[Mike. Watterson]

Also it's not the ABSOLUTE size that's important but the electrical size, i.e. what fraction of a wavelength.
There are different issues:
1) Aperture. Obviously an array of four dipoles spaced enough, picks up four times the signal. At shorter wavelengths it's easier to use a parabolic dish than an array of aerials to increase signal. A 1/4 wavelength whip aerial on the ground inherently has smaller aperture than a vertically mounted dipole. The whip has got a reflected virtual whip. Spacing four MW aerials to have four times the signal needs about half a kilometre of ground!

2) Efficiency. A folded dipole is efficient if the size 1/2 wave overall. Such an aerial curved to be a "halo" type is very inefficient. A Yagi, dish or some Log periodics can have apparent high efficiency because the beamwidth is narrower. The gain of a dish goes up with the square of the frequency times the square of the diameter! So a 1m dish (fictitious 70% efficient) at 1GHz is 18.8dB. It's 38.8dB at 10 GHz. Increase to 3m and it's 48.8dB. At UHF using a massive array of 16 off Yagis works better. I have a photo of such a thing used on a Tipperary mountain to get UK TV. They had TWO, one pointed to Wales and one pointed at NI. Later there was a licenced microwave link from Cavan (the first private one in Ireland) to carry four channels.

A 60m wire isn't as efficient for MW as a 0.75m wire for VHF radio (traditional whip on car). A typical home vertical wire might be only 10m high. Electrically short, as a 1/4 wave is about 75m.

3) Matching. Certain kinds of aerial can be electrically small, that is smaller than a 1/4 wave. The actual physical size depends on the wavelength for a particular design.

4) Bandwidth. A dipole or whip has wider bandwidth than a Yagi. A Log Periodic or Discone (or double Disccone) can be as wideband as desired, it just gets larger for the lower frequency end and tolerance of parts gets problematic for the high frequency end. Log Periodic and Discones are common for 27MHz to 1.2GHz, but the military, spy agencies and Radio Amateurs can use such for Shortwave. They are rather impractical below 3.5MHz to 7MHz. The discone is usually only vertical polarised. A Cage or barrel aerial is sometimes used MW to 7MHz (not in one band!) to have a broader bandwidth than a wire. A Log periodic, like a Yagi or dipole can be used vertical or horizontal polarised, but at lower frequencies the mast interferes with vertical and mounting can be more awkward.

The halo is evil for VHF radio as it has negative gain and for omni, a vertical whip is best.

A whip needs a ground plane, so on a mast it needs earthed radials. A cute way to do a vertical dipole is a sleeve over the mast, such that ratio of mast dia to sleeve inner is 75 Ohms. The coax goes inside mast and connects outer to sleeve and inner to whip. Thus no groundplane or radials are needed.

5) Matching. A 1/4 is easy. A 5/8ths gives narrower polar pattern thus more gain. A 1/2 wave is very hard to match. If the aerial is shorter than 1/4 wave, then you can add capacitance at the top (radial wires on MW, a disc on UHF), or more inductance at the bottom. As the aerial gets shorter than 1/4 the aperture is less, thus a 1/40th wave (10m long on MW) will pick up very much less radio signal. It will not pickup much less interference that is very local, E near field). Thus one system to reduce interference is a loop or ferrite rod (just a miniaturised loop really) and a short wire, say the the VHF aerial, which will be good at picking up interference. Then if added in to the loop/ferrite signal at the correct phase and level it will reduce interference! You can buy new standalone boxes that do that. Some German valve radios had a switch to use the internal foil dipole (for VHF) to do this on MW & LW.

An Aerial Tuning Unit is actually usually MATCHING, not tuning the aerial. That's why better Amateur and professional HF systems have the ATU (the Match box) at the aerial wire and then use 50 Ohms coax. The matching can be automatic (needs a small transmission signal) or manual. Putting more than 1/10th wave of coax or dual feeder between the aerial and an ATU at the radio can't match the aerial properly.

6) You CAN have a very long wire. That's one that's many wavelengths. Unlike other aerials that pick up at right angles to the element/wire/dipoles, the very long wire only receives ground wave and ALONG the wire.

So important aspects are:
Frequency. That decides what is electrically short.
Size compared to wavelength, not ACTUAL size.
Height off ground.
Feed cable if the aerial doesn't start at the radio.
Matching.

At 138kHz to transmit you need about 2kW into a 25m long wire (vertical or horizontal) to get ONE Watt ERP. Inefficient. If matched, the voltage at the far end is lots of kilovolts.

At VHF you can use 80W and detect the signal bouncing off the moon with four really big yagis. Maybe about 2.5m long beam & 13 elements. Using digital signal processing and correlation.