**1. (Mathematics) Estimating a
function at a point which is larger than (or smaller than) all the
points at which the value of the function is
known.**

*
***2.
Mathematics:**** To estimate (a
value of a variable outside a known range) from values within a
known range by assuming that the
estimated value follows logically from the known
values.**

Get out the calculator and learn
how "ratios" can be used to Extrapolate.....or
not!

You probably "extrapolate" many times during your
day around the house or on your job without knowing
it.

**Here is an example....you want to
make 1 cup of coffee but all you have is a 10 cup coffee maker
and you certainly don't want 9 cups just sitting there getting stale
or wasted.**

**You "know" that in order to make
10 cups of coffee, you normally would use, as an example, 5 scoops
of coffee for 10 cups of brew! But....you only want 1 cup, not
10!**

**So how do you "extrapolate" how
much coffee to take out of the can to make 1 cup of coffee using the
same strength as if you had made 10 cups?**

**Here's how using
extrapolation: (in the form of ratios)**

**You take the "knowns" and then
arrive at a final ratio of water to
coffee for that 1 cup of coffee you so desperately need to get
the body going!**

**It is "known" that 5 scoops of
coffee, plus 10 cups of water = 10 cups of coffee when brewed to
your taste. (Assuming this is the way you normally make
it)**

**Using math extrapolation we get
a ratio between scoops required and the
final pot of coffee:**

**10 cups / 5 scoops = 2 (a ratio
of 10 cups of water to 5 scoops of coffee) for 10
cups of brewed coffee.**

**We only want 1 cup as the final
result so we extrapolate the ratio of coffee to
water using:**

**5 scoops / 10 cups of
water = .5 (that's decimal
5 in case it's not clear on your browser)**

**So for 1 cup of coffee you would
use 1 cup of water and .5 scoops
(1/2 scoop) of coffee!**

**Now to prove the strength is the
same using math, as if you are making 10 cups, just
multiply .5 X 10 = 5 scoops of
coffee!**

**The whole
idea here is that you use ratios when comparing dissimilar
things.**

Another simple example using
extrapolation:

You want to make some instant pudding from an 8oz
package of mix you bought at the store.

When you
opened the mix, you accidentally spilled half of the mix on the
floor. Don't worry, the ants will be happy to clean up the mess! Now
you only have 4 oz or half of the mix left to make the
pudding.

You read the directions on the package and it says you
need 2 quarts of milk plus one 8 oz package of mix to make 4 cups of
pudding...but wait...you only have 1/2 of that 8oz package left to
use...so how much pudding will it make and how much milk will you
need to make the pudding as thick as it normally would be?

Now
working with the "knowns" that you have which came with the
instructions:

**"Knowns".... 8oz of mix plus 2
quarts of milk = 4 cups of pudding and you only have 4oz of
mix! **

So what is the "unknown"...how much
milk you need to use in order to use all of the
mix?

**Using the extrapolation
technique to get a ratio to work with:**

8oz mix / 2 cups milk = 4
(a 4 to 1 ratio)

So you need a 4 to 1 ratio of mix to milk to get
the same strength pudding.

You simply use 4oz of mix plus the
ratio of 4 to 1 milk to get the same
mixture.

**2 quarts / 4 = .5
or 1/2 as much milk as you would have needed for the full 8oz of
mix!**

Yum, Yum!

**Using these two examples about is
a very simple method that many of us use without really thinking
about the fact that we are using some simple math to find an
"unknown" using "knowns". It is sort of a "logical" excercise
for our brains that we use during many days and with many things in
life. **

This technique can be applied
to working with ham radio antennas in many cases....read
on.

**How to Use
Extrapolation when working with antennas!**

**Using this method described
above when working with many ham radio antennas can be a
fantastic aid if you don't have "formulas" to
work with when you are attempting to use antenna
plans designed for one particular band on another band or
frequency.**

**Now let's get to some examples
using antennas rather than staying in the kitchen and getting
FAT!:**

**Just pretend for a moment that
you have plans for a 10 meter "xyz" antenna and you want to build
one of the same "type" antennas for use on the 17 meter
band BUT...there are no formulas
mentioned in the original plans. You are in the dark...or are
you?**

The 10 meter "xyz" antenna is designed for
28.400mhz and has a total length of 20 feet!

28.400mhz
and 20 feet are your "knowns" for the "xyz"
antenna.

**The "unknowns" you are looking
for is to use the same antenna "extrapolated" to the 17 meter band
and you want to know the length...the
"Unknown".**

**Using some simple math and your
"knowns" and "unknowns" we have:**

"Known" 10 meter design
frequency = 28.400mhz

"Known" Total length = 20 feet

"Known"
new design frequency = 18.130mhz (in the 17 meter
band)

"Unknown" total length of new 18.130mhz
antenna

**The
math: (Remember, we need to arrive at a
ratio between 28.400mhz and 18.130mhz)**

28.400 /
18.130mhz = 1.5664644 (round that off to
1.56) << There is your ratio in
red!

So the ratio in physical size
would be 1.56 to 1, meaning the 18.130mhz antenna will be 1.56 times
LONGER than the 28.400mhz "xyz" antenna. (Remember your going
down in frequency so the antenna will be longer and/or
larger).

Now using this ratio of 1.56 to 1 and using our "knowns"
and "unknowns" we get:

__20 feet__ for 28.400mhz __X 1.56__
(the ratio) = 31.20 feet for the new 17 meter
"xyz" antenna!

**Using "real
life antennas" for extrapolation**

Now lets use a real
antenna and a standard antenna formula and not that "xyz"
antenna that does not exist and also use the "extrapolated" method
in this example as a comparison to see if this "method" really
works:

**Using a dipole as an example we
use the standard formula of 468 / freqmhz = total length in
feet.**

**At 28.400mhz the dipole length
would be 468 / 28.4 = 16.47 feet total length.**

**BUT...you want to use the design on
18.130mhz...what would the length be***.....(remember, you no
longer have the formula to work with in this
example* and you need to find the ratio between the 28.400mhz frequency and the
18.130mhz frequency...all you have is the
frequency and length of the original in the
plans......

The math: ( we did
not round off in this example)

**28.400 / 18.130 = 1.5664644 ratio
(so the 17 meter antenna is 1.56+ longer than the 10 meter antenna
length in the plans.**

**Original 28.400mhz total length =
16.478873 feet**

**We now have a "known" of
16.478873 feet for the dipole, and by using 1.56 as the ratio when
we did the math above, we can now us it to find the
length of the 18.130mhz frequency antenna!**

**16.478873 X 1.5664644 = 25.81 feet ( the new 17 meter antenna extrapolated length rounded
off).**

**Now lets check the
math results compared with using the standard formula.
(Remember, we did not have formulas to work with in the
original "antenna plans" for the 10 meter antenna but now we
do!**

**468 / 18.130 = 25.81 feet (using the
formula)**

**You will notice the
"extrapolated" length is the same as is you had the formula to work
with!!!!!**

**Another
example:**

You are looking at the plans for a
20 meter vertical antenna but want to use the antenna re-designed
for 2 meters on 146mhz! The plans state that the vertical length is
say....16.47 feet long and was designed for 14.200mhz...the author
of the 20 meter vertical forgot to say
what formula he used in designing the
antenna.

**You procede using the same
techniques as before:**

14.200 / 146.00mhz = .0972 ratio between
the physical length of the 20 meter version and the 2 meter version.
Remember that the length of the 20 meter version is much longer than
the 2 meter version.

**Using the math ratio we
get:**

16.47 X .0972 = 1.6 (this is still in feet) 1.6 feet X
12 to get inches would give us 19.2 inches!

So everything else
being equal, the new 2 meter antenna "extrapolated" to a 2 meter
length would give us the 20 meter version "scaled" to 2 meters and
should work fine.

**Now dust off that calculator and play with this
method. Practice, practice.**

*"It is
important to note that when using this method to arrive at the
"unknown" length of that antenna, that differences in construction
materials, frequency, size of elements or wire, the
surroundings, height above ground and many other variables
associated with the "nature" of various antennas will make this
method 'not perfect' by any means, but it should get you in the ball park...you now have to find your
section, row and seat for the game. *

In other words, you may
still have to experiment with the "new" extrapolated antenna to get
it to perform well while remembering that in the beginning, you had
no idea how to even get into the ball park without the "ticket" (the
formula)....that's the fun part of antenna
experimenting!* *

*Now go into the kitchen and
spill some pudding mix! You deserve a break! *

What's that......no milk?.....just make some
coffee....it should be ready by the time you get back from the
grocery store...I'll take 2 cups, the other (insert number of
cups here) are for you...do the math.........!

73
Don!"