Axiom²

This is why you should stop gram counting your bicycle

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Where I live it’s becoming increasingly common to see regular folks getting into their lycras to go for a bicycle ride with their friends on weekends and holidays or even using their road bicycles for regular commuting. Inside of those groups of individuals, once in a while there’s one that has contracted a mental disease, gram counting, and those who do it are, appropriately called by other cyclists, gram counters (or weight weenies).

Gram counting serves a legitimate purpose if you’re a professional cyclist, not so much if you do it to commute, enjoy the companionship and/or the great outdoors.

A hypothetical scenario

Joe is an experienced cyclist who weighs 65Kg, is able to put out 300 watts at the pedals, has a bicycle weighing 9Kg and is up against Bob that has equal weight and power output but a 7Kg bicycle (after gram counting and spending much more money that Joe), on a perfectly leveled 100Km stretch of road.

Counting the bicycles, Joe’s total weight is 74Kg and Bob’s 72Kg so, if speed was inversely proportional to weight, it’s obvious that Bob, being 2,8% lighter than Joe, would win by 2,8Km, but it isn’t, aerodynamics will be the main factor under such conditions, so, in fact, Joe would win by a mere 0,11Km.

Less weight won’t help very noticeably on the flats under such conditions as we could see, but if the gradient was 7% (uphill) Bob would win by 2,1Km, which is great if he was competing, but when we consider a commuting scenario (round trip) we realize that on the way down Joe would win by 0,9Km due to the added weight, which means that Bob’s weight savings only netted a 1,2Km (0,6%) advantage, compared to Joe, over the 200Km trip.

Stages and competitions can be, and many times are, lost and won only by a few centimeters, in that sense, and comprehensibly so, every gram counts, but for getting to work and back faster each day, not so much, it’ll save a few seconds at best over a realistic course.

Cost to benefit of shedding some weight

Bikeradar tested a Verenti Technique Claris that costs 399GBP and weighs 10,11Kg, then you start going up in price and down in weight and get to, as an example, a Canyon Ultimate CF SLX 9.0 LTD that costs 4299GBP and weighs 6.29Kg.

I’m not sure about you, fellow bicycle rider, but I’d rather spend the extra money in some relaxing vacations in a tropical country with my family or even donate it to those who actually need it as getting 1% (or whatever irrelevance) sooner to work, the beach, the hills, my house, or whatever, just isn’t worth that much to me, and, if you apply some healthy degree of perspective, it almost certainly won’t be worth it to you too.

While it’s good to avoid cast iron wheels and lead frames, where does it cross the line into an obsession? At what point have you gone so far that you put light weight ahead of durability or financial responsibility?
Corey Maddocks @ singletracks.com

My answer would be:
If you’re not a pro, even if you have the cash, it’s when you spend money without an appreciable gain in functionality/performance/comfort or you won’t make adequate use of said benefits. For less than 1000€ (many times a lot less than that) and if you picked your stuff well you’ll most likely have a lightweight, responsive, very satisfying and well-engineered bicycle, enjoy, just ride it and be happy.

The power to weight ratio talk

I’m sure that if you’re into reading more technical articles on the subject of cycling you’ve seen people saying all kinds of things regarding power to weight ratio, Matt Jones @ weightweenieblog.com, as an example, used that metric to figure out what goes faster than what, which to be true would only mean literally breaking the laws of physics. Even if you’re somewhat of a regular Joe and don’t care much about this stuff you might have seen this term being thrown around wildly on TV car shows.

We’ve already seen what modifying your power to weight ratio (by removing weight) does under various circumstances. In our first example Bob would win over Joe by 0,1% on flat terrain because of having subtracted 2,8% of his total riding weight, but, if Joe had the same power to weight ratio as Bob due to a 2,8% increase in his output power (308,4W) he would win over Bob by 0,9Km, in short, power to weight just isn’t a relevant/accurate metric for evaluating things going at speed.

For sprints, better power to weight (relative to the other riders) can be of great use as it will produce a better acceleration (from a standstill, if one’s already at speed this may not hold true as other riders may have far more power), however, time the sprint wrong and other riders with more available power will be able to catch up pretty fast even without slipstreaming behind (even though they will), meaning, a better power to weight ratio won’t necessarily make your sprint faster.

Side note:
I talked about this metric being used a lot in TV car shows, but it’s even more useless there. At highway speeds it doesn’t matter much if your car has 700Kg or 2000Kg as aerodynamic drag will be overwhelming, let alone at sports car speeds. Power to weight ratio isn’t even a good metric of how strongly a car can accelerate as pretty much all cars will produce wheelspin if you stomp on the gas or will have some system (traction control as an example) to limit the power that is transmitted to the wheels.

If you really insist on gram counting  just to impress your friends with pictures of your scale

Like JR @ moretolifethanbikes and Corey Maddocks @ singletracks.com state, you should find a ratio you’re comfortable with in terms of money spent per unit of weight saved (even though you really shouldn’t be spending any time and money with this futile endeavour), and that’s pretty much all there is.

If you’re a pro cyclist or you really want to improve your bicycle for riding (as opposed to taking selfies with it alongside a scale).

Like it was already mentioned, fix a ratio in money spent per weight saved, but instead of stopping there, read on.

Realize that the weight of your bicycle on the scale isn’t equal to the “weight” (how it responds) on the road. A heavier bicycle (on the scale), all other factors being equal, can still outperform a lighter one even if you’re going uphill.

This happens because while all of the mass of your bicycle can be seen as moving in a straight line relatively parallel to the road (translational motion) some of it will experience rotational motion at the same time (like the wheels) and the power for all of those motions more often than not will come mostly from your legs.

This means that you can modify your money spent to weight saved ratio in order to roughly account for the influence each component has, which is a much smarter way of spending money.

I’ll pick 1CU (CU stands for currency unit, use whatever currency unit you want and pick whatever value you feel comfortable with) per each gram of weight saved (or any other weight unit you want) in components that only experience translational motion or whose rotational motion is irrelevant for your riding performance, which means everything except wheels without the axles, cranksets, freewheels/freehubs/cassettes, chains, dérailleur pulleys and pedals.

The mass of tires, tubes/tapes, rims and nipples goes around almost as fast as the bicycle is moving forward so they experience as much translational as rotational motion, which means that for these components you need to spend 2 CU per each gram saved (at the scale) as each gram here actually means closer to 2 grams for practical riding purposes.

The weight of the spokes will be evaluated at 1,33 CU/gram as their moment of inertia is 1/3 of that of the rim/tire per unit of mass while having the same angular velocity (radians/second).

A 700C wheel has a 331mm radius with the thinnest tire, a 170mm crank arm represents 51,4% of that, which results, at the pedals, in a moment of inertia of 26,4% of that of the tire per unit of mass.

If Joe was climbing a 7% grade his 700C wheel would be doing 138RPM, a typical cadence of 90RPM represents 65,2% of that, and hence, 65,2% of the angular velocity. I’ll use this percentage and the one calculated previously as my reference to figure out how much each gram you can save at the pedals is worth like I’ve done thus far, and it would be about 1,11 CU/gram. I’ve used the climbing example as I think it makes much more sense to project to a realistically common steep incline (good compromise) than flat terrain or crazy hills but if you figure that you should project for flat terrain know that under those circumstances the 1,11 figure will drop a lot and if you feel you should project for crazy hills it will rise a lot.

For the matter at hand (that doesn’t need a lot of accuracy) 1,11 is so close to 1 that you can pick almost any number in between for the rest of the moving stuff (chainrings, crank arms, dérailleur pulleys, freewheel/cassette/freehub, wheel hubs ignoring the axle, and chain) and still be in the ballpark, I went for the middle term of 1,06 CU/gram.

For the bottom bracket axle you can either consider the weight savings to be worth 1 CU/gram as it moves so slowly that is almost stationary, or assign it a symbolic value just to establish that 1 gram off of it is better than, as an example, 1 gram off of your frame, I picked 1,02 CU/gram.

I surely could have gone for minutia and plan for a variety of scenarios but I figure that there’s no need as doing it this way is already a lot better than the other way (flat ratio for all parts) that there’s probably very little to be gained as far as money savings go, maybe I’ll revisit this in the future and plot this stuff so that pretty much all cases are covered to greater accuracy.

Other sites that I didn’t mentioned but were valuable to produce this article:

bikecalculator.com  is a great speed/power calculator for cycling, the results are pretty accurate, a lot of the numbers for this article were obtained there.
Moment of inertia calculator (for objects with the mass concentrated at the extremes) was used to obtain the moment of inertia of the pedals relative to that of the rim per unit of mass.
Rotational kinetic energy calculator was used to obtain the rotational kinetic energy of the pedals relative to the rim/tire per unit of mass.

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