I assume you want to know whether they suffer from acrophobia, the fear of heights? And I assume equally, that you are not speaking of ostriches or penguins? Vertigo, in the sense of dizziness when looking down, I would not expect in a healthy, functionally flying bird. Fear of heights as such, also seems to be alien to birds with good flying capabilities, but nestlings that can not yet fly do not like to risk falls.  They commonly will cling tightly to one's fingers if handled, and very sensible too.

Penguins crossing deep water are unlikely to feel any nervousness other than the fear of predators attacking suddenly from the depths. They would not fall at all if they lost control, simply float to the surface.

I certainly could expect birds like swifts, that can hardly walk and cannot even take off from level ground, let alone from grassy surfaces, might have a complementary fear of low surfaces. When they go scooting like so many ice hockey pucks across level ground at an altitude of a few centimetres in breezy, cloudy weather, hunting for low-flying midges, they are performing acts of death-defying bravado analogous to human BASE jumpers or high wire artists.

And then they had better not suffer from vertigo or any similar loss of nerve or control.

And the way they shoot into their nesting holes at full flight certainly would terrify me!

But I am no swift, and I have no fear of walking or lying on the ground.

Go well,

Jon

I set up a dove cote in my garden a few years ago so that i could keep free flying birds as pets. The birds that i bought to stock this dovecote, 'White Garden Fantails', had never been out of their rather small aviary in their lives until bought them and proceeded to release them from my dovecote.

The birds were of a considerable size and so had very little flying space in their previous aviary. They certainly had never had the chance to fly to any height. As i observed them settling into 'dovecote life' it became obvious that they had an aversion to flying high, staying sedately on their dove cote perch.

As i watched them on one occasion they became scared by a dog barking. This caused four of the doves to fly very quickly (and apparently accidentally) to a great height above the house. The doves circled the cote and could be seen tilting their heads to look down at it. Each time one of them tried to descend it appeared to get scared and regain the height with much loud flapping.

It was very comical to watch what appeared to be four airborne birds trying and failing to descend as they flew very haltingly in circles 50 metres up. Eventually they tired and sank slowly down in the same circles after a few minutes.

I believe this behaviour shows that these among all flying birds were truly scared of heights.

I would imagine therefore that acrophobia is an acquired fear among birds just as it is among humans due to lack of exposure at a young age. 

One always has to be careful in using human emotions to describe animal behaviour. In the case of the birds previously confined to an aviary, a more likely explanation is that their sensory input was adpating to new experiences. Being unaccustomed to flying at such heights can be described in terms of sensory input and consequent neural processing. The human concept of fear is not necessary to explain the behaviour.

Anthropomorphism is a great danger to understanding animal behaviour. We should always look to a more basic neurophysiological explanation first.