# Francesco Longo's formula



## franc1960 (Dec 13, 2016)

I have the honor to submit to your Lordships a new interesting little formula on the model trains. I chose this forum first, where talk about it:
I come to the point:
It uses a single measurement system, preferably the MKS.
Suppose you have a scale model and a real train.
we denote the scale with p (H0 example: p = 87)
we denote the speed of the model with v, [meters per second],
We denote the mass of the model with m. [Kg]
we denote with g the acceleration of gravity [about 9.81 meters per second squared]
denote by r the radius of curvature of the track [m]

Given the above:

the weight of the model will be :

(M) x (g) [newton]

while its centrifugal force, being the centrifugal acceleration = v squared divided by r:

(M) x (v ^ 2) / r [newton]

the weight of the real train will :

(M) x (g) x (p ^ 3) [newton]

while the centrifugal force of the real train will :

(M) x (p ^ 3) x (v ^ 2) x (p ^ 2) / ((r)x(p)) = (p ^ 4) x (m) x (v ^ 2) / r

So in summary it must be true that:

Kmodel = (p) x (Kreality)
where
Kmodel = the ratio between weight and centrifugal force in the model
Kreality = the same ratio for the real train
p = the scale factor
Which confirms that the models have a stability factor of their scale

Or in other words This leads to the conclusion that the ratio between weight and strength centrifugal force in the model is p times greater than in the real train.


Conclusion (a bit contrary to intuition would suggest that the same behavior):

Each model shows a cornering stability proportional to its scale (not the gauge)

therefore eg. H0 scale models shows a factor stability that is 87 times respect the true trains
H0e scale models shows a factor stability that is 87 times respect the true trains
N scale models shows a factor stability is that 160 times respect the true trains
z scale model shows a factor stability is that 220 times respect the true trains
Thanks for your attention: hello:


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