Why ADF & VOR both are installed on most of the aircrafts?

Question

Because both serve the same purpose of providing Bearing/Heading to/from a station

Answer 1

They are quite different.  

The NDB (non-directional beacon) used with the ADF provides no bearing from the ground, the ADF in the cockpit pointed to a relative bearing that would change as you flew toward the station with the wind, this was called "homing" and you would fly a parabola like path.  You could, though some mental gymnastics ( double the distance from the bearing to the head and add it to the tail -- it's been a long time) actually track straight (sorta) to a station.

The VOR (VHF Omni-directional Range) provides bearing information through the cockpit instrumentation by broadcasting two different signals.  The VOR head measures the difference between the two signals and displays the bearing TO or FROM the station in the cockpit.  Much easier than the NDB.

Also, a lot of LOM (Locator, Outer Markers) used to be NDBs and you could listen to AM radio stations on them during long boring flights.

Answer 2

you are absolutely right.

They provide backup for each other in many places.

Answer 3

Although both are rapidly becoming "old tech" these days, they actually operate in a different fashion.  Many smaller airports are equipped with an NDB approach only (although these are being replaced in many areas by GPS approaches) since the NDB is a simple, inexpensive piece of equipment.  The ADF is used, for example, to fly approaches to these airports.  Also, the ADF can be used to track to or from some high power stations that have a range beyond VOR, particularly at lower altitudes.  ADF is trickier to use than VOR, usually requiring some extra mental gymnastics (unless you have some relatively sophisticated equipment).  The equipment is susceptible to interference from, among other things, thunderstorms.  When you're trying to fly an approach in bad weather, that is not something you need.   On the other hand, if you're not using the ADF to navigate, you can alway use it to listen to the local AM radio stations.

VOR and VOR/DME was once the primary method of navigation.  It is much easier to use, and more accurate than ADF navigation.  VOR stations are still very common in the US and most other parts of the world, but you can expected to see them fade away at some point in the future.

Answer 4

ADF provides a bearing TO the station, but cannot be used to set a course FROM the station nor to determine TO or FROM orientation.  An NDB approach is the least precise approach.

VOR provides a heading TO or FROM the station, which is much more useful information.  The minimums for a VOR approach are considerably lower than those for an NDB approach.

In old time instrument flying, VOR and ADF complement each other, and the ADF is used to provide a cross-check on position when flying by reference to VOR stations or making a VOR or ILS approach.