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I am trying to understand the physics of bike weight. I have just made a switch from an 11Kg road bike to an 8Kg one (obviously there are many more factors and differences between the 2 bikes other than weight), and have noticed the benefit of reduced weight. However I am not sure I understand it.

Let's say for example My combined weight is 8+75 for a total weight of 83Kg. The difference between this and 86Kg is minimal, but is does make a difference seemingly beyond what I would expect.

Assuming I could equalise the total weight by carrying a pack or particularly heavy bidon/saddle pack) such that the combined weight could be the same, why is the lighter bike always seemingly faster?

I have read something about rotational mass, which seems to indicate that it's nothing to do so much with your combined weight as perceived through gravity, but with the equivalent lifting effort of the moving parts, namely your wheels, and in fact it's wheel weight that is the major factor because your are in effect having to lift half the wheel in order to produce forward momentum. Is this a sort of gyroscopic affect whereby the easier it is to turn your wheel the faster you go?

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I would have upvoted the question, if you had made some measurements e.g. are you really faster, and does the experiment with the backpack really work out as you describe. –  Vorac Oct 21 '13 at 13:48
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It would be really hard to measure, even assuming I could arrive at the same hill at the same time of day after having the same breakfast on a day with the same temperature and other conditions etc I couldn't do it justice with facts and figures, for a start the 2 bikes are very very different, everthing from frame size to chainset and gearing options, hence the more theoretical physics angle. –  stuffe Oct 21 '13 at 13:59
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Placebo effect. You just put $5K down on a shiny new toy. You will pedal harder to prove to yourself the "investment" was worth it every cent. –  mattnz Oct 21 '13 at 19:20
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"your are in effect having to lift half the wheel in order to produce forward momentum" -- That is totally bogus. The only effect wheel weight (vs weight elsewhere) has is on acceleration, and even then the difference is quite modest. –  Daniel R Hicks Oct 21 '13 at 20:24
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The three most likely answers: 1: if you measured it you wouldn't actually find much difference. 2: the new bike is more aerodynamic, it makes you ride in a more aerodynamic posture, and has much less mechanical resistance. 3: confirmation bias. –  user973810 Oct 22 '13 at 0:42

2 Answers 2

Some of the physics are simple. To move an object of mass m up an incline requires an amount of work proportional to the weight. This is the mass times the gravitational acceleration times the displacement W = m g d. So for the heavier bike it requires more work. It also requires more average power to lift it over the same rise in a fixed set of time.

But if in your experiment with the same weights are then this physical effect is not there, it is just perception, or another physical phenomenon. Also this is limited to climbing.

The angular acceleration of your wheels is a factor as you are accelerating. As you apply torque to increase the angular velocity of the wheel, the moment of inertia is a factor. This is basically an accounting of how much mass and how far away it is from the axis. Think of a figure skater spinning with their arms out and then pulling them in to spin faster. Gravity on the wheels is a separate consideration, described above.

Another physical phenomenon at play could be aerodynamic drag. In the simplest models, this is proportional to the cross sectional area, velocity squared, and drag coefficient. Some say a heavier bike with better aerodynamic performance performs more efficiently overall. Given the combined weight with the rider this could be true at sufficient speeds.

Finally there could be a variety of fit factors on the lighter bike that make it feel easier and more efficient to you. It may even be that the fit puts you in a more aerodynamically advantageous position. But you will feel better on a properly fitted bike.

Try the new bike with the old wheels and a loaded bag. If it still feels faster, it must be because it fits you better.

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Dynamic friction on moving surfaces comes into play - I'd put $ on it that the 8kg has better quality components and therefore bearing than the 11kg bike..... Nothing to do with weight, but in cycling weight and quality is inextricably linked. –  mattnz Oct 21 '13 at 19:25
    
Tires are another factor - I'm definitely faster on my light carbon fiber road bike than my heavy steel commuter bike, but the road bike has lightweight 23mm tires @ 110psi, compared with much heavier (puncture resistant) 32mm tires at 80psi on the commute bike so I suspect that most of the difference is in the wheels (and a more aerodynamic position on the road bike). –  Johnny Oct 21 '13 at 19:51
    
I didn't much consider tires in the response, as we're comparing two road bikes. –  Jason Brown Oct 21 '13 at 19:57
    
Stiffness also factors in. The stiffer the BB area, the less power lost to frame flex. How much, I couldn't say. But the reduction of mass for climbing, increased stiffness and reduced friction for increased power to the wheels combined probably add up to something noticeable. –  Stephen Touset Oct 21 '13 at 23:00

The two major "drags" on a bike, on level ground, are the rolling resistance of the tires and the wind resistance of the bike and rider.

In general, up to a point, a tire with higher pressure will have lower rolling resistance, as will a tire with a smoother tread. Tire width also figures in, but mostly in terms of how it influences pressure and tread.

Wind resistance is affected by tire width, number of spokes, tube size, and rider position. Generally, as the "raciness" of a bike increases, tire width and spoke count decrease and rider position becomes more prone (and hence more aerodynamic). Tube size doesn't tend to vary much (and may actually increase as you go steel->aluminum->carbon) but that effect is slight and subtle differences in frame design can be more significant.

There may also be ergonomic changes -- eg, the more prone riding position, while more fatiguing, is often somewhat better for peak power output.

Bearing quality hardly figures in at all. Even cheapo bearings have very low losses, and the difference in drag between them and top-of-the-line bearings is not likely to be measurable. (The bigger difference is in durability.)

Bike weight only comes into the equation when one must "climb" (and to a very minor degree for rolling resistance), but of course it's rare to have a route that does not go up/down by 0.5% or so most of the time. That 0.5% increases the power required to hold a steady speed by about 10% over a dead-level course. But the 3KG difference between the above two bikes would amount to about a 0.4% power difference on that 0.5% slope.

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Thanks - For info whilst most of my routes are circular and therefore have no loss or gain or height overall, they are often very hilly, and it's not unusual to see several hundred metres of climb per ride (with associated well earned descents!). –  stuffe Oct 21 '13 at 20:54
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Yeah, the "cost" of the climb generally swamps the "blessings" of the descent. But keep in mind that a 3KG increase in weight is about 3.6%, and that is the MOST increase in effort you'd see on the heavier bike. –  Daniel R Hicks Oct 21 '13 at 21:22

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