albert einsteinThis is an opinion piece by Reno Toffoli. Reno’s opinions don’t necessary represent the opinions of Your Group Ride or its advertisers but I always enjoy his rants. If you’d like to write an article for YGR, please email me at

Over the years, I have discovered a discrepancy in bicycle speeds. I’m not talking about gear ratios; I’m talking about the rate at which one is traveling. After years of countless observations I have constructed my own theory about this that states speed is relative to the rider, his or her abilities, the terrain, and the bike they are riding. I call it the Cycling Theory of Relativity.

In the same way that the laws of Newtonian physics break down at the quantum level or at very high velocities approaching the speed of light, I find that, under certain conditions, the speed at which you are traveling on a bike, the distance you have traveled, and the time it took you to get there start to break down and not really tell the whole story of what’s going on.

Kind of like Einstein’s theories of relativity, the cycling theory of relativity explains why one’s distance, rate, and time might be different depending on where you are in space. Where an outside observer might see a 2 hour mountain bike ride where you only cover 12 miles as slow, the rider may see it as a huge accomplishment. Oops, I’m getting ahead of myself…let’s lay the ground work for that first.

The standard formula for rate, time, and distance is:

d=rt or distance equals rate times time.

The problem with that is that it doesn’t take the variables of the cycling universe into account.

My first formula of cycling relativity* goes one further and states that:

r=2m. Where m=the miles ridden off road on a mountain bike and r=the miles ridden on the road on a road bike. What this really means is that 1 mile on a mountain bike equals 2 miles on a road bike.

That part is pretty simple but it’s not overly impressive so we should probably add some stuff to it to make it all cool and complex and make people’s brains hurt. Fortunately, cycling doesn’t usually make my head hurt (unless I crash on it, which has happened) but spicing things up a bit might be good.  Einstein had a lot of stuff in his theories about how the faster you go, the slower time goes and to an outside observer distance decreases as you go faster while you also age more slowly than the outside observer, etc. That’s some crazy-funky jazz right there. Any mathematicians or physicists out there can feel free to help me out. Bonus points if you can use cool irrational numbers, exponents, and anything having to do with Heisenberg’s Uncertainty Principle.  If you manage to pull it off, I will mention you in my Nobel Prize acceptance speech.


For my example, let’s discuss the two broad categories of cycling speed. They are mountain bike speed, and road bike speed. For these examples, assume one is riding a mountain bike off-road on dirt or gravel surfaces and a road bike on paved surfaces. If I look at average speeds, calories burned, effort involved, the r=2m equation really seems to hold up. Don’t start asking what happens when you ride a mountain bike on paved surfaces or a road bike on gravel, just don’t, you’ll screw everything up. Then the formula would be like 1.2r=2m or something like that and I’d have to re-write it for every scenario. It still wouldn’t have any exponents or cool irrational numbers in it either. Although now I’ve got the beginnings of an algorithm and there will be functions involved…maybe I can get a government grant. Someone really needs to get on this.

Mountain bike speed is pretty darn slow when one looks at the real numbers. I’m typically thrilled when I’m able to average over 10mph on a mountain bike ride that includes significant climbing and technical riding. Throw in stupid amounts of climbing and my average speed is probably going to be down around 7mph. This doesn’t sound very exciting, especially when you tell your non-cyclist friend or co-worker about a ride. “Yep, I averaged 9.6mph today” you tell them as they reply with raised eyebrows and a half-sarcastic “Wow, impressive.”

In real burly terrain, mileage figures don’t tell the real story either. Chugging up a few thousand vertical feet and over basketball sized rocks tends to make for a pretty slow average speed and therefore pretty low overall total mileage for a ride. I’ve found that the best way to mask the relative slowness of a mountain bike ride is to discuss it in time.** Saying that you went on a 3 or 4 hour ride is impressive. It’s often how I impress myself after looking at the rest of the data from my ride and feeling rather let down by it.

While average speed is good for racers and stats geeks, actual speed or maximum speed is where I like to concentrate my efforts.

In my experience, things start to feel pretty fast on a mountain bike on singletrack at around 17 or 18 mph. At these speeds and above, the scenery starts to blur in your peripheral vision, your brain is doing untold calculations per second, and all of your senses are focused to a very sharp point.

This is the point where I start to flow and feel like I’m one with the machine; it’s one of the reasons that I love to ride; it’s the serene pleasure of speed.

In my universe, singletrack speeds north of 25mph can get a little scary. Fire road speeds above around 35mph get scary. The tighter, steeper, and more technical it is, the lower these numbers go. This makes our ‘speed/pleasure threshold’ variable and rider skill level will factor in to this as well… someone really needs to write a formula for this too.

Climbing speed is another story. Chugging up ridiculously steep sections where grades are in the 20-30% range at 2mph or less is pretty damn slow but it still beats walking. I feel like I’m flying up a steep section if I can ride at 4mph. If the climb isn’t technical, I think a lot about all kinds of different things which helps to pass the time. Sometimes, I get a really annoying song stuck in my head. Since I have a 5 year old daughter, sometimes it’s a song about Disney Princesses.

I’ll admit that I’m not much in to climbing because it can be slow and torturous and not very fun. I do like the feeling of kicking gravity’s butt and cleaning technical climbs is also something I enjoy. But when it comes down to it, it’s the actual speed that I love; gravity trying to pull me to the center of the Earth. I guess I should have been a downhiller.

Switching to the road leaves me with one adjective: effortless. Well, at least relatively speaking. If a mountain bike is like a pimped out Jeep or rock crawler, then a road bike is like a Formula One car except that it doesn’t pull 4gs under braking.

Road bike speed is fun and effortless and fast. On flat terrain, I can usually average 18 or so mph over respectable distances. Get in a fast group ride or criterium and that speed can jump up 10 or more mph. Although I don’t do it a whole lot, riding in fast groups is a different kind of fun. The speed really becomes effortless and all of your senses are again sharpened to a point while you ride to stay inches off the wheel ahead of you and also play the tactics chess game over and over in your head. Sprinting is fun as well…how fast can you go for 30 seconds? Pretty fast. That’s really my only tactic…try to survive until the end and then go fast for 30 seconds. It works for me as long as the course is flat. If there’s climbing involved, I’m screwed. I guess I should have been a sprinter.

Unlike mountain bike speed and distance, road bike speed and distance are impressive. You rode 60 miles today? Cool. Averaged 20mph? Impressive. Sprinted to 40mph? Nice. The stats speak for themselves.  

Climbing speeds on the road are definitely much higher than off road. I don’t think I’ve ever gone 1.5mph on a climb on my road bike or even better…went so slow that the cyclocomputer wouldn’t even register the speed and simply read 0mph. I have definitely done that on my mountain bike. Descending speeds on a road bike can get pretty astronomical. If I remember right, I think my personal record for top speed on a bicycle is 62mph. I’ve definitely gotten north of 50 a bunch of times. These are straight bombs down long, straight descents on clean, wide roads. As roads get narrow, or rough, or busy, the speed comes down proportionally. The beauty of the road bike is that high speed descending is effortless as well. Descending on a mountain bike is like a gorilla crashing through the jungle. A road bike is like a raptor in a dive: smooth, silent, graceful, and effortless. By the way, in my opinion, the speed/ pleasure threshold on a road bike is around 30mph. It doesn’t matter if you’re descending or on the flats; at speeds above 30, you really feel like you’re getting somewhere fast.

So there you have it. Just remember that r=2m and you can now convert your mountain bike miles in to road bike miles. For the hardcore road riders out there, you now have a formula to relate someone’s mountain bike ride to your universe. They say a picture is worth a thousand words and that’s probably true. I’m not sure how many fake mathematical formulas a picture is worth but if anyone wants to skip all the conversions and look impressive all around, just take a picture of the burliest part of your ride and say ‘I rode this!’


*I’m sure there could be others but I have yet to formulate them…I’ll buy someone a Snickers if they can get on that for me.

**I don’t really believe time exists but that’s something for another…time?…Dammit! Never mind.