# Physics of weight loss on bikes

#### Red Lemon

##### New Member
Hi, I figured if I was going to find an answer to this anywhere, it'd probably be here. With so many PhDs knocking around, someone has to be a physicist or engineer. I hope it's not on the wrong part of the forum, I couldn't really find one that it fits into properly.

Right, here goes...

We're always told that the wheels are the best place to lose weight on a bike, as it's rotating mass, which has a greater impact on the force required to accelerate. What I'm looking for is a way (purely out of interest) to quantify the difference between rotating and non-rotating mass.

The rims on my bike right now are 525g per rim. I'll shortly be upgrading them to a set that weigh 400g per rim.

If this was non-rotating mass, big deal. I weigh 80kg, the bike weighs about 23. Seeing as F=ma, 102.75kg isn't going to accelerate much faster than 103kg.

Seeing as the 250g saving is rotating mass, is there any way to estimate roughly the amount of static mass you'd have to lose to have the same effect, or does it require knowledge of a whole bunch of other variables? The radius is approx. 330mm (13").

#### Monty Dog

##### New Member
Moment of Inertia calculations for a rotating object consider the mass squared and radius, therefore for a wheel of the same radius, the energy increase is calculated as the squared of the weight difference. For static mass, there is no 'squared' i.e. energy expenditure is linearly proportional to mass. Simple stated, halving the weight of the frame will only save half the energy, whereas halving the weight of the wheels will save your three-quarters for the same given speed and conditions. Obviously, it's a little bit more complicated, particularly as aerodynamic drag is the biggest factor above about 40kph.

#### Oddsos

##### Über Member
While saving rotating mass may seem a good plan you will probably find it has a negligable effect on your performance. Reducing the mass of your bike will only reduce the energy required when you are accelerating.

Unfortunately most of the energy expenditure on a bike is in struggling against air resistance to maintain speed rather than continuous acceleration. This means that a heavy, aerodynamic rim will trump a light box section rim in performance terms. Mavic Cosmic Carbones are pretty weighty, however they are popular because they are durable, aerodynamic and have an aluminium braking surface.

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#### Red Lemon

##### New Member
Thanks for the responses.

I should admit I'm an MTBer, so outright top speed isn't that important to me. Being able to accelerate hard out of tight corners and stomp up short, steep slopes is more important than being able to effortlessly maintain 30mph or more.

#### asterix

Oddsos said:
While saving rotating mass may seem a good plan you will probably find it has a negligable effect on your performance. Reducing the mass of your bike will only reduce the energy required when you are accelerating.

..and climbing hills of course!

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#### Red Lemon

##### New Member
Sorry, don't know where I got 23 from. 13 is what I meant to say, but got 23 stuck in my head...

#### derall

##### Guru
If you're interested in any of the physics of cycling - including the rotating mass problem - then Whitt & Wilson is the best place to look. I think it's out of print at the moment, but there are copies to be had if you hunt around.

#### barq

##### Senior Member
The third edition is in print, but authored by David Gordon Wilson with contributions from Jim Papadopoulos. David Whitt died so he is no longer listed as an author. It's a great book - really worth the money.