Farm Operations formula solvers

Aeration Airflow Requirement

Q = q \, M

Farm OperationsTotal fan airflow for a stored quantity of grain, from the aeration rate per tonne. The first number in sizing an aeration fan — though not the last, because static pressure decides the rest.

Auger or Conveyor Transfer Time

t = \frac{Q}{R}

Farm OperationsThe hours an auger, belt or conveyor takes to move a quantity of grain at its rated capacity. The check that decides whether the handling system can keep up with the combine.

Break-Even Price

p_b = \frac{C}{Y}

Farm OperationsThe price the crop has to fetch, at the yield expected or already in the bin, before it has paid for itself. The number that belongs on the wall beside the futures screen during marketing season.

Break-Even Yield

Y_b = \frac{C}{p}

Farm OperationsThe yield the crop has to make, at a price already contracted or assumed, before it has paid for itself. The most-used number on any grain budget, and the one that decides whether an acre gets seeded.

Cost of Production per Unit

c = \frac{C}{Y}

Farm OperationsWhat a tonne of the crop cost to grow: total cost per hectare divided by yield per hectare. The one figure that can be laid beside a market price and compared without further arithmetic.

Crop Revenue per Unit Area

R = Y \, p

Farm OperationsWhat a hectare of the crop is worth: yield multiplied by price. The top line of every crop budget, and the only line on it that two people can agree on before harvest is over.

Crop Share as an Equivalent Cash Rent

r = s \, Y \, p

Farm OperationsWhat a landlord's share of the crop is worth per hectare, so a share agreement and a cash rent can be compared in the same currency. The arithmetic behind every kitchen-table conversation about a lease.

Custom Hire Break-Even Area

A = \frac{C_f}{r - c_v}

Farm OperationsThe area at which owning a machine costs the same as hiring the work done. Below it the custom operator is cheaper; above it the fixed cost is spread thinly enough that ownership wins.

Drawbar Power

P = F \, v

Farm OperationsThe power a tractor delivers through the drawbar: draft force times travel speed. The figure that decides whether a tractor can pull an implement at the speed the job needs.

Effective Field Capacity

C = w \, S \, e

Farm OperationsHow fast a machine actually covers ground, from its working width, its field speed and its field efficiency. The number every other machinery calculation is built on.

Field Efficiency

e = \frac{C_e}{C_t}

Farm OperationsThe share of a machine's theoretical capacity it actually delivers, once turning, filling, unloading, adjusting and overlap are counted. Measured, it is the honest input to every capacity estimate.

Fuel Use per Unit Area

F = \frac{q}{C}

Farm OperationsFuel burned per hectare, from the burn rate per hour and the effective field capacity. The form the number has to be in before it can be compared to anything or budgeted against a crop.

Grain Cone Volume

V = \frac{\pi}{3} \left(\frac{d}{2}\right)^{2} h

Farm OperationsThe volume of a cone of grain: the peak above a level fill in a bin, or a whole pile dumped on the ground. One third of the cylinder that would enclose it, which is more than most people guess.

Grain Drying Energy

E = \frac{m_w \, \lambda}{\eta}

Farm OperationsThe fuel energy a dryer needs to evaporate a given mass of water, once its efficiency is accounted for. The calculation behind a propane bill in a wet harvest.

Grain Mass from Volume

m = \rho \, V

Farm OperationsThe mass of grain filling a known volume, from its bulk density. The step between a bin measurement and a quantity that can be sold, hauled or insured.

Gross Margin per Unit Area

G = R - C_v

Farm OperationsRevenue per hectare less the variable cost of producing it. The figure that ranks one crop against another on the same field — and the figure most often mistaken for a profit.

Machinery Cost per Unit Area

c = \frac{C_f}{A} + c_v

Farm OperationsWhat a machine costs per hectare: the annual fixed cost spread over the area it covers, plus the variable cost of covering it. The equation that explains why the same machine is cheap on one farm and ruinous on another.

Machinery Cost per Unit of Output

c_m = \frac{C_m}{Y}

Farm OperationsThe machinery bill expressed per tonne of crop rather than per hectare of land: machinery cost per hectare divided by yield per hectare. The form that makes an over-equipped farm visible.

Marginal Return on an Input

M = \frac{\Delta R}{\Delta C}

Farm OperationsWhat the last increment of an input actually returned: the extra revenue it produced divided by the extra it cost. The test for whether one more pass, one more unit of nitrogen or one more fungicide pays.

Overlap Loss from Swath Spacing

O = \frac{w - s}{w}

Farm OperationsThe share of a machine's swath that lands on ground the previous pass already covered, from the working width and the actual pass-to-pass spacing. The number a guidance system is bought to reduce.

Round Bin Capacity

V = \pi \left(\frac{d}{2}\right)^{2} h

Farm OperationsThe volume of grain in a round bin, from the inside diameter and the depth of grain. Answered in bushels or cubic metres — the conversion between them is geometry, not agronomy.

Safe Storage Time

t = t_0 \cdot 2^{-\Delta M} \cdot 2^{-\Delta T / 5.56}

Farm OperationsHow long grain will keep before spoilage, as a halving rule: storage life halves for every percentage point of moisture above the reference condition, and halves again for every 10 F° of warming.

Time to Cover a Field

t = \frac{A}{C}

Farm OperationsThe hours a field takes at a given effective field capacity. The calculation behind every decision about whether the crop gets off before the weather turns.

Tractor Wheel Slip

s = \frac{d_0 - d_L}{d_0}

Farm OperationsWheel slip measured the way it is measured in the field: mark a wheel, count the same number of revolutions loaded and unloaded, and compare the distances travelled. The check that decides ballast.