# 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

• 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?

• Cycling on a smooth road it's practical to compute speed mathematically based on weight, slope, and power. Off-road would be all over the map. May 27, 2014 at 11:28
• Well, off-road's main problem is how many times you hit your face on a rock. =) I suspect software like runkeeper and google maps have some rules of thumb builtin though. May 27, 2014 at 20:29
• Off-road there's also the question of how much bumping the rider will tolerate -- depends on the path, the bike suspension, and the ability of the rider to "levitate", in addition to his tolerance for abuse. May 28, 2014 at 1:18

For significant climbs, the VAM ( french? for meters climbed per hour ) is all you need to know. If you know your VAM and the height of the climb, then that's how long the climb will take. Road or MTB, it doesn't vary much in my experience unless the trail requires significant hike-a-bike.

Walking speeds just don't vary that much so Naismith's rule generally works pretty well. Biking speeds vary much more from rider to rider, so it's very hard to make any generally useful rules.

You can generalize Naismith's rule for bikes as follows:

Time for ride = (distance/average speed on flat ground) + (Total Elevation gain/VAM )

Naismith's rule works so well because the two variables are fairly constant for hikers. For bikers, you'll have to figure out what your avg. speed and VAM are to estimate how long a ride will take.

• VAM was coined by the Italian Michele Ferrari (the physician who has been banned for life from cycling for his connection with various doping scandals) and is an abbreviation for the term "velocità ascensionale media" (or mean ascension speed in meters per hour). It is sensitive to slope: at the same power output, the VAM you can produce on a shallow slope is lower than the VAM you can produce on a steep one. May 28, 2014 at 14:37

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.

Like said R.Chung, the wind can dramatically change the speed, and it's impossible to predict.

For my part, here's how I do for commuting in my city (so wind is blocked by building):

I enter in my favorite gps the from and to, and ask for an itinary using foot, then I take the total amount of kilometers, and I count roughly the time at 16/18/20 km/h.

• 16 is without sweating
• 20 is in a hurry...

I'm on a city bike, often loaded, so ...

But even with that simple rule, if you're lost, the time will vary :)