- #1

cyclemark

- 1

- 3

**v**given the rider's power output

**p**(watts), rider mass

**m**(kg) and hill gradient

**g**.

*For this particular model, headwind and tailwind beyond the drag force conditions are not relevant.*

In the model I use, there are three forces against the cyclist:

- Gravity: function of
**m**and**g**, - Rolling Resistance: function of
**m**and**g**and coefficient of rolling resistance**c** - Drag: function of
**v**^2,**CdA**and air density**rho**.

**F_total**.

So

**F_total**is a function of

**m**,

**c**,

**cdA**,

**rho**,

**g**,

**v**.

But, in my situation,

**m**,

**c**,

**cdA**,

**rho**can safely be assumed to be constant, so

**F_total**is really only a function of

**g**and

**v**

And the steady-state speed is reached when

**p**=

**F_resist ⋅ v**

*.**I currently solve this equation using a mid-point search in a loop feeding in potential velocities until the equation is satisfied with an error of less than 0.0001. But if there is a formula to answer this please let me know!*

Now, the tricky part for me, I'm looking for a way to estimate how long it takes to transition from one steady state velocity to another when either

**p**or

**g**or both change.

For example:

if

**p**=300w,

**g**=0% then

**v**=39kph and if

**p**=300w,

**g**=5% then

**v**=20.75kph. But how long does it take to go from 39 to 20.75kph?

Similarly,

**p**=300w,

**g**=0% then

**v**=39kph and if

**p**=400w,

**g**=0% then

**v**=43.35kph. But how long does it take for the speed to increase to 43.35kph?

I hope this explanation is satisfactory. Please let me know if any clarification is necessary.

Any help would be greatly appreciated!