# Altimeter Grade Graphing ("pain-o-meter")

The altimeter grade is the average grade over roughly 1/10 of a mile,
from my altimeter data. This is intended to convey the overall
difficulty of the climb, and put the max. grades in a proper context.
At this resolution, a 10-foot altitude error (the maximum precision of
my altimeter) translates to a 2% grade error.
I don't know the accuracy of this data, but it should give a rough
picture of the climbing involved.

The horizontal grid lines are at 10% grade intervals, and the
vertical grid lines are at 1 mile intervals.

I linearly interpolated my original altitudes to find a piecewise linear
grade before computing the 1/10 mile averages.

## Example: Redwood Gulch

I started with my list of distances and altitudes:

* Each horizontal line is 100 feet. *

Then I linearly interpolated the altitudes:

* Each horizontal line is 100 feet. *

And took the derivative (slope):

* Each horizontal line is 10% grade. *

Then I smoothed it using this filter, a gaussian, to get rid of
some of the noise in the data. (This is the impulse response,
from an instantaneous 50-foot climb.)

* Each horizontal line is 10% grade. *

And this is the result:

* Each horizontal line is 10% grade. *

Finally, I subsampled this function at 40 pixels per mile:

* Each horizontal line is 10% grade. *

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