UNIVERSITY OF CALIFORNIA COLLEGE OF AGRICULTURE AGRICULTURAL EXPERIMENT STATION BERKELEY, CALIFORNIA DETERMINING TONNAGE OF HAY IN STACKS R. L. ADAMS Results of a cooperative investigation conducted by the United States Department of Agriculture, Bureau of Agri- cultural Economics, Hay, Feed and Seed Division, and the California Agricultural Experiment Station BULLETIN 570 March, 1934 CONTRIBUTION FROM THE GIANNINI FOUNDATION OF AGRICULTURAL ECONOMICS UNIVERSITY OF CALIFORNIA BERKELEY, CALIFORNIA CONTENTS PAGE Introduction 3 Scope of the investigation 4 Determination of cubical contents of stacks 4 Rules for determining volume of stacks 4 The Quartermaster Rule 4 The Frye-Bruhn Rule 5 The Outlaw Rule 5 The Fowl Rule 5 Rules requiring height measurement 5 Analysis of the various rules 7 Suggested new rule 8 Example of calculating cubical contents of stacks by the Decimal Rule . 9 Effect of shrinkage upon volume of stacks 10 Shrinkage in heights of stacks 11 Factors affecting rate and amount of shrinkage 11 Determination of density of hay in stacks 12 Cubic feet per ton of hay 12 Factors affecting density of hay in stacks 13 Relation between age of stacks and cubic feet per ton (grain and volunteer hay) 14 Relation between size and age of stacks and cubic feet per ton (grain and volunteer hay) 14 Relation between size and age of stacks and cubic feet per ton (alfalfa hay) 14 Relation between size of stacks and cubic feet per ton (alfalfa hay) . 14 Relation between method of stacking and cubic feet per ton (alfalfa hay) 16 Relation between cuttings of alfalfa and cubic feet per ton of hay in stacks 18 Relation between variety and cubic feet per ton (alfalfa hay) .... 18 Conclusion 18 Suggested procedure for measuring stacks 18 Aids in determining cross section and tonnage of stacks 20 Table of cross sections of stacks 20 Chart for determining tonnages of haystacks 22 Summary 24 Acknowledgments 26 DETERMINING TONNAGE OF HAY IN STACKS 1 2 R. L. ADAMS 3 INTRODUCTION Production of hay in California annually amounts to approximately 4,000,000 tons. 4 Of this amount about 2,750,000 tons are of alfalfa, about 1,250,000 tons are of grain or grass, and a few thousand tons are of timothy or clover hay. A portion of this production is stacked in the field to be sold as loose hay, fed to livestock, or apportioned in payment of rent. Frequently information is needed concerning the tonnage con- tents of such stacks. Weighing is obviously preferable, but when weigh- ing cannot be done then some other means is required to assist in a fairly accurate determination of tonnage contents of stacks, particularly when a sale is being negotiated or consummated on a tonnage basis, when feeding operations are being planned, when rentals are paid in stacked hay, or when hay previously advanced to a tenant is being re- paid. To compute the tonnage of hay in stacks requires two steps : (1) deter- mination of the cubical contents of the stack by use of some acceptable rule, and (2) conversion of cubical contents to tonnage by dividing the cubical content, expressed in cubic feet, by some figure representative of the number of cubic feet occupied by 1 ton of hay. To calculate cubical contents of stacks, California farmers and stockmen have for years relied chiefly upon either the Quartermaster Rule or the Frye-Bruhn Rule, while occasional use is made of the Outlaw Rule, Because of a belief that no rule heretofore developed is sufficiently accurate or simple to serve satisfactorily the needs of both producers and buyers, the California Agricultural Experiment Station, in cooperation with the Bureau of Agricultural Economics of the United States De- partment of Agriculture, undertook an investigation to test the accu- racy of the various rules now in use, to attempt the development of a simple formula which would give more accurate results, and to deter- mine the number of cubic feet required for a ton of different kinds of hay. i Received for publication May 5, 1933. 2 Paper No. 51, The Giannini Foundation of Agricultural Economics. s Professor of Farm Management, Agricultural Economist in the Experiment Sta- tion, and Agricultural Economist on the Giannini Foundation. * United States Department of Commerce Bureau of the Census. Fifteenth Census of the United States, 1930. [3] 4 University of California — Experiment Station SCOPE OF THE INVESTIGATION During the course of this investigation a total of 563 California stacks were carefully measured, and later the actual weights of 364 of these stacks were determined. The stacks were located in Contra Costa, Marin, Merced, Sacramento, San Joaquin, Sonoma, Stanislaus, and Yolo coun- ties. Four hundred twenty-four stacks were of alfalfa hay, and 139 stacks of grain and volunteer hay. The stacks of alfalfa hay were prin- cipally of the square flat-topped type, ranging from 8 to 14 feet high, 16 to 22 feet wide, and 18 to 26 feet long. Most of the stacks of grain and volunteer hay were also of the flat-topped type with dimensions ranging from 10 to 16 feet in height, 18 to 26 feet in width, and 22 to 30 feet in length. Data were collected concerning the variety and texture of the hay, its stage of maturity when cut, the cutting (in case more than one were made), the method of stacking, the age of the stack, together with meas- urements (frequently repeated at intervals of time) of the height, width, length, and "over." 5 Later, if the hay were baled, weights as shown by the balers' tags were obtained. The data thus collected were subjected to searching tests, first by the Bureau of Agricultural Economics of the United States Department of Agriculture, and, later, by the California Experiment Station to deter- mine the accuracy of rules now in use, the influence of kind and quality of hay, the method of stacking, the rate of shrinkage, and other factors affecting the tonnage contents of stacks, and the number of cubic feet required to make a ton of hay under various conditions. The study de- veloped certain information concerning the accuracy of the various rules commonly used by buyers and sellers, a suggested rule to replace those now in use, and the effect of various factors upon the accuracy of determining the contents of stacks by formula. The more outstanding results are reported in this bulletin. DETERMINATION OF CUBICAL CONTENTS OF STACKS RULES FOR DETERMINING VOLUME OF STACKS Of the several rules for determining the volume of haystacks which have been advanced from time to time, the most commonly used rules are the Quartermaster, the Frye-Bruhn, the Outlaw, and the Fowl. The Quartermaster Rule. — This rule consists in adding the over to the width, dividing by 4, squaring the result and multiplying by the s "Over" is the distance from the ground on one side of and close to the base of the stack, to the ground on the opposite side of and close to the stack, measured at right angles to the length of the stack. Bul. 570] Determining Tonnage of Hay in Stacks 5 (0 + w\ 2 — - — ) L. G This formula is based on the theory that the cross section of the stack can be reduced to a square by adding the over and the width and then dividing by 4, a figure representative of the average length of each side of the square. Squaring this figure repre- sents the area of the cross section, which when multiplied by the length gives the cubical contents of the stack. The Frye-Bruhn Rule. — The Frye-Bruhn Rule, or Rule of Two, sub- tracts the width from the over, multiplies this result by the width, and divides by 2 in order to determine the cross section of the stack. This cross section multiplied by the length gives the contents of the stack as calculated by this formula. The formula is expressed thus ■Ci 2 ) WxL, or (O-W) y 2 W L, or (%0-%W) WxL = V. This rule is based on the assumption that the height of a stack can be found by sub- tracting the width from the over and dividing by 2; that the area of the cross section is equal to the height times the width; and that the cross section times the length gives the contents of the stack. The Outlaw Rule. — This is a simple formula which consists in multi- plying the over by the width, dividing by 4 (presumably giving the area of the cross section of the stack) , and then multiplying by the length. It is expressed thus : ( — - — ) L = V. <(*?)*- The Fowl Rule. — The Fowl Rule, or Department Rule, is expressed by the formula F xO xW xL = V, in which 0, W, and L represent the measurements of over, width, and length of the stack, respectively, and F is a factor varying from 0.25 to 0.37, according to the height and full- ness of the stack. For narrow stacks, three-fourths as tall as they are wide, the factor 0.25 is used, if moderately full the factor is 0.28, and if very full-sized the factor is 0.31. For stacks as tall as they are wide, the factors for narrow, moderately full, and very full-sized are respectively 0.28, 0.31, and 0.34. For stacks one and one-fourth times as high as they are wide, the factors for the varying degrees of fullness are 0.31, 0.34, and 0.37 respectively. 7 Rules Requiring Height Measurement. — Several other rules have been advanced from time to time, but as these require determination of 6 In the description of each of these rules given in following paragraphs, the sym- bols O, W, L, and H represent the dimensions of over, width, length, and height of stacks, respectively, in each formula presented. 7 For further discussion see : McClure, H. B., and W. J. Spillman. Measuring hay in ricks or stacks. U. S. Dept. Agr. Office Sec. Cir. 67:1-10. 1916. See also: U. S. Dept. Agr. Yearbook 1924:340-342. 1925. University of California — Experiment Station the heights of stacks — a figure difficult to obtain — and rather compli- cated calculations, they have never become popular. The Triangle Rule is an example. It is expressed by the formula (i/ 2 W H + S B) L, in which W is the width, H the height, and L the 222 Fig. 1. — A glance at these illustrations of cross sections of differently shaped stacks indicates the type of cross section and the factor to be used when the Fowl Rule is to be applied. (After McClure and Spillman.) length of the stack. S is the square root of a figure obtained by squaring one-half the width and adding to it the square of the height. B is the square root of one-fourth the over squared, minus one-half of 8 squared. The Triangle Rule has proved to be fairly accurate. 8 If it were not for the difficulties involved in determining stack heights and the complexity of calculations, the rule would be worthy of more extensive use. s Checks made of this rule by the United States Department of Agriculture indi- cate an average percentage of accuracy of about 96. Seventy-nine per cent of the cases were in error by less than 10 per cent. See: Hosterman, W. H. A method of de- termining the volume and tonnage of haystacks. U. S. Dept. Agr. Tech. Bui. 239:15. 1931. Bul. 570] Determining Tonnage oe Hay in Stacks ANALYSIS OF THE VARIOUS RULES As a basis for studying the accuracy of rules now in use, each stack when measured had recorded on coordinate paper a carefully drawn outline of the cross section of the stack. The areas of these cross-section sketches were subsequently measured by a planimeter calibrated to permit very close calculations of the actual areas of the sketched stacks. With these figures comparison could then be made with the cross sec- tions calculated according to the principal rules now in use, those se- TABLE 1 Comparison of the Cross-Section Areas of 366 Haystacks Calculated by the Frye-Bruhn, Quartermaster, and Outlaw Formulas with Actual Average Cross-Section Areas Determined by Planimeter Measurements Calculated average cross-section area of stacks Relative accuracy of computed average cross sections compared with actual average cross sections of all stacks (263 square feet = 100) Degree of error Formula Average for all stacks Range in error of measurements for individual stacks 1 2 S 4 Frye-Bruhn square feet 234 260 23b per cent 88 13 99 23 87.39 per cent 11.87 0.77 12.61 per cent 5.4 -20.8 0.0*-23.8 Outlaw 0.2 -32.8 * Four cases checked identically with the actual areas. lected for testing being the Frye-Bruhn, the Quartermaster, and the Outlaw rules. Cross-section areas were made for each of 366 haystacks, and the actual cross-section areas were determined by planimeter meas- urements. Comparison of the variation in accuracy of results obtained by use of the different rules is presented in summary form in table 1. As shown in column 1 of table 1, the average cross-section area for the 366 stacks when calculated by the Frye-Bruhn, Quartermaster, and Out- law formulas were found to be 234, 260, and 236 square feet, respec- tively. Column 2 indicates the degree of accuracy of each of the three formulas when compared with the actual average area of 263 square feet determined by planimeter measurements of the cross sections of the same stacks. Column 3 records the average degree of error of the calcu- lated results as compared with the actual average area of the cross sec- tions, and column 4 shows the range in error of calculated results com- pared individually with the planimeter measurements. Thus, the calcu- lations by the Frye-Bruhn Rule for individual stacks resulted in dif- 8 University of California— Experiment Station ferences of from 5.4 to 20.8 per cent greater or lesser than the plani- meter calculations of the same stacks. Similarly, the differences between the planimeter measurements and calculations by the Quartermaster Rule varied from 0.0 to 23.8 per cent. The zero means that some stacks (four in number) compared exactly. Prom this exactitude of zero, re- sults with other stacks varied to as much as 23.8 per cent difference in the Quartermaster Rule when compared with the planimeter findings. The Outlaw Rule was found to give results varying from 0.2 to 32.8 per cent from the planimeter measurements. TABLE 2 Comparison of Degree of Error Between Actual and Computed Cross-Section Areas as Calculated by Frye-Bruhn, Quartermaster, and Outlaw Rules Degree of error Number of cases in each group (366 stacks) Percentages in each group (above or below actual area) Frye-Bruhn Rule Quarter- master Rule Outlaw Rule Frye-Bruhn Rule Quarter- master Rule Outlaw Rule 83 232 46 5 188 123 34 11 10 49 64 82 87 84 0.0 22.4 63 4 12.4 1.8 51 4 33 7 9.2 3 2.7 13 4 17 4 22.5 23 8 22 9 Inaccuracy will, of course, favor either the buyer or the seller, ac- cording to whether more or less hay is actualty delivered than the cal- culated figures show. The significance is more apparent when one notes the frequency of errors resulting from the cross sections of the 366 stacks already referred to, when these are calculated individually by each of the Frye-Bruhn, Quartermaster, and Outlaw rules, and com- pared with the findings as shown by planimeter readings. The findings are set forth in table 2. SUGGESTED NEW RULE As a result of the findings set forth above, including similar work in other states, 9 Hosterman 10 evolved a new rule for determining the cross section of square, flat-topped stacks of the type commonly made in California. For purposes of identification the name Decimal Bute desig- 9 California, Colorado, Idaho, Minnesota, Montana, Nebraska, Nevada, "Oregon, South Dakota, and Utah cooperated with the Bureau of Agricultural Economics of the United States Department of Agriculture in this study. io For a full discussion of this rule see : Hosterman, W. H. A method of determin- ing the volume and tonnage of haystacks. U. S. Dept. Agr. Tech. Bui. 239:16-20 1931. See also: Hosterman, W. H. Measuring hay in stacks. U. S. Dept. Agr. Leaflet 72:2-3. 1931. Bul. 570] Determining Tonnage of Hay in Stacks 9 nates this new rule in this bulletin. This rule consists in multiplying the over by 0.56, subtracting 0.55 times the width, and multiplying the resulting figure by the width. Expressed as a formula, this rule reads as follows: V= [(0.56x0)- (0.55 xW)] W. This rule is a refinement of the Frye-Bruhn Rule in that instead of taking one-half the over and one-half the width, the Decimal Kule takes 0.56 of the over and 0.55 of the width, which figures are found to give more accurate results. The greater accuracy of this rule is shown when planimeter readings of 288 comparable stacks are compared with re- sults obtained by each of various rules. The planimeter readings of these 288 stacks indicated a total of the cross sections amounting to 74,619; calculating by the Decimal Rule the total amounts to 75,395. Calcula- tions according to the Quartermaster, Frye-Bruhn, and Outlaw rules gave totals respectively of 73,759, 66,447, and 64,266. Considering the planimeter readings as 100, indexes of accurac}^ for the other rules then become : Decimal 101.0 , Quartermaster 98.6 Frye-Bruhn 89.0 Outlaw 86.3 In other words, the results with the Decimal Rule average within 1.0 per cent of the planimeter readings; the results of the Quartermaster Rule within 1.4 per cent; while the Frye-Bruhn and Outlaw rules vary 11.0 per cent and 13.7 per cent, respectively. The area of the cross section multiplied by the length is designed to give the cubical contents. In all cases measurements are taken in feet so that the results will be in square feet for areas and cubic feet for volume. Example of Calculating Cubical Contents of Stacks by the Decimal Rule. — A haystack having an over of 51 feet, a width of 21 feet, and a length of 24 feet will have a cubical content of 8,573.04 cubic feet as cal- culated by the Decimal Rule. The procedure of calculation consists in determining the area of the cross section and multiplying the area of the cross section by the length to obtain the cubical content. The formula for this rule is : V= [ (0.56 x O) - (0.55 x W) W] x L. By inserting in the formula the values of O, W, and L for this stack and calculating the various steps, results are as follows : V = [ (0.56 x 51) - (0.55 x 21) 21] x 24 V= [(28.56-11.55) 21] x 24 V= (17.01x21) x24 V= 357.21x24 V = 8,573.04 cubic feet 10 University of California — Experiment Station EFFECT OF SHRINKAGE UPON VOLUME OF STACKS Before discussing the number of cubic feet required to make a ton of hay — the final step in determining the tonnage contents of stacks — at- tention should be directed to the settling of stacks and the influence of this shrinkage upon volume and consequently upon the number of cubic feet that constitutes a ton of hay. All stacks settle with the passing of time and become more dense. This factor has a direct influence upon the method of calculating the ton- nage contents. In order to determine the rate of shrinkage, 75 stacks of TABLE 3 Average Total Shrinkage of Alfalfa Haystacks Over Various Periods (Stacks of 10 to 30 tons in size) Ages of stacks at times of measuring Averag shown (perce cubi( e total shrinkage as by measurements First measurement Second measurement ntage decrease in feet of contents) Over 2 and under 3 months % 8.3 7 9 6.5 10 3 14 27 4 20 .7 alfalfa hay were measured to determine shrinkage in cubical contents at various intervals of time, the longest period being for 240 days fol- lowing the date of stacking. Of these 75 stacks, 22 were measured twice, 24 three times, and 29 four times. These measurements indicate that the shrinkage of stacks proceeds at the greatest rate during the first month after stacking, continuing at a gradually decreasing rate of settling, as long as dry weather continues, but showing a marked increase in rate after the stacks have been subjected to the influence of fall rains. The average total shrinkage taking place between measurements is shown in table 3. The rate of shrinkage indicated by these data show a gradual but not marked falling off in the rate of shrinkage as the stacks age, until the influence of rains hastens shrinkage. This influence is in evidence in connection with the last four figures in the final column of table 3. The rate of shrinkage for different stacks of the same kind and qual- ity of hay, of approximately the same size, and of about the same ages, Bul. 570] Determining Tonnage of Hay in Stacks 11 was by no means uniform. Ten individual and comparable stacks, which had been standing 30 to 59 days at the time of taking the first measure- ment and 180 and 209 days at the time of the second measurement, de- creased in volume by 17, 21, 22, 26, 29, 31, 32 (2 stacks), 36, and 46 per cent, respectively. Seven other stacks measured during the interval elapsing between measurements taken 60 to 89 days after stacking and 210 to 240 days later recorded shrinkages of 20, 21, 26 (2 stacks), 27, and 31 (2 stacks) per cent of volume. Shrinkage in Heights of Stacks. — During the several months when stacks continue to settle and hence to shrink in volume, no appreciable effect could be noted on either the width or length of the measured stacks. Reduction of volume is, therefore, primarily and principally due to a shrinkage in height. Measurements of height indicate that the greatest decrease occurs within the first 30 days after stacking but continues at measurable rates during the 8-months' period covered by these studies. The average height of nine small haystacks (10 to 16% feet in height) measured during the first 30 days after stacking was found to be 13 feet 8 inches. Second measurements taken 30 to 59 days, and third measure- ments 60 to 89 days after stacking gave average heights of 12 feet 2 inches and 11 feet 11 inches, respectively. The average decrease in the heights of these stacks between the first and second measurements amounted to 1 foot 6 inches, a decrease of 11.0 per cent; between the second and third measurement the decrease was 3 inches, or 2.1 per cent; and for the entire period a decrease of 1 foot 9 inches, or 12.8 per cent occurred. On larger stacks, from 15 to 23 feet in height, the shrinkage on nine stacks during the interval between measurements made 30 to 59 days and again 180 to 209 days after stacking averaged 4 feet 8 inches, or 24.5 per cent. On eight other stacks measured 60 to 89 days and 210 to 240 days after stacking, the shrinkage averaged 3 feet 6 inches, or 20.3 per cent. No uniformity of rate of decrease in heights could be noted. The nine stacks measured 30 to 59 days and 180 to 209 days after stacking, for example, individually registered shrinkages in height of 13, 19, 23, 24 (2 stacks), 29 (2 stacks), 30, and 32 per cent. The eight other stacks shrank 13, 16, 19, 21 (2 stacks), 25, and 27 (2 stacks) per cent, respec- tively. Factors Affecting Rate and Amount of Shrinkage. — Numerous fac- tors have been observed as affecting the rate and amount of shrinkage of haystacks, the more important of which are : 12 University of California — Experiment Station Kind of hay Maturity when cut Moisture content when stacked Amount and kinds of weeds Height of stack Method of stacking Eapidity of drying of hay in stack (influenced by size and shape of stack and atmospheric conditions) Data obtained during the course of this investigation were not ade- quate to permit a quantitative analysis of the effect of each of these fac- tors upon the rate and amount of shrinkage occurring in stacks. Atten- tion can only be drawn to them as causes of differences in rates of shrinkage. No correlation could be noted between height of stack and rate of set- tling. This is not surprising in view of variable influences due to differ- ent methods of stacking, different qualities and ripeness of hay, and similar factors. The findings do, however, emphasize the complexity of the problem. DETERMINATION OF DENSITY OF HAY IN STACKS As already indicated, calculation of the cubical contents of haystacks is but a preliminary step to a determination of the tonnage of such stacks. Once the cubical contents have been determined by means of any one of the rules discussed above (with emphasis being placed upon the Decimal Rule, since it tends to be more accurate) there arises a need for some figure that shall express as nearly as possible the number of cubic feet that represents a ton of hay. CUBIC FEET PER TON OF HAY In California the usual method is to assume that a ton of hay occupies a space equal to the cube of 6, 6.5, 7, 7.5, 8, or some similar figure, accord- ing to the size and shape of the stack, its age, and the character of the hay. According to our field observations, figures of 450 cubic feet per ton of alfalfa and 512 cubic feet of grain and volunteer hay are most fre- quently taken as the basis of calculations. 11 In order to check the accuracy of figures now in use representing the density of hay in stacks, comparison was made of the volume of 364 stacks (139 of volunteer and grain hay and 225 of alfalfa hay) with the final weights as shown by balers' tags. For grain and volunteer hay the density ranged from 429 to 926 cubic feet per ton with a general average ii This is a variation from the actual 343, 422, and 512 cubic feet which results if one cubes 7.0, 7.5, or 8.0 feet, respectively. Bul. 570] Determining Tonnage of Hay in Stacks 13 of 666 cubic feet per ton of hay for all stacks; for alfalfa a general aver- age of 448 cubic feet per ton of hay for all stacks with a range of from 271 to 597 cubic feet per ton. The greatest frequency group for all stacks of grain and volunteer hay ranged between 600 and 800 cubic feet per ton, the average for this frequency group being 696 cubic feet. The greatest frequency group for all stacks of alfalfa hay ranged between 400 and 500 cubic feet per ton, the average for this group being 453 cubic feet. FACTORS AFFECTING DENSITY OF HAY IN STACKS The number of cubic feet required per ton of hay in stacks is influenced by a number of factors of which the following are the more outstanding : Type and size of stack, especially its height Height from which the hay is dropped during stacking Type of stacker Amount of hand-placing and tramping Method of hauling to the stack Atmospheric conditions Dryness of hay Leafiness of hay Texture of hay Variety of hay Amount and character of foreign matter Lengtli of time in stack Eate of shrinkage Of these various factors the two most outstanding are (1) the mois- ture content of the hay, and (2) the compactness of the stack. The drier the hay the less it weighs per cubic foot. The per cent of moisture is ob- viously affected by the condition of the plants when cut, the method of curing, the atmospheric conditions occurring during the stacking and sweating process (especially the presence or absence of exceedingly dry- ing winds, hot spells, or fogs), and by absorption of rain. The density of the stack is influenced by the height, the kind and quality of the hay, and the method of stacking. From data compiled during the course of this investigation, compari- sons were made of the cubical contents and the resulting tonnages of (a) stacks of different ages; (b) various-sized stacks; (c) two methods of stacking (overshot and Jackson fork) ; (d) various cuttings of alfalfa hay; and (e) two varieties of alfalfa (Peruvian and Chilean or com- mon) . These studies clearly emphasize the difficulty of obtaining a figure that is likely to be generally reliable. 14 University of California — Experiment Station Relation Between Age of Stacks and Cubic Feet per Ton (Grain and Volunteer Hay). — Measurements of stacks at various ages resulted in data as given in table 4. "Relation Between Size and Age of Stacks and Cubic Feet per Ton (Grain and Volunteer Hay). — By dividing- the various stacks measured into group intervals data could be tabulated indicative of the cubic feet comprising a ton of hay for different-sized stacks and of different ages. TABLE 4 Relation Between Age of Stacks and Cubic Feet per Ton : Grain and Volunteer Hay (139 stacks) Age of stacks 35 days 50 days 80 days 110 14 6 42-26.42 697 410 926 18 20.7 14 15-35 35 499 429-695 11 27.7 20 26-35.16 533 488-587 Again it should be understood, because there are so many immeasurable factors which could not be included, that these averages are not absolute. The findings are given in table 5. Relation Between Size a/nd Age of Stacks and Cubic Feet per Ton (Al- falfa Hay). — Table 6 presents in some detail data of the cubic feet re- quired per ton of alfalfa hay in stacks of different sizes and different ages. No allowance has been made for differences in variety, cutting, method of stacking, or texture of hay. The data are the result of divid- ing the predetermined volume of each stack (using the Decimal Rule) by the tonnage weights obtained at the time the hay was baled out of the stacks. A study of table 6 shows no uniformity of relation between age of stack and cubic feet per ton of hay. It does indicate, however, that for most stacks up to 20 tons the cubic feet per ton fall within the range of 400 to 500 cubic feet. Relation Between Size of Stacks and Cubic Feet per Ton (Alfalfa Hay). — Measurement of 100 stacks of common alfalfa hay, put up with either overshot stackers or derrick and fork, and classified according to actual tonnage as shown by balers' weights, indicates a tendency, though not absolute, towards fewer cubic feet to make a ton of hay with the larger stacks. There is a wide range, however, in the density of stacks of Bul. 570] Determining Tonnage of Hay in Stacks 15 TABLE 5 Belation Between Size and Age of Stacks and Cubic Feet per Ton Grain and Volunteer Hay (139 stacks) Size intervals Under 10 tons Stacked 35 days 10 to 20 tons Stacked 35 days Stacked 50 days 20 to 30 tons Stacked Stacked 35 days 50 days Stacked 80 days 30 to 40 tons Stacked Stacked 50 days 80 days Frequency distribution Total number of stacks 400 to 500 cubic feet per ton 500 to 600 cubic feet per ton 600 to 700 cubic feet per ton 700 to 800 cubic feet per ton 800 to 900 cubic feet per ton Over 900 cubic feet per ton 18 77 11 15 5 6 2 6 3 2 2 5 4 2 2 4 3 36 1 6 10 31 7 4 5 1 Average size, tons 8.68 13 5 16.4 23.2 24 8 23.8 33 7 32 3 Average volume, cubic feet per ton 757 733 687 649 513 475 668 722 477 448 525 542 490 490 540 Greatest frequency group 540 TABLE 6 Cubic Feet per Ton of Stacked Alfalfa Hay Age of Size of stacks Number of stacks Cubic feet per ton of hay Greatest frequency group (mode) stack at time of measuring Average for all stacks Range for all stacks Group Number of stacks Average of modal group 5 days < Under 10 tons 6 469 402-514 400-500 4 446 1 10 to 20 tons 14 461 356-512 400-500 9 451 15 days < Under 10 tons 8 496 379-597 400-500 4 461 I 10 to 20 tons 12 359 380-550 500-600 6 525 20 days ■ Under 10 tons 6 433 346-484 400-500 4 466 { 10 to 20 tons 20 499 347-596 500-600 11 541 25 days Under 10 tons 8 447 338-540 400-500 5 469 Under 10 tons 10 463 391-534 400-500 6 448 30 days < 10 to 20 tons 32 463 311-589 400-500 16 466 20 to 30 tons 8 416 331-502 300-400 4 350 Under 10 tons 10 414 332-482 400-500 7 443 35 days 4 10 to 20 tons 30 437 338-596 400-500 14 431 20 to 30 tons 10 407 352-444 400-500 6 425 40 days < Under 10 tons 6 498 377-586 500-600 3 552 { 10 to 20 tons 11 462 314-588 475-588 6 536 50 days 10 to 20 tons 10 462 392-526 400-500 8 462 60 days < ( 10 to 20 tons 20 to 30 tons 7 480 425-546 400-500 5 458 7 439 271-524 500-600 3 512 65 days 10 to 20 tons 10 379 309-518 300-400 7 346 16 University of California — Experiment Station the same size. The 15 to 22% ton stacks, for instance, show a larger num- ber of cubic feet per ton on the average than do the 7% to 15 ton stacks. The evidence is set forth in table 7. TABLE 7 Relation Between Size of Stacks and Cubic Feet per Ton Common Alfalfa Hay (100 stacks) Grouping by stack sizes Less than J 1 ! tons iy 2 to 15 tons 15 to 22^ tons 22^ to 30 tons 30 to 371 2 tons Frequency distribution Total number of stacks measured Less than 300 cubic feet per ton 300 to 400 cubic feet per ton 400 to 500 cubic feet per ton 500 to 600 cubic feet per ton 600 and over cubic feet per ton 27 8 1 1 4 3 10 3 9 1 1 Average volume, cubic feet per ton All stacks Greatest frequency group. 478 459 455 458 475 457 415 422 396 366 TABLE 8 Cubic Feet per Ton of Common Alfalfa Hay in Stacks Made With Different Types of Stackers (Measured 20 to 35 days after stacking) Type of stacker Overshot Derrick and fork Number of stacks 10 28.5 20.8-34.1 414 337-493 7 Average size of stacks, tons Range in size of stacks, tons Average cubic feet per ton 35 6 22.9-40.9 381 Range in cubic feet per ton 351-481 Relation Between Method of Stacking and Cubic Feet per Ton (Al- falfa Hay). — Measurements of 17 stacks of second and third cuttings of common alfalfa, in stacks 20 to 40 tons in size, made 20 to 25 days after stacking:, indicate that in about seven and one-half times out of ten less cubic feet are required per ton of hay when the stacks are put up with derrick and fork than when stacked with the overshot stacker. The findings are given in table 8. Bul. 570" Determining Tonnage of Hay in Stacks 17 TABLE 9 Cubic Feet per Ton of Common Alfalfa Hay : Second and Third Cuttings Cuttings Second Third Frequency distribution Total number of stacks Under 300 cubic feet per ton 300 to 400 cubic feet per ton 400 to 500 cubic feet per ton 500 to 600 cubic feet per ton 600 and over cubic feet per ton Average size, tons All stacks 14 30 14.25 Average volume, cubic feet per ton All stacks 400 to 500 cubic feet per ton group.. 500 to 600 cubic feet per ton group.. 436.70 453.40 TABLE 10 Cubic Feet per Ton of Common (Chilean) and Peruvian Varieties of Alfalfa Variety of alfalfa Common Peruvian Frequency distribution Total number of stacks Under 300 cubic feet per ton 300 to 400 cubic feet per ton 400 to 500 cubic feet per ton 500 to 600 cubic feet per ton 600 and over cubic feet per ton 32 32 3 3 7 6 13 11 6 5 3 6 Average size, tons All stacks 14.16 15.04 Average volume, cubic feet per ton 450.60 466.00 479 00 440 00 18 University of California — Experiment Station Relation Between Cuttings of Alfalfa and Cubic Feet per Ton of Hay in Stacks. — The density of hay in 19 stacks of second cutting and 23 stacks of third-cutting alfalfa were found to be 491 and 437 cubic feet per ton of hay, respectively. Measurements of the individual stacks, how- ever, showed a range from 249 to 625 cubic feet per ton for second cut- ting, and from 197 to 615 cubic feet per ton for third-cutting hay. Fur- ther examination of the data, presented in table 9, reveals that nine times out of ten the stacks of second cutting are less dense than those of third-cutting hay. Relation Between Variety and Cubic Feet per Ton (Alfalfa Hay). — A study of 32 stacks of common (Chilean) alfalfa and 32 stacks of Peruvian alfalfa indicates that the variety has very little relation to the number of cubic feet per ton of hay. It will be seen in table 10 that com- mon alfalfa averages 450 cubic feet per ton, while Peruvian alfalfa has a slightly higher average of 479. A study of these averages, however, reveals that the difference is not significant but is due to wide variation in the individual stacks. CONCLUSION From the data presented above, which shows the wide variation in cubic feet per ton of hay resulting from the numerous immeasurable and un- controllable factors, it is evident that no rule of calculating tonnage of hay in stacks can be evolved which will produce highly accurate results under all conditions. However, some of the findings are indicative and should be helpful in more closely estimating the tonnage of hay in stacks. SUGGESTED PROCEDURE FOR MEASURING STACKS As a result of having taken and checked the results of more than 1,000 measurements of haystacks during the course of this investigation it is evident that a considerable variation in measurements is very likely to occur even though carefully done. No two men independently measuring the same stack at the same time are likely to obtain identical figures for width, length, or over. A major difficulty lies in the irregularity of most stacks. Most California stacks resemble a loaf of homemade bread. In some cases the loaf "falls" and in others it runs over, just as bread ex- tends beyond the edges of a pan. Because of the varying widths, lengths, and heights throughout the three dimensions of any stack, the measure- ments are certain to differ, according to just where and how the meas- urements are made. Not only do such irregularities in the shape of the stack, such as lack of uniformity in top lines and varying bulges in stack sides, make it Bul. 570] Determining Tonnage of Hay in Stacks 19 difficult to obtain accurate measurements of overs,* but also there is the ever present danger that the width and over measurements are not taken at right angles to the length. If stiff winds are blowing the chances for error are materially increased. Measurements made during or following heavy winds vary from those made during periods of calm weather because stacks tend to puff out under the influence of penetrating air drives. Sometimes winds are sufficiently severe to actually lift good-sized masses from the tops of stacks, the measurements made during or after this occurs are likely to be in error. Difficulties in measuring can be greatly decreased by building stacks as compact and regular in shape as possible. Pegs set along the base line will help to make straight sides. The hay should then be carefully placed to insure an even stack, corners being kept well squared, sides vertical, and sufficient tramping done so that 'equal settling will result through- out all parts of the stack. Stacks thus built are easier to measure and the calculations are likely to be more accurate than if stacks are built hap- hazardly and irregularly. When measuring stacks a sufficient number of measurements of widths, lengths, and overs should be taken so that the resulting aver- ages will approximate as closely as possible the actual dimensions of the stack. Measurement of widths should be taken carefully at both ends of the stacks, making proper allowance for bulges, and the average of the two measurements used in computing volume. The length should be measured in a similar manner along* both sides and the two figures aver- aged. Overs must be measured at right angles to the base line of the stack. The several points where these measurements are to be made should be carefully located by measuring from the ends on each side of the stack in order to insure placement of the tape in a proper position for taking these measurements. Lines or tapes used to measure overs should be drawn tight enough to fit to the shape of the top, but not tight enough to cut into the top of the stack. Because of the danger of wind interference and the need of pull- ing the line tight, a cloth tape is less accurate than a thick cord, such as is used by builders. This can be best thrown over the stack by means of a weight similar to those used by fishermen and sufficiently heavy to carry the cord. Feet and yards can be marked off with colored paints or strings securely affixed so that slipping will not occur. Measurements to a half foot usually are productive of sufficient accuracy for all practical pur- poses. 20 University of California — Experiment Station AIDS IN DETERMINING CROSS SECTION AND TONNAGE OF STACKS Notwithstanding the difficulties inherent in the use of formulas for de- termining the tonnage of stacks, as discussed above, circumstances may require the use of some formula. In such cases the Decimal Rule will best serve as a means for determining approximate cubical contents. Then individual judgment must govern the selection of a figure to rep- resent the number of cubic feet per ton. Study of the tabulated findings given in preceding pages will aid in that determination. To simplify the task of calculating cubical contents and tonnage, a table and a chart are given below. These aids provide means of determin- ing cross sections of stacks and their tonnage contents. As a preliminary, four figures are needed. These are (1) width of stack, (2) over of stack, (3) length of stack, and (4) number of cubic feet accepted as comprising a ton of hay. Table of Cross Sections of Stacks. — The chief calculation required in using the Decimal Rule is the determination of the cross-section area of any given stack. The rule calls for 0.56 of the over minus 0.55 of the width, multiplied by the width. Table 11 was constructed in accordance with this rule. The vertical column at the left shows a list of various widths of stacks. The caption, or horizontal row of figures at the top, gives a list of overs. The figures in the body of the table are the areas of the cross sections, in square feet, for stacks of the dimensions indicated in the column and row headings. A sufficiently wide range of measure- ments is given in the table to provide for most of the stacks put up in California. Others must be calculated individually. To use the table, one first finds the figure of width in the vertical col- umn at the left of the table that corresponds with the width of the stack, the cross section of which is desired. Next, the figure of over that corre- sponds with the over of the stack is located in the horizontal row at the top of the table. The figure at the point where the column and row inter- sect is the area of the cross section (in square feet) of the stack. To demonstrate this procedure, suppose one has a stack 22 feet wide with an over of 48 feet. By following the procedure just outlined the cross section of this particular stack is found to be 325 square feet. Or if the stack is 16 feet wide and has an over of 40 feet, the cross section is 218 square feet. Use of this table eliminates the necessity of making in- dividual calculations to determine the cross-section areas of the ma- jority of stacks as built in California. Bul. 570] Determining Tonnage of Hay in Stacks 21 CO :::::::::::::::::::::::: : co r^. 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In addition, as already pointed out, the length of the stack must be known and a figure determined, which in the judgment of the inquirer is representative of the number of cubic feet comprising a ton of hay. Directions for using the chart are as follows : 1. Determine the length, width, over, and number of cubic feet per ton of hay applicable to the stack. 2. Prom table 11 determine the cross-section area of a stack having these dimen- sions of width and over. 3. On figure 2 locate the length in Scale 1 and the cross-section area in Scale 2 that correspond to the length and cross section of the stack under consideration. Connect these points. 4. With a straight edge extend the line made by connecting the two points until it intersects Scale 3. 5. Locate on Scale 4 the number of cubic feet per ton that is pertinent to this stack. Connect this point with the previously located point on Scale 3. 6. Extend the line formed by connecting the two points on Scales 3 and 4 until the line intersects Scale 5. This last point of intersection will be the calculated ton- nage for this particular stack. The procedure to be followed in using this device for determining the tonnage content of haystacks may be demonstrated by an example. If a given stack is 50 feet long, has a cross-section area of 300 square feet (as determined from table 11), and it is assumed or determined that 500 cubic feet are required per tou of hay, the first step consists in con- necting with a straight line the figure "50" on Scale 1 and the figure "300" on Scale 2. The line is then extended to Scale 3. Next, this point on Scale 3 is connected with "500" (the number of cubic feet per ton of hay) on Scale 4. This line is then extended to Scale 5 and the tonnage read at the point where it crosses Scale 5 — in this case 30.0 tons. Bul. 570] Determining Tonnage of Hay in Stacks 23 FORMULA: TONS = '*" ^g«^ »?£ * LENGT " CUBIC FEET PER TON SCALE I LENGTH OF STACK (FEET.) 70 r 65 60 50 30 SCALE 2 AREA OF CROSS SECT/ON CSQ. FT.) 100 150 SCALE 4 FACTOR OF CUBIC FEET PER TON 400 SCALE S TONS 90 -17 16 15 14 13 12 EDNA FISHER 60 50 Fig. 2. — Chart for determining tonnages of hay stacks when length, cross section, and number of cubic feet per ton of hay have been previously determined. 24 University of California — Experiment Station SUMMARY The need of a satisfactory method for determining the tonnage of stacked hay, when conditions prevent actual weighing, resulted in the collection by the College of Agriculture of more than 1,000 measure- ments of 563 stacks of hay and final weights of 364 of these stacks, as shown by balers' data, in order to study the accuracy of prevailing methods of estimating the tonnage of haystacks, and to attempt the de- velopment of a better rule than any now in use. As a result of this study the following conclusions were made : A study of the Quartermaster and Frye-Bruhn rules, the two princi- pally used in California, indicates that on an average they will give re- sults within 99 per cent and 88 per cent, respectively, of actual volume of stacks. Results obtained with the Quartermaster Rule, however, may be in error as much as 0.1 to 23.8 per cent, and with the Frye-Bruhn Rule from 5.4 to 20.8 per cent of actual volume of stacks. The Decimal Rule, developed during the course of this investigation, is a refinement of the Fn^e-Bruhn Rule, and for measuring square, flat- topped stacks is expressed by the formula V= [ (0.56x0) - (0.55x17) 17] L in which O is the measurement of the over, W the width, and L the length of the stack. When stacks are measured in feet, to the nearest half foot, the results obtained by use of this formula give close approxima- tions of the actual volume of stacks. The volume of most stacks decreases steadily with ageing, but the rate of decrease is not uniform because of the factors of : Kind of hay Maturity when cut Moisture content when stacked Amount and kinds of weeds Height of stack Method of stacking Rapidity of drying hay in stack (influenced by size and shape of stack and atmospheric conditions) Rainfall On an average the rate of shrinkage was found to be : 8.3 per cent from 1 to 2 months after stacking 7.9 per cent from 2 to 3 months after stacking 6.5 per cent from 3 to 4 months after stacking 10.3 per cent from 4 to 5 months after stacking 14.0 per cent from 5 to 6-8 months after stacking 27.4 per cent from 1 to 6-8 months after stacking 20.7 per cent from 2 to 6-8 months after stacking Bul. 570] Determining Tonnage of Hay in Stacks 25 Stacks tend to shrink in height only, little change taking place in either width or length. Wide variation was found to exist in the number of cubic feet which comprise a ton of hay. The average cubic feet per ton for 139 stacks of grain and volunteer hay was found to be 666 cubic feet, with 696 cubic feet for the greatest frequency group. The average cubic feet per ton for 225 stacks of al- falfa was found to be 448 cubic feet. Studies of various factors, however, show the difficulty of indicating any single figure likely to be acceptable for general use. When a need arises for determining the contents of stacks by some formula, in lieu of weighing, if the measurements of width, over, and length are known and a figure indicative of the number of cubic feet per ton determined, then much of the task of calculating can be avoided by use of basic tables presented in the text of this bulletin. The tables and chart provide a means for quickly and easily determining ( 1 ) the cross-section area of the stack, (2) volume, and (3) tonnage. Suggestions to guide in measuring stacks stress the necessity of build- ing stacks as evenly as possible, and the exercising of care in taking the required measurements. The final conclusion, resulting from this study, may be summed up in the few words : There is no entirely satisfactory substitute for weighing. But when reliance must be placed on the use of some formula, then the Decimal Rule is advocated as a means of determining volume. From this determination the number of tons can be ascertained once a figure has been reached indicative of the number of cubic feet comprising a ton of hay. Aids designed to assist in the calculating of the cubical contents of stacks by this method eliminate the necessity of laborious calculations. 26, University of California — Experiment Station ACKNOWLEDGMENTS The Bureau of Agricultural Economics, United States Department of Agriculture, cooperated with the California Agricultural Experi- ment Station in the collection of data and the making of calculations which form the basis of this bulletin. Credit is due W. H. Hosterman of the Bureau for evolving the Decimal Rule. Measurements of 139 stacks of grain or volunteer hay and of 36 stacks of alfalfa were made by W. J. McCaleb during 1927. Measurements of 388 stacks, practically all of alfalfa, were made by W. S. Goodrich in 1928. Ben R. Olson assisted with office computations and analyses. Special acknowledgment is made of the contribution by Miss Edna Fisher, formerly of the Giannini Foundation of Agricultural Economics of the College of Agriculture. To her belongs the credit for working out the unique chart showing the tonnage content of stacks when length, cross section, and cubic feet per ton are known. 10m-4,'34