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Map scale is at the same time kind of
a straightforward idea, but also there's
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a few little details that I think
are important for us to elaborate on.
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So let's talk a little
bit about map scale.
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The purpose of map scale is just
to show distances on a map.
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If I'm looking at a map, and especially
if it's an area I'm not familiar with,
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it's really hard sometimes to get
a sense of how far is it from a to b?
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Is that a few blocks?
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Is it a kilometer?
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Is it really far?
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So that's the whole purpose of map scale,
is to indicate to somebody distance.
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On this slide here,
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I'm showing three different map
areas that are all the same size.
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In other words, the squares on
the slide are the same size, and yet
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they're showing very
different sized areas.
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So the distance from here to
here is very different on
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the ground than the distance
from here to here on this map.
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Which of course is very different
than the distance on this map again.
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So even though the size of the squares is
the same, the distance is quite different.
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So how do we tell people
what those distances are?
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We use a map scale.
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So what would be the walking distance
to get from point A to point B?
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If we're looking at this map and I
want to know, this is in London, England,
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near Buckingham Palace.
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If I want to know, well, how far is
it from this point to that point, for
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whatever reason,
how would I calculate that?
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How would I figure that
out if I needed to?
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So the map scale is needed
to calculate that distance.
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So scale is represented as a ratio of
the map distance to the ground distance.
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It's expressed as 1 over a number.
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The numerator is always 1,
the denominator can be any number, really.
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So we have a ratio of map
distance to ground distance and
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the scale is always 1 to something,
that's the way we would say it.
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So in this case, 1 to 250,000.
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And the important thing too here is
that there are no units to a math scale.
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As long as the units are the same for
both the numerator and the denominator.
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And what I mean by that is
if we said that, whatever,
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this is 1 foot to 250,000 feet.
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That would mean that if I
measured 1 foot on the map,
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that would equal 250,000 feet
on the ground in reality.
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But I could just as easily had said
1 meter on the map equals 1 meter on
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the ground, or 1 centimeter on
the map is 1 centimeter on the ground.
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Or 1 cubit, or fingernail, or whatever,
it could be any units you want.
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The point is, as long as they're the same,
that's the important part.
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And people get tripped up on this all
the time because especially if it's
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something like centimeters, then
the denominator is centimeters as well.
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You can then convert the distance
that you've calculated into meters,
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or kilometers, or something else.
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But when you first calculate it will be in
the same units that the map scale is that
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you measured it from.
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So on a map you probably are going to
measure, say if it was a paper map,
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the distance across that paper map in
centimeters, not in kilometers, and
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then you could calculate
the distance on the ground.
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And that then would make more sense to
convert it to some unit that's more
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relatable, like kilometers.
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Okay, so if we measure the map distance
from A to B here as being 10 centimeters.
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So, in other words if it was 10
centimeters on a paper map or
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it's 10 centimeters on this screen.
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Doesn't really matter, as long as we
know what this scale is and we know
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what the distance is on the map, we can
then calculate the distance on the ground.
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So let's do that.
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So 10 centimeters on our map,
if this map was at a scale of 1 to 5,000,
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that means that 10 centimeters on
the map is something on the ground.
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So we're going to solve for x,
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we're going to do a little
cross multiplying here.
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So x = 10 cm x 5,000, so essentially,
really, we're taking this and
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we're doing cross multiplying,
that's what we have there.
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And so we multiply those together, and so
the actual distance is 50,000 centimeters,
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and then if we wanted we could
convert that to something more useful,
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like meters, like 500 meters, okay?
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That's all there is to it.
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It is useful to know how to do,
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some people are more mathematically
inclined than others, but
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I think most people should to be able
to figure something like this out.
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And it's just a useful thing to
be able to know how to calculate.
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There are three main ways that
we can express a scale on a map.
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We can do it as a representative fraction.
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So that would be as a ratio like this,
1 to 500,000.
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Sometimes this is also referred
to as an absolute scale,
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you may see that in the software that way.
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Sometimes it's indicated
as a verbal scale,
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especially on maps with imperial
units like in the United States.
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A common scale might be something
like one inch to a mile.
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So 1 inch on the map is
1 mile on the ground.
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Now, that's kind of doing a unit
conversion as part of the way the scale's
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being expressed,
which may be more or less confusing.
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But maybe that's why metric's
a little easier to work with,
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just saying, as a Canadian,
a little editorial there.
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[LAUGH] And
we can also represent it as a bar scale.
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So depending on the scale of
the map that you're making,
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one or more of these might be more or
less useful.
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So when should you use each of these?
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It's a good idea to include
a representative fraction on virtually any
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map that you make.
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You can't really go wrong with that.
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So at the very least I would
include a representative fraction.
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A verbal scale is really only useful for
unusual map scales, like I said,
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like imperial units in the US,
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so in that case certainly that
would make sense to include.
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A bar scale is visually easy for
people to understand, it's quite useful.
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And as we'll see in later section though,
there are maps of certain scales and
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projections where a bar scale
doesn't really make sense,
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like the Mercator projection, for example.
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So there's a kind of a rule of thumb that
people often will use, or a convention,
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is that a bar scale only makes sense at
a larger map scale than say 1 to 250000.
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And larger map scale means actually zoomed
in, as we'll talk about it in a minute.
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But smaller map scale means zoomed out,
if you want.
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So if you have a map, say, of a state,
or province, or a country, or
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the world, a scale bar is really not
the most useful way to represent scale.
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I would probably just go with
a representative fraction.
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Okay, let's talk a little
bit about terminology.
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If I show you a map of the world and
I ask you, is this a large scale map or
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a small scale map?
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And you're probably thinking already this
must be some kind of trick question.
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And yeah, it kind of is.
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It's a small scale map.
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Now, this is one of those pedantic
little details that cartographers and
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GIS people pay attention to.
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Is that this is where the confusion comes
from, is that if you said you were working
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on a project that was in 20 different
countries, and it's a worldwide effort,
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and it's a big project.
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In everyday normal language you would
call that a large scale project,
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but it's not a large scale map.
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If you make a map of the world
it's actually a small map scale.
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And if you were making a map
of say a neighborhood,
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that might seem like a much smaller
project, but it's a much larger map scale.
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So why is it like this?
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Why do we insist on being
different like this?
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Well, let me explain.
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Here we have five different maps that
are all the same size on the screen.
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The squares are all the same size,
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but they're representing different sized
areas, so they're different map scales.
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They actually range from
a large scale to a small scale.
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So the large scale would be something
with a representative fraction of,
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say, 1 to 5,000 versus a small scale map
which would be, say, 1 to 3 million.
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So this is a map of really
just one individual building,
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this is actually Buckingham Palace.
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Versus at the other end of the spectrum,
let's say, is a map of the entire world.
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So where does this confusing
terminology come from?
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It's from these numbers,
1 over 5,000 is actually
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a larger number than 1 over 300 million,
okay?
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If we convert that to decimals,
then this is 0.0002 and
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this is 0.000000003333, okay?
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So it's actually a much smaller
number if you divided them,
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and that's where that
terminology comes from.
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Is that this is a larger number,
therefore, it's a larger map scale.
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This is a smaller number, therefore,
this is a smaller map scale.
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And that's the way I try to
avoid confusion with people.
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Well maybe I'm being pedantic,
but it's not like I'm going,
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excuse me, I think you used
that terminology incorrectly.
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I'm just trying to say,
you mean a large map scale or something.
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I try to be polite about it, but
sometimes all you're trying to do is,
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not that I'm trying to
make somebody feel bad,
153
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I just want to make sure we're
talking about the same thing.
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That's really what it comes down to.
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So really you can think of it
as a continuum of map scales.
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Sometimes I get asked well,
so what's the cut off?
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When does a map suddenly become large
map scale versus small map scale?
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I don't know that there really is
a hard and fast rule about this.
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I tend to think of it like, if you're
looking at a neighborhood, certainly
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that's a large scale or, I don't know, a
few neighborhoods would be a large scale.
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A city would be kind of medium scale,
a state or province would be small scale,
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and certainly a country or
the world would be small scale.
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So it's not a trick question or
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something it's just kind of
a relative term that gets used.
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And so I think after a while
the more you make maps and
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the more you talk about them you kind of
get a sense of what the correct range
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of scales would be in
terms of the terminology.15312
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