Regional management of animal manures—a model for collection, storage location and distribution

.I N,qri(‘. 1‘17,y~~q Res. ( 1974) 19, 233-244

Regional

Management

Collection,

of Animal Location

Storage

V. A. Dorm*;

D. F. LvoNst:

Manures-A

Model

for

and Distribution

J. R. O’CALLAGHAN:

The feasability of separating manure management from pig and poultry production units in the same way that feed production is separated from utilization is examined. The basic idea is that centralized storage facilities for manure should be provided for a group of pig and poultry units. The manure collected into the central store can be disposed of by land spreading on selected land areas in a separate operation. An analytical model is developed to optimize the siting of the store and the determination of the number of tanker wagons to collect and spread the manure. The model is applied to a specific example comprising 58 pig fattening units and the results indicate that the system may have economic application while at the same time minimizing pollution hazards and relieving the specialist pig or poultry farmer of the task of manure management. 1.

Introduction

It is assumed that land spreading must at least for the immediate future, be the principal method for the disposal of animal manures. O’Callaghan, Dodd and Pollock’ have put forward guidelines for the management of manures by land spreading. In order to minimize problems of soil, crop and water pollution, manures must be applied at controlled rates during the growing season. The amount applied is constrained by the rate of evapotranspiration of the crop and the quantities of NPK which are removed when the crop is harvested. In the future, it may be essential as part of land use planning, to maintain tracts of productive agricultural land in close association with animal production units. It is not uncommon for feed to be transported long distances to pig units, the location of which are often chosen solely on consideration of market outlets. As a consequence these units may be located on very limited land areas in the vicinity of towns. The separation of feed and animal production has enabled farmers located in areas of poor soil types in which grassland and tillage farming are difficult to carry out on an intensive scale, to develop “farmyard” type enterprises. In addition such “farmyard” enterprises are used to generate additional income on intensive grassland or tillage farms of small area. In pig and poultry units, animal manures may be regarded as a liability and any investment in manure management considered as a charge on the enterprise. Due to climatic conditions manure storage facilities for up to 6 months may have to be provided in certain areas’ and this represents a considerable investment-approx. f6 per pig place. The acquisition of spreading rights on land may not be practical; land owners may be unwilling to grant such rights because of the consequent encumbrances that are placed on the holding. [n addition the acquisition of land by the pig or poultry farmer may be impractical first because of the capital investment required and second, having purchased the land for spreading it becomes necessary for him tc engage in crop farming. The provision of manure storage tanks and land of themselves do not ensure utilization of manures in crop production. It has been submitted’ that manure be managed on a regional basis to ensure an orderly expansion of livestock production against a background of land use and water resource planning. This paper examines the feasability of separating manure management from pig and poultry production units in the same way that feed production is separated from utilization. The basic idea is that centralized storage facilities for manure should be provided for a group of pig and * Agricultural Institute. Dublin t Agricultural

Institute

! fkparrment

of Agricultural

Scholar,

Statistics

Department,

Engineering.

University

Dublin

University

of Newcastle

on Tyne 233

234

REGIONAL

MANAGEMENT

OF

ANIMAL

MANURES

poultry units. The manure collected in the central store can be disposed of in a separate operation. An analytical model is developed to optimize the siting of the store and the selection of the number of tanker wagons to collect and spread the manure. The model is applied to a specific example comprising 58 pig fattening units. 2. Assume k pig units located . . . . . . . kl.

at points

The model

xi, J’~ in some arbitrary

co-ordinate

system (i -: I, 2, 3,

Consider the ith unit: No. of pig places = ni Volume of manure storage tank -= vi gallons. Distance from central store = di miles*. q =volume of manure produced per animal per day. In the case of pig fattening houses the volume of manure produced per day in gallons is equivalent to the number of pig places.* No. of tankers collecting and transporting manure to central store = N. Capacity of each tanker collecting manure = C, gallons. Speed of travel of tankers collecting manure = S, mile/h. Effective working period = 11, h/day. Time to load and unload a tanker at store == I, min. Capacity of central manure store = P gallons. Position of central store X, 9. Manure is transported from store and spread on j parcels of land located at xi’ yi’ (i ~- I, 2, 3 . . . . . . . . . . .i) Consider the ith spreading area: Amount of manure to be spread = nil gallons/annum. Distance of nearest point in ith area to central store = dil miles*. Location of nearest point in ith area to central store = xil, J’il* No. of tankers transporting and spreading manure from store = M. Capacity of tanker transporting and spreading manure from store -= C, gallons. Effective working period = h, h/day. Speed of travel of M tankers from store to spreading areas := S, mile/h. Speed of travel within each spreading area = S, mile/h. Time to load each tanker with C, gallons of manure = I, min. Time to spread nil gallons within ith area = fir min. Note that this does not include time required to travel to the edge of ith area; til can be assessed knowing the area of land, number of tanker loads to be spread, shape and topography of the area. Spreading period = W days per annum. Required parameters are (a) capacity vi of tank at each pig unit, (b) collection period T days for each pig unit, (c) the number of tankers N and M (d) capacity P and location 2, j of the store. Determination of vi 2.1, Two approaches have been examined as follows: (a) Vi = niq T with T being constant for all units. In this case each tank is emptied once in T However ri may not be a multiple of C,, indeed it days and the demand for tankers is uniform. * In the calculation d( can be taken as the straight line distance from a pig unit to the store ti/(?i --X)’ t+(yr -hs. The road distance. how-

ever, will

in getma

be greater than this value and a correction

factor

may be necessary in a specUic situation

:\

L

I)Oi)I)

1 I).

t

I YONS:

J.

R.

_,:i

O’CALLAGIIAN

may even be a fraction for small pig units, so that unless routing procedures are introduced some tanker runs, the tankers may, on occasions, be only partially full. In practice, however, of a given situation rule hill be a route of pig unit to store to pig unit. In an examination c.lpaclty

of each pig unit

calcul;\ted.

11~

and each tank

volume

l‘i could

be measured

The value of T chosen would then be the lowest value of ?“i

against (b)

and the values

fol the the -“!-

and this would ensure 4

any tank overflowing. l’i

C,.

In this case each tank is emptied

at intervals

of 2

days so that all tankers

are

full at all times and no routing procedure is required. Howeve; because the period between emptying tanks varies with pig unit size the demand for tankers will not be uniform and some tankers must stand idle for a period of time if overflow is to be avoided. In addition, for large pig units the period between emptying tanks would be so short as to require shift work. This would be overcome by making vi equal to a multiple of C,. However this procedure will not alter the total number of tanker runs required to operate the system. Approach (a), viz. I’~ y- niq T, would appear to be the most suitable. The number of tankers is constant: it is easiest to operate and can be made efficient in a given situation by routing procedures for the collection of manure from very small pig units. It is pointed out that the number of tankers required to operate the system is independent of time T between emptying tanks. 2.2. Determination of N, number of tankersjbr manure collection Applying approach (a), tji = ni q T and assuming the tanks on the pig units are large compared to the tankers, time ti to empty tanks of capacity vi gallons at ith unit

i.e.

(la)

Note that this expression Applying

approach

is independent

of T.

(b), I’~ = C, i.e. T = 2

The ith unit will be emptied

L ni times in C, days.

I’i Time to empty the tank of ith unit once = c

120 rl, s

1 L

Time to empty the tank of ith unit ni times = + Time to empty k tanks over period

C, days =

[y

-I-- 1111

min.

jlj min.

REGIONAL

236 i.e.

OF

ANIMAL

MANURES

...(lb)

N > Cl”

Note that this expression approach (a).

Consider

is independent

of T and is the same function

Total time to travel to and spread

, It]

x1’ llil gallons

E Zig x,‘.il

as that obtained

with

2.3. Determination of M, number qf’tankers for spreading manure the ith area. Time to travel to and spread tiil gallons of manure on ith area. ~z!!.?[!Z!$?

Note

MANAGEMENT

+tilmin.

of manure

on j areas

[!J!$

+ j2] + C,jtil

min.

MSN,

it is necessary

to combine

= Cl” niq

.. i.e. To determine the number Eqns (la, b) and (2).

Put K, = cl” KI +K,

w 4 6Oh,C,

of tankers,

and K, =

can be evaluated

the two functions

in

Ci

as all terms are known.

r1

N+M>/C,+Wh&

Clkniqdi-t

1, c2s 2 21

w

Cj~?~'dil

... (3)

The minimum value of the expression on the right hand side gives the optimum location .X,p of the store. Knowing ,?‘,y the individual components of theexpression on the right hand side can be evaluated and hence from Eqns (1) and (2) the least values of N and A4 can be ascertained.

To find 2, j an iterative

procedure

2.4. l‘ocation of store due to Kuhn and Kuenne3

can be used.

Let K = K,+K, zfori= and ri = I i

1. . . . . . . . k

111

2 nl( i--k) h c s Wfor 2

i=(k+

1). , . . . . . .(k ii)

2'2

d,+i=dilfori=

1 . . . . . . . . .j

‘+.

.\.

l)ODD:

[).

I-‘. LYONS;

J.

R.

O’CALLAGHAN

and let tli ( V. p) 2 J,. Now substitute

into Eqn (3) as follows h -tj N t A4 2 K .. 2 ridi. i ~~I

J.-tj

Put The optimal

f(,F-, j) = K 2. C ridi. I point .?, 4; is given by the solution of the pair of simultaneous

equations. (4)

kfj

o

(x[ --.q

7 ri 7

which are

..

=L

k~+jri(yi -j)

o

?7=

Eqns (4) and (5) cannot gives :

However

in general be solved for 1 and j. k+irlxi

kfj

rearrangement

of the equations

ri

Fd,=ff;z ,.. (4a)

or

k 1-jriyi

Similarly

7%

Y =

f:z

The following procedure at the qth iteration.

is rapidly

convergent. jut k X

‘To

20 E ~)I

start, define

1 (5a)

ktjri I

Define R4 and ~7 to be the values of .? and p i-tk C

ri Xi

jP ;z- 1

j+k 7

ri ?‘i / i-k 7

ri

ri

i.e. the centre of gravity

(4b)

Put

-q+1=

Y

and

k-J

7 di (P, forq==O,

I,2 ,.....

.........

. (5b)

rf j”)

238

REGIONAL

MANAGEMENT

OF

ANIMAL

MANURES

The procedure may be stopped when successive values of both R and j change by less than some small specified amount. In a practical situation two possibilities as follows can be considered: (i) manure spread on an area concentric with the store; in this case the centre of gravity Ci” ni4Yi Cik niqxi of the pig production units approximates to the optimum store ’ Cikniq [ Cikniq I location: (ii) manure transported from the store to several spreading areas; in this case the centre Ci”

of gravity of the whole system to the optimum store location:

n[qxi

[

2.5.

xi

+

li t?iq

Ci”

-1

Hi1

2:

xi1

_Cik

Hi1

12iq Xi”

Yi

+ Cij nil

Yi’-

approximates

niq $- cij nil

I

Determination of store capacity P

The capacity of the store is dependent on the quantity of manure produced, & n,q gallons per day, and the period of time, W days, during which spreading of manure is permikible. The value of W will vary with regions but on average will be the length of the growing season. Assuming manure spreading to be permissible throughout

W the value of P is (365-W)

i niq. I

Day0 I store

7i

‘I

rz

t3

6.

‘2

‘-----‘T-T+ m

r4

m

empty

In some situations in which specific cropping routines prevail it may not be possible to spread uniformly throughout the period W. A general expression for ris thus developed as follows. Consider the year as starting immediately after the store has been emptied. Let T, days be the length of the first period when the store is filling and no manure is spread, t, days be the length of the first period during which manure is drawn out of the store, T2 days be the length of the second period when the store is filling and t, the length of the second period during which manure is drawn out of the store and so to T,,, and t,, where m is the number of periods when the store is being either filled or emptied I/ = Jpti

Let

I

L = C”‘T, U + L _ 365 At any time t days the volume of manure in store 365 Ckniqz:’ ti = t Ckniq-1

Maximum volume in store

=-

T kniq

Max

r’

o < f < 365 t

Fmtc-

C”’ti w-365C’ti 1

maximum number of days storage required 365 s’

= Max 0 4

f <

365 t-

f;“:’

ti

1

\

et.

i)Olll).

I).

t.

I.YONS:

J.

R.

-.’ 10

O’(‘ALLAGfI.\h

The m;rximum value obviously occurs at the start of a spreading period and hence such times only 7‘2 need consideration : the times at the start of a spreading period are T,, (T, + T, f ,I, (T, T., I, : I,J and so on to (T,+T,tT,. , . , T,,,-t(tp f,~l-t, , . r,, 1). (‘onsider the beginning of the Rth period t = CR Tilx=R I I Maximum

number

-1 ti

of days storage required _ Max i

I ~Rsrn

1

T, + xR-l I

CR

I

ti-

:= Max I
Ti + CR--’ ti I

7”

i

= U and U $- L

C”t,

Hut

1

Maximum

number

365

of days storage required = Max 1 c R < m

CR

Ti

_\ +/ CR

Therefore

the minimum

volume

1 fi/

I

1

of the store,

Consider the following example-3-cut mid May-mid June and during August.

silage system in which manure

Day 0

is spread during

March,

365 T,=45

7j=46

j *

), -31

7i = I81 days

store

r2=31

empty

U =

Then

5=3t;

Cm ti = 31 f31{-31

=- 93 days

1 1,

=

Cm

I Consider

Ti = 181145-k46

mu 272 days.

the number

of days that storage would be required

1

=

18 1 days manure

CtTi

=

226

x11 ti

:= 31

March May 15

Ti

272.3 1 There are 226 - - 93 days stored = 1355 days

stored

at March

1, May 15 and August

1

240

MANAGEMENT

REGIONAL

August I

OF

ANIMAL

MANURES

&” Ti = 272 Cl2 ti

=

62

272.62 There are 272- - 93 days stored = 908 days Hence the number of days for which manure storage must be provided is 181 days and B = 181 Ckn,q. I

3. Application of model Farming patterns in the area of Lough Sheelin, a valuable trout fishing lake in Co. Cavan, Ireland, illustrate how manure produced from enterprises, the feed for which is purchased, can be a liability rather than an asset. In general the farms are small, the soil of poor quality and pig production forms the main farming enterprise. Under such circumstances the demand for manures for use in crop production is low and resort was made in the past to land spreading at “dumping” rates. A rapid increase, 9,000-19,000 pig places, in pig production took place in the area over the period 1968-71; the levels of nutrients in the lake, particularly N and P, increased over the same period culminating in an extensive “bloom” of blue green algae in spring 1971. The deterioration in the lake water quality was a cause of public concern as a result of which an examination of the management of manures in the catchment area was carried out.4 Data from the survey of pig units is used to illustrate the application of the analytical model. The distribution of pig fattening units and soil types in the catchment area, 27,000 ha is shown on Fig. I; the pig units total 58 and range in capacity from 40 to 3,500 places with 4 units accounting for almost 60% of the total. The values of ni, xi, yi, vi are given in Table I and q = I. The following values are assigned to the parameters in Eqns (l), (2) and (3). Capacity of tankers = C1 = C, = 1,500 gallons Speed of travel of tankers collecting manure m=S, = 10 mile/h Speed of travel of tankers distributing manure = S, = 3$ mile/h Time to load tanker at pig unit and unload at store = I, = 8 min/load Time to load tanker at store prior to spread = I, = 1.5 min/load Effective working period h, = 4 h/day Effective working period h, = 8 h/day Spreading period, W, to be 184 days, spreading to be in accord with following routine: March, mid May-mid June and August. Rate of spread to be 3 equal dressings of 6,400 gal/ha. Area on which manure is spread to be circular and concentric with store. The volume of manure produced per day x1” Q gallons, is estimated at 19,000 gal. Storage period required is September-February inclusive viz. 181 days; this period has been shown to be adequate for the proposed spreading routine. Capacity of store, p, therefore, required is 181 Cl”%, or 3.44 m. gallons. The minimum number of tankers, N, required to collect manure is indicated by the expression N > 0.42 +

C,“” nidi 3oooo

. 3

The value is 2.5; a correction factor of 1.2 is applied to allow for road travel so that a total of 3 tankers are required. The optimal location of the store _?,3 is estimated at 4.53, 9.75 which point by coincidence lies on a pig farm; in this context it is relevant to note that the centre of gravity of the pig units is 5.77, 9.03 so that this approximation is reasonable in the present case.

TAISLE I I.oration(.I i, v,),number of pigs (n,), daily

\-,

-T

(miles)

manure production (~~(1)~estimated required in individual system

-

storage

-

E.ui.Y/irrg .~tWUge

Yi (miles)

cr/pocit.r

(10:’gul) _~. ~.

_____

6.12 6.90 6.35 1.73 5.21 6.32 4.82 X.03 647 7.26 9.75 3.06 2.10 6.43 3.57 13.56 8.68 2.30 4.55 2.25 7.20 6.70 9.31 5.30 7.66 4.07 6.95 5.96 6.20 5.90 9.10 I .90 6.41 6.55 6.28 4.28 5.00 5.08 7.70 3.97 5.95 2.15 4.70 6.10 5.75 5.30 7.52 7.30 6.30 6.16 8.72 6.85 3.97 6.42 6.93 I .63 6.34 1.25

existing

13.42 8.22 6.30 8.67 12.40 6.80 11.20 14.64 625 5.90 I.39 10.35 a.75 13.42 9.82 7.20 9.34 IO.65 9.75 8.16 6.10 6.46 6.10 13.04 6.55 6.30 8.35 12.94 10.65 8.22 IO.45 IO.50 3.20 12.70 13.55 10.65 9.25 12.22 6.80 10.95 5.80 IO.25 10.79 4.15 6.10 11.11 6.80 13.40 6.40 6.25 4.71 12.90 10.55 9.20 7.94 9.36 10.59 10.02

40 40 40 50 50 50 50 52 56 51 60 15 82 86 92 93 100 100 100 100 100

-

100 100 100 110 112 115 116 120 120 130 145 150 150 150 150 I58 I80 200 250 260 300 300 300 350 370 3x0 400 400 400 400 400 500 590 1000 2500 2500 3500

0

0 4.8 0 0 5.4 5.7 0 5.3 0 5.4 15.2 0 0 IO.2 14.7 8.2 8.9 8.9 8.9 9.5 14.4 18.6 31.5 15.4 0 16.8 19.9 8.6 12.7 9.2 13.0 0 12.2 20.4 40.1 14.4 7.6 21.4 IO.3 19.3 I.4 I I.0 20.8 41.9 21.7 21.7 15.4 15.4 18.2 IX.5 30.8 48.4 40.9 131.6 260 217 76

Additiotrtrl stortrge required ( 10:’ gtrl ) 7.2 7.2 2.4 9.1 9.1 3.7 3.4 9.4 4.8 IO.3 5.5 0 14.8 15.6 6.5 2.1 9.9 9.2 9.2 9.2 8.6 3.7 0 0 4.5 20.3 4.0 I.1 13.2 9.1 14.4 13.2 27.2 15.0 6.8 0 14.2 25.0 14.8 34.9 27.1 46.9 43.3 23.5 21.5 46.3 47.7 57.0 57.0 54.2 53.9 41.6 42.1 65.9 49.4 193 176 558

capacity

and storage

242

REC;[OIGAI.

MANA(;EMEi‘;T

01; ANIMAL

MANURt:s

Fig. I. Map showing &trihrrtior~ of pig units and soil types it1 catchment cwea of‘LON~/ISheeiin In this example the manure is assumed to be spread on an area concentric with the store so that dil is zero. The area required for spreading manure is estimated at 361 ha viz. a circle of 2 km diam. The number of tankers, M, required to spread manure is estimated at 1.69. This was determined by dividing the spreading area into 7.5 m wide annuli; (7.5 m is the width of manure spread by a tanker and manure is spread by a single pass of a tanker). The tanker is assumed to travel out

\’

,?.

I:Oi)l):

I).

I.

I.jONS:

J.

R.

247

O’CALLAGHAN

to each annulus and then to travel around the annulus. In the case of annuli receiving more than I tanker load radial routing from the annulus to the store and back again is assumed. In practice. therefore, to operate the system a total of 4 tankers would be required. Such ;I fleet nould provide for I stand-by machine during the winter period assuming 4 h effective working, day and 0.8 stand-by machines during summertime assuming 8 h effective working day for all machines. The estimated cost of a tanker-tractor unit is &3,800 p.a.“’ so that the cost of manure collection and distribution is estimated at &15,200 p.a. or 28~ per pig fattened assuming a throughput of‘ 3 pigs per place per annum. The cost of manure storage tanks depends primarily on tank capacity and form of construction. Approximate current costs for tanks of various types over a capacity range of lO,OOO-200,000 gallons are shown in Table II. The costs can only be regarded as approximate because of the significant influence of site location and excavating conditions. Unlined underground tanks are excluded because of the danger of ground water pollution and the ditTiculties in emptying them. r:tciially

Approximate costs of manure storage tanks Tuuk cupuci7y (gul )

10,000

20,000

60.000

40,000

cost/gul

__

100,COO 150,~JOO

80,000

2f10,OOf~

(/I)

-

-

I Underground roofed reinforced concrete* Underground unroofed reinforced concrete (nett) Underground unroofed reinforced concrete (grossjt Overground unroofed reinforced concrete (nett) Overground unroofed reinforced concrete (gross) Overground roofed reinforced concrete Overground unroofed steel (nett): Overground unroofed steel (gross)

-

I.3

5.6

5.1

4.5

6.3

4.6

3.5

I.6

5.5

8.3

I I

4.1

3.9

3.7

3.4

3.0

2.7

3.6

2.3

2.1

4.2

3.6

3.2

3.0

2.7

2.5

5.3

3.5

2.8

2.5

2.3

1.9

I.6

9.6

6.2

4.2

3.4

3.0

2.7

2.3

2.1

9.3 9.2 10.1

6.3 6.3 7.0

5.1 4.3 4.8

4.3 3.3 3.7

3.9 2.8 3.1

3.6 2.6 2.9

3.3 2.1 2.4

3.0 1.X 2.1

-

-

Estimates based on the following: *Concrete tanks, 9 ft deep square in plan. Unit costs: Excavation f0.75/yd” Floor slab (6 in) f2.OO/yd’ Walls (9 in) .f9,OO/yd” Roof (precast beams) fS+K)/yd” + Allowance for 24 in depth for wmter rainfall. 1 Based on suppliers’ current estimates.

It is useful to compare the cost of operating the central storage system of manure management with that of each pig unit having its own manure storage and spreading facilities. The estimated cost of the central store is E72,OOO; this figure is based on providing a group of 13 tanks each of 0.28 mg capacity. There is at present a lack of knowledge on agitating and emptying manure from tanks of greater capacity. The estimated cost of additional storage capacity at individual pig units is &78,000. Although economy of scale is attainable in manure storage tanks it is not significant * Labour 1,800 pa. investment in tanker-tractor unit-f4,500 at 10”; assuming linear depreciation over 5 years-f1,200 ~_a. Fuel-t 200 p.:~.

Maintenance

and

repairs--fWl

p.s.

244

REGIONAL

MANAGEMENT

OF

ANIMAL

MANURES

in the present example because of the 4 major pig units. The estimated total minimum cost, assuming hired equipment, of each pig farmer spreading manure from each unit on an area concentric with the unit amounts to approx. 22,500 p.a. or 4.4~ per pig fattened. The cost of the system therefore amounts to approx. an extra &12,500 p.a. This is offset, however, by the cash value of the manure, estimated at &20,000 p.a. The example illustrates that the separation of manure management and pig production can be achieved without cost to the pig farmer while at the same time minimizing pollution hazards. It must be pointed out however, that the cost of operating the system would increase in the event of the available spreading areas being located some distance from the store. 4. Discussion and conclusions The manure from the store may be disposed of by land spreading on an area concentric with the store or on selected areas located at some distance from the store. Alternatively manure may be sold to farmers on a supply or a supply and deliver basis, the cost of the product with the latter method being dependent on the haul distance. Where manure is to be “conditioned” before spreading, for reason of quality control, odour suppression or pathogen removal, centralizing the treatment facilities offers further economies of scale in the areas of capital investment and operation of equipment. Although the model optimizes the collection, storage location and distribution of manure withn a given area it does not optimize area boundaries within a region. However, in a practical situation the economies of including or excluding specific units and manure spreading areas may be easily ascertained and indeed external circumstances will in many cases determine the area boundaries. The fact that the centre of gravity of the pig units and the spreading areas together approximates to the optimum store location enables near optimal solutions for the store location and number of tankers required to be determined by simple calculation. Acknowledgements

The authors are grateful to the Agricultural Research Council for provision of funds to the University of Newcastle on Tyne for research work on animal manures, to the Director, Agricultural Institute, Dublin for his co-operation and the financial support of the Institute to Dublin University. REFERENCES ’

O’Caliaghan,

J. R.; Dodd, V. A.; Pollock, K. A. The long term management of animal manures. J. agric.

Engng Res., 1973 18 l-12 z O’Callaghan, J. R.; Dodd, V. A.; Pollock, K. A.; O’Donoghue, P. A. J. Characterization of waste treatment properties ofpig manure. J. agric. Engng Res., 1971 16 399 3 Kuhn, H. W.; Kuenue, R. E. An efficient algorithm for the numerical solutions of the generalized Weber problem in spatial economies. J. Regional Sci., 1962 4 (2) 21 4 The Management and Disposal of Animal Manures in the Cutchment Area of Lough Sheelin, Co. Cavan, Zreland. Agricultural Institute, Dublin, April 1972