In this final installment of the Bikerumor *Weight We Wear* series, we look at the most critical component of all, shoes. Like wheels and tires, cycling shoes are rotational mass, which means the impact of their weight gets amplified with every pedal stroke. We’ve all been there, when we’re chugging up a hill and it feels like we’re slogging through molasses. Yeah, your wheel and tire selection (and fitness) has a lot to do with that, as does the incline, but this video helps illustrate how much more power is required when you’re riding in heavy shoes.

## Because F = m • a

We used Northwave’s mountain bike shoes as an example, but the science applies to any type of shoe in any situation. And before you science-types go nuts in the comments, we recognize and fully admit that the math used here does not fully and totally accurately explain what’s going on. Newton’s Second Law is usually explained in terms of moving mass in a linear path, not a rotational path, but it gets us close enough. And the calorie expenditure is not perfectly coordinated with the Newton force required to move the pedals, for three reasons: First, because it’s not a perfect, direct correlation. Second, because everybody is different in their calorie expenditure. And third, because you’re not actually accelerating the shoes from a standstill at all moments. In fact, you are most often maintaining momentum, so the actual energy expenditure will be much, much lower than what’s shown here.

Basically, the numbers here are to help paint a picture. We spoke with Zipp’s engineers about rotating mass, too, and they (along with any other wheel manufacturer worth their salt) will tell you the same thing: Once you’re up to speed, the rotating mass matters very little and aerodynamics are much more important. It’s when you’re accelerating that the weight really matters. Where we believe this matters more for shoes is when you examine your pedal stroke. As Pioneer display shows above, you’re never pedaling perfect circles, so there are micro accelerations on every stroke.

We tested two of Northwave’s shoes at the extremes of their weight range. The lightweight Ghost XC came in at just 396g/397g, and the Enduro Mid at 616g/619g. We chose Northwave (who, for full disclosure, agreed to sponsor this video experiment) because I like their shoes and knew they had something both very light and very heavy…and everything in between. It’s not always the top end shoes that are the lightest, so check claimed weights (or bring a gram scale) to your bike shop and see where things line up and match your needs, style and budget.

If you want to recreate this (or pick it apart), here’s some of the equations we used:

- F = ma (Force equals Mass multiplied by Acceleration, usually explained as a Newton being the amount of energy it takes to move 1kg a distance of 1 meter in 1 second)
- 175mm crank arms @ 90rpm cadence = approximately 0.52m/s linear movement from top of stroke to bottom (350mm = 0.355m; 90rpm = 1 rev per 0.667s; so, 0.355m ÷ 0.667 = 0.52m/s).
- Actual foot movement would be more because it’s not traveling in a straight path across those 350mm of total distance, but we wanted to keep it simple.
- 1 Newton-Meter = 0.2388 Calories
- Make sure to double individual shoe weights to account for the pair

There are a couple of takeaways we’d like to highlight:

- The amount of energy required to move your shoe (and pedal, and sock, and leg) increases at the same rate as the increase in weight, assuming speed is kept constant.
- Energy expenditure (calories) does, too.
- If you want to get faster without training, get lighter shoes.
- Lighter weight shoes also
*feel*faster on the bike, which provides a huge mental advantage. Or, more precisely in our experience, heavier shoes can feel*really*heavy and provide a distinct mental disadvantage when you’re already struggling up a hill. Or in a sport like cyclocross where there’s tons of accelerations and running, everyone is suffering, and you need every psychological benefit you can get.

Be sure to check out Part One (Clothing) and Part Two (Hydration) to see how everything you wear and use adds up. Got another category you want us to explore? Leave a comment and we’ll check into it for a future story here on Bikerumor!

What about comfort? I bought a new pair of lighter shoes this year and even went down 1/2 a size based on input from the bike shop where I bought them. They were fine for shorter 90 minute training rides, but on my first century my feet were killing me by the end. I googled and found that stiff/light shoes not only improve power transfer to the pedals, they also allow road vibration from the bike to your feet.

Is there a way to have both light/stiff shoes but not be in agony after a long ride?

Possibly put a small piece of Dynamat on the outsole? Run lower pressure in your tires? Just ideas, never tried that first one, but some sort of material like that might help reduce vibration transmission without adding significant weight. But yeah, I feel your pain. I can put up with some very stiff shoes for shorter stuff, but I have my go-to long distance shoes when I know comfort matters more.

Better insole solve that.

Maybe try Specialized’s bg insole?

If your feet hurt, get shoes that don’t hurt them! Who cares if they’re light, really? Ergonomics is far more important UNLESS you’re racing, in which case you’ll suffer through some discomfort in the name of speed.

Don’t bother looking at shoe weights. This is just a silly precedent. If you want to ride medium to long distances here’s the order to optimize:

Tire Pressure/Frictional Losses/Maintenance>Ergonomics>Fitness>Rider Weight>Aerodynamics>Rim weight>Bike Weight

When looking at the effect of rotational mass of bicycle components, one needs to keep in mind the they are part of a system that includes both an entire bike and a rider. When including the total mass of the bike and rider together, a 100 gram difference at the rim becomes negligible:

https://www.slowtwitch.com/Tech/Why_Wheel_Aerodynamics_Can_Outweigh_Wheel_Weight_and_Inertia_2106.html

and

https://www.cyclingpowerlab.com/AccelerationAndInertia.aspx

This certainly follows for shoes.

Rotating mass is a flywheel. It stores energy when you accelerate, and releases energy when you decelerate. When you climb a hill, it’s acceleration/deceleration at the rate of your cadence. The net effect, for all practical purposes, is zero.

Not sure about this since there is no inertia involved in the biomechanics of pedaling. Some might be with fixies, but not when you are using a flywheel.

the cog of the shoe is actually describing a circle so yes there is some pseudo inertia effect here and also with the fact the whole bike accelerate decelerate. For road riding definitely negligible beacause speed does not vary that much. But XC racing on modern tracks is permanent acceleration deceleration and it’s not true you’ll get your inertia back when decelerating because most of the time you’re braking so wasting that power in brakes. So yes, slightly lighter shoes might help and a touch more than slightly lighter other part. Still one hsould not worry about that too much.

I’m glad I’ve never worried about ‘pseudo-inertia.” Jeeeeeeeezus

I’m going to pseudo-worry about this.

jycouput – My background is in a lot of different motorsports. The “stored flywheel effect” is a widely “known fact” that has been dis-proven many many times by top testers/teams. Depending on specific circumstances/combinations you can prove a razor thin advantage/disadvantage can be gained/lost. But 99.9% of the time the gains balance the losses for a net zero. On paper it can look like there can be an advantage gained. But when you get out into the real world and the massive number of variables that you can’t incorporate into your “on paper” test come into play the data gets so thin that it falls well within the testing margin for error. One of the simplest tests is to run manual trans drag car with a lightweight then “heavy” flywheel. This is a very narrow window to test in so has pretty good results. The results, which I have seen from multiple sources show that you always end up at a net zero.

Shoes don’t work like wheels. One shoe is heavy and pushes down while the other is being pulled up. So the two shoes offset each other in rotational weight. All you are really calculating is total weight that the shoes add to the bike/rider.

*sigh* The physics here isn’t even wrong.

Yes, the rotational moment of inertia goes up (linearly!) with mass, but that only matters during rotational acceleration. Constant* cadence == no* rotational acceleration. It doesn’t matter how hard you have to push (down, etc.) to keep that cadence, the inertia doesn’t come into play.

Now, the bio losses of having to haul a big heavy mass around at the end of your leg, that’s no joke, but it has almost nothing to do with the math you’ve presented. 🙁

All, thanks for the comments…I figured there’d be plenty. I’d argue that there’s not a lot of energy stored in your shoes/pedals/socks as you rotate them around, and that the weight of your legs likes to bring them to a quick halt as soon as you stop pedaling. So, you have to get all of that weight moving each time you stop pedaling, and, really, each time you’re changing from the up stroke to the down stroke. So sticking heavier shoes on the ends of those pistons certainly won’t help. Which is yet another reason why the math on this one is so hard to get right.

Jon, I mentioned in the article (and you’re right) that when in motion, the energy used to maintain that motion is far less than the energy needed to accelerate that motion.

Mike W, I’d say the “weight” of the shoes would balance each other out if you were simply leveling out the cranks and seeing which side would fall. But when we’re actually riding, it’s not that the weight of one is negating the other’s weight like on a balance. Instead, you (with your muscles) are having to move them through space and it’s that forced movement that’s using energy. Yes, it might be easier to get one moving down than the other moving up, but the net force required to spin those shoes around the cranks is equal from side to side as they go through the rotation. So, yes, they do act as rotational weight and not static weight.

Dkrenik, to expand on your comment and perhaps shed a slightly different light on it, think of it this way: If your bike weighed 100g and your rim/tire combo weighed 100g, I would think it would take more effort to move the rim/tire within the bicycle system. Here’s why. I can push a 100g weight (mass) across a table easily because it moves at the speed at which I push it (acceleration). However, if I need to spin a wheel up to speed to move it that same distance across the table, I’m effectively having to apply my force to accomplish two things: First spin up the wheel’s mass, then also move the mass. I’m not doing a great job of explaining it, but hopefully that helps explain why shoes (and wheels) matter more. Not only are you moving their mass through space linearly along with the rest of the bike, but you’re also moving them radially.

I understand your example Tyler and it has a flaw. You’re giving the same value to the bike and the wheels. The bike weighs much more. The bike + rider weighs evermore yet. A wheel set might weigh ~1.5kg. The entire bike (including wheels) might weigh ~7-8kg. Now add a rider (me) at 80 kg and the system is 87-88 kg’s. A 100 gm difference at the rim is nothing in that scenario.

Thanks for your response Tyler. Did you check out the link to cyclingpowerlab?

For me (~80kg), complete bike (7.3kg) I did an example with 100 gm difference for each wheel (front and rear). The power cost to accelerate from 20 – 50 kph in 15 seconds was a little over a ½ watt.

My point is/was that when looking at components alone, significant differences exist. When including the whole “system”, they become negligible.

There is a blog post from many years ago that is still relevant (unfortunately I can’t find it). The poster showed (mathematically) how differences in rim mass/rotational inertia become negligible when the entire bike and rider are included in the measurement.

Sorry to break the news on you Tyler, but this is complete non-sense. I’m a professional physicist, and can’t help but feel pain when I hear so many conceptual errors and misconceptions, justified as “crazy science” details.

The best way to think about this is in terms of torque. The main torque accelerating a bike is produced by the force exerted on the pedals by the rider. The leg pushing down produces a positive torque, while the leg going up, if it has part of its weight still on the pedal, produces a negative torque. The sum of the two torques is the net torque, which is transmitted to the rear wheel (also as a torque) to fight the torques on the back wheel that slow you down (e.g. friction, wind or gravity) or to accelerate the rider.

The torque produced by the weight of one shoe (and pedal, and sock, and whatever) is always almost exactly equal, but with opposite sign, to the torque from the other shoe. The net torque is zero. That’s why your crank doesn’t start to magically spin by itself if you clip both shoes in the pedals and stare at it.

The only time where shoe mass plays a role is when you change your cadence. Let’s take a pretty extreme example: going from 30 RPM to 90 RPM in just one second. The torque required to do this, for two 100g masses at the ends of the cranks, is about 0.04 N m (Newton – meters; details below). At 90 RPM, that’s an enormous 0.4 W.

0.4W is how much power you need to accelerate a shoe that is 100g heavier than another one from 30 RPM to 90 RPM in one second.

0W is the difference between a heavier and a lighter shoe at constant RPM.

Of course, you have to carry shoes uphill, so they add to your total weight. 100g is the same as 100 ml of water in your bottle; about half a cup.

— details —

Angular velocity at 30 RPM is 3.1 rad/s, 90 RPM is 9.4 rad/s, accelerating constantly between the two gives the angular acceleration of 6.3 rad/s/s.

The torque to produce this acceleration is equal to inertia times angular acceleration; inertia is 2 (because two feet) times cranks length squared, times 0.1 kg. That’s 0.4 Nm for the torque. Power is torque times angular velocity; that’s 0.35 W at 90 RPM.

And of course, linear superposition applies: if you were to really accelerate from 30 RPM to 90 RPM, much of the required torque would go to accelerating your big muscular legs (and you on the bike), not spinning around a few extra grams in your shoes.

Check out https://en.wikipedia.org/wiki/Rotation_around_a_fixed_axis

^^This

The kinetic energy of 1000g of shoes on 175mm cranks turning at 90rpm is 1.36Joules of rotational energy. Thats one watt extra for 1.36 seconds. To put that in perspective thats the energy required to accelerate those same shoes from zero to about 4 miles per hour. For nino that matters for you its a personal call…

That being said, while its easy to flame an article from across the web while citing mis-remembered physics from highschool or college, I truly appreciate the effort put into a scientific analysis as opposed to the ‘cool new color / 15% stiffer’ marketing hype. Thank you.

> cycling shoes are rotational mass, which means the impact

> of their weight gets amplified with every pedal stroke.

Sorry, but the majority of commenters here are correct, and the premise of this article is 100% baloney.

The effect of the weight of shoes is of course real, but it is so small that it is totally negligible. In the real world, you wouldn’t be able to measure it.

Tricky, fun stuff. Easy to argue complex physics, but with that said, I can say with assurance that for kicks, I’ve done identical, short-ish rides in my light racing shoes and my heavy winter shoes, and my legs sure feel the difference during and after the ride.

It’s not HUGE, but it’s there!

Thanks Tom, and that’s really the point at the end of it. 100g of additional weight may not sound like much when you look at the energy expenditure to accelerate them, but it adds up over a multi-hour ride. I can feel it, too, and I definitely appreciate a lightweight shoe for longer rides and explosive disciplines like cyclocross.

Indeed, most don’t understand the complex mechanics interacting with aerodynamics. Shoe weight?? Otherwise they would have thought to shield ONLY the upper wheel. We now have proven the fastest conventional road bike, simply by shielding the upper wheel — in downhill coast tests. In this case, a Cervelo P3. Hint Tyler. See you in Reno?

https://youtu.be/tnjEacJybyQ

I laugh at all the chubby chub chub guys eating bacon thinking that lighter shoes will make them climb faster xD

Yay physics fail Tyler. How about consulting an engineer/physics instructor first before posting things like that in the interwebs?

Waiting for a corrected version of this article, else these types of anecdotes will show up in the cafes how their $500 shoes made them so much more efficient and they can “feel” it.

> I can say with assurance that for kicks, I’ve done identical,

> short-ish rides in my light racing shoes and my heavy winter

> shoes, and my legs sure feel the difference during and after the ride.

That’s proof alright. Proof that the mind is an easy thing to fool. Look up “cognitive bias” on wikipedia.