How wide is the cone of confusion above a VOR and NDB?
The value +/-40° is correct, but need to be interpreted. The primary reason of the existence of a &quot;silence&quot; (confusion) cone is a design choice to increase navaid range. Range and &quot;isotropy&quot; are antagonistic.
However, when the aircraft approaches the confusion cone, say at 45° elevation, while flying at 9 km above the station, its slant distance to the station is about 13 km. Even with a small apparent power (say a few RF watts), the radio link being not attenuated by obstacles, is still very good. It should not prevent the signal from being demodulated.
There is a second phenomenon, which is more critical for a D-VOR: The Doppler shift is created by the antenna scan in the horizontal plane only, and is maximum when the receiver is on the station plane. As the relative elevation increases, the apparent displacement in the direction of the receiver is reduced. This reduction of the distance results in a reduced apparent velocity toward/away from the receiver, hence a smaller Doppler shift.

Without the correct shift, -480 Hz to +480 Hz, bearing determination is inaccurate (for a detailed explanation of VOR principles, see this answer). For conventional VOR there is a similar problem but related to the amplitude.

Detailed case: D-VOR
A VOR radiates a signal that can be interpreted in the horizontal plane, so the system is designed with antennas radiating horizontally. There are two types of VOR, the most modern is the D-VOR (Doppler VOR). A common antenna for D-VOR is the Alford loop antenna which is horizontally polarized:
 
Left: Source, right: Source
The D-VOR antenna system consists of a circular array of antennas:

Source
This array has a radiation pattern similar to this in the vertical plane:

How to interpret:

The straight lines are elevation angles, 90° being the zenith. The brown circles are a scale for power radiated, the large circle is the power measured in the direction where it is maximum. The next circle is where power is only -3dB of the maximum. Using decibels to measure ratios is frequent when working with radio signals because this is a logarithmic scale. -3dB is half the power, -6dB is 1/4 of the power, etc.

The red curve is the radiation power curve of the VOR for any vertical angle. It is maximum around 30° and minimum at 90°. For 60° its about -20dB which is a ratio of 1/100th only.

VOR cone of silence/confusion is where the signal is too small to be correctly interpreted by the VOR receiver, and you can see there is a strong signal fall around 50°-60° (that is 30°-40° from the VOR zenith)

As visible, power is mostly radiated to one side, the other side of the antenna array radiates only a parasitic power. This is due to the way the D-VOR works: Interfering pattern between all the antennas of the array. Power is destructed on the right side of the diagram, while it is cumulated on the left side.

The interfering pattern is rotated electronically around the vertical axis at 30 rounds per second (1,800 RPM, 30 Hz), so the antenna actually radiates power in an annular volume (donut).


Doppler cone of confusion
Specific to the D-VOR, due to the way this VOR works:

In the conventional VOR relative bearing is obtained by sensing the phase difference between a reference modulation (FM) and a varying modulation (AM) which depends on the direction the VOR antenna is currently pointing to.

In the Doppler VOR, the varying signal is actually obtained by electronically moving the center of the antenna array. This creates a frequency shift that is equivalent to the AM modulation of the C-VOR, but in frequency (and the D-VOR electronically &quot;rotates&quot; in the other direction so that the inversion between AM and FM modulation is not visible, ensuring compliance between C-VOR and D-VOR with the receiver).


However the Doppler effect can be sensed only when the receiver is on the same plane than the electronic &quot;displacement&quot;, i.e. the horizontal plane. When the receiver is located too close to the VOR zenith, the frequency shift becomes small, and cannot be sensed correctly. This is why, even with an isotropic antenna, the system cannot work at high relative elevations. So there is actually no point to have an isotropic antenna for the D-VOR.

C-VOR and NDB
A conventional VOR (C-VOR) works with a vertical antenna which radiation pattern is naturally similar to the one above without the need for interferences. The antenna actually rotates physically.
NDB use long wire antennas of many kinds. The power is radiated with nearly no particular preference (omnidirectional antenna), but the radiation pattern is still similar to the C-VOR one, except that there is no need to rotate it. The donut volume is obtained with the antenna stationary.
As the NDB is omnidirectional, the energy in the horizontal plane is not focused as strongly as for the C-VOR and D-VOR. However NDB range is still reasonable because:

NDB uses the LF/MF portions of the radio spectrum which are less subject to propagation losses.

NDB receiver doesn't require a strong signal to locate the beacon, as simply detecting the carrier is in theory sufficient.



Why is that done this way?
You may ask why not using an antenna (or an antenna array) with a circular radiating pattern radiating the same power in any vertical direction. Such &quot;isotropic&quot; antennas exist in practical.
The reason is the same than for rotating the antenna: It's to concentrate power in one direction, to increase the range. In technical terms this is to increase the effective isotropic radiated power (EIRP).
A good similarity is the one of a light bulb and a torchlight:

A light bulb has an omnidirectional radiating pattern, it lights up in all directions, but the power received at a distant point is limited (unless the light bulb is a very powerful one).

A torchlight focuses light in a small solid angle, multiplying by a large factor the intensity in the privileged direction. A high intensity can be perceived in this direction without using a huge power, and the range is increased at equal power. However to scan all points in space, the torchlight must be rotated.