Antenna wavelength calculation problem

[Prdufresne]

I'm struggling with what appears to be an inconsistency in the way wavelengths are calculated for antennas in the sample questions for the Canadian Amateur Radio Basic Exam. The following question for example:

Approximately how long is the driven element of a Yagi antenna for 14.0 MHz?
• 5.21 metres (17 feet)
• 10.67 metres (35 feet)
• 20.12 metres (66 feet)
• 10.21 metres (33 feet and 6 inches)

The correct answer, according to the Industry Canada application is 10.21, however if I'm doing the straight math using the speed of light (divided by 4), and the frequency, I get 10.71 metres.

Mathematically, I can see that the delta for all the answers are 95% of what I calculate, so where does that 95% come from?

ThanX!

 

[LtDoc]

That question is asking you several things, not just one. First, you'd need to know that a typical yagi antenna's driven element is a 1/2 wave length long. Then it's wanting to know it's approximate length because there are several factor which can affect that length. So, what's a 1/2 wave length at 14 Mhz? It's in the neighborhood of 33 feet, right? Right, and that's the 4rth answer.
So why isn't it an exact number? Several reasons. You don't know the exact frequency of use. A thingy called velocity factor, the speed of an electron isn't always the same. It changes with what it's traveling through. The 'right' length is also determined by the antenna's environment to some extent. I'm afraid there are no exact, always the same, calculable lengths for antennas in each and every case...
- 'Doc

 

[kb2vxa]

A half wave conductor is 90% of a half wave in free space so it becomes 0.9 X 492 or 468. The formula then becomes 468/f in MHz for a half wave in feet. SO... if you use the speed of light equation which gives free space results just multiply by 0.9 or skip all the nonsense and use 468/f. Just to be pedantic the precise length is 33.428 feet but 33' 6" is close enough for government work, IC is satisfied.

Don't ask me what the metric formula is, unlike Canada we told the French where to go after buying Louisiana. (;->)

 

[talkpair]

A half wave conductor is 90% of a half wave in free space so it becomes 0.9 X 492 or 468. The formula then becomes 468/f in MHz for a half wave in feet. SO... if you use the speed of light equation which gives free space results just multiply by 0.9 or skip all the nonsense and use 468/f.

Actually, 95% of 492 is 468....which matches the OP's findings.

Length in meters = 143 / Freq in MHz

 

[kb2vxa]

As long as you're being pedantic (;->) someone mentioned velocity factor but didn't explain. Electrons flowing in a conductor are slower than the speed of light owing to mass, therefore wavelength in a conductor is shorter than free space. Not being a physicist I'm at a loss to explain why this can be as great as 0.6 in transmission line which for certain applications must be factored in accordingly.

"Length in meters = 143 / Freq in MHz"
Lacking a meter stick I really didn't have to know that. (;->)

 

[Prdufresne]

I really appreciate the help guys. I didn't consider the effect of the transmission medium on the speed of light.

Ironically, I was voicing my frustration to my 15 year old son earlier today and he explained it to me, referencing his grade 10 high school optics unit where they were learning about light refraction.

Okay, now I can move on to propagation and interference. Once I get through those and learn my Q codes, I should be ready to take the test.

ThanX!

 

[kb2vxa]

I'm glad you learned something, that's what we're here for. Hmmm, knowing about light refraction helps when you go spear fishing, that is unless you're doing it underwater. (;->) It seems IC has a few subjects in the test the FCC doesn't require, then again they're good to know since when working DX or SWLing you need to know which band to use at which time of day to hit the target area. One thing to remember about Q codes, primarily they're CW abbreviations. They're of little use with voice and data although some common ones are occasionally used.

Take your time and you'll get there, when you receive your callsign we'll welcome you with open dipole arms.

 

[Prdufresne]

I downloaded a forum app for my ipad, and this thread showed up in my list of subscribed threads. I had completely forgotten about it.

For the record, I got my licence, went on to get my Advanced and have since been pretty active with APRS. I've been writing an application to act as a gateway between SMS and APRS messaging.

ThanX again for the help.

 

[KF5YDR]

Nice! Hopefully you'll share with the group once you get that figured out?

 

[Prdufresne]

I actually started a separate thread about it, but it's running now. You can get more information on the project website.

http://smsgte.wix.com/smsgte