Why are the spokes in motorcycle wheels not arranged perpendicular

A motorcycle wheel is designed to have low moment of inertia and reduced air resistance. The first is achieved by reducing the mass of the wheel and the latter by improved freedom for airflow across the wheel. Both the benefits arise from use of spokes to bind the metal rim to the central hub.

It is necessary for the hub to have a definite width from side to side so that the essential components like the brake and the bearings can be housed in the hub. It is therefore essential to align the mid plane of the hub to that of the rim.

This is done by arranging tightened spokes from the circumference of the two sides of the hub to the middle of the rim. After tightening the spokes the hub and the rim integrate into a rigid structure.

So, the spokes are tightened sufficiently hard. In order that the forces balance exactly on all sides, the spokes are arranged regularly and uniformly on all sides so that the net radial force vanishes.

When a spoke is tightened it experiences a tensile stress along its length. If this stress can be reduced while not compromising on either the tightness or the rigidity, its life increases.

Instead of increasing the cross sectional area by making the spokes stouter, an ingenious method is adopted to reduce the force along the individual spokes, but ensure good amount of radial force along any radial direction.

This is achieved by arranging two spokes at some angle symmetrically about a radial direction. By this, even if relatively low force is applied along each spoke, their combined effect is to generate a sufficiently high resultant force along the radial direction.

This is because the resultant of two forces can be made higher than the individual forces by choosing the angle between the components properly as is done in the design of the motorcycle wheel.