33.4.2. Underwood Exponential Model

Try these first

1. 1.

   What does the variable k represent in the Underwood model?

   Hint

   Think about how many cars there are in a certain length of road.

2. 2.

   Explain how the Underwood model predicts speed as density increases.

   Hint

   Consider the behavior of vehicles as they become closely packed.

3. 3.

   What does 'v_f' represent in the Underwood model?

   • Traffic flow rate
   • Free flow speed
   • Density constant

   Hint

   Think about the top speed vehicles can achieve without constraints.

4. 4.

   True or False: The Underwood model predicts that speed reaches zero when density is zero.

   • True
   • False

   Hint

   Consider what happens in highly congested scenarios.

5. 5.

   If the free flow speed is 80 km/h and k0 is 250 veh/km, calculate the speed when density is 125 veh/km. Explain your steps.

   Hint

   Square away the substitution before calculating the exponent!

6. 6.

   Describe how you would use the Underwood model in a real-world scenario for traffic engineering.

   Hint

   Consider how you would monitor a highway’s traffic conditions.