i ;:*;. siKJt Class _^2^iZ Book i P^ f pe Copyri^htF mcrement increment ^c I m(*rement CDPmiGHT DEPOSm Vol UniCS i^^ve been written on vch. j;iue ^mi 'itten on quality and price BJItmore Timber Tables BY HOWARD R. KRINBILL COPYRIGHT. 1911 BY HOWARD R. KRINBILL FOR THE USE OF THE BILTMORE FOREST SCHOOL WORKING FIELDS, 1911-12: ADIRONDACKS, SOUTHERN APPALACHIANS, LAKE STATES. PACIFIC COAST AND GERMANY INTRODUCTION 63> W^v\ This booklet has been prepared for the use of the slu- dents of the Biltmore Forest School and may prove of interest to foresters and lumbermen in general. The original material consists of Compound Interest Keys for solving financial problems, Keys for the mental calculation of areas of circles, and Form Height Factors for estimating standing timber in board feet of lumber and in cords of wood and bark. The Mill Factor Method of estimating standing timber is employed by Dr. C. A. Schenck, who publishes a handy booklet of Cruiser's Tables giving contents in board feet for trees of any diameter, any number of logs up to 6, any taper per log from I inch to 4 inches, and any Mill Factor from 5 to 8. The Volume Tables of "The Woodman's Handbook" have been used as a basis for working out Form Height Factors. The Tables for Use in Germany were compiled during an excursion through the forests of Germany. This booklet is the right size for inserting in ''The Woodman's Handbook" by Henry S. Graves, published by The United States Forest Service, or in "A Manual for Northern Woodsmen" by Austin Gary, published by Har- vard University. CCI.A2SSS63 PROBLEMS IN FOREST FINANCE To Illustrate the, Utility of the Compound Interest !''eys 1. The Report on the Standing Timber of the United States by Herbert Knox Smith, commissioner of corpora- tions, gives as examples of "enormous increase in value with great profits to the owners" during an interval of 40 years: From $5 to $30 an acre, $7 to $40, $20 to $150, $1 to $18, $4 to $140, $1 to, $50. Question: What rate of interest do these "great profits" represent? 2. Southern pine sold by the government 40 years ago at $1.25 per acre is now worth $60. Douglas Fir sold at $2.50 is now worth $100 to $200. What has been the annual price increment? 3. If Yellow Poplar log run averaged $14 in 1895 and $30 in 1910, what has been the annual increase in stumpage value, assuming that the expense of production was $10? 4 Timber worth $8 per acre in 1906 has increased yearly in volume 1 per cent, quality increment 2^ per cent, price increment 4 J per cent. Value in 1911? 5. If stumpage prices increase 8 per cent, yearly, when will the investment double? When will investment increase threefold? Tenfold? 6. In 1911 White Pine stumpage is worth $6 per M, Poplar $5, Oak $4, and Yellow Pine $3. What were the prices in 1890 and in 1900 if the annual price increment has been 10 per cent for White Pine, 8 per cent for Poplar and Oak, and 12 per cent, for Yellow Pine ? PROBLEMS 7. In 1901, $1200 was paid for marked trees, equal volumes of White Pine, Poplar and Oak. The trees were to be cut in 5 years but in 1906 $700 was borrowed at 6 per cent, to pay for the privilege of letting the timber stand until 1911. How much was gained (or lost) by waiting until 1911? The annual increments in volume, quality, and price were: White Pine, 3J per cent, 3 per cent, 8 per cent; Poplar 3 4-5, 2, 9; Oak 1 4-5, 1, 6. 8. In 1900 a forest of 10,000 acres was bought for $70,- 000. Taxes in 1900 were 6 cents per acre and advanced gradually to 15 cents in 1910. The lumber cut in 1900 was 1000 M and increased steadily each year to 2000 M in 1910. Stumpage netted $2 per M in 1900 and rose steadily to $5 in 1910. In 1904, a right of way was sold for $150; in 1905, a waterpower site brought $2500; in 1906, mineral rights, $3800; in 1907, tan bark $2750 net; in 1908, extract wood, $1320 net. In 1910, the property was sold for $20,000 cash, $10,000 yearly for 5 years, and shares of U. S. Steel, some common at 77| and the rest preferred at 119. Question: How many shares of each were secured to make 7 per cent, on invest- ment, including taxes? ANSWERS 1. $5 to $30= Aft- Value 6. Key 184. 184^40=-4.6 per cent. (Case 3.) Similarly, the other rates of interest are 4.5 per cent, 5.2 per cent, 6.6, 9.1, and 10.1 per cent. 2. $1.25 to $60=Aft- Value 48. Key 397. 1 397^40=10 per cent. I $2.50 to $100= Aft- Value 40. Key i /p,,^ o\ 378. 378^40=9i per cent. | ^^^^^ "^^ $2.50 to $200=Aft- Value 80, Key | 449, 449-^40=11.2 per cent. I I 3. $4 to $20= Aft- Value 5. Key 165. 165^15=11 per cent. (Case 3.) 4. 8 1-5 per cent. X 5 years=Key 41. Aft-Value 1.5. 1.5X$8=$12. (Casel.) 5. Aft-Value 2=Key 71. 71^8=9 years. (Case 4) 6. Case 2. 7. Case 1. 8. Case 1, 5 and 6. COMPOUND INTEREST KEYS (Aft-Value is value at the end; Pre- Value is value at the beginning) Aft- VALUE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 50 100 500 1,000 10,000] 100,000 TENTHS 0.0 .1 0.2 0.3 0.4 0.5 0.6 0.7 0. 8 0.9 KEYS (Number of Years x Rate of Interest) KEYS 71 113 142 165 184 199 213 225 236 246 255 262 270 278 284 288 296 301 307 330 401 472 637 708 944 1180 10 19 27 34 41 48 54 60 76 81 85 90 94 98 102 106 116 119 122 125 128 131 134 137 145 147 150 152 154 157 159 161 167 169 171 173 175 177 179 180 186 187 189 190 192 193 195 196 200 202 203 205 206 208 209 210 214 215 217 218 219 220 221 223 226 227 228 229 231 232 233 234 66 109 140 163 182 198 211 224 235 To obtain key of any omitted Aft-Value, add the keys of its factors. For example: Key of 29= Key of 10 plus Key of 2.9=345. Key of 36 =Key of 6 plus Key of 6 =368. Many problems may he solved mentally by remembering the Key for doubling, 71. How TO Use the Keys: Dase Given Wanted Solution 1 2 3 4 5 6 per cent, and years per cent, and years Aft-Value and " per cent. & Af t-V. per cent, and years per cent, and years Aft-Value Pre-Value per cent. Years Aft-Value of $1 paid yearly Pre-Value of $1 paid yearly per cent, x years=Key to Aft-V. IH— Af t- Value= Pre-Value Key H— years =per cent. Key H— per cent.=years. Aft-Value of Key— 1 per cent. Aft-Value of Key— 1 per cent. X Aft- Value of Key MILL FACTORS The Mill Factor of a saw mill is its productive efficiency expressed in board feet of saw cut per cubic foot in the log. For example, Mill Factor 7 indicates that the mill produces 7 and wastes 5 board feet for each cubic foot in the log. The unavoidable waste depends upon the following fac- tors: soundness of logs, taper of logs, diameter of logs, thickness of saw, thickness of boards, smallest width per- missible, quality ofmill machinery, skill of sawyer, inspection rules followed in edging and trimming, lowest marketable grade, and shrinkage. Under the most favorable conditions, in the case of straight, sound logs, a band mill will have a Mill Factor of 8, while a circular mill will generally be rated not higher than 7. The 40 or 50 different log rules used in the United States represent either constant or variable Mill Factors. Among the former are: The N. Hampshire or Blodgett Rule (115 Blodgett Feet per M) -Mill Factor 6. The Square of Two-thirds Rule ' " 6.8 The Vermont Rule " " 7.6 The Square of Three-fourths Rule " *' 8.6 The most common log rules with variable Mill Factors are: It is evident that any given log rula is accurate for any given saw mill only where the Mill Factor of the log rule equals the Mill Factor of the saw mill. A standard method of log measure- ment would be to allow a certain number of board feet per cubic foot in the log. By comparing the solid cubic contents of a number of logs with the actual output in board feet of lumber, the Mill Factor of a mill is readily obtained. Page 8 shows the contents of sound trees in feet board measure by the Mill Factor Method. H w «.H a a J 3 ■^ ?5 J Z J (M 13 ca w 3 •-; j3 s« ^_S i^ = S BB .2- ^^ i^ ^U Q fe fe c^ 6 1.3 6.1 6.1 9 3.6 5.7 7.2 12 5.2 6.3 8.3 15 6.2 7.3 8.2 18 6.9 7.4 8.2 21 7.6 7.9 8.7 24 8.0 8.0 8.7 30 8.6 8.4 9.0 36 9 8.2 9.1 40 9.2 8.6 9.0 50 9.7 8.6 60 10.0 8.6 120 10.7 8.8 DOYLE BOARD FEET IN SOUND TREES (Taper above butt log=i to 3 inches) Diameter Taper and No. OF Fourteen Foot Logs Breast-High Bark of Outside Bark Butt Log 1 2 3 4 12 2.7 25 44 53 63 15 3.4 51 92 117 127 18 3.8 92 165 217 260 21 4 146 260 357 435 24 4.5 211 387 541 669 27 4.5 297 549 773 963 30 4.6 400 745 1050 1310 33 5 506 946 1340 1660 36 5.1 630 1190 1660 2060 39 5.6 754 1410 1980 2510 42 6.1 890 1670 2350 2970 45 6.6 1030 1950 2740 3470 48 7.1 1190 2250 3170 3990 51 7.7 1350 2550 3620 4540 54 8 1540 2890 4080 5080 57 8.8 1710 3220 4540 5650 60 9.2 1920 3560 5010 6250 The lumberman wastes timber to save money; the con- sumer wishes him to waste money to save timber. CONTENTS OF SCUND TREES IN BOARD FEET MILL FACTOR 7 (Taper above butt log=two inches per log) Small Diameter OF Number of Fourteen Foot Logs Butt Log Inside Bark 1 2 39 53 69 3 4 5 6 7 8 9 26 34 43 83 10 11 12 53 65 77 88 108 130 107 134 164 147 184 13 14 15 90 105 112 155 182 210 198 235 275 224 269 318 238 288 344 16 17 18 137 154 173 241 275 310 318 365 415 372 430 492 406 473 545 19 20 21 193 214 236 347 387 428 468 524 583 558 629 703 623 706 794 22 23 • 24 259 283 308 472 518 566 645 711 780 782 866 953 887 986 1090 30- 36 42 480 686 938 896 1309 1792 1260 1855 2569 1568 2338 3262 1827 2758 3878 48 54 60 1225 1554 1918 2359 3003 3717 3395 4340 5397 4340 5572 6951 5194 6699 8400 5964 7735 9737 KEYS FOR MENTAL CALCULATION OF AREA OF CIRCLES Diameter Class Base Key 6 inches to 12 inches 6 in ches = .2 sq. ft. .1 sq. ft. per in. 12 " '' 24 *' 12 '' =.78 '' .2 " " " '* 24 " '' 36 " 24 " =3.14 " .3 " " " " 36 " "40^ " 36 - =7 4 .. .. .. .. m " " 50 " m " =9 .5 " '' '' ' 50 '' " 60 " 50 '' =13.6 " .6 " '* '* '' The key to Square Feet Per Inch is the tens figure of the upper limit of the diameter class. How to use the Keys: Area 27 in. -=3.14+ (27 Area38in.=7 -f (38— 36X.4) 24X.3)=4.0sq. ft. ~ 7.8 sq. ft. ESTIMATING STANDING TIMBER AT SIGHT After the Keys for Area of Circles are memorized, standing timber may be estimated at sight quickly and ac- curately by the Sectional Area— Form Height Factor Method af follows: No. OF 14 ft Logs (Taper above butt log equals 2 in. per log.) COTTENTS OF SOUND TREES IN BOARD FFET. MILL FACTOR 7 Area of small end of butt log inside bark x 100 Contents of a one log tree x If x3 x3i The above method may be applied to any log rule having a constant Mill Factor by simply changing the length of log. For example: M. F. 8, log 12 ft. and M. F. 6, log 16 ft. FORM HEIGHT FACTORS Sedional Area Breast iiigliXf. H. f =[ords of 128 Cubic feel of Wood TOTAL HEIGHT IN FEET D tf t^ 1 1 M 1 1 O W Q ^ ^ M 1 1 1 1 1 I SPECIES Q Ph p:; hH O S ^ 3 § w ►^ 405060708090100110120140 160 J H O < p^ ffi O fe q" 6 20 23 28 Q 9 18 21 25 30 O 12 18 21 23 27 31 s i 15 17,20 22 26 29 34 38 18 119 22 25 28 321 36 in vl 90 21 |192l 24 27 31 34 1 < 24 1821 24 27 30 33 27 18 21 24 27 30 32 34 ^ H 30 20 23 26 29 31 33 X 36 22 25 28 31 33 W 45 26 28! 30 32 Q o 6 2631 36 £ o 7 2631 37 ° ^ S 1 80 8 27|32 38 down 9 33 38 to 1 inch 10 35 40 11 37 43 w ^ m C/2 12 39 45 o^ 6 18 22l28 34 9 20 2630 35 95 12 26|30 34 "^ .. >y down 15 30 33! 38 SPR (For Fii Multip] to 4 in. 18 29 32:36 42 21 3213640 24 32S35 38 27 134^37 6 22 28 9 22 27 33 12 27 32 37 43 48 53 15 31 37 42 47 52 57 63 P-t 18 35140 45 50 55 60 W 90 21 38 43 48 53 57 24 42 47 52 56 66 K 27 42 46 51 56 65 ^ 30 36 46 45 50 50 55 54 64 63 72 45 62 70 SHORT-CUT FORM HEIGHT FACTORS S. A. Breast liighxf. H. f =Cords of 128 cubic feet of wood Species Cords of 128 Cu. Ft. Containing Total Height of Tree Feet F. H. F. Chesnut Second growth Hardwood Spruce Fir White Pine solid cubic feet (For Long Cords of 160 cubic feet with 112 solid cubic feet) solid down to 1 in. solid down to 4 in. 95 solid down to 4 in. 90 solid cubic feet 75 ft. and under Over 75 ft. 75 ft. and under Over 75 ft. 30 ft. to 60 ft. 65 ft. and under Over 65 ft. 65 ft. and under Over 65 ft. 80 ft. and under 90 ft. to 100 ft. 110 ft. to 120 ft. 130 ft. to 170 ft. + 10 + 11 + 8 + 9' -^ +D JH 2 3^H 10 ja 2 2 H 5" H 2 _H^ 2 H 2 2JH 5 13 - 2 + 2 + 2 -2 ^ + SpJCOD s ^ T— 1 § JO aaquinu si^nBg 1 1 1 1 SHOXOV^ HHiawvia Qco^ Q Q ^^o. |B0 mm-) 300^HaH HAY TABLES FOR USE IN GERMANY FORM HEIGHT FACTORS S. A. BreastHighXf. H. f.=Cordsof 128 cubic feet with 90 of solid wood over 2 3-4 in. 1 pq 1 12; 1 o 05 6 H m C/2 tt, 8 C/2 10 18 19 14 16 21 22 20 20 21 25 26 24 25 25 28 29 26 28 28 32 32 28 32 31 34 35 31 35 35 37 38 33 38 38 40 41 35 41 41 42 43 38 44 44 45 46 40 48 47 48 48 42 51 50 50 51 45 54 53 53 53 47 58 56 54 54 50 60 58 57 57 52 63 60 59 55 68 63 + 60 + a| =^ K ^ a ^ .-V ^^ 1 -"t 4J <4H 1 W s g CD «D a; > o m 0) > o tfi a> CD Eh S TO Q^ 22 25 27 30 33 35 37 39 42 43 45 47 50 (DO) 13 0) ^ CO sL W2 "^ *- CO . •1- II o 3 -P -^ CD ;2S ^Oi 'O II X 0) 0) offi Hi(M ?H ?H "^ -Sol :::5 OS 0) a; CO CD •• ^ rn "^ 0) 0) q; P- Sh ?-4 ^, CO C« ,^ o) a; 5^^^ CO 03 CO a c3 a32gaS ^ ~H3 "^ "o3 "^ "^ .S .S ;3(73!=Si73:3^55m?h 00 .5 ^ CD CO 0) -lJ 0) «+H if " 3 I g II O "=*. HICO T-H C^^ LO CO O X ^ X -^ 0) S o q5 ^ ^ c3 o Q ffi ^ CO ffi a The German Foresters Are. growing Oak in rotations of 150 years at $100 to $200 per thousand board feet, the Corner Stone of Conservative Forestry being High S'" age Price. The foundation for Destructive PVestry m aid by low prices and low tariff, high taxes an I high freight rates, /'hot iires and cold logic- free trade and unlimited competition. liiiifiii