With so much time/$$$/attention given to reducing bike weight and streamlining it for aerodynamics, I’d like to better understand the relative role of the various factors that affect the work/effort necessary to propel a bike. Perhaps someone knows the equation and can provide general/typical values for the primary coefficients so we know where best to concentrate our efforts (other than on personal fitness). For example, I assume the equation must be something like the following:

Work/effort = Speed x Mass x Friction x Drag x Incline, where

S = speed the bike is moving
M = weight of the bike and rider (would the equation differentiate ‘static‘ weight and ‘rotational/dynamic' weight?)
F = friction created by contact between moving parts
D = aerodynamic resistance (drag)
I = slope of the road

Intuition/experience suggests that F is pretty inconsequential relative to the other factors given the ready availability of good bearings and high pressure tires. I is beyond our control. If there’s little difference between static and dynamic weight, then losing personal body weight is probably far more effective for all but those few athletes who have ideal body weight as spending BIG $$$ to shave off a few grams on bike components. Is reducing a pound of body fat as effective as spending $$$thousands to drop a pound off the weight of the bike?

If any of this is generally on-target, then commonsense suggests that most of us should focus on 2 variables: lose body weight and improve bike/rider aerodynamics.

Ok you engineers and physicists, what’s the math underlying the motion of a bike?

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Wilier Cento Uno, 13.25 lbs / 6.01 kilograms
http://weightweenies.starbike.com/forum/viewtopic.php?f=10&t=95887

I'd suggest a foray over to http://www.analyticcycling.com

Quite a bit of info/hypothesis there.

as above, the analytic cycling site is a good place to start

for road cycling, it's mostly about aerodynamics, and most of the drag is due to the rider not the bike

You are forgetting genetic predisposition...

A lazy sod with awesome 'genes' is still a lazy sod.

No way they would step on a bike and smoke someone with 'inferior' genes who trains.


Just my .02

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Baum Ristretto, Baum Mondrian Corretto & the '89 Merckx! | "If you could eat it in one sitting, hold your line." | twitter.com/Tinea_Pedis

What about fast / slow twitch fibres? Training Specificity TP?

Every spring after focussing on and racing a winter of TT’s (my preferred event), I’ll dust off the track bike for summer… Here are guys at my club who were top sprinters in the past and who now don’t train much anymore due to other commitments, but will easily out sprint me if I haven’t dropped them before the last lap.

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http://climbinglama.blogspot.com.au

Almost. Instead of losing body weight, what you really want is to improve your Watt/Kg figure. This translates to "train more, eat less" (with a tongue-in-cheek, of course you need to eat, so you can exercise).

As regards rider- (and to a lesser extent bike-) aerodynamics, spot on. Get your torso in shape so you can sustain a low position. Exercise so your legs and back are flexible. Get rid of the spacers below the stem one by one, and you'll find each step will speed you up.

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Bikes: Raceur, Beateur

You'd think so, but it ain't the case.

I remember having a Team Leader who was such an indvidual. Now, it wasn't that he never rode, but he wasn't anything close to the rest of us. He would go weeks without riding. At all. He smoked, drank like a fish and just generally couldn't care (he was 'forced' into it by his father, a former professional rider back 'in the old country'). I remember one Provincial Championship road race where he was pre-warned by Staff that if he didn't win outright, he wasn't going to get selected for Nationals due to his bad attitude. We were driving around all night trying to find him, which we eventually did, passed-out at a house party. We got him to the line, where he was puking like a dog. The course was really tough with multiple ascents of steep climbs. He finished second in a sprint. Go figure.

Thanks all for the discussion. I explored the Analytic Cycling site, altho for my general, non-racer-related questions it's almost TMI. But having read all the pertinent threads I can find here and on other forums, here's what I've concluded as an avid, middle-aged recreational rider who has some (but not unlimited)disposable income to spend on bike toys. FWIW, here are John's 5 golden riding rules:

#1: The purpose of biking is personal refreshment, fitness and fun, albeit with modest challenges/goals. Keep it that way.

#2: There are no universal truths regarding THE BEST frame, wheels, components, etc. There are lots of great options in all categories, whether top-end off-the-shelf, mass produced parts, or small, boutique custom parts. Stop trying to split hairs. So, shop carefully and then buy products you believe in, that please you, and enhance your riding experience. Remember, what makes you happy and adds to your riding pleasure is what's best. And style is personal/subjective: don't look to others to tell you what color, paint/finish scheme, etc. is best... express your taste in building-out your ride. If others approve of your stylistic choices, great; if they don't, SCREW-'EM! And GET A BIKE AND SET-UP THAT FITS!

#3: Lighter weight is generally better, however don't get insane over mere grams. (I know that violates a core WW goal; but I suspect many of the forum readers are like me: outsiders seeking general advice/wisdom from the experience of the 'true believers"). Don't risk safety and dependability/performance for uber-light, off-brand carbon fiber stuff. The BIG $$$, super light stuff won't make an appreciable difference in performance. For we non-elite athletes, dropping a few pounds of excess body fat and improving our cardio-vascular conditioning, especially our 'red-line' limit at our aerobic/anaerobic threshold, yields better results.

#4: Aerodynamics trump weight. And by far the biggest aerodynamic factor is the rider: use the drops and wear appropriate kit. Wheels come next. After that, the aero benefit of various components is trivial for all but the most advanced racers/TTs. And, lastly,

#5: While chosing the best quality components you can afford, be sure to use really good tires and bearings as they have a measurable affect on rolling resistence and friction. No need for ceramic bearings; high quality steel is just fine. However, if you use ceramic, get top-end ones w/the best seals and proper lubrication or don't bother.

Again, these ideas apply to we mere mortal riders... Any suggestions from you super-humans?

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Wilier Cento Uno, 13.25 lbs / 6.01 kilograms
http://weightweenies.starbike.com/forum/viewtopic.php?f=10&t=95887

I think you guys are quoting the (very rare) exceptions to the rule.

Plus relying on their say so 'not doing much'.

We all know how well cyclists sandbag.


Happy to concede differing POV's though.

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Baum Ristretto, Baum Mondrian Corretto & the '89 Merckx! | "If you could eat it in one sitting, hold your line." | twitter.com/Tinea_Pedis

As usual, the answer is on Sheldon Brown's site.
http://sheldonbrown.com/rinard/aero/formulas.htm

Rainer Pivit is a university type guy in Germany and has measured exactly what you're asking: typical values for the various forces that oppose a cyclist. His equation is:

(quote)
The force resiting the motion of the bicycle Ftotal consists of the sum of rolling friction Froll, aerodynamic drag Fwind, the force needed to accelerate Faccel, the upward slope resistance Fslope, the bearing friction resistance and the drive efficiency h. Unlike the other quantities, acceleration and upward slope resistance can also be negative - usually a positive thing for the cyclist - thus propelling rather than retarding the bicycle. Naturally the drive losses h apply only if the bicycle rider really pedals the bicycle and does not just let it roll. Bearing friction, such as friction in the hubs, is usually added to rolling friction; accordingly the bearing friction forces in the drive train are added to the drive efficiency h, specifically, pedals, bottom bracket, freewheel and partially also the hubs (the additional forces on the hub due to chain tension). Thus one arrives at the formula:

Ftotal = (Froll + Fslope + Faccel + Fwind)/h
where h : drivetrain efficiency, dimensionless.

(end quote)

Also there are two charts, Figure 1 graphically showing the Forces in the equation above, at different speeds, for a "typical" rider on flat goround. This might be the "work" you're asking about.




The second chart, FIgure 2, graphically shows the Power needed to overcome those Forces, again at different speeds, for a "typical" rider on flat ground. This might be the "effort" you're asking about.




What's interesting to me is that: you're right, aero is a bigger source of resistance than weight. But remember these charts are on flat ground, where weight only affects rolling resistance; on uphills, low weight really starts to matter. (On down hills, heavier is actually better!)

The usual question is, since we can all agree that aero+heavy is faster on the flats, and non-aero+lighter is faster up very steep hills, at what gradient does lighter weight become more important than good aerodynamics...?

My guess is somewhere around 4% grade

Edit...
But it is probably more rider specific than one might think.
Maybe someone that puts out lots of power would be able to push the aero benefit to 5% grade, but a smaller rider who can't put out those watts will benefit from less weight starting at 3% grade.
or maybe it is reversed...

And wouldnt the length of the climb affect this as well.

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TIME RXR