Is there a cycling equivalent to Naismith's rule After doing some training rides on courses without bigger ups and downs where I didn't make significant elevation gains, a recent ride was in more rough terrain. Of course, the relief changes the average speed one can achieve and I was wondering, if there are some rules of thumb to estimate the influence of the relief.

From hiking I know there is Naismith's rule which allows to calculate the time needed for a certain route based on distance and elevation. I am aware of the fact that with cycling the rule would be less general and require more calibration depending on


mountain vs. road bike 
different surfaces
greater difference between uphill and downhill speeds.


On outdoors.SX.com also someone presented a slightly different approach that translates different parameters (elevation gain, trail conditions etc.) into distance travelled, which could be another useful approach here.

So my question is, is there some rule of thumb or a set of rules of thumb for cycling as well?
As you have noted, the problem is slightly more complicated for a bicycle since aerodynamic drag is a larger component. However, one can combine two rules of thumb which are given in these two bicycles.stackexchange answers (How do I calculate power to climb a hill and How many miles of riding are equivalent to one mile of running) to make an estimate of either speed or power on the flat and on climbs. 

If you are only concerned about climbing the rule of thumb is simpler: on a steep hill, multiply the hill's gradient by your speed in km/h, then by ~ 3. If you measure your speed in mph, multiply by 5 rather than 3. That will give you a ballpark estimate of the watts/kg you need to produce. Since you're trying to calculate riding speed, just "solve backwards" given the equivalent power (in watts/kg) for a given slope. For flat roads where aerodynamic forces predominate, you will need to have a ballpark estimate of your "drag area" which mostly depends on your position on your bike.