Why do we feel we are travelling fast while riding a motorbike

Our perception of size of an object or of its spatial extension is based on the relative displacement between two spatial points at the extremes of the object. This is easier and better expressed in terms of the angular displacement.

A good practical measure of this is given by the ratio of the separation of the two points to the distance between the object and the observer.

This is clear from our observation of the starry night sky where the stars appear only short distance apart although they are away by thousands and millions of kilometres from each other.

Similarly, a house across the street looks much bigger than the stars; the sun and the moon look to be of the same size as that of a football.

Speed, technically, is the distance covered in unit time interval. But the feeling of speed comes from the rate at which we cover the angular displacement corresponding to an object.

Further, the sense of speed arises from the usual experience of relative motion of the observer and the objects nearby with respect to which the observer moves.

When we are riding a bike, we do observe the objects in the proximity like, the trees, milestones, lamp posts, etc which protract a large angle owing to their proximity to the observer. And this is covered in a small time interval giving us the feeling of a high speed.

When we travel in a rain, we observe only the distant objects, which subtend a smaller angle at our eye, thus it appears as if the object is almost static and we feel as if we are moving slowly.

However, if the observer goes near the door of the compartment and looks outside, the objects near the railway track can be seen to be moving with great speed and the actual speed with which we are moving can be perceived.