PRC ABE cheat sheet

Soil water content on a mass basis: θm = (wet mass − oven-dry mass) / oven-dry mass; gravimetric samples are dried at 105 °C to constant mass.

Volumetric water content: θv = θm × (bulk density / density of water); porosity φ = 1 − (bulk density / particle density), with particle density typically near 2.65 g/cm³ for mineral soils.

Available water capacity = (θ at field capacity − θ at permanent wilting point) × root-zone depth; field capacity is roughly −10 to −33 kPa and permanent wilting point is −1500 kPa.

Infiltration and unsaturated flow are governed by Darcy's law q = −K(ψ) dH/dx, where H is total head (pressure plus elevation head); saturated conductivity Ksat falls sharply as clay content rises.

USLE/RUSLE soil loss: A = R × K × LS × C × P, where R is rainfall erosivity, K soil erodibility, LS slope length-steepness, C cover management, and P support practice.

Manning's equation for open-channel flow: V = (1/n) R^(2/3) S^(1/2), with R = A/P (hydraulic radius) and Q = V·A; n rises with vegetation and channel roughness.

Irrigation scheduling: net irrigation requirement = ETc − effective precipitation, where ETc = Kc × ETo; application efficiency = water stored in root zone / water delivered.

Drainage spacing for parallel subsurface drains follows Hooghoudt-type relations in which spacing decreases as drain depth, soil Ksat, and allowable water-table rise increase.

Livestock environmental control uses psychrometrics: relative humidity = (actual vapor pressure / saturation vapor pressure at dry-bulb temperature) × 100, and wet-bulb temperature marks the evaporative cooling limit.

Tractor power take-off (PTO) power relates to drawbar power by tractive efficiency: drawbar power = PTO power × tractive efficiency; drawbar pull = drawbar power / forward speed.

Draft of tillage implements rises with soil strength, depth, and width; specific draft (force per unit area of soil disturbed) is the standard scaling coefficient.

Wheel slip = (travel speed with no load − actual travel speed) / travel speed with no load, expressed as a percentage; excessive slip wastes fuel and damages soil structure.

Engine power is reported as brake power at the flywheel; PTO power is lower because of transmission and accessory losses, and drawbar power is lower still because of traction losses.

Sprayer calibration: application rate (L/ha) = (nozzle flow per minute × 600) / (boom spacing in m × travel speed in km/h).

Precision agriculture: variable-rate application maps prescription zones from yield maps, soil sampling, and remote sensing; GNSS guidance with RTK correction reaches centimeter-level repeatability.

Grain combine performance is set by cylinder speed, concave clearance, fan speed, and sieve openings; losses are measured as a percentage of total grain entering the machine.

Machinery economics: total annual cost = fixed cost (depreciation, interest, insurance, housing) + variable cost (fuel, lubrication, repairs, labor); field capacity (ha/h) = (implement width m × speed km/h) / 10 × field efficiency.

Design live loads for agricultural floors, grain bins, and manure tanks are set by local building codes; silo and bin wall pressures increase with depth and follow Janssen-type relations that account for wall friction.

Confined livestock ventilation rate is set per animal unit (m³/h per head) and rises with temperature; minimum winter rates control moisture and gases, while maximum summer rates control heat.

Beef and dairy housing: open-front barns rely on natural ventilation with ridge openings; the ridge opening area should be sized relative to the eave opening to sustain stack effect.

Greenhouse energy balance: solar gain + supplemental heat = transmission losses through glazing + ventilation losses + latent heat for evapotranspiration.

Manure storage must be sized for the animal population, storage period, wash water, and precipitation; anaerobic lagoons require a treatment volume plus a sludge and freeboard allowance.

Fencing and corral design uses animal-unit spacing; handling facilities use curved chutes and solid sides because livestock tend to circle and balk at shadows and contrasts.

Structural design of light-frame agricultural buildings assumes load combinations of dead, live, snow, and wind loads, with wind pressure proportional to velocity squared times a shape coefficient.

The hydrologic cycle balance for a watershed: P = ET + Q + ΔS + G, where P is precipitation, ET evapotranspiration, Q streamflow, ΔS storage change, and G groundwater recharge.

Peak runoff estimation uses the Rational Method Q = C·i·A, where C is a runoff coefficient, i rainfall intensity, and A drainage area; it applies to small catchments.

Riparian buffers remove sediment, nitrogen, and phosphorus; effectiveness depends on buffer width, slope, vegetation type, and concentrated versus sheet flow.

Animal waste nutrient content is expressed as total nitrogen, P2O5, and K2O; land application rates are limited by the nutrient in greatest excess relative to crop removal.

Composting requires a carbon-to-nitrogen ratio near 25–30:1, moisture of 50–60%, oxygen above about 5%, and temperature maintained in the thermophilic range for pathogen reduction.

Water quality monitoring uses grab and composite sampling; parameters include BOD, COD, total suspended solids, nitrate, ammonia, phosphorus, pH, and dissolved oxygen.

Constructed wetlands treat agricultural drainage through sedimentation, plant uptake, microbial denitrification, and adsorption; performance depends on hydraulic retention time and loading rate.

Thermal process lethality: F = D × (log N0 − log N), and the z-value relates D-values at different temperatures; a 12-D reduction is the classic target for low-acid canned foods.

D-value is the time at a given temperature to reduce a microbial population by 90%; z-value is the temperature change that changes D-value tenfold.

Moisture sorption isotherms relate equilibrium moisture content to water activity (aw); microbial growth is generally inhibited below aw of about 0.6.

Drying rate curves show constant-rate and falling-rate periods; the constant-rate period is controlled by external heat and mass transfer, the falling-rate period by internal diffusion.

Heat transfer in food processing: conduction q = kA(ΔT/L); convection q = hAΔT; radiation q = εσA(T⁴); heat exchangers are designed using log-mean temperature difference.

Refrigeration capacity is rated in tons of refrigeration; 1 ton = 3.517 kW, the rate of heat removal to freeze 1 ton of ice per day.

Material balance in a food process: mass in = mass out + accumulation; component balances track solids, water, and nutrients through unit operations such as evaporation and drying.

Differential leveling: elevation difference = backsight − foresight; the height of instrument = known elevation + backsight.

Traverse closure: sum of interior angles of a closed polygon with n sides = (n − 2) × 180°; angular misclosure is distributed by the compass rule.

Horizontal distance from a total station: HD = slope distance × cos(zenith angle); vertical difference = slope distance × sin(zenith angle).

Area by coordinates (shoelace method): A = ½ |Σ(Xi·Yi+1 − Xi+1·Yi)| for a closed boundary.

GNSS positioning: absolute accuracy depends on satellite geometry (DOP), ionospheric and tropospheric delay, and multipath; RTK correction provides centimeter-level accuracy.

Map scale: scale = map distance / ground distance; a 1:24,000 scale means 1 unit on the map equals 24,000 units on the ground.

Contour lines connect points of equal elevation; contour interval is the vertical distance between adjacent contours, and contour spacing indicates slope steepness.

Simple interest: I = P·i·n; compound amount: F = P(1 + i)^n; present worth: P = F / (1 + i)^n.

Capital recovery factor: A = P × [i(1 + i)^n] / [(1 + i)^n − 1], used to convert a present sum to equal annual payments.

Net present value is the sum of discounted cash flows; a project is acceptable when NPV is positive at the chosen discount rate.

Internal rate of return is the discount rate at which NPV equals zero; a project is acceptable when IRR exceeds the minimum attractive rate of return.

Annual depreciation by straight line: (cost − salvage value) / useful life; declining balance uses a fixed rate applied to book value.

Payback period = initial investment / annual net cash flow; it ignores the time value of money and cash flows after payback.

Benefit-cost ratio = present worth of benefits / present worth of costs; a ratio greater than 1 indicates a favorable project.