Tudor MT5402 - Balance Wheel Size

[mzinski]

I’ve finally succumbed to my multi year interest in the Tudor Black Bay Fifty-Eight (M79030N). Yay for me! 

(Gratuitous wrist shot, can’t help it)

So what’s the first thing I do? Obviously open the case back to have a look at the in-house calibre MT5402. It’s a handsome, if not utilitarian movement. But what struck me immediately was the size of the balance wheel - it’s small. 

Can anyone offer some insights or speculation as to why it would be designed so small? 

My first instinct is the small balance wheel allows for a smaller movement. But clocking in at 26mm diameter I don’t think this would be the rationale. That larger than an ETA2824 but smaller than a Rolex 3135. But the Tudor has the smallest balance wheel. So maybe, maybe not. 

My next thought is the smaller wheel somehow has an impact on the timekeeping. But here’s where my limited knowledge ends. Why would a smaller balance help timekeeping? It is a COSC movement and goes thru Tudors own superlative testing. 
 

Let me know what you think. 

[Nucejoe]

In basic dynamics,

Moment of intertia   I     is equal to product of m mass by square of its distance from axis of rotation.

I=m×r**2

Lets plug in some numbers for r

r=1    >>    I=m

r=2     >>   I=4m

3=3     >>  I=8m 

r=4     >>   I=16

so, you see the effect of increasing the radius of balance wheel. Bigger balance was the answer to attaining certain moment of inertia out of less mass, which is one of the two good that came out of bigger balance.

The smaller the mass the samller the impact of shocks on pivots.

Obviously Tudor has chosen to increase the mass of balance wheel, perhaps they are so sure of their shock system and hardness of the pivots as well as their poising and adjustments technique.

Regs 

Joe

[mzinski]

14 hours ago, Nucejoe said:

In basic dynamics,

Moment of intertia   I     is equal to product of m mass by square of its distance from axis of rotation.

I=m×r**2

Lets plug in some numbers for r

r=1    >>    I=m

r=2     >>   I=4m

3=3     >>  I=8m 

r=4     >>   I=16

so, you see the effect of increasing the radius of balance wheel. Bigger balance was the answer to attaining certain moment of inertia out of less mass, which is one of the two good that came out of bigger balance.

The smaller the mass the samller the impact of shocks on pivots.

Obviously Tudor has chosen to increase the mass of balance wheel, perhaps they are so sure of their shock system and hardness of the pivots as well as their poising and adjustments technique.

Regs 

Joe

So what’s the desired result of a balance wheel? Low moment of inertia? 
Based on the equation, doubling the mass results in a lower moment of inertia compared to doubling the radius. 
What is the goal when designing a balance wheel? Make it as big (largest radius) as possible? Or as light? Or as heavy? 
 

[Nucejoe]

4 hours ago, mzinski said:

What is the goal when designing a balance wheel? Make it as big (largest radius) as possible? Or as light? Or as heavy? 
 

Hi M,  Nice watch.

Invisige/ ink mark a point on the rim of the balance wheel, you want the point to travel max distance per unit time without rebanking, the larger the wheel the longer the distance the points travels, increasing  the frequency/beat produces the same result.  Higher beat in modern watches increases accuracy, which is why you want to maximize the said traveled distance.

A repairman's accuracy to regulate a watch is limited, by his skill and the regulator design, so regulating is inexact, we can only improve accuracy when regulating.

Apart from inexactness with regualtor pin- boot slot. The ratio of the inaccuracy in moving the regulator arm to regulate ,to the distance the said point ( on the wheel) travels is practically the inaccuracy of regulation. 

I hope johnR concurs and finds us some illustative explanation on this, but he is smart he waits until I say all I know in ten words or less before showing up.  

As to why Tudor has chosen to increase the mass, I am just guessing they would like to see watches go to their authorized centers for service.

I see no dynamic enhancement in massive wheels other than making some space available for other components in the escapement.