Arsenal Collection: Stadium Sightline

One of the challenges in designing an Olympic stadium is to make sure that spectators can see the event without their views blocked by others.

Suppose the horizontal distance (D) between the spectator and the event is 30m and the vertical height (R) is 10m. What is the viewing angle of the spectator?

If the depth of the seating row (T) is 1m, how much should the riser height (N) be such that the view of the spectator does not get completely blocked by the person in front?

The spectator's ability to see the event over the head of the person in front is measured by the 'C' value (see the illustration below)

(Image taken from Paul Shepherd's website: http://people.bath.ac.uk/ps281/)

A reasonable number for C is 15cm. To make sure that the spectator can comfortably watch the event, how much should the riser height (N) be?

In what other ways can we improve the C value of the spectators? The C value can be calculated using the formula

$$C = \frac{D(N+R)}{D+T} - R$$

(Try derive it yourself!) Can you relate everyday experience to the formulae above?

Which factor affects the C value most? Suppose the seating area is limited by the overall stadium design to be 20m in seating depth and 10m in vertical height, how can you optimize the viewing comfort while accommodating as many spectators as possible?