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Crank length: science!

964cup964cup Posts: 1,359
edited June 2017 in Road general
Thinking about this because all my bikes have 175mm cranks (something about which I've been obsessive) except for my new single-speed, which has 170mm. I don't quite have the physics to work this out for myself, so I thought I'd see if someone has already done it, or can be bothered to...

The point, apart from comfort factors, of longer cranks is leverage, right? Longer crank = more torque, therefore lower RPM to produce the same power. However, longer crank also means larger pedal circle, so faster foot movement to produce the same RPM. The question is whether the foot speed at the pedal circle is constant for a given power output, irrespective of crank length.

Anyone know?
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  • ugo.santaluciaugo.santalucia Posts: 25,093
    Same RPM to produce the same power I am afraid.

    Long cranks are better if you are a grinder, short cranks are better if you are a spinner... difficult to spin long cranks faster than 100 rpm
  • joncomelatelyjoncomelately Posts: 658
    Same RPM to produce the same power I am afraid.

    Isn't power equal to force times velocity? So wouldn't that be same foot speed to produce same power, rather than RPM (that is, if we're ignoring all the other variables that contribute to power)?
  • ugo.santaluciaugo.santalucia Posts: 25,093
    Same RPM to produce the same power I am afraid.

    Isn't power equal to force times velocity? So wouldn't that be same foot speed to produce same power, rather than RPM (that is, if we're ignoring all the other variables that contribute to power)?

    I don't understand...

    if you are spinning a given ratio at a given RPM you produce the same power, regardless of whether you do so with short or long cranks. Longer cranks might give you more leverage, but shorter cranks will make spinning easier, as your leg has to travel a shorter distance up and down. The net result is the same.

    You only notice a difference if you try to spin at 140 rpm with long cranks... difficult! In practice it only matters if you can't change gear, so SS or FG
  • imposter2.0imposter2.0 Posts: 11,003
    Taken from the link I posted earlier:
    Summary: Common crank sizes are nearly all equal in efficiencies. Cranks size can be chosen for reasons such as ground clearance for cornering/obstacles (shorter), aerodynamics (shorter), or rehabilitation/flexibility (longer). Sprinting 120 rpm is best. 60 rpm is better than 100 rpm aerobically (generally lower cadences are more efficient than higher). Natural pedal stroke is best (do not pull up), crank length has no effect on fatigue, no effect on metabolic efficiencies and very small effect on maximum power.
  • joncomelatelyjoncomelately Posts: 658
    Same RPM to produce the same power I am afraid.

    Isn't power equal to force times velocity? So wouldn't that be same foot speed to produce same power, rather than RPM (that is, if we're ignoring all the other variables that contribute to power)?

    I don't understand...

    if you are spinning a given ratio at a given RPM you produce the same power, regardless of whether you do so with short or long cranks. Longer cranks might give you more leverage, but shorter cranks will make spinning easier, as your leg has to travel a shorter distance up and down. The net result is the same.

    You only notice a difference if you try to spin at 140 rpm with long cranks... difficult! In practice it only matters if you can't change gear, so SS or FG


    I read the OP as talking about a theoretical treatment of the situation at the cranks, rather than anything related to gear ratios etc:

    "The question is whether the foot speed at the pedal circle is constant for a given power output, irrespective of crank length"

    I agree with what your saying if you're talking about the effective power delivery from the rider to drive train, but if we just think of the cranks and rearrange the OP's questions I slightly: a 1cm crank spinning at 100 rpm clearly will generate less power than a 15m crank spinning at 100 rpm. So in our theoretical model, the power generated will be proportional to crank length at a given cadence. But crank length and cadence combine to create foot speed, so the OP is correct - to hold our same theoretical power, you must vary cadence and RPM in tandem.

    Which doesn't apply in the real world, as many people have demonstrated.
  • svettysvetty Posts: 1,904
    The limiting factors are down to the individual and their physiology not crank length. Power is a function of the rider and there is little evidence that variations in crank length within the usual range (165 to 180mm) make any significant difference in power produced.

    Shorter leg lengths will find shorter cranks slightly more ergonomic due mainly to hip and knee angle variation during the pedal stroke and vice-versa for those longer legs but the effect on power is minimal.

    The other issue is that shorter cranks facilitates a slightly lower saddle height which may in turn give slight improvements in aero performance (and hence higher speed).
    FFS! Harden up and grow a pair :D
  • amrushtonamrushton Posts: 773
    Shorter crank = HIGHER saddle height.

    Shorter cranks means your feet are describing a smaller circle so you will be spinning more. Cyclefit advocate shorter cranks for many people as you are pushing a shorter lever and many people are better at spinning rather than grinding

    http://www.cyclingweekly.com/news/produ ... ter-188288 may be of help
  • Simon MastersonSimon Masterson Posts: 2,740
    svetty wrote:
    The other issue is that shorter cranks facilitates a slightly lower saddle height which may in turn give slight improvements in aero performance (and hence higher speed).

    Assuming you mean higher? In any case, higher saddle can make you lower at the front, but you could just make yourself lower at the front by other means, and use longer cranks to lower your saddle, and thereby make your body lower to the top tube.
  • buckmulliganbuckmulligan Posts: 1,031
    Tom Anhalt had a good post on this topic; worth a Google if you're interested in the real world implications.

    The take home message was that crank length doesn't matter.
  • fenixfenix Posts: 5,437
    I'm with the crank length not mattering either. I rode with odd cranks for a few months - couldn't tell the difference. I put them on as my LH crank cracked - and then i completely forgot about it.

    We are only talking mm here on what is a fairly large length of leg and foot.
  • mamil314mamil314 Posts: 1,103
    Same RPM to produce the same power I am afraid.

    Isn't power equal to force times velocity? So wouldn't that be same foot speed to produce same power, rather than RPM (that is, if we're ignoring all the other variables that contribute to power)?


    With longer crank velocity is higher, but force lower to achieve the same RPM and power as shorter crank.
    I like shorter cranks better for more ground clearance and easier hip angle.
  • paul2718paul2718 Posts: 471
    For the same power and rpm shorter cranks imply higher forces.

    I would expect the choice to be primarily determined by leg length.

    But, if you are spinning at a nominal rpm and power, and put longer cranks on, the effect is to reduce the force required and increase the leg speed (but not the rpm). So spinnier. If you shorten the cranks then the force goes up and the leg speed down, so grindier.

    But if anything matters it will be leg length.

    Paul
  • svettysvetty Posts: 1,904
    amrushton wrote:
    Shorter crank = HIGHER saddle height.

    Shorter cranks means your feet are describing a smaller circle so you will be spinning more. Cyclefit advocate shorter cranks for many people as you are pushing a shorter lever and many people are better at spinning rather than grinding

    http://www.cyclingweekly.com/news/produ ... ter-188288 may be of help
    svetty wrote:
    The other issue is that shorter cranks facilitates a slightly lower saddle height which may in turn give slight improvements in aero performance (and hence higher speed).

    Assuming you mean higher? In any case, higher saddle can make you lower at the front, but you could just make yourself lower at the front by other means, and use longer cranks to lower your saddle, and thereby make your body lower to the top tube.

    It depends....

    The limiting factor in a TT position is generally hip angle and 'thigh hitting abdomen/chest' issues. These are eased with shorter cranks so shorter cranks are often advocated by 'marginal gains' time trial riders to enable a lower position.
    FFS! Harden up and grow a pair :D
  • DeVlaeminckDeVlaeminck Posts: 6,037
    It's surprising there haven't been more studies on crank length.

    It must make a difference, it might not make much difference, there may be pluses and minuses for longer and shorter, but given the time and money even some amateurs spend on marginal gains if you can get another few watts, avoid an injury or decrease drag even by a small amount just by speccing a different length crank who wouldn't do it.
    AFC Mercia women - sign for us
  • imposter2.0imposter2.0 Posts: 11,003
    It's surprising there haven't been more studies on crank length.

    It must make a difference, it might not make much difference, there may be pluses and minuses for longer and shorter, but given the time and money even some amateurs spend on marginal gains if you can get another few watts, avoid an injury or decrease drag even by a small amount just by speccing a different length crank who wouldn't do it.

    Did you not read the link I posted earlier?
  • DeVlaeminckDeVlaeminck Posts: 6,037
    Imposter wrote:
    It's surprising there haven't been more studies on crank length.

    It must make a difference, it might not make much difference, there may be pluses and minuses for longer and shorter, but given the time and money even some amateurs spend on marginal gains if you can get another few watts, avoid an injury or decrease drag even by a small amount just by speccing a different length crank who wouldn't do it.

    Did you not read the link I posted earlier?

    Yes but the link to the article he's based it on no longer works - are we supposed to take that blog as definitive?
    AFC Mercia women - sign for us
  • imposter2.0imposter2.0 Posts: 11,003
    Imposter wrote:
    It's surprising there haven't been more studies on crank length.

    It must make a difference, it might not make much difference, there may be pluses and minuses for longer and shorter, but given the time and money even some amateurs spend on marginal gains if you can get another few watts, avoid an injury or decrease drag even by a small amount just by speccing a different length crank who wouldn't do it.

    Did you not read the link I posted earlier?

    Yes but the link to the article he's based it on no longer works - are we supposed to take that blog as definitive?

    The blog is simply an overview of the study. The link may be dead, but you can still find details on the study by googling it..

    https://issuu.com/superhandydave/docs/3 ... gtechnique
    Similar study by same author - https://www.ncbi.nlm.nih.gov/pubmed/11417428
  • reacherreacher Posts: 416
    Surely all their testing is the end result ? Having worked with tools all my life I can safely say that leverage matters repeat it several thousand times and I would have thought it matters a lot. I can't see how they can test what is required by an individual to apply that force, the end result might be the same but how each person sets about applying it has to be very differant. Also it changes as you adapt to it, to simply say try x length then move to the next length on a test is all well and good but I would have thought you need to try them for a considerable period to get a definitive answer on do they work for you.
  • svettysvetty Posts: 1,904
    reacher wrote:
    Surely all their testing is the end result ? Having worked with tools all my life I can safely say that leverage matters repeat it several thousand times and I would have thought it matters a lot. I can't see how they can test what is required by an individual to apply that force, the end result might be the same but how each person sets about applying it has to be very differant. Also it changes as you adapt to it, to simply say try x length then move to the next length on a test is all well and good but I would have thought you need to try them for a considerable period to get a definitive answer on do they work for you.

    You are framing this as a power/force issue in the same way that the 'strength' thread went. Again the nub of the debate is that cycling all about is aerobic power, not leverage or force. This is why crank length has negligible effect on aerobic power (within the usual range of crank lengths).
    FFS! Harden up and grow a pair :D
  • reacherreacher Posts: 416
    svetty wrote:
    reacher wrote:
    Surely all their testing is the end result ? Having worked with tools all my life I can safely say that leverage matters repeat it several thousand times and I would have thought it matters a lot. I can't see how they can test what is required by an individual to apply that force, the end result might be the same but how each person sets about applying it has to be very differant. Also it changes as you adapt to it, to simply say try x length then move to the next length on a test is all well and good but I would have thought you need to try them for a considerable period to get a definitive answer on do they work for you.

    You are framing this as a power/force issue in the same way that the 'strength' thread went. Again the nub of the debate is that cycling all about is aerobic power, not leverage or force. This is why crank length has negligible effect on aerobic power (within the usual range of crank lengths).

    Not at all, all I'm saying is that leverage is a fundamental fact nothing to do with strength that's your take on it not mine, longer lever means easier to turn something, does that apply to a crank I have no idea other than at some level for some people depending on riding style it may do, for others it may not.
    Why you keep referring back to previous threads iI have no idea other than you seem obsessed with anybody that does not agree with certain ideas about training, no ones arguing that cycling is not an aerobic sport, their does that clear up that particular debate
  • 964cup964cup Posts: 1,359
    Fascinating. So no-one can do/has actually done the physics. I wasn't asking the usual question about crank length; we've all been there. I was asking a specific question about the relationship between crank length, power, RPM and foot speed. Let me see if I can make any sense of it myself:

    Let's start by establishing that power is a measure of the *rate* at which work is done. Torque is the measure of work done. So, to produce more power you can apply more torque, or apply the same torque faster.

    The conversion is:

    Power (W) = Torque (Nm) x RPM / 9.5488

    So 250W at 80rpm requires 29.8Nm

    Simplistically, a 175mm crank requires application of a force of 170.3 Newtons to generate 29.8Nm. A 165 crank requires 180.6 newtons.

    So to get the same power at the same RPM with shorter cranks, you have to press harder. 6% harder, obviously, since the 175 crank is 6% longer. Or, of course, you can turn the 165mm crank at 85rpm (6% faster) and push the same 170.3N to get the same power.

    The pedal circle of a 175mm crank is 1099.6mm; at 80rpm your foot is moving around this circle at 1.466m/s.
    The pedal circle of a 165mm crank is 1036.7mm; at 85rpm your foot is moving around this circle at 1.469m/s.

    Allowing for rounding, it looks like foot speed is constant for a given power (which isn't really a surprise, as I thought).

    On the 110mm cranks I used at Rollapalooza the other day, I'd have to spin at 127rpm to do 250w at 170N. That's a foot speed of...1.462m/s.

    Whether you prefer to push harder or spin faster is of course personal preference. There is also the matter of the included hip and knee angles, which will vary with crank length (and therefore relative saddle height). But that's trig, and I'm tired.

    What this does suggest, though, is that shorter cranks suit lower gear inches. Consider a fixed wheel. Assume I have a 270W FTP; that means 38kph sustained on the drops on the flat. My current bike has 170mm cranks and 48x18 (70.64"); roughly 110rpm to get 38kp/h at 270W (22.4Nm, 131N). If I switch to 165mm cranks to meet Velodrome regs I should be spinning at more like 113rpm to keep the same foot speed, Newtons etc. So I should also change to a 49x19 (68.26"). Hadn't thought of it like that before.

    Obvs the actual gears at a Velodrome would be different - 48x18 is a commuting gear - and the speeds and power outputs would be higher, but that just exaggerates the effect. Take 50kph as the measure, and 120rpm. Closest match is 50x15 (88.1"). Go to 124rpm and it's 48x15 (84.66").

    [All ratio/speed/cadence calculations assume a 700c wheel with a 25c tyre, and are approximate. Your mileage may vary. I am not a lawyer. I'm not a performance coach either. Or a physicist. End disclaimer.]
  • reacherreacher Posts: 416
    Are you not over thinking this a bit ? surely just pick the crank length that suits your particular type of riding. A lever is a lever longer is easier, the Egyptions found that out stone age man before that, its a fundamental principle, you can apply all the science you want but the fact remains some people are going to exploit that principle some are not
  • LimitedGarryLimitedGarry Posts: 400
    Let's be honest here: if you can't tell the difference through any observations or feel, does it REALLY matter?

    Me, personally, 170mm on my roadbike. Helps keep up cadence. On the MTB, 175 (do a lot of slow climbing on it).
    Shorter crankarm allows you to put your seat slightly higher, thus further reducing how high you need to raise your knee on top of the pedal stroke, so the help with maintaining cadence is greater than one may initially think. Also, the range of motion is smaller (one of the factors that helps keep higher cadence)
    However, in situations where maintaining constant cadence is difficult or even impossible (generally mountainbiking over rocks), you don't really need to be able to spin fast, you need to be able to crank reasonably hard when needed. The longer crank gives you not just more leverage, but also more modulation. In technical climbs, smashing the cranks as hard as you can usually isn't the answer. You need enough power to be able to go up, but not too much power to cause the wheel to loose traction.

    No matter what the science says, it should be a matter of preference.
  • 964cup964cup Posts: 1,359
    I'm only going to say this one more time. This wasn't meant to be a "what crank length should I use" thread - to which the answer is "whichever one you like best". This was a question about the underlying physics, which I hoped someone had already worked out, or could work out faster than me. I've done it now.

    Anquetil used to fit a 177.5mm crank in place of his normal 175mm when he was "feeling strong"; this was a signal intended to induce fear into the peloton. I guess the logic was that he meant to maintain the same pressure and cadence, but gain 1.4% more output power (effectively by increasing his foot speed). I wonder if anyone can evidence physiologically that it's easier/better/more sustainable to increase your foot speed to go faster rather than raising your RPM or pressing harder on the pedals in the first place. Or is it purely psychology (whether directed at himself or at his rivals)?
  • reacherreacher Posts: 416
    964cup wrote:
    I'm only going to say this one more time. This wasn't meant to be a "what crank length should I use" thread - to which the answer is "whichever one you like best". This was a question about the underlying physics, which I hoped someone had already worked out, or could work out faster than me. I've done it now.

    Anquetil used to fit a 177.5mm crank in place of his normal 175mm when he was "feeling strong"; this was a signal intended to induce fear into the peloton. I guess the logic was that he meant to maintain the same pressure and cadence, but gain 1.4% more output power (effectively by increasing his foot speed). I wonder if anyone can evidence physiologically that it's easier/better/more sustainable to increase your foot speed to go faster rather than raising your RPM or pressing harder on the pedals in the first place. Or is it purely psychology (whether directed at himself or at his rivals)?

    It's not exactly rocket science to determine that a longer lever is easier to turn or move something just go in the workshop and try two differant length tools you don't need anything else to figure that one out
  • reacherreacher Posts: 416
    As the other post says mountain bikers exploit the leverage so clearly it can be done, but then your into a whole differant question debate which as is constantly pointed out you don't need any strength other than that of an old lady to go up a mountain on a bike, unfortunately I haven't found that to be the case
  • LimitedGarryLimitedGarry Posts: 400
    Yeah, the thing about how mountain bikes make climbing easier is a bit twisted. Sure, when you take a road bike on regular road, the road bike will climb faster but it'll also take more effort. Mountain bike CAN go at a much lower effort, but it will not climb at the same speed under the same effort. (personally found that road biking is great for extending aerobic strength on climbs)
    And when you actually go mountain biking (steep hills, rocks, dirt, loose terrain), it's almost a completely different sport. So much more is required than just pedalling.

    When it comes to what is better for going fast, it really depends on how you train yourself. It's as simple as anaerobic vs aerobic strength. Both are very important for cycling, but you can have a preference.
  • reacherreacher Posts: 416
    To be fair I have changed my opinion on strength and as a consequence I have changed my riding style, it's pretty enlightening to watch those pro riders all simply just spinning up climbs compared to the old days
  • cyclecliniccycleclinic Posts: 6,865
    I can spin my 175mm cranks at 150 rpm for cadance intervals. So that statement at the beginingn of the thread is wrong.
    In fact I have cranks from 165mm to 177.5mm and all work just fine for me. I adjust my seat height a bit and saddle fore and aft.

    I have come to the conclusion you can use almost any cranks you like withing reason and it wont make much if any any difference so long as you adjust your saddle. From a biomechanical point of view optimal crank length is meant to be much shorter than 170 to 175mm, it should be around 150 mm. Bicycle science volume 3 gives a detailed account of this well as detailed as the published evidence allows as there is hardly anything. Why is there hardly anything because changing crank length makes sod all difference so there is nothing to investigate.
    http://www.thecycleclinic.co.uk -wheel building and other stuff.
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