The Why - Rotational Mass Moment of Inertia

March 22, 2018

“Rotational mass moment of…. What? Yep. we're geeks, no surprises there.

But this should explain a different way to consider wheels.

What are we on about here? If you’re going to fixate on the weight of a wheelset, you really should be asking more on its rotational mass moment of inertia.

Rotational inertia affects how lively a wheel feels and it’s responsiveness to acceleration changes. In essence, it has a greater impact on how a wheel performs than its static weight.

As cyclists we’re fixated on static weight, it’s because it’s a primary unit of measurement (i.e distance, time, mass) so it’s easy to rationalise this, especially since all other cycling components are measured in static weight. Mass moment of inertia is a multivariable and multidimensional unit (mass square meter or kg.m^2) and far more difficult to rationalise, it’s why we don’t hear much of it as it’s almost a 2nd language. Ok, promise, geek part over, kinda.

Percentages are helpful, they can be visualized. For comparison purposes, If we take a shallow wheel (say 38mm) and a deep wheel (say 50mm) and keep all factors of hubs, spokes and nipples the same. There is approximately 7-9% difference in rotational inertia depending on the rim mass, which will also form a baseline number to compare against.

This percentage difference is significant enough to justify different products (i.e. climbing wheels vs aero wheels), otherwise climbing wheels wouldn’t exist when considering aero gains do exist.

Geek Fact: The further an object is from its center of rotation, the greater the impact on its rotational inertia. So with that in mind, rims, nipples, and spokes in that order have the biggest impact on how lively and responsive a wheel is. Hubs on the other hand, barely have an impact on rotational inertia due to its close proximity to being at the centre of rotation.

One good example where we applied this knowledge is our 3 Series wheelset where:

  • A 5-6% favourable gain was achieved by having 20g lighter rims developed for us and using aluminium nipples (saving a further 15g) when compared to the original standard rims built with brass nipples (with spokes and hubs considered the same).
  • By contrast, weight differences between a 240g and a 180g rear hub produced a 0.2% difference or negligible effect.

This 5-6% improvement isn’t to be scoffed at, especially when compared to our baseline number previously mentioned. This should give some insight into what a little extra care and development yields.

By targeting rotational mass over static mass (i.e. hubs) we ensure our wheels are among the most responsive and lively on the market.

It’s also one of the reasons we committed to tubeless road wheelsets as the tyre and tube (or lack of tube) is the furthest mass from the center of rotation.

So in conclusion, if wheelset weight is of primary focus to you, please consider the devil in the details. You may find yourself riding wheels that accelerate and respond faster had you not. 

Should you wish to know more, please don't hesitate to get in touch and I’ll be happy to discuss the above, including the maths behind it.

Regards

David

Ronin Cycling

Post Note: In saying all this, it’s an accumulative gain here and every little bit helps, our previous blogs covered rear wheel lacing patterns and preference for 2X both sides of a rear wheel, the benefit of hub selection in gaining a favourable geometry to optimize spoke tension balance and now rotational mass.

In my next technical blog, I’ll be sharing the aerodynamics of our rims and the Computational Fluid Dynamics work that we undertook to verify they don’t just look aero.