NDB's are non directional and VOR's are omnidirectional.
What is the difference between a signal that is non directional and a signal that is omidirectional, if any?
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Think of an NDB as dropping a small pebble in an otherwise still/static mass of water like a lake. It generates ripples that expand radially from the point in which you dropped the pebble, in the shape of a circle.
If you see the ripples, by judging in which direction they move, you can determine where they come from and all you know is that if you follow that track, you'll eventually find out where the source is. You don't really know (unless you work it out mentally, use a compass and some charts) on which bearing of such NDB you are just by getting the signal (ripples), and it gets even more complicated if you were not flying towards it already
Now, think of a VOR. VORs are fundamentally different as they broadcast 360 different signals (one for each degree of azimuth). Instead of dropping a pebble into a large mass of static water, imagine you placed 360 different colored lasers (I know this may be difficult, just bear with me for simplicity's sake), each one emitting a straight light beam, each color/wavelength on a predictable azimuth from the source. Once you get in the path of one of these (let's say 524 nanometer green), you can instantly tell not only where the source is (it's along the propagation line of the beam) but also you can tell in which exact bearing (relative to the VOR) you'd approach the source if you followed that specific track (called a Radial)
Why is the difference important? When you're airborne, you are subject to forces other than the basic lift vs gravity and thrust vs drag. There's also winds aloft which almost all the time mean that flying a 300° heading will not equate to a 300° track. If you were to use an ADF needle to fly towards an NDB in any condition other than completely static air, you'd keep the ADF needle at the 12 o'clock position (flying towards the NDB) but you'd trace a curve over the ground. This is very non-precise way to follow a track. VOR's on the other hand, let you know exactly where you are relative to them and by following a specific radial you'd be sure you'd be approaching the VOR from the exact direction you should be approaching from. Hence, airways built on VOR's are so very much more precise than NDB-based ones
Now regarding specific differences in the signal:
1.- NDB signals are usually in the KHz wavelengths while VOR and other directional beacons transmit in the Mhz ranges (right below the air band for radio comms, by the way)
2.- As stated above, the NDB broadcasts a single ommnidirectional signal. Directional beacons will (excuse me for the over simplification) transmit slightly different frequencies on each azimuth. No two azimuths will be on the same frequency, so for each VOR each frequency uniquely identifies a specific radial.
3.- In real life, radials are not completely straight and non-overlapping "lines". They have a cone-shaped dispersion pattern (just as a laser produces a dot of different diameter as travel distance increases) so being "on the radial" still has some margin of error and thereforce VOR-based airways are still a couple of miles wide from the centerline... if you are 100 miles away from a VOR and "centered" on a specific radial, you may still be offset by as much as a mile. As you track the radial inbound, your offset becomes smaller until you overfly the VOR
"Omnidirectional" may not be the most descriptive word for the actual radio signal emitted by a VOR, as contrasted with the signal from a NDB. We could note that a VOR and a NDB actually both share the characteristic of broadcasting in all directions, as opposed to the narrow beam emitted by a landing approach aid, or the characteristic pattern emitted by the "four course" radio ranges of long ago.
But as for the difference between the radio signals emitted by a VOR and a NDB--
Think of the signal from a VOR as a collection of beams radiating out from the transmitter. Each beam carries data: it is encoded with the azimuth from the station. You can easily find more information about how this done: in actual practice the azimuth information is encoded in a phase shift between two different signals.
With a NDB, we also have beams radiating in all directions from a transmitter, but all the beams are the same. That's why you can only get a relative bearing from a NDB.
To add to @quiet flyer's answer, the practical result is:
With Non Directional you only know the radio aid's bearing from the aircraft's longitudinal axis and not the aid's geographic orientation to the aircraft's position (until you mentally work it out).
With Omnidirectional, you only know the aircraft's geographic orientation to the radio aid's position; that is, its bearing from the radio aid itself (but not the range), but not its bearing relative to the aircraft's longitudinal axis.
Put another way, with an ADF you only know whether it's in front, behind or off to the side at a given azimuth of the airplane at any moment. With an OMNI you only know whether the aircraft is north, east, south, or west (or any azimuth angle in between) of the navaid itself.
My understanding was that a VOR was not a series of different signals being sent out in narrow cone shapes. I understood VORs to be just a few signals being sent out to include the station identifier, an optional voice signal, a reference signal, and a variable phase signal, as well as some other discrete signals.
The navigation part is done by sending out a reference signal that is sent out in the same phase in all directions. We will say this signal has a phase of 0. Then, a highly directional antennae sends out a very concentrated signal as it is revolved around the center of the antennae array. As the antennae revolves, it rotates the phase of its signal in correlation to its angular position in its revolution. In other words, when the antennae is broadcasting in the direction of Magnetic North, its signals phase is 0. As the antennae moves in its clockwise arc, the signals phase will shift 1 degree of phase for each degree of movement. By the time the antennae’s signal is broadcasting Magnetic East, the signal’s phase has shifted 90 degrees. And so on, and so forth. The receiver in your Nav radio can receive both the reference signal and the variable signal, sense their phases, and compare the difference. The difference in the phases is the Radial on which you are located.
As far as NDBs, think of old pictures you’ve seen of pre-jet-age planes. The older ones had loop antennaes on the top and/or bottom of the fuselage. These loops were used to pick up the signal of an NDB. The NDB just sent out one navigation signal in one phase. But, by rotating the loop antenna, you could tell which direction the signal was coming from by sensing whether it got weaker or stronger as you rotated the loop. There was a second simple sensing antennae on one side of the loop antennae to ensure that you did not make a 180 degree mistake.
The DME portion of the VORs and NDBs are a whole different baileywick. These are call and response devices on a whole different frequency than the VORs and NDBs. Your DME radio sends out an encoded and timed call signal. The DME station sends back a coded and timed response signal. The DME calculates the time difference to determine the slant range distance. The bandwidth space on these station is finite. That is why you will see in your charts and chart supplements requests to turn your DME off when entering certain terminal approach areas like DFW. The Maverick VORDME (TTT) only has so much bandwidth. The FAA wants to reserve its use to those airplanes that really need it. Especially those at or above FL240.
ILS and Glideslopes are a unique kettle of fish. Each has antennae that send out two different frequencies. These antennae were highly directional and concentrated. The ILS has antennae that are side by side. So the two frequencies are effectively the left frequency and the right frequency. If your Nav radio is picking up both frequencies equally, you know that you are right in the middle of the ILS. If your Nav radio is picking up one frequency more than the other, you know which side of the ILS you are on. The Glideslope works the same way except the antennae are one on top of the other. Now, most of the antennae are uni-directional, but not all of them are. Some are still bi-directional. And, since the antennae are fixed in place either side by side or one on top of the other, so are their signals on the back side. So, if you have an ILS that is sending a signal to the North, its right-hand signal, as you face the antennae from the North, is on the West side. Its left-hand signal, as you face the antennae from the North, is on the East side. But, if you face the antennae from It’s backside on the South (its Back Course), its Right-hand antennae is still on the West side. Which is your left-hand side. Its Left-hand antennae is still on the East side. Which is your Right-hand side. People call this reverse sensing. It’s really true sensing. We are reversing it in our heads. Be careful on the backcourse to get this correct. The same is true of the glideslope. But it is not as prone to confusion because top is still top and bottom is still bottom. Up is still up and down is still down. And, the backcourse signal is pointing 3 degrees into the ground for the most part.
Oh, and to answer the original question:
Non-directional means that the signal is broadcast out everywhere without any focus on direction.
Omni-directional means that the signal is broadcast out in every and all directions, but with focus on each direction.