Sprayer Application Rate

Every printed calibration table gives this equation with a constant baked into it, and the constant is the reason so many people find spraying arithmetic mysterious. In metric it reads $\text{L/ha} = 600 Q / (v w)$ with output in litres per minute, speed in km/h and spacing in metres. In US customary it reads $\text{GPA} = 5940 Q / (v w)$ with gallons per minute, miles per hour and inches. Two different equations, apparently, for the same physical act.

They are not two equations. Both are $V = Q/(wv)$, and the constants are nothing but unit conversions wearing a disguise. The 600 is 10,000 m² per hectare divided by 1000 litres per cubic metre divided by 60 seconds per minute. The 5940 is 43,560 ft² per acre times 12 inches per foot divided by 88 feet per minute per mph. Neither number contains a scrap of agronomy. Because this site converts units for you, the solver above carries the clean form and you may enter litres per minute alongside miles per hour if that is what your equipment reads — a combination no printed table has ever allowed.

Two errors account for most miscalibrated sprayers. The first is entering the whole boom's output as $Q$ instead of one nozzle's, which multiplies the answer by however many nozzles are on the boom. The relation works per nozzle because each nozzle is responsible for exactly one strip of ground, $w$ wide. The second is trusting the tractor's speedometer. Wheel slip, tyre pressure and a part-full tank all put real ground speed several percent away from indicated, and since rate is inversely proportional to speed, that error transfers straight into the application. Time yourself over a measured 100 metres with the tank half full and the boom running, and use that number.