## Equations For Livestock

Where:

AAP = annual average population NAPA = number of animals produced annually

Equation 10.2

Coefficient for calculating net energy for maintenance

Where:

Cfi = a coefficient which varies for each animal category as shown in Table 10.4 (Coefficients for calculating NEm), MJ day-1 kg-1

°C = mean daily temperature during winter season

Where:

= net energy required by the animal for maintenance, MJ day-

Cfi = a coefficient which varies for each animal category as shown in Table 10.4 (Coefficients for calculating NEm), MJ day-1 kg-1

Weight = live-weight of animal, kg

Equation 10.4 Net energy for activity (for cattle and buffalo)

Where:

NEa = net energy for animal activity, MJ day-1

Ca = coefficient corresponding to animal's feeding situation (Table 10.5, Activity coefficients)

NEm = net energy required by the animal for maintenance (Equation 10.3), MJ day-1

Equation 10.5 Net energy for activity (for sheep)

Where:

NEa = net energy for animal activity, MJ day-1

Ca = coefficient corresponding to animal's feeding situation (Table 10.5), MJ day-1 kg-1

weight = live-weight of animal, kg

Where:

NEg = net energy needed for growth, MJ day-1

BW = the average live body weight (BW) of the animals in the population, kg

C = a coefficient with a value of 0.8 for females, 1.0 for castrates and 1.2 for bulls (NRC, 1996)

MW = the mature live body weight of an adult female in moderate body condition, kg

WG = the average daily weight gain of the animals in the population, kg day-1

Where:

NEg = net energy needed for growth, MJ day-1 WGlamb = the weight gain (BWf - BWi), kg yr-1 BWi = the live bodyweight at weaning, kg

BWf = the live bodyweight at 1-year old or at slaughter (live-weight) if slaughtered prior to 1 year of age, kg a, b = constants as described in Table 10.6.

Equation 10.8

Net energy for lactation (for beef cattle, dairy cattle and buffalo) NE1 = Milk • (l.47 + 0.40 • Fat)

Where:

NEi = net energy for lactation, MJ day-1

Milk = amount of milk produced, kg of milk day-1

Equation 10.9

Net energy for lactation for sheep (milk production known)

Where:

NEl = net energy for lactation, MJ day-1 Milk = amount of milk produced, kg of milk day-1

EVmilk = the net energy required to produce 1 kg of milk. A default value of 4.6 MJ/kg (AFRC, 1993) can be used which corresponds to a milk fat content of 7% by weight

Equation 10.10

Net energy for lactation for sheep (milk production unknown)

[(5 • WGwean )]

NE1 —

• EVmilk

NEi = net energy for lactation, MJ day-1

WG wean = the weight gain of the lamb between birth and weaning, kg

EVmilk = the energy required to produce 1 kg of milk, MJ kg-1. A default value of 4.6 MJ kg-1 (AFRC, 1993) can be used.

Equation 10.11 Net energy for work (for cattle and buffalo) NEwork = 0.10 • NEm • Hours

Where:

NEwork = net energy for work, MJ day-1

NEm = net energy required by the animal for maintenance (Equation 10.3), MJ day-1

Hours = number of hours of work per day

Where:

NEwool = net energy required to produce wool, MJ day-1

EVwooi = the energy value of each kg of wool produced (weighed after drying but before scouring), MJ kg-1. A default value of 24 MJ kg-1 (AFRC, 1993) can be used for this estimate.

Productionwool = annual wool production per sheep, kg yr-1

Equation 10.13 Net energy for pregnancy (for cattle/buffalo and sheep)

Where:

NEp = net energy required for pregnancy, MJ day-1

Cpregnancy = pregnancy coefficient (see Table 10.7)

NEm = net energy required by the animal for maintenance (Equation 10.3), MJ day-1

Equation 10.14

Ratio of net energy available in a diet for maintenance to digestible energy

CONSUMED

25.4

Where:

REM = ratio of net energy available in a diet for maintenance to digestible energy consumed DE% = digestible energy expressed as a percentage of gross energy

Where:

REG = ratio of net energy available for growth in a diet to digestible energy consumed DE% = digestible energy expressed as a percentage of gross energy

Where:

GE = gross energy, MJ day-1

NEm = net energy required by the animal for maintenance (Equation 10.3), MJ day-1

NEa = net energy for animal activity (Equations 10.4 and 10.5), MJ day-1

NEl = net energy for lactation (Equations 10.8, 10.9, and 10.10), MJ day-1

NEwork = net energy for work (Equation 10.11), MJ day-1

NEp = net energy required for pregnancy (Equation 10.13), MJ day-1

REM = ratio of net energy available in a diet for maintenance to digestible energy consumed (Equation 10.14)

NEg = net energy needed for growth (Equations 10.6 and 10.7), MJ day-1

NEwool = net energy required to produce a year of wool (Equation 10.12), MJ day-1

REG = ratio of net energy available for growth in a diet to digestible energy consumed (Equation 10.15)

DE% = digestible energy expressed as a percentage of gross energy

Equation 10.17

Estimation of dry matter intake for growing and finishing cattle

DMI = BW0 75 •

(0.2444 • NEma - 0.0111 • NEma' - 0.472)

_ NEma _

DMI = dry matter intake, kg day-1

BW = live body weight, kg

NEma = estimated dietary net energy concentration of diet or default values in Table 10.8, MJ kg-1

 Equation 10.18a Estimation of dry matter intake for mature beef cattle DMI = BW075 • (0.0119 • NEma 2 + 0.1938) _ NEma _

dry matter intake, kg day-1 live body weight, kg estimated dietary net energy concentration of diet or default values given in Table 10.8, MJ

Equation 10.18b

Estimation of dry matter intake for mature dairy cows

' f(5.4 • BW"

DMI =

i 500 J

( (100 - de%)y

LI 100 JJ

DMI = dry matter intake, kg day-1 BW = live body weight, kg

DE% = digestible energy expressed as a percentage of gross energy (typically 45-55% for low quality forages)

Where:

kg"1

Where:

Emissions = methane emissions from Enteric Fermentation, Gg CH4 yr-1 EF(T) = emission factor for the defined livestock population, kg CH4 head-1 yr-1 N(T) = the number of head of livestock species / category T in the country T = species/category of livestock

Equation 10.20 Total emissions from livestock enteric fermentation

Where:

Total CH4 = total methane emissions from Enteric Fermentation, Gg CH4 yr-1

Ei = is the emissions for the fh livestock categories and subcategories

Where:

EF = emission factor, kg CH4 head-1 yr-1 GE = gross energy intake, MJ head-1 day-1

Ym = methane conversion factor, per cent of gross energy in feed converted to methane The factor 55.65 (MJ/kg CH4) is the energy content of methane

Where:

CH4Manure = CH4 emissions from Manure Management, for a defined population, Gg CH4 yr-1

EF(T) = emission factor for the defined livestock population, kg CH4 head-1 yr-1

N(T) = the number of head of livestock species/category T in the country

T = species/category of livestock

Equation 10.23

CH4 emission factor from manure management

/ \

r 3 MCFSk ] B0(t) • 0.67 kg / m3 • • MS(t,s,k)

EF(t) — (S(T) • 365)

EF(T) = annual CH4 emission factor for livestock category T, kg CH4 animal-1 yr-1 VS(T) = daily volatile solid excreted for livestock category T, kg dry matter animal-1 day-1 365 = basis for calculating annual VS production, days yr-1

Bo(T) = maximum methane producing capacity for manure produced by livestock category T, m3 CH4 kg-1 of VS excreted

0.67 = conversion factor of m3 CH4 to kilograms CH4

MCF(S k) = methane conversion factors for each manure management system S by climate region k, %

MS(TSk) = fraction of livestock category T's manure handled using manure management system S in climate region k, dimensionless

EQUATION 10.24 VOLATILE SOLID EXCRETION RATES

EQUATION 10.24 VOLATILE SOLID EXCRETION RATES

Where:

VS = volatile solid excretion per day on a dry-organic matter basis, kg VS day-1

GE = gross energy intake, MJ day-1

DE% = digestibility of the feed in percent (e.g. 60%)

(UE • GE)= urinary energy expressed as fraction of GE. Typically 0.04GE can be considered urinary energy excretion by most ruminants (reduce to 0.02 for ruminants fed with 85% or more grain in the diet or for swine). Use country-specific values where available.

ASH = the ash content of manure calculated as a fraction of the dry matter feed intake (e.g., 0.08 for cattle). Use country-specific values where available.

18.45 = conversion factor for dietary GE per kg of dry matter (MJ kg-1). This value is relatively constant across a wide range of forage and grain-based feeds commonly consumed by livestock.

Where:

N2OD(mm) = direct N2O emissions from Manure Management in the country, kg N2O yr-1

N(T) = number of head of livestock species/category T in the country

Nex(T) = annual average N excretion per head of species/category T in the country, kg N animal-1 yr-1

MS(T,S) = fraction of total annual nitrogen excretion for each livestock species/category T that is managed in manure management system S in the country, dimensionless

EF3(S) = emission factor for direct N2O emissions from manure management system S in the country, kg N2O-N/kg N in manure management system S

S = manure management system

T = species/category of livestock

44/28 = conversion of (N2O-N)(mm) emissions to N2O(mm) emissions

Equation 10.26 N LOSSES DUE TO VOLATILISATION FROM MANURE MANAGEMENT

Nvolatilization-MMS S S

Frac

GasMS

Where:

Nvolatlllzation-MMS = amount of manure nitrogen that is lost due to volatilisation of NH3 and NOx, kg N yr-1 N(T) = number of head of livestock species/category T in the country

NeX(T) = annual average N excretion per head of species/category T in the country, kg N animal-1 yr-1

MS(T,S) = fraction of total annual nitrogen excretion for each livestock species/category T that is managed in manure management system S in the country, dimensionless

FracGasMS = percent of managed manure nitrogen for livestock category T that volatilises as NH3 and NOX in the manure management system S, %

Where:

N2OG(mm) = indirect N2O emissions due to volatilization of N from Manure Management in the country, kg N2O yr-1

EF4 = emission factor for N2O emissions from atmospheric deposition of nitrogen on soils and water surfaces, kg N2O-N (kg NH3-N + NOx-N volatilised)-1 ; default value is 0.01 kg N2O-N (kg NH3-N + NOx-N volatilised)-1 , given in Chapter 11, Table 11.3

Where:

Nleaching-MMS = amount of manure nitrogen that leached from manure management systems, kg N yr-1 N(T) = number of head of livestock species/category T in the country

Nex(T) = annual average N excretion per head of species/category T in the country, kg N animal-1 yr-1

MS(T,S) = fraction of total annual nitrogen excretion for each livestock species/category T that is managed in manure management system S in the country, dimensionless

FracleachMS = percent of managed manure nitrogen losses for livestock category T due to runoff and leaching during solid and liquid storage of manure (typical range 1-20%)

Where:

N2OL(mm) = indirect N2O emissions due to leaching and runoff from Manure Management in the country, kg N2O yr-1

EF5 = emission factor for N2O emissions from nitrogen leaching and runoff, kg N2O-N/kg N leached and runoff (default value 0.0075 kg N2O-N (kg N leaching/runoff)-1, given in Chapter 11, Table 11.3

Where:

NeX(T) = annual N excretion for livestock category T, kg N animal-1 yr-1

Nrate(T) = default N excretion rate, kg N (1000 kg animal mass)-1 day-1 (see Table 10.19)

TAM(T) = typical animal mass for livestock category T, kg animal-1

Where:

Nex(T) = annual N excretion rates, kg N animal-1 yr-1

Nmtake(T) = the annual N intake per head of animal of species/category T , kg N animal-1 yr-1 Nretention(T) = fraction of annual N intake that is retained by animal of species/category T, dimensionless

Where:

Nmtake(T) = daily N consumed per animal of category T, kg N animal-1 day-1

GE = gross energy intake of the animal, in enteric model, based on digestible energy, milk production, pregnancy, current weight, mature weight, rate of weight gain, and IPCC constants, MJ animal-1 day-1

18.45 = conversion factor for dietary GE per kg of dry matter, MJ kg-1. This value is relatively constant across a wide range of forage and grain-based feeds commonly consumed by livestock.

CP% = percent crude protein in diet, input

6.25 = conversion from kg of dietary protein to kg of dietary N, kg feed protein (kg N)-1

Equation 1G.33 N RETAINED RATES FOR CATTLE

retention(T)

Milk

Milk PR% 1GG

6.3S

 í 7.G3 • NEg WG • 26S - g WG iGGG 6.25 Where: N retention(T) = daily N retained per animal of category T, kg N animal-1 day-1 Milk = milk production, kg animal-1 day-1 (applicable to dairy cows only) Milk PR% = percent of protein in milk, calculated as [1.9 + 0.4 • %Fat], where %Fat is an input, assumed to be 4% (applicable to dairy cows only) = conversion from milk protein to milk N, kg Protein (kg N)- 6.38 WG = weight gain, input for each livestock category, kg day 268 and 7.03 = constants from Equation 3-8 in NRC (1996) NEg = net energy for growth, calculated in livestock characterisation, based on current weight, mature weight, rate of weight gain, and IPCC constants, MJ day-1 1000 = conversion from grams per kilogram, g kg-1 6.25 = conversion from kg dietary protein to kg dietary N, kg Protein (kg N)-1 Equation 10.34 Managed manure N available for application to managed soils, feed, fuel or CONSTRUCTION USES Fracj iGG Where: NMMS_Avb = amount of managed manure nitrogen available for application to managed soils or for feed, fuel, or construction purposes, kg N yr-1 = number of head of livestock species/category T in the country Nex(T) = annual average N excretion per animal of species/category T in the country, kg N animal yr-1 MS(T,S) = fraction of total annual nitrogen excretion for each livestock species/category T that is managed in manure management system S in the country, dimensionless FracLossMs = amount of managed manure nitrogen for livestock category T that is lost in the manure management system S, % (see Table 10.23) beddingMS = amount of nitrogen from bedding (to be applied for solid storage and deep bedding MMS if known organic bedding usage), kg N animal-1 yr-1 S = manure management system T = species/category of livestock

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