Re: Grade Conversions

[David Johnson <trainman@ozemail.com.au>]

Graham Fry wrote:

> However, he constantly refers to grades in
> percentages. Can someone provide me with the conversion to our method of
> defining grades in 1 in ??. Thanks in advance.

These questions were asked a while ago in relation to the Scenic Railway at
Katoomba in February.  My reply to that thread states:

                    > >For these formulae,
                    > >Gradient in % = "GP"
                    > >Gradient in degrees = "GD"
                    > >Gradient in rise:horizontal distance = 1 in "GH"
                    > >
                    > >GP = (tan (GD)) * 100
                    > >GP = (1 / GH) * 100
                    > >
                    > >GD = inv tan (GP / 100)
                    > >GD = inv tan (1 / GH)
                    > >
                    > >GH = 1 / (GP / 100)
                    > >GH = 1 / (tan (GD))

I also went to the trouble of creating a BASIC program to do the conversions by
computer.  It is listed below:

                    1 REM Copyright David Johnson
                    5 RAD = 3.141592654# / 180
                    10 CLS
                    20 PRINT "Gradient Conversion Program"
                    30 PRINT "Enter Number of known data"
                    40 PRINT "1 = Rise : Distance (1 in x)"
                    50 PRINT "2 = Angle (Degrees)"
                    60 PRINT "3 = Percentage"
                    70 INPUT G
                    80 CLS
                    90 IF G = 1 THEN 200
                    100 IF G = 2 THEN 300
                    110 IF G = 3 THEN 400
                    120 GOTO 10
                    200 INPUT "Enter Horizontal Distance - 1 in "; GH
                    210 GP = (1 / GH) * 100
                    220 GD = ATN(1 / GH) / RAD
                    230 GOTO 500
                    300 INPUT "Enter Angle in degrees "; GD
                    310 GP = (TAN(GD * RAD)) * 100
                    320 GH = 1 / (TAN(GD * RAD))
                    330 GOTO 500
                    400 INPUT "Enter Gradient Percentage "; GP
                    410 GD = ATN(GP / 100) / RAD
                    420 GH = 1 / (GP / 100)
                    430 GOTO 500
                    500 CLS
                    510 PRINT "Gradient is:"
                    520 PRINT "1 in"; GH
                    530 PRINT GD; " degrees"
                    540 PRINT GP; "%"
                    550 END

I hope this is of some help to you.  For further discussion on the subject, do a
search at http://www.deja.com for "Katoomba Scenic Railway not steepest?"


--
David Johnson
trainman@ozemail.com.au
http://www.ozemail.com.au/~trainman/