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Posted

1Hill, think of a triangle...

Modelling gradients as percentages using metre rulers and elastic

 

http://www.ordnancesurvey.co.uk/images/userImages/misc/education/triangle.jpg

 

To develop children's skills in measuring and expressing gradients

as percentages, metre rulers were used. A metre ruler laid flat on the

ground gives a convenient horizontal distance of 100 units (cms) and

another ruler held upright at one end gives a selection of the same

units for vertical climb. A length of shirring elastic can be used to

link the two rulers for example, a triangle formed in this way with a

100 cm base and 20 cm height has a 20% gradient. This means that a toy

car would climb 20 cms vertically for every 100 cms it travels

horizontally. 20 units out of every 100 = 20%.

 

Using the same triangle, it is also possible to translate

percentages into ratios and vice versa. If the child travels 4 cms

along the horizontal ruler with a toy car and then measures up

vertically from this point to the elastic slope, the height will be 1

cm. This is a 1: 5 triangle. These ratios can be multiplied e.g.:

 

  • 8 cms along .......................... 1.6 cms up
  • 12 cms along .......................... 2.4 cms up
  • 16 cms along .......................... 3.2 cms up
  • 100 cms along .......................... 20 cms up (20%)
http://www.ordnancesurvey.co.uk/oswebsite/education/teachingresources/mapwork/investigatinggradients.html

 

 

Posted

I'll try explain further. A 1/1 gradient is 45 degrees and expressed as 100%.

 

The calculation to get 45 is (100/100) ARCTAN = 45 degrees.

 

For 12% the calculation is:

(12/100) ARCTAN = 6.8 degrees

 

On a scientific calculator to get this you hit INV (12/100) TAN and hey presto.
Posted
12percent on 1km climb =120m of climbing in altitude

 

And to make things even more confusing...

 

This isn't 100% correct. Seeing that the 1km climb is on the "diagonal" part of the triangle. You're supposed to use the vertical / horizontal distances, not the vertical / diagonal.

 

But on "normal" climbs the figures would be pretty close.ConfusedEmbarrassed
Posted
12percent on 1km climb =120m of climbing in altitude

 

And to make things even more confusing...

 

This isn't 100% correct. Seeing that the 1km climb is on the "diagonal" part of the triangle. You're supposed to use the vertical / horizontal distances' date=' not the vertical / diagonal.

 

But on "normal" climbs the figures would be pretty close.ConfusedEmbarrassed
[/quote']

 

shoosh! Wink

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