xt7rjd4pmp71 https://exploreuk.uky.edu/dips/xt7rjd4pmp71/data/mets.xml   Kentucky Agricultural Experiment Station. 1937 journals kaes_circulars_291 English Lexington : The Service, 1913-1958. Contact the Special Collections Research Center for information regarding rights and use of this collection. Kentucky Agricultural Experiment Station Circular (Kentucky Agricultural Experiment Station) n. 291 text Circular (Kentucky Agricultural Experiment Station) n. 291 1937 2014 true xt7rjd4pmp71 section xt7rjd4pmp71  3,-
COLLEGE OF AGRICULTURE
Extension Division
THOMAS P. COOPER. Dean and Director
CIRCULAR NO. 291
SIMPLE PROBLEMS IN LAND MEASUREMENT
Lexington, Ky.
March, 1937
Honplibmlifil in commotion with the agrioulturul cxtciisiou work r:uY1'i<‘d 011 UY €00D*~‘i'i*‘
Agmc(LltU‘° COUGEG of Agriculture, University of Kentucky, with the U. S. Department uf
uf MM §ri·g*;·:d diSIl'ibuted in I·lll`T.hEI`{l,Il(f(> of tho work providod for in tho Act of CuI1gl‘<’SS

 C O N T E N T S
and
··—‘— acci
acci
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'I`0 measure a Held ............. 3
mea
T0 calculate [lie area 0f a Held ...,..... ·l lm
avci
'l`0 lay 0uL a Held of a given area ......... 8 age
are
'I`0 convert acres L0 square feet, Table N0. l ..... I? aim
thc
'I`0 (`()IE\'(‘l`l square feet L0 acres, Table N0. 2 ..... I3 Pm
V _ V _ VI Mci
Number 0I plains per acre. [able N0. 3 ...... l· `
A homemade chain for measuring land ,,,_,.. ll "“1|
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. Circular N0. 291
Simple Problems In Land Measurement
By EARL G. WELCH
.-\ farmer needs to know how to ascertain the area of a field
and how to lay off a held to contain a given acreage, with reasonable
accuracy. This circular describes simple, practical and suiliciently
accurate methods for solving these problems. The need for instruc-
mg tion in land measurement is shown by a recent experience in the
' measurement of 270 fields, most of them irregular in shape, on 106
A _l lanns, in 6 counties. Fifty-nine farmers, whose tobacco acreage
ateragecl 41.40 acres per farm, overestimated the acreage by an aver-
_ 8 age of nearly one acre per farm. Thirty-four farmers, whose acre-
age averaged 7.50 acres per farm, underestimated the acreage by an
. l? average of nearly an acre and a quarter per farm. Only thirteen of
I3 the ·lO6 farmers estimated their acreages correctly to within 0.l acre.
· Pacing or stepping distances does not give accurate measurements.
I M Mtn Seldom agree on distances determined by this method.
l’rol>lems in land measurement are easier if the helcls are of
_ l=l *l¤1|>lC, regular shapes, with straight boundary lines. CUl`VC(l, il`l`Cg`-
ular boundary lines make computations more dilhcult and increase
the chances for error. This should he kept in mind when a held is
being laid out.
TO MEASURE A FIELD
Equipment. A cloth or steel tape marked in feet may be used
{nr making measurements. If no tape is available, it is suggested
that a surveyor’s chain be made according to the instructions in this
circular. Use of the chain as the unit ol measurement simplifies
Calculation.
.lfeasureme21t in C/HIIUIIX. The most convenient unit of meas-
Elrernent is the surveyor's chain which is 66 feet long. A square
iainlis equal to 4356 square feet (66 l`t. x 66 ft,). Since an acre
contains 43560 square feet, l0 square chains are equal to one acre.

 —l Ken/zzcky EX/('}I.VI·O)I Circular t\'o. 29l
A standard chain is divided into I00 links each 7.92 inches long. .\ ‘
distance measured in chains should be expressed decimallv; Ia. HH
’ example, 6 [ull lengt.hs of the chain and I8 links should be recortlgtl I is
as 6.l8 chains. ll a rectangttlar held is 6.18 chains long and 5.IlI
chains wide the area 1nay be obtained by multiplying 6.lS chains In
5.l0 chains. The product., 3l.5l8 square chains, is reduced to ;ttr<·~
by dividing by I0, or moving the decimal point one place to the Ielt,
so that 5l.5I8 square chains equals   acres.
· il[(’((.$`I(l`{’7II('}I/ in Fcc/. ln many instances distances will It
measured in I`eet. Tables lor converting acres to square |`t·et antl
square feet to acres are provided in this circular (Tables I antl 2;.
The use ol` these tables avoids tedious multiplication and tlivision.
‘ Iiozzrizlririar. In measuring an area planted to a row crop or in
laying oIl’ an area to be planted, the measurements should inclutlcen
distance beyond the rows on all sides equal to hall the (ll5I§lIItl‘
between rows. In Iields seeded to wheat. a tlistance oI` one loot out-
side the drill rows should be included in the seeded area.
Nzzm/zcr of P/rm/s [wr Acre. \\’here tobacco is checked. as it i~
in western Kentucky, a common practice is to estimate acreage In
the 1lUnlI)c1‘ ol plants set. This tnethotl is satisllactory lor t1lIt¤|·
lating acreage in connection with tobacco production, protitlul
the correct number ol` plants per acre is used in the calculatitm.
Table 3 shows the number ol` plants on an acre ol ground lor spu-
ings ranging by inches lrom three to I`our leet. The total mtmllu
of plants to be set may be determined by multiplying the intmllu
ol pla-nts per acre which corresponds to the adopted spacing In tht
number ol` acres to be set.
TO CALCULATE THE AREA OF A FIELD
.\cre equivalents.
I acre ; -I?’»5li0 square Ieet, or I0 square chains.
I acre 1 ·l8·I0 square yards, or I00 square rods.
$<]l12ll`C ICCL Lll`t‘ l`t‘tll1t‘t‘tI to acres by tlivitlittg by lfiallll *’I lll l H-]
means ol Table 2. sit
, . . . . _ I I CN
Square chains are reduced to acres by dividing by I0. ot mount Il
. . . I { I)
the decimal point one place to the lelt.

 F?
${111.]}/tr [)I`()f}f(?IIl.\` /11 Luna! t\»Imt.s`111‘t¢111<¢11I 5
long. .\ ‘ jtytrtattgles. Rectangular and square Helds are those in which
ally; fm all interior angles are right angles. The area of a rectangular lieltl
1‘er t;1It11-
I)I`tl\IlIl‘tI V _ V _
I mlm 5t>Iuttt>n. (Measuretnents in chains.)
t·11 ; 1 _ _ _ _ _
1. I lm III chains X :1 chains :410 square cltatns.
() ` N 1 ` _ _
I lllllI)t‘| :10 square chains + IO —.; 5.0 acres.
ll
~ IIllIllItt‘I
112 I1) 1*1* A L 7'/7`L/DE
1 (
I
I
im lg In _ III`f(UIg`f<’.v. 'l`l`l2ll]gl1I;|l` fields are those with three si<>site (`()l`ll('I`. YIIIIU i1\`l'i!
11I a triangle is equal to half the lJl`(>(Ill(`l <>I`tI1c· base by the altitude.

 6 Kentuc/cy Exlension Circular N0. 291
Problem. \\’hat is the area ol a triangular held which liasa V
base of 792 feet (12 chains) and an altitude of 800 feet (12.12 _
J chains) P
_ base altitude
Formula. Area :-—%——
Solution. (Measurement in feet)
792 ft. 800 ft. L . is
, Area —; L-li;-— ; 516800 square feet.
- zi
316800 square feet ;— 7.3 acres (see conversion table No. Yr
Solution. (Measurement in chains)
I 12 chains 12.12 chains _ ,_ .
Area:   ::12.1 square chains.
72.7 sq. chains ; 7.27 acres.
sms A li
|"" " ‘ ‘I
I I |
I l">QL7'/Tl/D5, . it
Trapczoizls. .—\ trapezoid is a l`our—sided figure that has only nm
sides parallel. The altitude ol` a trapezoid is the shortest clistaiitr ’
between the parallel sides. The average length of a L1`2ll)CZ()l(ll*
hall the sum ol` the parallel sides. U
_ . ., lu
Problem. \\'hat is the area ol` a traliezoid in which side .·\1S·l'*J \k
feet (7 Chains), side B. 594 feet (9 chains), and the alt.itullC- 111* .l
feet   chains)?
Formula. Area ; average length >( altitude.
Solution. (Measurement in feet)
462 lt F941t. . , t
Area ;i —¥ X 198 lt. : lt)—lg4»l square lect.
l0·l5·l—l square leet ; 2.~l acres (see conversion talrlr tj
No. 2). "

 Simple Problems In Land Measurement 7
:h has a n Solution. (Measurement in chains)
t (12.12
7 chains 9 chains . _
Area :   3 chains : 24 square chains
24 square chains ; 2.4 acres.
Tmpezzitmrs and Fields of More I/mn Four Sides. A trapezium
ie; a four—sided Hgure that has no two sides parallel. The area of such .
zi ligure is obtained by dividing it into two triangles and calculating
No. 2i.
? I
, * 4
\*`<'e>4
_ { xx
ms. /ILT/Tl/Of `\ `
the area of each triangle separately as explained under triangles.
The base and altitude ol` each triangle should be measured.
The illustrations show how various shaped helds may be divided
into triangles, rectangles and trapezoids. By careful preliminary
\\
\
\\
\
only l11'·*
d·$l,Hm, · Ktriangles 1 trapezoid, 1 triangle 1 rectangle, 2 triangles
pezoitl ir
examination the best method ol` subdividing an irregular field can
. .,, be determined so that unnecessari measurements are avoided. .—\
: .~\ 15 ’l"- . , ) .
[ IC W, ~l<€lt‘h ol the held should be made belore measurements are taken.
ut . -· .. _
lhe sketch should be kept lor reference.
/\ !°—\
// \ //\ / E
\\/// v `_/
1`cc1· ·'llW!5 lt'!.//1 I)`)`(’g'[(/(l)` or (][;;·z»(»([ S[([(·,s‘, A11 i1`i`eglll2ll` $l(lC of IU]
I urea may be measured as a straight line, as indicated by the solid
ion tzilit line in the diagram, provided the amounts of land on opposite sides
ol the straight line are equal or approximately equal.

 S [{021/itr/cy lixtezistiou (Ifr<·ulur ,\'o. 2£}l
\\`het·e sides ol` il Iield are (`lIl`\'(‘(l, us they lietlttetitly tue wliew i
V nontour planting is done, the ztpproximzite meet muy be obtztined lit
multiplying the ztvetwtge width ()li1l strip by its ziverznge length. Ilia-
i1\`CI`2Ig(? width und length should be determined [rom two or iiiutv _
mezisurements. The Iigute above illustrzues an area with ctttwl
I sides which has been subdivided into two strips ol dillerent lengtlh
und widths. '1`he sum ol the two ill`(‘1lS is the totnl ztre;1.
----1
t I
I I
I
I
AI--- ·
I I
I I
| BARN I
. I I
.. ...... ...l
The ll`1`CglllZll` shztped Iield shown above muy be mezisured tts tt
rectztngle. By Slll)I4l`ZI(`llIlg the znezis between the dotted lines tttitl
the solid lines, l`t·om the ztrezt ol` the I`C(Cl2llIglC, the plzmted tulett mnt
be determined in less time und more 2l(`(`llI`ZllCl}' thzm by amy otliu
method. The Iield sketcli should include the necessary tliinetistttw
lor rleterniining the 1ll`C2lS to be subtrzieted in addition to the :Iili leet. or IIIII st;tnd;u·d links ezltli YW lll lit
tlies long. int
l liomenizade cltuiu :; titi Ieet, oi- Ii) long links (guilt 5 st2lt1il>C
IIIullil)li(i(i   [i](j Q[l[i[[l(l(j_   i~()ll()\\`$ lllill lll(j illikiil klivldcd   hull.
_l;mil;tt·l llw hztse gives the altitude.
l)l`()l)lClll. .·\ triztngulztr field is to contznin 3%.5 ztcres. The bztse

 f
10 Kmzlttc/c)· E.v/rrrtximt Circular No. 291
B is ll chains, or 726 feet. \Vhat; should be the length
( of A, the altitude?
J Method. Convert the area to square feet or square chains, zit-
cording to the unit of measurement to be used. atttl
1 divide this figure by 1/Q the length of the base. 'fltt
t answer is the altitude.
Formula. Altitude : area of triangle 4- 1/2 base
Solution. (Measurement in feet.)
( 3.5 acres ; 152#l60 square feet (see conversion tztlllt
N0. 1)
152460 square feet 4- 363 feet (1/2 of 726 feet) :1211 V
feet (the altitude)
· Solution. (Measurements in chains)
( 3.5 acres : 35 square chains.
35 square chains+ 5.5 chains (% of ll chains);t
6.36 chains (the altitude).
[_' B __` F-,
O'  tAv:A·A.s·£ Lsrvcrn ' l l
. Q? JAOFES l t
--J
C=/at?
Trapczoicls. Because the area of a trapezoid is equal to tltt .
product of the average length by the altitude, it follows that tht
area di·vided by the altitude gives the average length.
Problem. A field in the shape of a trapezoid is to contaitt it
acres. The altitude A between parallel sides ll zttttl
C is 5.00 chains, or 330 feet. Side (Q is 12 chains. ··¤
792 feet. \\'hat should be the length of side ll?
Method. 1. (Ionvert the area in acres to square feet or sqtttttt
chains, according to the unit of measurement l·* t
be used.
2. Divide the area in square feet or square t’l121lll* lt
the altitude in feet or chains, The result will lt
the average length of the field or the sum ol tltr
opposite parallel sides B and (I divided bv 2. V
Pl. Multiply the average length of the held bv Y Wi

 V
Sf?77./)](? Prob/ems In Land llfertsttrcnicitl I I
e length subtract the known side C. The result will be the
. length of the side opposite C or side B.
mlm All . _ _ V _ sum of parallel sides
sed, arrtl Formulas. Average length ;  2 
ae. 'lltt
Average length ; area + altitude.
An unknown parallel side ; 2 X average length
minus known parallel side.
lm mm Solution (Measurements in feet.) I
5 acres:2l7800 square feet (see conversion table
rr :»¤¤<· Sl? ll r . . M
al/800 square leet + 530 feet (altitude, A); troll
ft. (the average length of the held).
660 ft. X 2 : 1320 ft.
rains);. I320 ft. — 792 ft. (side C) : 528 lt. (side B)
Solution. (Measurements in chains)
5 acres : 50 square chains
50 square chains + 5 chains :10 chains (the aver-
' age length of the Held)
I0 chains X 2 : 20 chains
X 20 chains — I2 chains (side C) : 8 chains (side B).
l
--l B
I to tltt . \ 3
that tlrt 8\ D
ontairi J
es ll zuitl I Z
hains. ·>¤
tre A
rr sqrtzttt Tmpcziitnzs. The area of a trapezium is equal to the sum ol
srnt-nr r·i the areas of two triangles.
lll`0l>Ien1. To lay oll a given acreage where three l>oun68#6%£715i75E11T1§§;1;[1;§§§;2 1678821114  

 Simp/ri Problmns In [,(l7I(i tllmstzrcnimil IS I .
I wml CONVERSION TABLE N0. 2. SQUARE FEET TO ACRES
trea to . Locate tl1e block within which the number lalls. Travel to lel`t
e acre- margin where acreage is shown in units. Travel upward to where
:itltlitional fractional parts of acre is shown. By coinbining these
to com- the total acreage is obtained to the nearest 0.1 acre.
LTQEIZZ 421;; -2 I -3 = -4 I -5 I -6 I -7 t;;_
Igclhcl- OI I I 6535 I 10891 I 15247 I 19603 I 23959   28315   32671   37027
  I 6534 I 10890 I 15246 I 19602 I 23958 I 28314 I 32670 I 37026   41382 `
`i11999 I 45739 I 50095 54451 | 59z§n7I_5E5§ 67519 719?7V&H1790587
`llllll1‘(I II 45738I 50094I 54450I 58806I 63162I 67518I 71874I 76230I 80586I 84942
IC nett. ww 89299 I 93655 98011 I 102367 106723 I 111079 I 11%»I@91iIii1A24147
U) {lu.   89298I 93654 I 98010 I 102366 I 106722 I 111078 I 115434 I 119790 I 124146 I 128502
I-(IM. `3 E%>§F3 §EF§>2§§Ii'15E5@,§9§£sT1é§é5i@5770*
e blotl 132858 I 137214 I 141570 145926 I 150282 I 154638 I 158994 I 163350 I 167706 I 172062
nrc 190  Q@§Ii11@ @7T1i99§§9H99ii§555 I7205911   211267
 ___i_ _ 4I176418 I 180774 I 185130 I 189486 I 193842 I 198198 I 202554 I 206910 I 211266   215622
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*23199* ` If5 11Q§@E51¢& I92E9W929979iI 999295 I 337591 I 341947
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$§é§7‘3mI_I I 3I?>[§58 I 355014 I 359370 I 363726 I     385506 I 389862
    SM389863 I 394219 I 398575 I 402931 I 407287 I 411643 I 415999 I 420355 I 424711   429067
  _   I 398574 402930 I 407286 I 411642 I 415998 I 420354 I 424710 I 429066  433422
MIQAVIIISQI 10433423 I 437779 I 442133 I 446491 | 450847 I 455203 I 459559 I 463915   468271 I 472627
§)08»51S964 > 437778 I 442134 446490 I 450846 I 455202 I 459558 I 463914 I 468270 I 472626 I 476982
}g§gL591914 1 1I41§83 IE9%@9'AI50H75 I511831   515187
{129   __‘¥81338 I 485694 490050 I 494405 I 498762 I 503118 I 507474 I 511830 I 516186   520542
159964901* 12   5@ "IE4i&;79 V551095 I`555991 I 559747
    I524898 I 529254 I 533610   537966 I 542322 I 546678 I 551034 I 555390   559746   564102

 {
I4 K('}III(('/i’)‘ Exlension Circular N0. 29l
TABLE N0. 3. NUMBER OF PLANTS PEB ACRE‘*‘ .
  -.7 _..; -?._T;Ti-ii.,-;;-; 2- --—--j-. ~--—;;;iT_--. shi
- V Sq. Ft. N0. Plants Z lh,
Spacing Per Plant Per Acre
  4340
3* -1** X 3* -1** 9.48 #@0
‘ 3  10.03 2 4343
3i37>;3§ —f 10.56 #?Y~E5
y   SVAMK0
3* -5** X 3* -5** 11.6*: _—i%E33
 ;f#l§5
3i*?:¢?*? 12.81 AFEE
‘ 3* -8** x 3* -8** aét 13.40   3250
QE X 3* -9** wk? 4777;}.06 Ad 3100
  2-22   in
BGFKSEVIA-.*4-; 4”E§1l2"#'Q 2 MK2
4 *l2l2i-2 A 222 diiitnt tltl wmm”5?é2
*43560 square feet equals 1 acre.
A HOMEMADE CHAIN FOR MEASUBING LAND
.\ homemade chain can be made easily out of baling wire or Nw. lm;
I2 wire, on the device shown below. Make each long link 39E¤i;" . as
long, which is equivalent in length to live links of the stand:ll‘ll M
surveyorls chain. Twenty links f%9%;" long make a chain 66 lecl lll mq
length. .»\t one end of the chain 5 standard links 7.92 inches ill (lk
length may be made in place of one of the long links, to be used in ·
measuring short distances.
'.i-230%;,.,1-L A 
.715
· . T5 .
I:. JH N I, .
I fg ¤ 460LT W/T/1 mma /?£MOL/E0 I I
» J
J. ,, | 6
l-;  -0 .——.}—?»{

 . if
Simple Problems In Land illeaszzremeizl I5 V
. The length of the finished link should be 3.3 feet, but the bolts
,;__ Slmiiltl be placed 399/W" apart, outside measurement, to allow for-
mts l the tendency of the link to lengthen while making the eye joints.
DPC
) S/eps in lllrtlcing ri Homemmle C/min.
l l. Cut l9 wires ¢l3" long for long links.
3 2. Cut Eve wires ll]é" long for short links.
5 il. With a pair of pliers bend and twist the wire around the bolts
J to form an eye in each end, being careful to keep wire taut ‘
3 between bolts.
i ~l. Slip the end of the wire of next link thru the eye of the preced
3 ing link before forming the eye on it.
ll 5. After the 66 ft. chain is completed, check the length of each
li link and the length of the chain with a standard steel tape.
6 The length of a link can be made to conform to the standard
E) link by bending the eyes to make them shorter or longer.
e2 li. A harness ring or a piece of rawhide should be fastened to
c each end for greater ease of handling.
 ri 7. When the chain is not in use, the links should be folded into
T 7 a bundle and tied with at piece of string or rawhide.
T0 MEASURE WITH A n01v1E1v1ADE CHAIN
ln making measurements with the homemade chain, fractional
<>l` N"- [Mills of a chain are expressed deciinally. Each long link is counted
3€l?»l:" V as 5 links, or 0.05 chain. The short links at the end of the chain
llllllllll lll? l link or 0.01 chain each. For example, if a given distance is
lccl lll lllC?1$ll1`€(l as 9 full chains plus 8 long links, plus G Sll<>1`l lillliS, fll€
ili€5 lll llhlance should be recorded as 9/l-0 chains.
.1sed in
 
./

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