapner the spring will be about one-half compressed, or one- 
 half of its free movement will carry or balance the contemplated load. 
 The reason is that this gives some leeway for additional load in the 
 car without compressing the spring too much, and also permits the great¬ 
 est movement above and below the normal medium position. It is 
 believed that the conditions of longest life and least severe fracturing 
 strain upon the car spring are met when the calculated ordinary load 
 will thus compress the spring one-half of its total free movement. 
 
 For pop valve service, on the other hand, the conditions are different; 
 the exact pressure load is determined from the exposed area of the 
 disc and the steam pressure, and when the valve opens there is an 
 added load governed by the additional area of the disc and the steam 
 pressure, which rapidly decreases as the steam directly below the valve 
 escapes and the boiler is relieved. Under no conceivable conditions of 
 actual service can sufficient steam pressure be brought upon the valve 
 disc to compress the spring so that the coils will be solid, metal to 
 metal, if it has been reasonably designed for its original fixed load; 
 and the additional spring compression to permit the valve opening in 
 order to relieve the boiler is comparatively little, possibly 0.08 inch, 
 more commonly and preferably less, and never under any conditions 
 as much as 0.12 inch or say ^ inch as an extreme amount. If after the 
 
8 
 
 SAFETY VALVE SPRINGS 
 
 fixed load pressure is reached, the spring has still 15-32 inch of unused 
 possible compression, of which less than 3-32 inch will be required to 
 accommodate the desired lift of the valve, there will be still 3-8 inch 
 more before the spring would go solid at which point all further com¬ 
 pression would be impossible; therefore the valve spring can be properly 
 designed to carry its set load at much more than half of its total free 
 compression, and nearer to its solid condition than would be wise with 
 a car spring where the amount of amplitude of total motion is not 
 limited. 
 
 If springs are properly proportioned, the point of greatest resilience, 
 elasticity and reaction, securing sharp action in the valve, and permitting 
 the most sensitive and accurate adjustment of opening pressure, is in 
 the last one-third of the total possible free compression, and this is the 
 part of the spring action which should be utilized for safety valve service. 
 I believe it proper to proportion the spring so that the set load is carried 
 at about two-thirds or three-fourths of its total free compression, 
 making the length and dimensions of the spring such that the remaining 
 unused compression of the spring will be ample for the lift of the disc, 
 and a safe margin beyond. 
 
 While it may be said that the springs will never be subjected to 
 the extreme compression required to force them solid in service, yet 
 the working compression is a large proportion of the total free move¬ 
 ment and the spring might be dangerously near the point of setting or 
 fracture unless properly proportioned and tempered to take the solid 
 test. In making boiler tests the head bolt may be set down until the 
 spring is solid, to close the valve; and if the valve is fitted with a lever, 
 the spring may be at any time lifted or compressed an indefinite amount 
 by that means, even to solid. I would not consider it proper to use in 
 a pop safety valve any spring that would not safely take the solid 
 test, capable of being compressed until the coils are metal to metal any 
 number of times consecutively, without showing any permanent set or 
 strain. Otherwise there will be nothing to prevent the spring from 
 being screwed down, even through ignorance, until the danger point 
 may be once passed, and the spring then takes a permanent set, after 
 which it becomes entirely ineffective as a valve spring and a source of 
 danger if its use is ignorantly continued. 
 
 One prominent manufacturer of safety valves requires all springs 
 to be designed to take this solid test indefinitely. After the springs are 
 made and tempered, they are closed solid in a press at least three times; 
 and again before they are put into valves for service, at the time when 
 
SAFETY VALVE SPRINGS 
 
 9 
 
 the ends are dressed and fitted, they are tested three times solid and the 
 compression at the proper load for which they are designed is noted. 
 If any spring shows a set or shortening, even temporarily, of as much 
 as 1-16 inch in any of these tests, or if there is much variation in the 
 compression at normal load, it is condemned and rejected. Out of 
 the great number of valve springs made and tested every year under 
 these conditions less than one-third of one per cent are rejected on 
 this account, which shows that the requirements are commercially 
 practicable and that the method of calculation and design is sound and 
 conservative. Breakage of these springs in service is practically 
 unknown. Such results demonstrate what modern methods with care 
 and accuracy can accomplish, in producing uniformity of performance 
 and reliability, and would be remarkable in any manufacturing opera¬ 
 tions where the number of pieces is so considerable, without taking 
 into account the peculiarities of springs and steel. 
 
 If after the winding, tempering or testing, the finished spring is a 
 little shorter than the standard length, there is a temptation to reheat 
 it and pull it out a little to make it the full length, but such treatment 
 is undesirable even if it be so skillfully done that the steel is not burned 
 or overtempered. Not all springs so reheated would be inferior, but 
 perfect security lies in accepting the small losses that may occur rather 
 than assume any risk. 
 
 Springs of comparatively poor design, if well made of proper steel, 
 heated uniformly to the temperature for working and tempered skill¬ 
 fully, are to be preferred to springs of better dimensions but improperly 
 made. In most small shops where springs are wound by hand, the 
 long bar of steel must be heated in comparatively short sections in a 
 small furnace or forge fire, winding about a foot of the steel at each 
 operation, drawing the bar by hand-tongs around a cold mandrel and 
 then sticking the remainder of the straight bar again into the fire until 
 it is soft enough to wind another coil or two. Each foot of the steel 
 has been heated to a different temperature, and where the heated 
 sections have overlapped, the steel is likely to be burned. The same 
 difficulty arises in tempering, where it is necessary to move a large 
 spring rapidly around in the fire to try to get all parts of it heated up 
 at the same time; one end sticks out into the cold air while the other 
 end is in the hottest part of the fire in the blast. No two springs made 
 in this way can be alike, and different coils of the same spring will differ 
 considerably in load-strength, temper, elasticity, resilience and breaking 
 strain, for generally about one coil is all that can be wound at each 
 
10 
 
 SAFETY VALVE SPRINGS 
 
 heating. The bars measure from five to twelve feet long for making 
 springs for valves of the larger sizes, and for locomotive valves the 
 lengths would be about four to six feet. The whole bar of steel should 
 be evenly heated at one time, without being exposed to any direct 
 de-carbonizing flame or forge blast, then wound accurately and quickly 
 at one operation, and plunged in the tempering bath at exactly the 
 proper moment. 
 
 These springs should be wound of a special grade of steel, kept up 
 to standard specifications, in bars of the various sizes and shapes 
 required for different loads and pressures; and although they are wound 
 in the same general manner and have much the same outward appear¬ 
 ance as ordinary coiled helical springs that are used for car springs and 
 other commercial purposes, in reality they are very different in treat¬ 
 ment and character, and proper results can never be obtained if springs 
 of ordinary steel are substituted. No railroad should attempt to use 
 car springs of similar shape that may be on hand, or to buy springs for 
 safety valves by specifying simply the measured dimensions. 
 
 In measuring springs, it is the custom and better practice to state 
 first the inside or mandrel diameter, then the free length of the finished 
 spring and last the diameter and form of the steel rod used, the measure¬ 
 ment of the cross-section being that of the straight bar before winding. 
 For long springs it is sometimes necessary to use a taper mandrel to 
 facilitate the drawing off of the spring, although generally the slight 
 natural expansion of the spring after winding will sufficiently release it; 
 where the mandrel is tapered, the mean diameter, approximately half¬ 
 way between the two ends, is the dimension to be specified. The over¬ 
 all outside diameter will generally be slightly more, and the outer face 
 of the coiled square steel will be less, than the commercial dimensions 
 would indicate. 
 
 In any design and calculation of springs the factor of proper or 
 permissible fibre stress must enter; and it is obvious that this amount 
 of fibre stress can be stated or calculated to be any quantity which 
 may be desired or may seem comfortable or convenient in the judgment 
 of the engineer, by properly proportioning the various assumed factors 
 and constants, which must be determined more or less arbitrarily in 
 operating under any formula whatever. Whether we reason from 
 Hooke’s Law, or from the general statement that every action has an 
 equal and opposite reaction, or appeal directly to the doctrine of the 
 conservation of energy, it is plain that we can get no more work out of 
 a spring in reaction than is put into it, and the more force or power in 
 
SAFETY VALVE SPRINGS 
 
 11 
 
 compression that is put into a spring of given dimensions, the greater 
 the amount of work which it will return and the sharper and more 
 positive will be its action in controlling the valve. The way to get proper 
 work out of a spring is to put force into it in effective stress. 
 
 In a paper by a member of the Society, Mr. H. V. Wille, of the 
 Baldwin Locomotive Works, printed in the January number of the 
 Journal of the American Society of Mechanical Engineers, he discusses 
 difficulties that have been met with in designing stay bolts for locomotive 
 fire boxes, where by reason of the expansion the bolts are stressed above 
 the elastic limit, in flexure more than in tension. He argues that the 
 obvious remedy does not lie in the use of a slow-breaking material but 
 in the employment of steel of sufficiently high elastic limit to meet 
 the conditions of service, and thus also to reduce the necessary diameter 
 of the bolt and proportionately reduce the fibre stress in flexure. He 
 states that stay bolts have recently been made of the same grade of 
 steel as that used in the manufacture of springs, oil-tempered, to safely 
 stand a fibre stress of 100,000 pounds per square inch, its high elastic 
 limit making it possible to reduce the diameter so that the fibre stress 
 in flexure is less than one-half that in the ordinary type of bolt and the 
 material is capable of being thus stressed to a high degree. This same 
 reasoning applies aptly to the problem of making suitable springs for 
 safety valves, and practical experience has demonstrated that every 
 argument and consideration is in favor of putting the steel under the 
 highest practicable fibre stress. Safety here lies not in allowing a 
 factor too large, but in using material of known and uniform quality 
 and greater strength. 
 
 Low fibre stress is not a measure of safety but of ineffectiveness. 
 To properly develop the resilience of the most trustworthy and suitable 
 steel available today requires a stress that would be inadmissible with 
 material of inferior temper or uncertain quality and subject to ordinary 
 commercial defects. Experience shows that springs may best be 
 stressed at from 60,000 to 75,000 pounds per square inch at the fixed 
 load, which should compress the spring about 70 per cent of its total 
 possible free movement, the remaining movement should be three or 
 four times the further lift of the valve in opening. This is low enough 
 for good steel and gives safe working limits and conditions, and under 
 the same formula the stress when the spring is solid will not exceed 
 100,000 pounds per square inch. 
 
 The limit of elasticity, beyond which a permanent set occurs, is 
 different for torsional strains than for elongation and is independent of 
 
12 
 
 SAFETY VALVE SPRINGS 
 
 the tensile strength, and for steel of the proper characteristics for 
 spring-making, this torsional elasticity is relatively high. Car-springs 
 have sometimes been calculated upon a fibre stress as low as 30,000 
 pounds per square inch at normal load, and this may have seemed 
 reasonable for common grades of steel under circumstances where the 
 springs might be frequently subjected to the extreme compression or 
 extension. But the material to be used today does not properly 
 develop the power in reaction at any such small percentage of its total 
 strength, and the fibre stress now recommended in the hand-books 
 and in the modern text-books on applied mechanics is generally 80,000 
 pounds. This is not a question of keeping within limits of safety, 
 but of stressing the steel to its point of proper efficiency. For example, 
 it would be absurd to expect a spring suitable for use in a valve at 200 
 pounds pressure to show proper performance and lift or permit satis¬ 
 factory opening and closing of the valve at only 50 pounds pressure; 
 its reaction and resilience could not be at all reasonably developed. 
 
 If a spring is designed upon a formula which may indicate a fibre 
 stress of 70,000 pounds per square inch at normal load, and as much as- 
 100,000 pounds per square inch when compressed solid, yet is made 
 of such steel that it can remain assembled in the valve indefinitely 
 under pressure without perceptible set, and can be compressed solid 
 an indefinite number of times without injury, it is evident that it is 
 more properly proportioned and is used at a better and safer percentage 
 of its elastic limit than springs made of less virile steel, that although 
 calculated by some formula which indicates only 30,000 pounds per 
 square inch fibre stress at normal load, will suffer a gradual set or 
 deterioration in service or will become permanently set if tested solid. 
 Of course it is obvious that certain grades of steel, whether on account 
 of cheapness in methods of manufacture, lack of uniformity in character, 
 or poor judgment in adaptation to the special purposes in hand, may 
 show a set at a comparatively early point beyond the normal load, no 
 matter at what figure it may be fixed; and therefore a fixed limit of 
 fibre stress has no meaning unless the characteristics of the steel be 
 also specified or known. Springs wound of bronze are notoriously 
 inefficient and unenduring, and their depreciation and permanent set 
 in service at comparatively low fibre stress will more than counter¬ 
 balance any possible advantage of slow corrosion; and certain grades 
 of steel may be as poorly adapted for the making of valve springs. 
 The torsional elasticity and power depends not upon the tensile strength 
 so much as upon the temper and resilience. Therefore some of the 
 
SAFETY VALVE SPRINGS 
 
 13 
 
 new alloy steels have proved disappointing for this service and the 
 name of any alloy can not as yet be used either as a fetich or a selling 
 phrase. 
 
 Observation of many thousand springs in continuous daily service, 
 under severest conditions of constant use, shows that springs calculated 
 upon a very high fibre stress are entirely reliable for indefinite periods 
 of service and do not develop any measurable percentage of faults or 
 fractures; the failure of valves under operating conditions attributable 
 to such springs is practically unknown and is less than the percentage 
 due to the rare defects of the other structural parts. 
 
 The theory of the action of helical springs was developed between 
 1814 and 1848 by Binet and by Professor Thomson, who argued mathe¬ 
 matically that the force opposing the elongation or contraction of the 
 spring is the elasticity of torsion, which is independent of the elasticity 
 of compression or extension in the rod; but all mathematical discussions 
 of the nature of the action of helical springs have been simplified or 
 made possible by eliminating or disregarding all consideration of 
 certain practical conditions met with in practice. Green showed in 
 1830 that the general investigation of the relations between the stresses 
 and deformations of any solid body depends in its simplest form upon 
 the solution of a quadratic equation having six unknown quantities 
 and twenty-one terms whose coefficients are essential, therefore we 
 may pardon all the later investigators who have refused to include the 
 further complications that consideration of the means of applying the 
 pressure upon the ends of the spring and the flexural stresses would 
 introduce, and have made a short cut by imagining the spring unwound 
 and resolved back into the original straight bar of uniform section, 
 in order to obtain any workable formula whatever; and we can under¬ 
 stand why more do not rush in with easy experiments and confident 
 amendments. 
 
 The very complete mathematical discussion of this whole subject 
 by St. Venant, the French physicist, in 1855, with graphic illustrations 
 of his conclusions, includes the consideration of round, square, triangular 
 and many peculiar sections. He demonstrates what may seem at first 
 rather startling, that the points of greatest distortion at the surface 
 are nearest to the axis of the twisted section, that the least distortion 
 occurs at the points farthest from the center, and that the stress and 
 strain tend toward zero at projecting angles, either acute or obtuse. 
 Thomson and Tait followed this with elaborate mathematical discussion 
 and practical experiments. The more important flexural distortions, 
 
14 
 
 SAFETY VALVE SPRINGS 
 
 in bending the steel and winding the spring, as well as the torsional 
 strains, are along the outer and inner faces of the square section in each 
 coil and to a less degree along the lateral faces, at both the short di¬ 
 ameters of the section and not through the corners; as may be very 
 roughly illustrated by winding a square rod of soft rubber into helical 
 form. 
 
 But the actual spring is not even approximately a straight bar 
 held firmly at one end and twisted uniformly; and the pressure is not 
 applied at the extreme end of the bar but upon a flat plate or thimble 
 at either end, fitted when the spring is free and not when more or less 
 distorted under load, but intended to transmit the pressure as nearly 
 in a straight line along the axis of the mandrel as conditions will permit. 
 The violent distortion of the cross-section of the square steel rod, which 
 by no stretch of imagination can be considered as still rectangular, 
 sets up internal stresses in the tempered steel, which must be recognized 
 even if they cannot be conveniently measured. The strain of deflection 
 of each coil, of even moderate pitch, amounts to a serious item, but is 
 expressly brushed aside and ignored in deriving the ordinary working 
 formulae. 
 
 Springs should be very gradually and uniformly heated without 
 decarbonizing the surface skin by exposure to any flame, and the 
 excessive hardness or temper of the surface afterward drawn by 
 reheating to a relatively low temperature. This reheating seems to 
 give a toughness to withstand greater tensile strain and is especially 
 important in proper consideration of the generally neglected factor of 
 lateral or flexural strain which becomes so large when any set or fracture 
 of the spring occurs. I am persuaded that much of the virtue and 
 special character of the spring lies in the molecular tension and condi¬ 
 tion of the surface skin after tempering. 
 
 Although the chief element in the power of a spring is its torsional 
 strain developed in the compression, and the flexural stress may be 
 comparatively a small part of the useful power or resilience, yet the 
 destructive set experienced from over-compression in springs of few 
 coils with steep pitch, can be shown, I believe, to be more commonly 
 due to exceeding the elastic limit in the bending strains than to any 
 severe strain in torsion; and this flexural stress increases as steel of 
 larger cross-section is employed; but no one has yet been willing to 
 risk a statement of the influence or effect of variation of pitch, as a 
 definite factor in any generally accepted formula. 
 
 In springs made of square steel it may very well be that the re- 
 
SAFETY VALVE SPRINGS 
 
 15 
 
 heating to draw the surface temper affects the corners most and the 
 lateral faces only slightly less, and that the toughened metal in the 
 corners backs up or strengthens the harder interior portions; the internal 
 strains would be relieved, while an approximately cylindrical interior 
 would retain a high temper to resist the truly torsional stress of com¬ 
 pression. The slightly variable temper in the corners and lateral faces 
 of the square steel may be the better disposed and adapted to accom¬ 
 modate the several varying strains in a helical spring; for the sym¬ 
 metrical form of the round steel, even when the temper is slightly 
 drawn after hardening, permits little relative adjustment of the several 
 lateral and torsional strains, and the round section can be considered 
 as subject to considerable unrelieved internal strain in flexure. 
 
 The spring must have sufficient compression to afford the amount 
 of valve-opening fixed upon as reasonable and practicable, yet be kept 
 within the least amount of movement that will satisfy these demands, 
 for every spring has considerable eccentricity, depending upon the 
 pitch and proportions of the coils, and under the increasing compression 
 or extension as the valve opens or closes, the ends have a movement 
 which may be likened in some degree to the actions of the free end of a 
 fire-hose under pressure. The side-thrust due to this twisting and 
 untwisting eccentricity is transmitted to the valve disc and guide wings, 
 and increases rapidly with each fraction of increased lift or opening 
 of the valve. 
 
 Large movement of the spring in compression is undesirable; it is 
 but a necessary means to an end, an evil to be kept within minimum 
 limits. The chief object of a safety valve is not to lift the disc but 
 to release steam; not to perform internal work in the valve but to 
 relieve the boiler. It would be an advantage if satisfactory discharge 
 through the valve could be attained with even less spring compression 
 than at present. Large lift of the disc is not merely a measure of 
 capacity but of inefficiency; for the valve which releases the steam 
 with the least proportional lift or spring compression is to that degree 
 the more efficient for its purpose and at the same time more safe and 
 reliable. 
 
 The specifications which require valve seats to be made of non- 
 corrosive metal and the rules which compel every valve to be tried 
 and lifted by the lever every day, aim to overcome the ever-present 
 danger that the valve may stick upon its seat and fail to open at the 
 critical moment; but the greatest cause of the sticking of the valve, 
 when it does occur, is not corrosion of the seat face but the binding 
 
16 
 
 SAFETY YALYE SPRINGS 
 
 friction of the disc-guides against the side of the well or throat of the 
 valve. This cocking or binding effect can be decreased by any modifica¬ 
 tion of design which will reduce the diameter of the cylindrical guide, 
 or which will eliminate the friction of the lower ends of the guides and 
 bring the guiding surface close to the plane of the seat; both of these 
 modifications reduce the moment of the friction or cocking stress. 
 Any device which reduces the lift of the disc and the spring movement 
 to the least possible amount will also reduce the eccentric spring action 
 and its effect, and of course any valve design which requires or con¬ 
 templates an unnecessarily large lift or compression disadvantageously 
 magnifies this effect. It is perhaps important to point out that as the 
 primitive and still common form of safety valve has a seat opening 
 beveled at an angle of 45 degrees with the vertical spindle, the effective 
 passage through the seat is measured by the sine of 45 degrees and is 
 approximately only 0.7 of the actual vertical lift or compression of 
 the spring when the valve opens, so that the spring must necessarily 
 compress about one and one-half times the effective lift, and even this 
 does not always afford a free passage for the steam to the air where 
 there is vertical overlap of the regulating ring against the lip of the 
 disc in order to increase the lift against the greater pressure of the 
 shortening spring. 
 
 In the well-known annular type of valve, the area of the disc 
 between the seats open to the constant pressure of the steam is ap¬ 
 proximately only four-fifths of the total initial area of the disc under 
 load in the bevel-seated form of valve having the same diameter and 
 seat circumference; therefore the use of the familiar annular, flat-seated 
 valve is the logical way to reduce to a minimum all the difficulties of 
 spring making, especially where the space available for the spring is 
 absolutely limited by the over-all dimensions permitted by locomotive 
 builders and boiler makers; for the spring need thus be of dimensions 
 and strength to carry only four-fifths of the load necessary in the lip- 
 type of valve; the vertical lift and spring compression require to be 
 only 0.7 as much, or for the same lift will give one and one-half times 
 as much discharge area; and no preliminary lift is required to relieve 
 the overlap of an adjusting ring, for the work of giving to the disc its 
 sudden pop lift is performed by an auxiliary steam discharge by-passed 
 through the central passages. This by-passed or auxiliary discharge 
 adds its volume to the main discharge capacity and leaves an absolutely 
 unrestricted and unthrottled free escape for the main flow of the released 
 steam directly to the open air, without any tortuous expansion chamber 
 
SAFETY VALVE SPRINGS 
 
 17 
 
 or deflecting ring; the outlet is across a flat seat which not only utilizes 
 the full vertical lift but gives a discharge opening of cylindrical form 
 with efficient rounded edges. This form of disc has the further ad¬ 
 vantage that it is impossible for it to jam or stick and it is easily refaced 
 by rubbing on a face-plate instead of grinding to a bevel; and as the 
 disc can be made entirely without the ever-cocking and sticking guides, 
 the efficiency of the spring can be thus aided and utilized to the greatest 
 possible degree. My emphasis upon this point of spring limitation and 
 the helpful effect of suitable valve-seat design is because attention has 
 not been generally called to its importance and experience has shown 
 the serious difficulties which may be thus minimized if not entirely 
 avoided. 
 
 It is not within my purpose to recommend any definite formula 
 for the calculation of helical springs. My investigations have led me 
 to believe that there are not in this country today many men who have 
 experienced the fortuitous concurrence of time, inclination, business 
 necessity and proper manufacturing and testing facilities to lead them 
 to develop a practical working formula very far beyond the very un¬ 
 satisfactory rules laid down in the hand-books. Experiments have 
 been carried out upon springs wound of comparatively small wire, 
 but every one who has had occasion to use the conventional formulae 
 must have realized that no matter how well they cover a few types of 
 car-springs within a limited range, they lead us far astray in this special 
 branch of the problem; especially in cases where the limitations upon 
 the free length of the spring will not permit the use of either round or 
 square bars and some special flat or rectangular section must be used 
 to secure the required area of steel and still leave room for movement 
 between the coils. 
 
 One engineer to whom I wrote replied: “ I would say in reference to 
 the questions raised by you, that I do not consider it good practice to 
 use a stress of over 95,000 or 100,000 pounds for valve springs, although 
 we have in our various experiences stressed springs as high as 145,000 
 and 150,000 pounds, but we do not under any circumstances recom¬ 
 mend this or any approximate stresses for the extreme service to which 
 valves are subjected. Regarding this question of stress, I would 
 further say that a long time ago we demonstrated that while various 
 published formulae are correct within certain limits for springs made of 
 round steel, they were far from being correct for springs made of squares 
 and special sections. We devoted a great deal of time to both theory 
 and experiment to demonstrate the formula which we now use, and 
 
18 
 
 SAFETY VALVE SPRINGS 
 
 which we have proved by exhaustive experiments to be correct. 
 We know that by using numerous published formulae that some springs 
 will show very excessive stress; however, these excessive stresses are 
 not actual, but apparent, due to errors in the formula. The formula 
 which we use being the result of years of experience, experiment and 
 calculation, you can readily understand is not published, and further¬ 
 more, would be useless without the accumulation of data and special 
 information which we have.” 
 
 My aim has been rather to state conclusions derived from experience 
 and observation and from the counsel and advice of those oldest and 
 wisest in this work as well as from an inheritance of the results of thirty 
 years of special study and experiment in this limited field. I have 
 reviewed the several practical considerations that must be taken into 
 account, so that in the discussion of the general subject this important 
 element of the spring may have its due attention. 
 
 Nearly every engineer of education and experience would be 
 qualified and perhaps ready to suggest at least one apparently simple 
 and more or less obvious improvement in the design of safety valves or 
 springs, but nearly every such possible detail will be found to be already 
 old. Almost every conceivable device and modification has been the 
 subject of a patent, and most of these have been thoroughly tried, 
 with much expense and enthusiasm, before being condemned and dis¬ 
 carded. The various subterfuges of double or concentric springs, one 
 more flexible than the other, of spiral springs with coils of increasing 
 diameter, whose first movement in compression is rapid until the smaller 
 and stiffer coils are brought into action, springs suspended in all sorts 
 of universal bearings, and every method of end bearing and fitting, 
 have all been tried and abandoned by almost every maker and user of 
 safety valves, but are periodically revived or rediscovered by some new 
 designer or foreman and brought forward for consideration again and 
 again. Before any such expedients are advocated, a study of the 
 old file of long-expired patents would be enlightening and interesting. 
 Attempts at using extension springs, in place of springs to be compressed 
 as the valve opens, can be seen in patents and experimental valves of 
 twenty-five years ago; but the idea has been generally abandoned, for 
 not only is it difficult to devise any satisfactory end-fastening which will 
 take firm hold of the steel without inducing a fracture there, but such a 
 spring could be easily and ignorantly overstrained and set, wdiile a 
 safely proportioned compression spring can not take a set within its 
 possible limit of movement, even to solid; and the side-thrust due to 
 
SAFETY YALYE SPRINGS 
 
 19 
 
 unevenly disposed coils is found in extension springs also, wherever the 
 springs have not the suitable length to permit proper proportioning and 
 balance. 
 
 It would serve no useful purpose were each engineer to attempt 
 to specify the exact dimensions of the springs to be used in safety valves 
 for each pressure and service, for the limitations of special cases and the 
 several conditions to be taken into account, with their relative im¬ 
 portance and weight in the problem, would require the exercise of 
 judgment to be derived only from personal experience, and any general 
 rule would be burdened with a long catalogue of exceptions more 
 troublesome than helpful. But the general principles rest upon a solid 
 foundation, and any one may judge whether the springs in his safety 
 valves satisfy certain rational requirements; but we must not expect 
 to reconcile mechanical contradictions nor ask for valves that would 
 demand miracles in springs.