# Agricutural Calculations

A cylindrical silo has a diameter of 20 feet and is filled with grain to a depth of 35 feet, how much grain is in there? (Volume = pi R^2 H)
```pi * (10 feet)^2 * 35 feet ? bu
= 8835.64 bu
```

You meet your neighbor at the CoOp and he tells you he had an avarage Corn yield of 2.1 millimeters this season, is that good?

In the US Corn yield is traditionally measured in bushels per acre, dimensionally that's VOLUME / AREA, or LENGTH^3 / LENGTH^2, which is just a length... So what's 2.1 mm in bushels/acre?

```2.1 mm ? bu/acre
= 241.164 bu/acre
```
Pretty good Corn!
Note: What "2.1 mm" really means is that if the Corn were just lying on the ground it would be in a layer about one kernal thick.

Let's say you need to apply an inch of moisture to a 160 acre field over the next week. What is the avarage flow rate of the irrigation water?
```160 acres; 1 inch; 1week ? cfm
= 57.619 cfm
```
What's with the semicolons?

Now lets say you are pumping this water from a well that is 60 feet deep, and you need 40 psi of head pressure to run the sprinkler, how big an engine do you need? (Power = Pressure * Flow) note: wc stands for water column.

```(60 feet wc + 40 psi) * 58 cfm ? hp
= 16.707 hp
```
If you buy energy at 6 cents/kWh, how much will you spend on power for this irrigation?
```16.707 hp * 6 cents/kWh * 1 week ? \$
= 125.581 \$
```
And how much for water, assuming you pay 1 cent per 1000 gallons?
```160 acres * 1 inch * 1 cent/1000 gal ? \$
= 43.4469 \$
```

You are deep plowing using full power with a 110 hp tractor and all you can do is 3 mph. What is the drawbar force?
```110 hp; 3 mph ? lbs
= 13750 lbs
```

Suppose you want to know what flow rate to set on a liquid applicator given that you need to apply 20 gallons per acre driving at 6 mph with a 45 foot boom.
```20 gal/acre; 6 mph; 45 feet ? gal/min
= 10.9091 gal/min
```

What is the plant spacing for a population of 25000 plants/acre on 30 inch rows?
```25000 plants/acre; 30 inches ? inches/plant
= 8.36352 inches/plant
```

Say a 6 inch diameter auger has a pitch of 8 inches and turns at 200 rpm, how fast will it move grain?
```pi (3 inch)^2 * 8 inches/rev * 600 rpm ? bu/hour
= 3786.7 bu/hour
```
How long will it take for this auger to empty a truck box that is 30 feet long, 7 feet wide and 8 feet tall?
```30 ft * 7 ft * 8 ft ; 3786 bu/hour ? min
= 21.3944 min
```
Get the dump box!

A combine is cutting 30 ft swaths of 210 bu/acre Corn at 5 mph, if Corn sells for 3 dollars/bushel, what is the hourly "take".
```30 ft; 210 bu/acre; 5 mph; 3 \$/bu ? \$/hour
= 11454.5 \$/hour
```

What's a good Corn yield in England?
```230 bu/acre ? cubic meters / hectare
= 20.0279 cubic meters / hectare

230 bu/acre; 56 lb/bu ? ton_metric/hectare
= 14.4366 ton_metric/hectare
```

Calchemy Software Inc.
Fort Collins, CO

Last Updated 6/21/2009