I posted this in the EMD TR5A build thread. It probably belongs here....I guess. Maybe under layout builds/design.........oh well.
In regards to "percent of grade".
Most may know this but this info is for those that do not.
Lets start with a 2% slope. Correctly shown as 2.00%. Now, move the decimal point to the left 2 digits. Now we have 0.02000.
0.0200 is now the tangent of an angle .
Most handheld calculators have Sin Cos Tan functions. Most also have a button to achieve the inverse functions usually referred to as arc-sin, arc-cos and arc-tan.
Back to our 0.02000 number. Enter this number in your calculator do the arc tan function and you should now have 1.1458. This is the angle in decimal form as 1.1458 degrees which equates to 1 degree, 8 minutes and 45 seconds.
This angle may be a bit hard to set up on your layout so lets do something else.
That tangent number, 0.02000 is the tool to use for figuring the slope dimensions on your layout.
Take 0.0200 and multiply by 12 (number of inches in a foot) and we get 0.2400.
12 inches represents the base of a right triangle (horizontal length) times the tangent gives the rise, the 0.2400 number. 0.2400 equates to 3.84 sixteenths of an inch. You can round this up to 1/4 (4/16ths) inch rise in 12 inches of horizontal length. But using this rounded up number will accumulate as you add more 12 inch lengths. So........
For more accuracy lets take an even rise number like 1 inch. To achieve 1 inch rise at 2% slope you need 50 inches of horizontal length.
So now 12 1/2 inches gives us 1/4 inch of rise exactly ; 25 inches gives us 1/2 inch rise ; 37 1/2 inches gives us 3/4 inch rise.
To sum up: 1% slope use .01000 as a tangent
1.5% slope use .01500 as a tangent and so on.
If you have a sloping section on your layout and you want to know the percent of slope (grade) of that section of track, then set up a level, lets say a 3 foot level. Set one end of the level on the high end of the track (roadbed, etc) and while keeping it level, measure the distance between the top of the track (roadbed etc) to the bottom of the level. Lets say you measured 3/8 of an inch.
Now 3/8 of an inch equates to .375 decimal and your 3 foot level converts to 36.00 inches. (we have converted all numbers to decimal inches)
Dividing .375 by 36 will give you 0.0104. That 0.0104 number is the tangent of the angle so move the decimal point 2 digits to the right and now you have 1.04. This is 1.04 % of grade. Not bad.
I hope this helps and is not confusilating to you. It is just trigonometry.
There may be a better way but this is what I use.
Take care....John
Donuts woulda helped.
