Expanding a Football Stadium: The Geometry of More Seats
Geometry & Trigonometry
Arsenal have discussed a major expansion of the Emirates Stadium that could force them to play home matches at Wembley during construction. What geometric constraints would such an expansion face?
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Expanding a football stadium means adding seats without compromising sightlines, structural limits or the roof span. This exploration models a stand's cross-section: seat count depends on row depth and the rake angle of the tier, and every seat must have an unobstructed sightline to the pitch. Students can compare a proposed expansion's capacity gain against the cost and disruption of relocating matches to Wembley for a season.
Guiding Questions
- Arsenal want more seats. What constraints (footprint, sightlines, roof span) shape a stadium expansion?
- Model the stand cross-section: how does seat count relate to rake angle and row depth?
- Every seat needs to see the pitch. Express the sightline condition mathematically and test your design.
- Compare your proposal's capacity gain with the cost of moving to Wembley for a season. Which is better value?