How long does it take to reach terminal velocity?  Up hill, down hill, at start of time trial, in a break?

Down Hill, Up Hill 

On a long downhill, a rider typically accelerates for a long time due to the force of gravity.  How fast will a rider be going when at terminal velocity?  How long will it take to reach terminal velocity?  

Terminal velocity downhill in the sample case takes about 60 seconds. 

 

Under the same conditions, but going up hill: 

 

Acceleration at Start of Time Trial 

Assume that a rider is starting a time trial at maximum, steady-state power.  How long will it take at maximum, steady-state power to reach maximum speed?  The plot bellow shows that for the example rider, it can take about 70 seconds.  (Power= 350 W, Slope= 0) 

 

Acceleration at start of a Break 

Now assume that the same rider is starting a break, how long will it take to reach steady-state from some relatively fast start?  Again, about 70 seconds.  Be patient, let your speed increase in a natural way.  (Power=350 W, Speed at Start=12.5)