Antenna Design Lengths
Wire antennas need to be made a bit long and cut to resonance. They are affected by height above the ground and surrounding objects. In order to get an idea of the right place to start, certain formulas are generally accepted.
Various formulas are given for calculating antenna lengths. You will find some variation in the factor required. While 468 is often cited as the formula for a dipole, it assumes some loading effect from the loops at the end where the wire goes through the insulators, and a thin, but finite wire diameter. Use of tubing changes the length needed for resonance. Making bigger end loops starts to turn them into significant "capacity hats" and shortens the resonant length. But most important, environment changes resonance dramatically.
High and clear is seldom the case for a real antenna. They are often mounted too low, too close to trees, houses, power lines and other things that will detune them. One very useful method for adjusting an antenna in a highly detuned situation such as one mounted inside an attic space, is to install it based on the formula for free space,
[ 492 / freq in Mhz ].
This will be low in frequency most likely. Measure the resonant frequency. Now calculate your own constant to replace the 492. Using this new "custom created" constant which will probably come out as something like 476 or so, recalculate the length required for the desired resonance. Often this method will zero in on an acceptable tune in just one or two trims.
Some of the antenna types listed here will require matching networks or tuners. The 5/8 wave vertical and the extended double zepp for instance are both capacitatively reactive and require inductance to tune them to resonance. Other antennas like the dipoles should be a good match for 50 ohm or 75 ohm line depending on how high and clear the mounting is. Low mount dipoles often match 50 ohm line better.
A high and clear dipole should have about 72 ohms of input impedance and be a great match for 75 ohm coax. An inverted V has reduced input impedance and is often a good match for 50 ohm cable. The folded dipole needs a 4:1 balun to match coax, but is a good match for 300 ohm twin lead. Even the quarter wave and three quarter wave verticals can often benefit from some kind of linear transformer matching since they can have feedpoint impedances as low as 35 ohms, or even lower with proximity effects from surrounding objects.
Don't forget that dipole type antennas can be mounted vertically, or sloping. Even inverted V's can be sloped. Ends of dipoles can be bent if necessary. None of these "fixes" are likely to make an antenna work better, and all will change the resonant length, but they will often make an antenna fit the space available and get you on the air. People have constructed Yagi type antennas entirely of wire, hanging the elements from a rope between two trees. The same has been done with delta loops and quads, even inverted V's have been used for beam elements hanging from a "boom" that was just a rope between two supports.
Here are some precalculated figures for the bands from 160 to 6 meters to help you decide what will fit at your QTH and save some brain strain. Just remember that these will need to be cut and adjusted to resonance once installed at your height, in your location. Also there is some argument about the right values, especially for things like full wave loops. Some people insist that [1005/freq in Mhz] is way too short and the factor should be closer to 1030.
There is no substitute for having a few extra inches initially, hanging the antenna where it is going to be installed, measuring the resonance, and then calculating our own custom factor and using this to adjust the antenna again. Expect to hoist and lower the antenna several times before you get it just right with the minimum SWR where you want it in the band. The closer you can get to mounting an antenna high and clear of the ground and other structures, the closer the typical factors will apply and the closer your first calculated length will be to optimal.
Use of insulated wire is fine, and there is something in its favor. The insulation somewhat protects the copper inside from corrosion. But the insulation will change slightly the velocity factor of the wire, throwing off the calculated length by a few percent. This is yet another reason to be a few inches generous on your first trial size for an antenna. Cutting is always easier than stretching. There is no substitute for hoisting a first version of an antenna into its working location and doing an SWR plot or similar measurement to find out how critical the tune is and what the current resonant frequency is. Then using that data to custom adjust your length factor and fine tuning.