Building Antennas Using "Extrapolation"
So what is "extrapolation"?
Where do I buy it? How do I use it in antenna work?
Actually, extrapolation is a method using math to arrive at an "unknown" or a set of "unknowns" when you have a set of "knowns" to work with and is a logical method of arriving at the "unknowns" you are looking for. So what does all this mean......
First, we must know the definition of
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.
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.
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
"Knowns".... 8oz of mix plus 2 quarts
of milk = 4 cups of pudding and you only have 4oz of mix!
2 quarts / 4 = .5 or 1/2 as much milk
as you would have needed for the full 8oz of mix!
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.
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 "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:
(Remember, we need to arrive at a ratio between
28.400mhz and 18.130mhz)
Using "real life
antennas" for extrapolation
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.
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......
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!!!!!
You procede using the same techniques
Using the math ratio we
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.