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Global Skywatch

I did math today


I have been off the air for A LONG TIME. As most of you know, I try to remain connected to the amateur radio bands – those folks who will still be able to share information over significant distances when the phones stop working.

Since we began the move from our riverside cabin to The Homestead, I have been off the air. My FCC-licensed radio stations have been silent, and worse, unlistening.

I have worked at remaining sanguine about it. As I continue to progress on EVERYTHING THAT HAS TO BE DONE, the radios I packed away several months ago will reappear … when they are supposed to … in the right order, in the grand scheme of things.

TODAY THE RADIOS SHOWED UP
Okay, I got serious about finding them, if you wanna be persnickety about it.

Rather than “Oh! Crap! Now I have to install all that gear”, I was enthusiastic, excited and energized. I ran myself in a frenzy to get on the air TODAY!

As usual, I grossly under-estimated the task … by a score. My body is feeling abused, yet the radios are unconnected, and the second shortest day of the year is GONE. Dang good thing… And not just because my body was SHOT.

As, in my evening mood, I decided to CALCULATE what it would take to lower and raise my antenna system to work on it. I figured it would be a good time to check and see if the 100 feet of rope I was about to use would accomplish the task.

Well, heck, how much leverage do I need?

A strong man and I lowered and raised it
(twice, actually, with two different strong guys). I figure the other guy was well over half the horsepower. I better plan on a minimum of three times the leverage before I get that forty feet of oil field pipe out of control.

The school-of-hard-knocks, older, wiser me says I had better go for 4:1

Okay. Four to one.

I sketch that out.
It is one double-pulley that I do not currently own, one single-pulley ( have two of), anchor points at both ends, and one guy pulling the weight.

Geeze. How many feet of quarter-inch line is that?

IDEA!
That is probably calculable.

Oh my!
Before there was dirt, I earned an A in college trigonometry. Dumb luck, I am convinced. But I have this vague confidence I can KNOW how much rope I need before this big, long, heavy antenna support system is part-way down and I can no longer control it alone.

Enter, stage left: MATH
(better still, old-school math)

I have THE BOOKS
But as long as it is easily accessible, I asked the Internet for the geometry I needed.


The Pythagorean Theorem is expressed as A2+B2=C2

Uh oh!

I have to stop and think.

I break out the slide rule and sketch pad.

I have a 90-degree triangle with two 15-foot legs.

Heck, can it be that straightforward? The square root of 15 squared plus 15 squared???

I throw 15 squared at my slide rule,
then add 225 + 225 with paper and pencil,
then ask my slide rule for the square root of 450.
21.2
Huh?
21.2 what?
21 is not a reasonable answer to my question. My gut instinct suspects that 100 feet of line is going to come up short. Running out of line with the heavy antenna support approaching contact with the earth would be bad.
21 feet does not seem right at all.

Oh yes it is.
You asked for ONE LEG. Yet the answer you seek is four lines of your 4:1 leverage. That means 84 feet of line does the job.

I then apply the sniff test. Does that smell like the truth?
Hmmmm. That is possible.

However, being pretty dang conservative as the stakes go up, I will have more than 100 feet to feed the block and tackle. I’ll need some for knots, tie-off and margin for error.

Update. I did the deed with 250 feet of line. Which turned out to be more than twice what I needed … which is just an unnecessary tangled mess.

I also regretted saving a few bucks by using 1/4″ line which was a bit hard on my hands. Thicker line would have been much better for gripping. I am also thinking 5:1 would be nice, but heavier counter-weight inside the base would serve as well or better.

While I successfully got the VHF and UHF antennas up for local comms, the HF long-distance antenna needs further work. That is another drop-and-raise the mast experience … opportunity to test an improved process.