Geared architecture for high speed and small volume fan drive turbine

A turbofan engine comprising:

• a propulsor section including a propulsor shaft in driving engagement with a propulsor having blades extending from a propulsor hub and being rotatable about a central longitudinal axis of said turbofan engine;
• an epicyclic gear system in driving engagement with said propulsor shaft and having a gear mesh lateral stiffness and a gear mesh transverse stiffness;
• and
• a gear system input to said epicyclic gear system defining a gear system input lateral stiffness and a gear system input transverse stiffness, wherein said gear system input transverse stiffness is less than 5% of said gear mesh transverse stiffness;
• a first turbine section in driving engagement with said gear system input and rotatable about said central longitudinal axis and said first turbine section includes an inlet and an outlet;
• and
• a second turbine section,
• wherein said first turbine section has a first exit area at a first exit point at said outlet and rotates at a first speed,
• wherein said second turbine section has a second exit area at a second exit point and rotates at a second speed, which is faster than said first speed,
• wherein a first performance quantity is defined as the product of said first speed squared and said first area,
• wherein a second performance quantity is defined as the product of said second speed squared and said second area,
• wherein a performance quantity ratio of said first performance quantity to said second performance quantity is between 0.5 and 1.5.