# Is the weight of a bicycle frame significant compared to the body weight?

Some of my colleagues had a discussion about the question if the weight of a bicycle frame is significant compared to the weight of the rider‘s body. One argues that the weight of the frame can simply be added to the body’s weight when the rider accelerates or keeps the bicycle in motion. Hence, it doesn’t matter if a specific amount of the weight is subtracted from the body and added to the frame and vice versa.

The other one said that a bicycle with a smaller frame weight is significantly easier to e. g. accelerate (especially when steepness increases) compared to one with a heavier weight. So, this suggests that it matters where the weight is actually located.

When applying the laws of physics to this question: Which statement is closer to the truth?

Edit: To summarize the question: Does a change in the weight distribution from frame to the body or vise versa affect the energy needed to keep the system (Rider+Bike) in motion.

• I find it is my mass that takes the most effort to accelerate - I'm 110kg - if I borrow my son's bike it is about 10 kg... carbon fibre... – Solar Mike May 29 at 20:15
• @SolarMike But is this scientifically backed? I would think the same but it seems somehow too simple. – Bastian May 29 at 20:21
• These hypotheses aren't incompatible. A lighter bike is easier to ride than a heavier one, because you don't typically strap the weight difference to your body to keep the total weight constant. A change in the total weight of the bike+rider doesn't necessarily change the distribution of the weight in any way. I don't see how the second hypothesis is related to the distribution of weight. – Nuclear Wang May 29 at 20:42
• So it doesn’t matter in terms of energy if the distribution is changed? – Bastian May 29 at 20:48

One argues that the weight of the frame can simply be added to the body’s weight when the rider accelerates or keeps the bicycle in motion. Hence, it doesn’t matter if a specific amount of the weight is subtracted from the body and added to the frame and vice versa.

In general that's correct. If you're accelerating the system (bikle + rider) forward, or you're pushing them up a hill against gravity, then the energy required is proportional to the total mass, plus any losses. Most losses will not be proportional to the mass of the frame, so the distribution doesn't matter much.

a bicycle with a smaller frame weight is significantly easier to e. g. accelerate (especially when steepness increases) compared to one with a heavier weight.

Also true. Now, most riders can't do this experiment where the total mass remains constant. In general, a less massive bike means a less massive system. Unless they're wearing a weighted vest while riding the light bike, I'm don't think the experience contradicts the first one.

Second of all, the rider may be noticing how the lighter bike can easily be accelerated out from underneath them. It might feel "nimble" and light, but still take the same amount of energy to accelerate the entire system. The actual energy expenditure and the rider experience do not have to correlate perfectly.

There are a couple other things you might consider. One would be if there's a different biomechanical response. Your body isn't 100% efficient. Conceivably, there's a reason that the heavier frame would make the body more inefficient. But, I'm not aware of anything that would obviously make this true, and such effects are a bit outside the realm of "physics".

Another thing is the differences in the bikes themselves. It costs more to make a super-light bike. If you're already paying more, you might also pay to have better tires, better bearings, etc. It could be that bike efficiency is correlated with lower mass. So the effects that some would see are real, but not due to the mass difference.

From a physics standpoint: $$F=ma$$ and $$E = Fd$$. If the mass is identical in both situations, and the uncorrelated energy losses are the same, then energy expended is the same.

• Thankful you. That seems plausible but isn’t there more to consider? – Bastian May 29 at 21:04
• Expanded a bit. – BowlOfRed May 29 at 21:37

What are you trying to do? If you're doing physics homework and the bike is not moving relative to the rider, then yes, you could move weight between the rider and the frame (assuming some really talented surgeons working with even more talented materials scientists).

But in practice, the bike moves with respect to the rider. It moves when you're pedaling hard (look at riders sprinting, or doing an intense hill climb). It moves when you're traveling over bumpy surfaces, and for a rigid-frame bicycle becomes unsprung mass, to the detriment of handling around corners.

So I believe that overall, the mass of the bike frame has a significantly higher detrimental effect to the ridability of the bike than it's effect on straight-line acceleration.

• It’s actually not my homework but thanks for your answer. – Bastian May 29 at 20:46
• Sorry -- I didn't mean to imply that. If you're doing a typical one-dimensional physics homework problem, where theory and the real world match, it's simple. But in the real world, things are different. – TimWescott May 29 at 20:59
• That’s why I’m asking this question. I’m interested in the real world effects of the weight distribution. It seems somehow too simple to assume that it doesn’t matter...but it could be true still. – Bastian May 29 at 21:02
• Accelerating hard on a really light bike is a joy, and not because of the forward part -- it's because you can work the thing side to side without feeling it. – TimWescott May 29 at 21:49