Viewing 40 posts - 1 through 40 (of 93 total)
  • F1 style Bike Maths
  • Kryton57
    Full Member

    No, not a what bike justification, but I found myself wondering about this but am too dim to come up with the answer;

    So, given the same virtual rider, virtual bike & course & therefore amount of output & resistance, could we come with an equation of:

    How many pounds lighter would a 26er need to be to offset the increased “rollability” of the same frame with 29″ wheels?

    There must be an “I can travel X miles for Y energy with…” style of thought…?

    njee20
    Free Member

    No

    PJM1974
    Free Member

    I suppose that it all depends on the terrain and conditions. My 30lb 29er climbs better than my 27lb 26er and on slippery mud it’s a no contest in favour of the wagon wheeled wonder. I guess I need to do some back to back testing this weekend.

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    Kryton57
    Full Member

    I suppose that it all depends on the terrain and conditions.

    We are assuming a virtual terrain here, same across the board.

    njee20 – Member
    No

    I’m sure there is something close, but it gave me a headache trying to get there…

    Nobby
    Full Member

    No, and it would be useless without a similar equation to work out the extra energy needed to get the 29er up to speed (as and when needed) on the same course.

    On paper, most would say that Vettel is a better driver than Ricciardo yet driving the same cars on the same track with the same everything else this is not the case. It seems the car, whilst the same, suits one driver’s style more than the other….

    matt_outandabout
    Full Member

    It depends if the bike is on a conveyor belt….

    ahwiles
    Free Member

    Kryton57 – Member

    We are assuming a virtual terrain here, same across the board.

    exactly, what are the conditions?

    you’d have to start by establishing a ‘terrain roughness’ measurement, an Ra value of sorts.

    (there’s much more to roughness than Ra, but it’s a start)

    and then you’d have to quantify grip,

    and then, etc.

    Kryton57
    Full Member

    Exactly ahwiles. Assuming the same (whatever you deem that to be)… Surely its not too difficult for the heavy hitters on here to establish a base and go from there?

    PJM1974
    Free Member

    My head hurts already…we’d have to agree on the type of virtual course (ie gradient, technical level, soil type, rootiness etc), but I do get the X miles for Y energy type equation which does exist but in a very simplified form and thus doesn’t take into account those game-changing variables that will extend your ride like saddle comfort, geometry, tyre choice ad infinitum

    I keep coming back to the notion that I should ride both of my bikes back to back around my local loop on an “ideal” summer’s day (ie dry, dusty and at roughly 20 degrees) and then report back. I’ll revisit this thread in June with my findings.

    mrblobby
    Free Member

    If it wasn’t too difficult I’m pretty sure there’d be data all over the web for it (I think some manufacturers, e.g. Giant, claim that they’ve “done the math” but then don’t present any data!)

    You could probably have a stab at some ideal model that involved a bike being rolled along a course with a constant input of power, but it wouldn’t be very representative of real world riding. Reckon there’s just too many variables with all the rider input (weight shifts, pumping, hops, etc.) and being on and off the gas, different types of surface, roots, rocks, etc.

    sandwicheater
    Full Member

    What colour is the 29er?

    Kryton57
    Full Member

    For the purpose of this thread, assume they are both pink camo.

    nemesis
    Free Member

    The problem is that the answer will depend so much on your assumptions and model and neither will likely be that close to real life given that mtbing by definition is over different terrains – eg you could probably make the answer whatever you want just by adjusting the parameters.

    aracer
    Free Member

    On paper, most would say that Vettel is a better driver than Ricciardo

    Not me – this season has shown what a useless lump Vettel really is, and how lucky he’s been previously to get a car which was so good and exploited his peculiar driving style.

    As for Kryton’s question – absolutely no way to do this as a paper exercise without lots of real world testing.

    sandwicheater
    Full Member

    assume they are both pink camo

    Aaah, so we’re riding in a ladies under garment section of M&S and being stealthy. Well, at least we know the terrain.

    maxtorque
    Full Member

    And of course, crucially, the only “Improvement” you get from a lighter bike is when you are accelerating or climbing. So a flat course, that you cycle around at a steady 20mph isn’t going to help the 26er at all.

    In fact, in my experience, on typical XC racing courses, you don’t actually accelerate that much, and speed is surprisingly constant for the vast majority of the time.

    Stevet1
    Free Member

    seeing as 29’ers are for novice riders suspect that the 29’er would have to be the lighter bike.

    nemesis
    Free Member

    And how do you factor in the exploding wheels?

    moshimonster
    Free Member

    You would have to start with a very simplified model and then attempt to add the various parameters later to build up a more useful model. But I haven’t even seen the simplest model yet ie. flat ground 26″ v 29″ at constant speed. So I think we’re a long way off a meaningful mathematical model, but I would have thought the big manufacturers would have the resource to develop one. But if they did it would not be in the public domain in the same way that F1 dynamic vehicle models are not freely available.

    In short I’m pretty sure it could be done to a level that would be meaningful. Could make a good phd project for somebody.

    mrblobby
    Free Member

    I wonder if for bigger riders if a lighter bike makes less difference too as it’s a smaller overall weight saving? Probably hurt the rollability of the 26er too more so than the 29er. So if you’re a portly gent then you’ll probably be better off with a 29er 🙂

    nemesis
    Free Member

    If you’re talking simple models, flat ground and constant speed then there won’t be any difference between 26, 29 or any other wheel size.

    cynic-al
    Free Member

    Look at that bloke’s (Matt?) test where he saved however many seconds over a certain loop.

    Then try calculating that into a weight gain for a 26er.

    That’d be a start

    TiRed
    Full Member


    One of my favourite books (Sorry). You need some clear definitions. Level smooth surface for rolling resistance and effects of contact patch, constant power for rider (otherwise the rider can increase power to negate any difference).

    I don’t think weight per se will be a huge factor here for these design parameters (flat), so you’d probably want a 3, 6, 9, 12% gradient for starters.

    Addition of surface terrain is probably a harder one, so you’d need some form of input for non-flat surface, say a sinusoid with period of 2.5, 5, 10, 20 cm to get some effect for wheel size.

    Should be easy 😉

    SamB
    Free Member

    If you’re talking simple models, flat ground and constant speed then there won’t be any difference between 26, 29 or any other wheel size.

    Correct. So that’s your starting model.

    Next step would be to add in “number of accelerations”, some way of quantifying the time difference due to getting back up to your constant speed (at the start, after tight corners etc). That would tip things in the 26ers favour. For the basic model above, there are zero “accelerations” so 26=29.

    After that you might add a “rollability” factor, i.e. the gain for a larger wheel over a given “roughness of terrain”. Again for a smooth course 26=29, as roughness increases so does the 29er advantage.

    That would get you a reasonable way towards modelling a twisty, rough course at a constant altitude. If you wanted to try and track weight, you’d need to add in a height variance over the course distance.

    It’s definitely do-able, but would get complicated quite quickly. Also, it would be very difficult to come up with the equation constants (e.g. by how much a given 90 degree corner slows down a 29er vs a 26er). Without a real-world testing ground (unlikely) it would be quite hard I think…

    nemesis
    Free Member

    Of course it’s doable, it’s just IMO pointless as I said – you’ll get whatever answer you want to get unless you’re going to put it all into a supercomputer with a huge amount of data gathering beforehand and also some actually agreement on what ‘typical’ riding actually is…

    jameso
    Full Member

    Imo.. a very difficult if not futile question even if you could create a complex enough model to be representative of enough reality to be of interest. Wheels and weight are inter related and lighter is rarely simply better (within normal bike ranges) it’s always a trade off. Look at both parameters in isolation for benefits then figure out the balance of the two.
    eg, my most efficient bike over a longer distance happens to have heavier wheels than normal, I see that as part of its advantage and I’m in no rush to change that aspect.

    aracer
    Free Member

    If you’re talking simple models, flat ground and constant speed then there won’t be any difference between 26, 29 or any other wheel size.

    Well no. If you’re going that simple, then everything else being equal the larger wheel will be faster.

    ahwiles
    Free Member

    agreement on what ‘typical’ riding actually is…

    aracer
    Free Member

    One of these will be fastest in that scenario

    nemesis
    Free Member

    I’m assuming a rigid wheel (eg no tyre), aracer – simple – hence no difference.

    Though come to think of it, even if you do assume a tyre and hence a contact patch, you’ve got the question over tyre pressure then between wheel sizes. Then maybe a question on pressure vs grip. And pressure vs pinch flat risk. Then tyre size. Then suspension travel. and it goes on and on…

    jameso
    Full Member

    The issue that throws the spanner in all the maths is human ergonomics. Cycling is much more about the rider than say the f1 driver. The human element is more dynamic and variable in riding style so the model has to be so specific as to be near impossible.
    Either you find the answer yourself through trial and error or you won’t know, even then the answer may be more placebo than anything.

    aracer
    Free Member

    Well that’s pretty pointless and unrealistic then.

    even if you do assume a tyre and hence a contact patch, you’ve got the question over tyre pressure then between wheel sizes.

    I was assuming equal tyre pressure, which seems like a good place to start, and no obvious reason to do otherwise given the same tyre type and width.

    aracer
    Free Member

    One interesting possibility does occur to me to get some answers to this. The availability of e-bikes does provide the opportunity to get rid of one of the most variable factors involved in real world testing – though clearly it is still not that simple to keep everything the same.

    digga
    Free Member

    To further muddy the already murky waters of the discussion, you also need to factor in – if we’re talking full suss mtbs here – the pedaling efficiency of the suspension system.

    My AM bike is a pound or two on the heavy side, but it climbs extremely well because the suspension design is so good, I never even need bother to lock the rear shock out.

    Any flat or inclined fire trail where there are imperfections over, say 20mm size, will always IMHO favour the bigger wheels rolling ability.

    Kryton57
    Full Member

    My view of this was to eliminate as many variables as possible. So same “virtual” rider, same bike components with the exception of the frame & wheels, same virtual course etc….

    The arguments above are introducing variables, so how about a simulation which elimates as much variability as possible…

    mrblobby
    Free Member

    But then you’ll have an riderless ebike rolling around a velodrome in a vacuum. What’s the point of that? Not really representative of the riding I do 🙂

    Kryton57
    Full Member

    Eh? Why? Why wouldn’t you have a virtual trail, with bumps, hills and curves, not a velodrome track?

    moshimonster
    Free Member

    If you’re talking simple models, flat ground and constant speed then there won’t be any difference between 26, 29 or any other wheel size.

    There would still be a difference in power output (however small) to maintain the same constant speed as there is more energy stored up in those larger wheels at constant speed. But yes, the model would need to be developed much further to be of any practical use.

    ahwiles
    Free Member

    on flat ground, smaller wheels are faster – they’re more ‘aero’

    Kryton57 – Member

    Eh? Why? Why wouldn’t you have a virtual trail, with bumps, hills and curves,

    because that stuff is practically impossible to define, measure and model.

    nemesis
    Free Member

    Define the virtual trail for us and once we all agree that it’s representative of what mtbing is, we’ll do the maths… Shouldn’t be difficult to get agreement on that, should it? 🙂

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