Sur la Plaque: Mechanics of the Big Ring

I’ve been riding for long enough to know that what “feels” good and and what “is” good in terms of technique are two independent sets with a small intersection; it’s very important to put a lot of thought and research into what you’re doing to make sure it offers a benefit.  Research takes “work” and “time”, so I’m not very fond of that approach.  Instead, I like to do a lot of “thinking”, leveraging both my inadequate expertise in mechanics and my unusually high degree of confidence in my ability to reason in order to jump to conclusions that benefit my initial assumptions.

For example, I believe there is an advantage to riding sur la plaque, or in the big ring, as opposed to riding in the same size gear on the small ring.  I generally find that when I’m strong enough to stay on top of my gear, climbing in the big ring feels less cumbersome than when I climb in the small ring at the same speed.  The downside is that it is like playing a game of chicken with your legs; it works very well if you are able to keep the gear turning over smoothly, but should you fall behind the gear, and your speed evaporates as you fall into a spiral of downshifting and decreasing speeds (not to mention morale).

All this can be explained away by having good legs or not (un jour sans), but I think there is a mechanical advantage as well.

First, there is the duration of the effort.  As they say, it never gets easier, you just go faster, but I firmly believe faster is easier, provided you are strong and fit enough to support the effort.  The faster you climb, the less changes in gradient and road surface impact your speed.  Not to mention that while all athletes perform the same amount of work when they cross over the same climb regardless of the duration of their effort, athletes doing so in less time suffer for a shorter period of time than do those who go slower.  Marco Pantani claimed that despite knowing the suffering that was just around the corner before his attacks, he was motivated to go as fast as possible in order to make the suffering end sooner.

Second, there seems to be a mechanical advantage of riding in the big ring.  I’m a little bit hazy on the physics here, but it seems to me that the crank arm is in effect a second-class lever and, while maintaining the same length crank arm (lever) and fulcrum (bottom bracket), by moving into the big ring, you are moving load farther out on the lever, providing a mechanical advantage over the small ring.

WikiPedia defines leverage as:

load arm x load force = effort arm x effort force

In our case, since the speed is constant, that means that the load force (to turn the pedals) is also constant.  And, since the load arm (crank) is a fixed length and the effort arm length is increased when moving the chain to the large chainring, the effort force is reduced in order to maintain a balanced equation, meaning that it doesn’t just feel good to ride sur la plaque, it actually is good.

All that said, this theory completely ignores the energy loss of bending the chain as you start to move the chain from straight at the center of the cassette towards the edge of your cassette, in particular when riding in the big ring and crossing to bigger cogs.  Q-Factor has an impact on how much your chain is bending as you ride in bigger and bigger cogs, but I think there’s a measurable loss if you are crossing your chain completely (big ring to biggest cog); and I suspect is is entirely possible that the big ring’s mechanical advantages are outweighed by losses in chain friction.

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130 Replies to “Sur la Plaque: Mechanics of the Big Ring”

  1. @frank
    leverage, that’s the monkey. bang on the me

    but crank length is important to correct positioning on the bike. And being able to pick and choose cranklength is fine for those deep-of-pocket or in the trade, but most bikes that have compacts are not sold with optimal performance in mind but with ratios that are lower to get up hills easier without the need for the weight penalty of a triple and with longer cranks to allow more leverage to get up hills more easily.

    I run 172.5, but compact’s generally come in 175. Now this next bit might be an old-wives tale – I am no physcist – but the longer the crank the more leverage and so the longer it takes to turn the crank. Fine for getting up hills more easily, but not so good for jumping on the wheel of the guy’s who has attacked down the opposite gutter.

    Also, if compacts are lighter and have a better range of gearing as that slowtwitch article suggests, then why don’t the all the PRO’s use them in races as well as for training?

  2. @Jarvis
    I’m gonna have to do some sums now…

    Basically, if we model it physically, the friction/resistance forces aren’t going to change much between the two. So all that matters is moments (leverage). I’ll do some sums.

    Btw, I think the cranks on my new Boardman are 172.5 anyway.

  3. Ok Physics done… If the ratio of chainring to cassette is the same (basically if you are pulling the same length gear – how do you work out that inches thing for gears?) it doesn’t actually matter how big either of them are, what actually matters is the length of the cranks compared to the radius of the wheel. Longer cranks mean less force required, but as Jarvis pointed out you have to push through further and less responsive. So it probably makes no difference at all.

  4. @Nathan Edwards
    Are you taking into account the placement of the fulcrum? I mean, in your equations, are you also taking into account where on the crank the load is being placed? To make an extreme example, if you put the chain directly on the bottom bracket, you’ll have very little leverage to turn the gear. Conversely, if you put the chain on the pedal, you’ll have loads of leverage. The length of the crank is only a part of the equation.

    Also, we’re all ignoring the distribution of the load across the chain ring.

    Also, here’s chart on the friction table for gear ratios. Here’s an interesting block I just found in a blog post that linked to this article (which also claimed my assertion in the article is bullocks):

    Big is Better, By Mick Hamer

    The difference between winning the cycling gold medal at the Olympic Games in Sydney in 2000 or settling for the silver could depend on something as simple as the size of the bicycle’s sprocket wheels. To save weight, world-beating designs of bicycle all try to minimise the size of the two sprocket wheels that carry the bicycle chain. However, Stuart Burgess, a mechanical engineer at the University of Bristol, has proved that this design philosophy is wrong. Tests by Burgess have shown that larger sprocket wheels are more efficient than smaller ones, because larger wheels reduce friction in the chain drive, which is more important than the marginal increase in weight. “Designers have concentrated on minimising losses from what they can see,” says Burgess. “They can’t see the chain losses.” When Chris Boardman broke the world distance record for cycling in Manchester in 1996, he completed 56·38 kilometres in an hour-breaking the record by more than 1 kilometre. In a paper to be given to the Engineering of Sport conference in Sheffield in July, Burgess says that if Boardman had doubled the size of his sprocket wheels, he would have added 100 metres to his record. Although the increase in efficiency is small-equivalent to a saving of 6 seconds over 25 miles-a few seconds can mean the difference between first and second place, says Burgess. Modern aluminium sprocket wheels are so light, he says, that doubling their size is relatively unimportant. “It is extremely marginal, no more than fractions of a second over 25 miles,” says Burgess. Far more important is the impact that larger sprockets have on friction in the chain drive. Competition cyclists typically have a chain wheel with 52 teeth and a sprockets with 13 teeth on the rear wheel. Burgess tested two different sizes of sprockets to demonstrate his point. One pair of sprockets had 26 teeth on the chain wheel and 13 on the rear wheel. He also tested double-size sprockets, with 52 teeth on the chain wheel and 26 on the rear wheel. At 50 kilometres per hour, the force on the chain with the smaller sprockets is about 45 kilograms. The force on the double-size sprockets is half that. “The cyclists is still putting in the same torque, so if the radius doubles the force would be halved,” says Burgess. The reduction of the force on the chain is accompanied by a similar fall in the frictional force in the chain. Each link of the chain is coupled with a pin that fits inside a roller, and the chief source of sliding friction is the pin sliding in the roller, says Burgess. In his tests, Burgess showed that doubling the sprocket size increased the efficiency of the chain drive from 98·8 per cent to 99·4 per cent. Even so, doubling the size of the sprocket wheels may not be practical for all competition cyclists, says Burgess, because there has to be clearance between the chain wheel and the ground. But competition bicycles could easily be made with sprockets that are up to double the normal size, and racing cyclists could order to larger sprockets tomorrow simply by going to a specialist supplier

  5. @Jarvis “compact’s generally come in 175.”

    Wrong. The crank lengths are determined by bike size. I’ve just done a scan of all the bikes on the shop floor, and for e.g Tarmacs (standard) and Roubaixs (compact) all have the same crank lengths for each comparitive size. Small (52cm) have 170s, Mediums and Larges (54, 56cm) have 172.5 and XLs (60cm) have 175.

  6. @brett
    Have you ever found one in a 177.5? My failure to find them has kept me out of the potential client pool for a set myself.

    It’s a shame, too, because cranks are so easy to switch these days, it would be nice to engage in some pedal doping every now and again.

  7. Dura Ace compact comes in 177.5 and 180. SRAM Red comes in 177.5, and also offers a 52/36 compact.

    Campy doesn’t offer a 177.5.

  8. @brett
    That’s what I thought.

    One more thing on the compacts before I retire from this absolutely awesome conversation:

    The argument that a compact has less rotating mass is ridiculous; given the size of a crankset, unless you’re comfortable spinning at 4356 rpm, there can’t be a measurable difference. It makes a difference in wheels which, at 700c are much bigger than a crank, and rotate several orders of magnitude faster than you pedal. But on a crank set? I’m not buyin’ it.

  9. frank :One other thing to keep in mind, however, is that being overgeared is also bad. Despite the physics, you have to match your gearing to your ability to turn it. I have gradually been shifting to lower gears, and my speeds increase on the steepest slopes. For more on that, just watch Basso and Evans on the Zoncolan.

    Of course I’m not, and I doubt Jarvis is, advocating 50 rpm big gear climbing. Like I said, the science is clear. Higher rpms on climbing is better. But surely spinning up hill at 90 rpm in a 39×23 is better than spinning up hill in a 39×25.

  10. @Marko Sorry. Didn’t see you were quoting someone there. “The tradeoff is easier climbing as the expense of a small loss of top speed. This is the lightest configuration for either set up.” Which, any way, I still assert is crazy, either for a road racer or a tri-guy. There’s some strange stuff in that article I”m not familiar with. Because fat is the most available source of energy, you should pedal at 90 rpm? Huh?

  11. @david
    I’m with you, David. That article makes some big jumps that I’m not following. I’m not a physio, but I always thought many of the things the article attempts to standardize were based on physiology and vary pretty significantly from person to person. Oh, well. I guess next year every pro will be riding a compact at 90rpm, all day, every day.

  12. frank :@david
    Oh, well. I guess next year every pro will be riding a compact at 90rpm, all day, every day.

    Then Brett will be able to move all his compacts off the floor, and get a new bike for himself.

  13. @frank
    Basically, the smaller the Chainring, the less opposing turning force there is against you pedaling

    BUT in order to keep the gear ratio the same the cog will have to be smaller, which will be creating less turning force. So the change in size of the chainring and cassette cancel each other out.

  14. @david

    I posted that article in here primarily for the technical data, not the dude’s assesment. That said, my assesment of the tech data underscores that it’s really so dependant on the cassette that all this back and forth about the chainrings is a bit like hitting our heads against the wall, again and again and again

  15. Well, I appreciate what the article is saying, and I would say it just depends.

    Where I ride it is mostly rollers, all over. Hill after hill after hill. We big ring everything because it maintains momentum, and once over the hill you recoop so much momentum so much faster it really is significant. Our hills though range from 1/2k to 2-3k at the longest, up from 100m to 300m at the most. They are just short intervals. That said, I can beat and out run most compacts given the same routes and all because of the length of the gear. And forget triples, I just don’t like them at all.

    I don’t agree that big ringing the Alp’s however is better. The long mtn pass’s that go on really require one to find a cadence and spin that is optimized for it. Big ringing isn’t it til descending.

  16. @Marko
    Well, the back and forth on chain rings (at least for me) has to do more with mechanical advantage than speeds and cadences, which is what the data you provided speaks to.

    To me, it definitely feels better to ride the same size gear in the big ring versus the little ring.

  17. @Nathan Edwards
    But that doesn’t take into account the considerably bigger diameter and angular momentum of the wheel, not to mention that the diameter (and then also the leverage from the cog) is relatively much smaller between the 16 and 21 (for example) that you would be switching between when riding roughly the same size gear in the big vs. small ring. Whereas on the crank set, you’re looking at something closer to a 1/3 bigger diameter/more leverage.

  18. @Souleur
    Aside from the weight and aesthetic concerns associated with triples, I’ve found it incredibly hard to maintain shifting quality with a triple because the rear dérailleur just can’t accommodate the changes in chain tension between the rings. Then you start looking at medium or long-cage dérailleurs and I don’t think we even want to start that discussion.

  19. @brett
    so it’s the taller people who are forced by manufacturers false assumption of physiology into buying bikes with cranks that are too long for them?

    I appreciate the science that smaller gears are lighter and by customising your gearing should give you equivalent gearing. So in that respect are better.

    It certainly doesn’t equate in practice, especially for racing cyclists.

    Anyway, this has been a fascinating discussion and I will leave it with the fact that compacts are wank and have no place in the Velominati.

  20. @Jarvis, @brett
    Crank length based on frame size is as good an assumption to make as any, but it’s something that the rider/bike fitter should definitely take into account and have the option to swap out for their optimal length.

    Brett, I have to say I’m puzzled by the choices that Specialized has for crankset types – the Tarmac gets a standard while the Roubaix has the compact? With the Tarmac being the better climber, I’d definitely expect those to be the other way around. Any thoughts on why they went that route?

  21. I’m late to the conversation, but I’ll relate my own experience. For years, I was on a 52/42. Moved to a 53/39 on my Colnago in ’96 and realized climbing seated was nicer on my knees, less energy wasted and my speed increased. Bought a cross bike in ’06 to also use as a commuter and found that the supplied 46/36 sucked as I was spinning out all the time. I like to pedal down hills, and found I couldn’t. So I bumped to a 50/34 compact. Still had a 53/39 on my nice bike and just adjusted to whatever I was riding that day. The compact was great when pulling 2 kids in a trailer (over 100 pounds) up 15% hills. HTFU!

    Curretly (and sadly) a one bike guy for the first time in 20 plus years, and I’ve got a 50/34. Last year when the car snapped my tibia and fibula, I needed a compact to spin the easiest gears possbile. I’m making due this season with the one bike, and finding that as my legs have come around I’m not using the easiest gears. I do most of my climbing in the 19, and will move up if I’m riding the steep stuff. I say if you adhere to Rule #5, you will choose the gear that makes you fastest. We all know if you have the legs, nothing else matters. I’d be happy to invite anyone to Portland for a hilly ride that includes plenty of 20% or more hills. A compact can be handy at times. And I can pedal up to 45 mph going down in the 50/11. That said, I don’t know if I’ll do compact or standard on the nice bike that I’ll be getting over the winter. The aesthetics issue isn’t bad for me as I’m on a 50cm bike with 170’s. The compact looks fairly “normal”. I feel like I’ll have a better idea of which direction to go after this season. A compact on a 15 pound bike might be overkill.

    On a side note, my best to all who are doing the Tour de Blast tomorrow. You’ll have a great time. It can be very different weather on top, so be prepared.

  22. compacts are a combination of mountain biker’s that have turned to road and want to spin and roadie’s getting off the juice and saying its okay to spin a smaller gear

  23. Seeing Leif has bumped this post (and without having a hope of reading through several hundred replies to find out if I’m just restating the bleeding obvious) I’d like to answer the original proposition in the negative. It makes no real difference whether you’re in a given gear in the big or small rings – you still only travel x distance per pedal revolution. And the smaller ring is stiffer than the big ring anyway.

    Also, the Tarmac has 53×39 because it’s perceived as the “racing” bike and racers are all Rule V, whereas the Roubaix is really the punters machine, hence requiring the nancy gears…

  24. Ok I’ll say my bit since someone bumped it too.

    I put on a compact crank when I was out of shape and fat. It was by necessity more than anything else, get up the hill or not, ride or walk. I’m about to graduate back to the regular crank and it’s because of aesthetics and the fact that I can now ride a 39×24 equivalent up almost every hill now.

    I’m 5’10” and I rode 172.5s for 3 months in attempt to make a change as it seems there is a trend to go to longer cranks and I didn’t want to miss out. For 3 months I felt awful on the bike, I thought it was my age, fitness, flexibility, cadence or bike fit and was really getting frustrated that I never felt good on my rides no matter how easy/hard I went, what I ate, the temperature, the hills etc. I put 170s on and within minutes I knew this was the issue. I don’t know if the 172.5s were too long for me physiologically or if it was 15 years of riding 170s in the past. Either way I think 3 months is a pretty good try for something like this and I’m convinced that I must stick with 170s.

  25. The lever is about the centre of the crank pivot, not the top of the chainring. No difference due to leverage.

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  27. @michael

    Hmm very interesting self appraisal ‘re cranks length, I think I have the same issue going from 170 to 172.5. They just feel doughy while seated.

  28. Just finally learned the physics.  Its not the physics of gear ratios.  Its the physics of wind resistance.  Of my first 8,000 serious miles only 50 of them (and only the last two weekends) were proper group rides hitting over 25 mph for long stretches on flats and over 30 mph in some sections.

    From my experience, it doesn’t matter what gears I would have when the riding is solo or small groups. I had a loaner bike with a 53/39 instead of a 50/34 and figured the bike was just crap when in fact it was simply I was a gear or two off.

    I can barely get over 30 pushing all the wind myself, however in a group the difference in wind resistance means I can do it.

    If  did regular group rides I would see the benefit of a 53 because you need 53/12 to do over 30 mph at around 90 cadence.  If you have a 50/12 you need to hit like 110 cadence.

    Same thing if the group decides to drill a downhill at over 35 mph.

    Thats the physics.  Unless you are a total stud riding by yourself with pro chainrings basically means you are a pro.

    And I’m not a pro, so that’s that on the chainrings.

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