12 Calculating Fall
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In the last section we looked at the three ways grade is expressed and how to work between them. Now we need to put that to work in an equation which can give us the total fall of an object.
Take a look at the guy above. Any guesses on the grade he’s falling at?
The first thing we do is look at what we are calculating and then figure out what variables we need. Let’s go back to this drawing from the last section.
If we start from the basics which is one foot and go from there we can build our formula.
I think we would all agree we need grade. In this particular case we can use a grade of inches per foot as we have a one foot piece of pipe falling three eighths of an inch. In our drawing we dealt with one foot but in reality we’ll more than likely be dealing with pipe that is longer than that. In the end it works out that we also need the length.
In conclusion we only require two variables.
1) Length
2) Grade
From this we can now build our formula.
It’s not actually the toughest formula to remember as there are only 3 variables if you include the answer. The trickiest part might just be dealing with the units as there are a few ways to express grade.
Usually we start off with the easiest example and then go to the harder ones but in this case we’ll start with the hardest.
Working With The Grade in Inches Per Foot
Expressing grade in inches per foot sets the formula up in a certain way.
Attention! The following is a very important point.
As the grade in this particular case is in inches per foot we MUST have the length in feet.
Grade is expressed in inches per foot.
The length must be expressed in feet.
The total fall ends up being in inches.
Here’s how it works mathematically.
or written another way…
The feet and the foot cancel each other out leaving just inches.
Example
A plumber must install 250 feet of pipe in a parkade. The pipe is to be graded at ¼ inch per foot. How far does the pipe fall vertically in the 250 feet.
Step 1: Start with the formula.
Step 2: Define your variables and make sure they are in the correct units.
Step 3: Plug the variables into the formula.
I know we’ve already talked about this but I want to bring up one point again. Note the total fall ends up in inches for this particular situation. This is key and very important.
Having said that let’s move on to another example involving grade in inches per foot. Maybe take a shot at doing this one yourself before moving on to the answer.
What is the total fall of a piece of pipe which travels 439 feet at a grade of 3/8 inches/ft?
Step 1: Start with the formula.
Step 2: Define your variables and make sure they are in the correct units.
Step 3: Plug the variables into the formula.
Note: What you might think of doing at this point is to change the 3/8 into a decimal which might make it easier to work with.
You could then plug that into the formula.
Either way you end up with the