GRIN:  4 steps to convert (almost) anything

Precision application depends on precise conversion of units of measure.   Some real examples were generated in class as part of a Fertilizer calibration.

Turfgrass managers must accurately mix and apply chemicals and other materials.   Examples include the use of herbicides, irrigation water, and wetting agents.   Reasons to be accurate are the cost of material, its narrow window for selectivity, and the law.  It is a violation of Federal law to apply a pesticide in a manner inconsistent with the label.

Inaccuracy can occur many ways, with serious consequences.  It takes only a tiny math error, in converting units of measure, to cause a lethal overdose of product per unit area.  What wasn't noticed in the pencilled notes becomes obvious when the lawn dies.

Herbicides sometimes cost more than $100 per pound of active ingredient.  But the price of wasted product is not what the turfgrass manager is thinking, when he has to explain to a client that he has just "smoked" her yard.  Professional Pest Control?  "Nice uniforms, but can't multiply."

Precise application is a powerful business advantage in turfgrass management.  So how do you convert units to get the math part right?  Don't depend on what most people do.  Be able to GRIN

Most turfgrass conversions are based on rules of thumb.  You "know" your spray tank covers 2 acres, the label says, "apply 1 pound per acre," so it's pretty obvious that to spray one full tank, you need to throw in 2 acres of product, that is, 2 pounds, per tankful.  Simple problem, no risk in figuring it in your head?   Yes, R-I-S-K.  Because when you change out the nozzles, you might not get 2 acres from one spray tank.  Or what happens if you have to switch to a different spray tank?  And the person who used it last isn't around to tell you how much it sprays.  What do you do? Just GRIN

GRIN is a simple bookkeeping system for getting the math right.

G = Given, i.e., what are you given to do?  Apply 1 pound of product per acre and apply product to 2 acres.

R = Required, i.e., what are you required to do?  Put so many pounds of product in a spray tank.  When you convert, what is required is always equal to what is given.

I = Identity, i.e., what units are identical?  As an example, area covered by one spray tank = 2 acres.  We could express this as a fraction,
     1 = (2 acres/area covered by spray tank)
The nice feature of this is that the identity principle says you can multiply any expression by 1 and not change it.  So, gather all similar identities and write them into a formula.  I'll show you in the example how this is done.

N = Nullify units.  Whenever you have a unit of measure, such as acres, which occur once in a denominator, and in another place in a numerator, just cancel them both out.

Other than a little multiplication, you're done.

An example

Sports Park Manager Leslie Leftowitz is purchasing fertilizer to apply to four football fields and adjacent turf areas, totaling 6.5 acres.  The fertilizer being purchased is 16-4-8 analysis (16% nitrogen) and it is to be applied at 1 pound of nitrogen per thousand square feet.  Fertilizer bags contain 50 pounds of fertilizer.  How many bags should she buy?

G = Given, 1 pound N per thousand square feet and 6.5 acres.

R = Required, number of bags of fertilizer.

	Required =	Given
	Amount =	Rate	x Basis
		1 pound N
	number of bags fertilizer =	________	x 6.5 acres
		1000 ft2

I = Identity, 1 bag fertilizer = 50 pounds fertilizer; 1 unit fertilizer = 0.16 units N; 1 acre = 43,560 square feet

	Amount =	Rate	x Basis	Identities
		1 pound N		1 bag		fertilizer		43,560 square ft2
	number of bags fertilizer =	________	x 6.5 acres x	_____	x	______	x	___________
		1000 ft2		50 pounds		0.16 N		1 acre

N = Nullify units.  Whenever you have a unit of measure, such as acres, which occur once in a denominator, and in another place in a numerator, just cancel them both out.  Items in red are being canceled.

	Amount =	Rate	x Basis	Identities
		1 pound N		1 bag		fertilizer		43,560 ft2
	number of bags fertilizer =	________	x 6.5 acres x	_____	x	______	x	___________
		1000 ft2		50 pounds		0.16 N		1 acre

Other than a little multiplication, you're done.

number of bags fertilizer = (43,560 * 6.5 bag fertilizer)/(1000*50*0.16) = 35.4 bags

So Leslie buys one pallet containing 40 bags, and has a margin of a few extra bags.

Comments

What's required and what's given are sometimes difficult to put together.  There are three basic relationships:

Conversions to memorize:

Why do GRIN?

This is a good method because: (1) it involves a logical, one-step setup; (2) it involves no mental gymnastics; (3) there are only three metric-to-English conversions needed to solve most problems; (4) GRIN can be applied to all kinds of situations; and (5) it never yields a wrong answer.