Sprayer Calibration Math Question
March 5, 2022 12:07 PM Subscribe
My husband is studying for a spray applicator license. We have a math question on one of the study guides - I'm hopeful someone here can help.
The study guide is this PDF. On page 73, it says:
oz per nozzle (collected per 200 ft) x 20.5 / nozzle spacing (inches) = GPA
14.8 oz x 20.5 / 20 inches = 15.2 GPA
What does that number represent, and how would he calculate that in real-world conditions?
The study guide is this PDF. On page 73, it says:
Calculate the delivery rate in gallons per acre (GPA). Using the following formula, insert the average nozzle output over a 200- foot course and the nozzle spacing in inches. (20.5 is a mathematical constant accounting for changes in volume and area measurements on a 200-foot course for these problems only.)He is wondering what the bit about 20.5 being a mathematical constant means, and how he should calculate this sort of thing outside of the study guide - that is, for the formula below, would he always use 20.5?
14.8 oz x 20.5 / 20 inches = 15.2 GPA
What does that number represent, and how would he calculate that in real-world conditions?
P.S. This dimensional analysis tutorial or this video might be a little better, but I included the other link in my answer above because it shows how I write down the problems -- using a grid pattern to represent fractions:
--|--|--|-- etc, where for 1/2 gallon per acre you'd put "1 gallon" on top in the first slot, and "2 acres" on the bottom in the first slot, and so on for whatever you needed to convert.
I find this easier to look at and cross out units than writing separate fractions, but it's just personal preference.
posted by cnidaria at 12:39 PM on March 5, 2022 [1 favorite]
--|--|--|-- etc, where for 1/2 gallon per acre you'd put "1 gallon" on top in the first slot, and "2 acres" on the bottom in the first slot, and so on for whatever you needed to convert.
I find this easier to look at and cross out units than writing separate fractions, but it's just personal preference.
posted by cnidaria at 12:39 PM on March 5, 2022 [1 favorite]
Best answer: The indicated constant is 12 * 43560 / (128 * 200), where 12 is the number of inches in a foot, 43560 is the number of square feet in an acre, 128 is the number of fluid ounces in a gallon (US units), and 200 is the length of the test run in feet.
(1) Work in gallons and calculate the output of one nozzle. This is [oz per nozzle] / 128
(2) Work in square feet and calculate the area one nozzle will cover, then divide by 43560 to get the area in acres. This is [nozzle spacing] /12 * 200 / 43560
(3) Divide the gallons delivered by acres covered to get gallons per acre. This is {[oz per nozzle] / 128} / {[nozzle spacing] /12 * 200 / 43560} which is [oz per nozzle] / [nozzle spacing] * 20.5
posted by StephenB at 1:07 PM on March 5, 2022 [6 favorites]
(1) Work in gallons and calculate the output of one nozzle. This is [oz per nozzle] / 128
(2) Work in square feet and calculate the area one nozzle will cover, then divide by 43560 to get the area in acres. This is [nozzle spacing] /12 * 200 / 43560
(3) Divide the gallons delivered by acres covered to get gallons per acre. This is {[oz per nozzle] / 128} / {[nozzle spacing] /12 * 200 / 43560} which is [oz per nozzle] / [nozzle spacing] * 20.5
posted by StephenB at 1:07 PM on March 5, 2022 [6 favorites]
Response by poster: I really love ❤️ this site. Thank you both!
posted by hilaryjade at 1:10 PM on March 5, 2022 [3 favorites]
posted by hilaryjade at 1:10 PM on March 5, 2022 [3 favorites]
Outside the guide, change the 200 to suit the length of your test run.
posted by StephenB at 1:11 PM on March 5, 2022
posted by StephenB at 1:11 PM on March 5, 2022
This thread is closed to new comments.
An example of a constant is that there are always 60 seconds in a minute. To go from minutes to seconds, you always multiply by 60. Since this number never changes, it's a constant.
An example of a variable is time -- for example, how long you leave the cookies in the oven. You could plot how crispy the cookies are on a scale of 1-10 versus how long you left them in the oven -- the time (and also the crispiness) is going to "vary" so it's a variable.
20.5 is just, in this situation, a constant to convert from (ounces per nozzle per 200 feet)/(nozzles per inches) into (gallons per acre). There's some tedious arithmetic behind it but if you have all the conversions handy (ounces to gallons, etc) you could calculate it yourself. I use dimensional analysis to solve problems like this, which is basically a fancy way of saying I combine multiple unit conversions together to get the answer. For example: 1 hour is the same as 3600 seconds. I know this because:
1 hour * (60 minutes / hour) * (60 seconds / minute) = 60*60 = 3600 seconds
The hour / hour units cancel out, and minute / minute units cancel out, and the only unit left is seconds. You can google "dimensional analysis" for more examples/YouTube videos.
Tl;dr it's basically same as saying if I have 5 minutes, I take 5*60 and I know I have 300 seconds; you just have a few more units involved.
posted by cnidaria at 12:32 PM on March 5, 2022 [4 favorites]