July 1, 1998
Forage Systems Update
Vol 7, No. 3
Grazier's Arithmetic
Jim Gerrish
At our May FSRC grazing school we failed to cover the topic of
"Grazier's Arithmetic" and I told the attendees that I would cover
it in the next newsletter, so here it is. This is basically
reproduced from our 1997 Missouri Grazing Manual, but it does draw
your attention to the topic. There are several components in a
grazing system that can be calculated or estimated. This is an
up-front disclaimer that these calculations are basically intended
to get ball park estimates to work from. They do not give you "the
Answer". We will look at calculating seasonal carrying capacity,
grazing period stock density, paddock size, and paddock number.
Seasonal Carrying Capacity: Carrying capacity is the stocking rate
which is economically and environmentally sustainable for a
particular grazing unit throughout the grazing season. Carrying
capacity is largely determined by four factors: 1) annual forage
production, 2) seasonal utilization rate, 3) average daily intake,
and, 4) length of the grazing season. These terms can be expressed
in the mathematical formula below:
Annual Forage Production X Seasonal Utilization Rate
Carrying = ------------------------------------------------------
Capacity Average Daily Intake X Length of Grazing season
Annual forage production is the total amount of forage dry matter
produced per acre on an annual basis. This would include both hay
and pasture harvested from grazed acres. In the formula, this term
should be expressed as lbs forage/acre. Seasonal utilization rate
is the percentage of the annual forage production which will
actually be harvested by the grazing livestock. This will be very
dependent upon rotation frequency and expected level of animal
performance. Utilization rate is expressed as a unitless decimal
fraction in the formula.
Average daily intake should be set at the level that will be
required to yield the desired animal performance level. This may
well be the most difficult part of the entire process. To
accurately determine the appropriate intake value, some estimate of
forage digestibility and energy is required. These values cannot be
reliably determined without careful forage sampling and laboratory
analysis. For this reason we tend to insert arbitrary values in
this space and err on the side of overestimating intake. Average
forage intake values for high, medium, and low performance of either
steers or cow-calf pairs would be 3.5%, 3.0%, or 2.5% as a
percentage of the animal's bodyweight. For example a 1200 lb cow
of medium milking ability would consume about 36 lb of forage dry
matter on a daily basis. In the calculation, intake would be
expressed as .03 lb of forage/lb of liveweight. Length of the
grazing season is how many days this grazing unit needs to feed the
livestock and is expressed as days.
When the appropriate values have been entered into the equation and
calculation made, the resulting answer is the pounds of animal
liveweight that each pasture acre of the grazing unit will support
for the indicated grazing season. As an example, we will assume
that an average acre will produce 7600 lbs of forage annually. If
we plan to use an average 3 day grazing period the seasonal
utilization rate might be around 70 %. The livestock will be steers
we hope to have gain 1.5 to 2 lb/hd/day. This would be a moderate
performance level, so intake is entered at 3 percent of bodyweight
which is .03 lb of forage/lb of liveweight. It is important to
enter intake in this format, not as 3 percent so that units cancel
out. We will anticipate grazing the steers from April 20 to October
1 or a total of 164 days.
We make the following calculation:
7600 lb forage/acre X .70
---------------------------------------- = 1080 lb liveweight/acre
.03 lb forage/lb liveweight X 164 days
The 1080 lb liveweight/acre is an indication of the carrying
capacity of this unit. If we purchase 540 lb steers, can we stock
the unit at 2 steers (1080 lb liveweight/acre ÷ 540 lb/steer) to the
acre? Only on the first day of the season! Why? Because the
animals are, hopefully, gaining weight every day and quite likely
the average forage availability in August is lower than that in May.
If expected average daily gain is 1 3/4 lb/hd/day, the average weight
of steers at mid-season will be 683 lb (540 lb + (82 days X 1 3/4
lb/day)). Initial stocking rate could be set at 1.6 steers/acre
(1080 lb liveweight/acre ÷ 683 lb liveweight/steer). Remember this
is a guideline to help make initial stocking decisions not, a
magical recipe for universal financial success.
Grazing Period Stock Density: After making basic farm stocking
decisions, the time comes for every beginning grazier to make the
actual decision of where to place a break fence or how many animals
to place in a particular paddock. That decision is based on the
same principles used in the carrying capacity equation discussed
above but modified to represent single grazing period conditions
rather than seasonal values. The carrying capacity equation becomes
the stock density equation with the following modifications:
Available Forage X Grazing Period Utilization Rate
Stock = ----------------------------------------------------
Density Average Daily Intake X Length of Grazing Period
Available forage is the quantity of forage dry matter that is
actually allotted to the animals for a grazing period. Accurately
measuring forage availability is time consuming and expensive so we
tend to rely on estimations of yield. The simplest method is to
look at a pasture and make an educated guess as to what the forage
availability is likely to be. With practice, a good grazier can
consistently estimate within 10 to 20 % ± the actual yield. A second
method relates height and condition of the pasture to dry matter
yield. This process was fully described in the
April 1997 Forage
Update (Vol 6:No. 2) or can be accessed at our website
(aes.missouri.edu/fsrc/)
The following example illustrates how to determine where to place a
temporary fence to create a paddock to feed a herd of 100 steers
weighing 600 lb/hd for 1 day with a rate of gain objective of 2.25
lb/hd/day. The pasture is Orchardgrass-red clover 8-10 inch tall
and the area where the steers have just finished grazing has about
20 percent bare ground. The pasture is 40 acres that is 660 ft
wide. To use the stock density equation we must first determine the
appropriate values.
Forage availability can be estimated from above mentioned
height:yield table using the average sward height of 9 inches and
the stand condition as good. The corresponding value for an
Orchardgrass-legume pasture is approximately 250 lb/acre-inch so the
available forage 2250 lb/acre (9 inch X 250 lb/acre-inch).
As an average daily gain of 2.25 lb/hd/day is a high performance
objective, utilization can not be excessive or else intake will be
limited. To maintain an intake rate of 3.5 percent of bodyweight, a
50 percent utilization rate with one day grazing would be
appropriate to use in the calculation. Assuming the 1 day grazing
period, we can make the following calculation:
2250 lb forage/acre X .5 utilization rate 31,365 lb
-------------------------------------------- = liveweight/acre
.035 lb forage/lb liveweight X 1 days
The steers weigh 600 lb/head and each acre will support 31,365 lb
liveweight, so the pasture can be stocked at the rate of 52
steers/acre/day (31,365 lb liveweight/acre ÷ 600 lb liveweight/steer).
The herd of 100 steers will require 2 acres/paddock (100 steers ÷ 52
steers/acre).
It is very important that values used for the parameters in the
equation are realistic in how they relate to one another. All of
the parameters are interrelated and inserting an inappropriate value
for any one parameter will result in erroneous conclusions. For
example if available forage is below 1500 lb/acre, an intake of 3.5
percent would be impossible to achieve. For this reason, the
equation cannot be used as most mathematical formulas where if all
but one value is known the remaining value can be calculated. A
calculation can be made, but the result may be biologically
meaningless.
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