> On the 12"/ft railroads, the leading truck on a steam engine must
> work to keep the engine from derailing by transmitting some torque
> to the engine frame on a curve. (I suppose the smaller wheels have
> less of a tendency to jump the track, or there wouldn't be any point
> in having them.)
Indeed the big driving wheels have a bigger tendency to climb on the
flanges, as, when the flange touches the rail, this occurs under
a smaller vertical angle. Thats why shunter locos without leading
axles are limited to comparativly slow velocities.
> So how come almost all of the leading trucks
> on model steamers are fastened with just one screw, so they can't
> actually help keep the frame rotating into the curve? Doesn't
> the physics scale down?
They do scale down, but under quite sophisticated laws,
which cannot easily be applied to model railways.
I my company we run a 1:5-scale experimental bogie on a roller
rig, so we know the similarity laws quite well.
Masses, inertias, stiffnesses, velocities and so on
all have a different scaling factor, if the dynamical running
behaviour of the model shall be the same as of the prototype vehicle.
(This can be compared to the similarity laws used in aerodynamics
to reproduce the flow and turbulences. Perhaps you remember
the Reynolds factor)
For example, if the scale of length is 1:n,
the masses scale with n**2, the inertias with n**4,
the velocities with SQRT(n), and the stiffnesses with n.
So in order to reproduce the running behaviour of a 100-tons loco
running at 100 km/h, a HO-model would have to weigh about 13 kg
and to run at 11 km/h. You see that those parameters are very
different from those known on model railways.
So you would have to scale the density, which leads to a scaling
factor for the stiffnesses of (n**2) * (scaling of density),
lets say about 5000.
Assuming a stiffness of the bogie-centering-spring of 1.000.000 N/m,
the model spring would have about 200 N/m.
A lateral displacement of 1 mm would result in a force of 0.2 N
(corresponding to 20 Gramms).
This might be a sensible amount for true-scale curves.
But model railways run much, much narrower curves, so the
lateral force would cause a derailment, and not avoid it.
As mentioned above, the physics of model railways are completely
different of those of the prototype: The curves are narrover, and
the masses and inertias cannot be compared at all.
So the model vehicles have to be designed for their special
purpose, and cannot be a "scaled" copy of the prototype.
For most locos the guiding forces of the drive axles are
sufficient, and the leading bogies exist just for optical reasons.
> (One exception was the Varney Casey Jones I had in the 50's,
> which had a very nice centering spring on its lead truck.)
Fine. Of course thats possible, but if the bogie shall have a
real leading function, it has to be pressed to the rail with
a considerable amount of the locos weight, and not just by its own
gravity. So a suspension is needed, which is probabely very hard
to adjust, and might cause problems at the "bumps" and sharp changes
of gradient found on many layouts. Again, also the suspension cannot
be scaled correctly, and most model locos dont have any suspension
at all. And in case of a lead bogie suspension, the friction force of
the drive axles becomes less, and the traction force decreases.
Not to forget the danger of the drive axles to derail now.
And the mass of a model loco and therefore the vertical force is
already much to small according to scaling laws.
I think for all these reasons most manufacturers dont do so,
as the centering spring is not really needed on models,
the effort would be considerable, and it would be a lot of
engineering work to be done to adjust the undercarriage
in order to work safely under all conditions.
Deutsche Forschungsanstalt fuer Luft- und Raumfahrt