Formula for working out drag on curves

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I am almost at track bed stage and as on my previous live steam layout want to incorporate a 16’ dia spiral. Through experimentation I have found my Accucraft (battery) K27 will haul 4 AMS Jackson Sharpe coaches up a STRAIGHT 1:60 gradient. It wheel span at 1:48. The gradient on the spiral would need to be 1:60 but I wonder if the drag on the radius (8’) may tip the balance. I can’t set up a trial spiral without extensive work so wondered if there’s a simple rule of thumb way to find the extra drag.
The coaches could probably do with roller bearings. I have already removed the electrical pickups which made a slight difference.
 
Not sure that anyone will be able to come up with a mathematical formula for your problem. But 10/10 if they do, problem is that each coach is likely to have a different rolling resistance and then likely different locomotives will have different pulling powers. You may find perversely that a Stainz may manage your consist with no problems. Being a heavy 0-4-0 helps with pulling power whereas you K27 also has a Tender to lump up the grade.

Why not turn a hinderance to a feature and have a siding for a helper loco to assist the K27 up the Spiral?
 
I hadn’t thought of that idea :-)
The tender is extremely heavy especially with the batteries etc on board. I could live without the spiral as I could sink part of the layout to keep the whole lot dead level, but not such an interesting line to play with!
 
Cuttings are a pain! - They collect debris, and can get waterlogged..

And, as you say, you can't see the train! :(
 
rusty spike said:
I hadn’t thought of that idea :)
The tender is extremely heavy especially with the batteries etc on board. I could live without the spiral as I could sink part of the layout to keep the whole lot dead level, but not such an interesting line to play with!
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I would have thought that at 16 ft diameter, the drag will be fairly minimal. I don't notice any drag at 10ft, but I definitively do on the few 8ft curves that I have (I have some curves that go 10ft - 8ft - 10ft).

Just because I don't notice it, doesn't mean it's not there - equally, I only have one AMS Jackson Sharpe.

However, Murphy's law suggests that the curvature could be the last straw .......................
 
Flip your stock over, and spin the axles by hand.. - You DO lubricate your axles, don't you?

You sometimes find a tight axle, or two.. These can make one heck of a difference.
Also, any bogies (trucks, US) that do not articulate freely? - All adds to drag..

PhilP.
 
So don’t forget either the inside or outside wheels will always slip on a curve, any curve, when on a fixed axel, so the friction on the slipping wheels will cause the drag.
 
JimmyB said:
So don’t forget either the inside or outside wheels will always slip on a curve, any curve, when on a fixed axel, so the friction on the slipping wheels will cause the drag.
Click to expand...

Allow me to expand on that comment. That is the reason that railway wheels are not flat, but rather, coned (usually 1 in 20). This is to allow the wheels, fixed on the same axle, to rotate and travel around curves with minimal slippage. The inside rail of a curved track, is a shorter distance than the outside rail. The cone shape of the wheels means that the further away from the flange you are, the smaller the diameter of the wheel. So then, the larger diameter follows the outside (longer) curved rail, and the smaller diameter, the shorter inside rail. This is why we also have gauge widening on curves.... to allow sideways movement of the wheels so that the wheels can adjust their line.
 
Gavin Sowry said:
Allow me to expand on that comment. That is the reason that railway wheels are not flat, but rather, coned (usually 1 in 20). This is to allow the wheels, fixed on the same axle, to rotate and travel around curves with minimal slippage. The inside rail of a curved track, is a shorter distance than the outside rail. The cone shape of the wheels means that the further away from the flange you are, the smaller the diameter of the wheel. So then, the larger diameter follows the outside (longer) curved rail, and the smaller diameter, the shorter inside rail. This is why we also have gauge widening on curves.... to allow sideways movement of the wheels so that the wheels can adjust their line.
Click to expand...
Allow some further clarification:

The taper in the treads is not for curves, it is for self centering down the straights.

The fillet (between the tread and the base of the flange) provides the larger diameter to allow travel without slippage.

This is one of the reasons we have slippage in our scale, as the fillet is not sufficient to allow a large enough diameter on the outer wheel on our over tight curves, way tighter than prototype.

That's also probably the reason that many wheels don't even have a fillet.

Also the gauge widening on curves is normally to accommodate the wheelbase of the trucks which again is woefully "long" compared to our curves (way tighter than prototype)

(I was schooled by a long time railroad track inspector, who has taught me many things about how stuff works)

Greg
 
Greg Elmassian said:
Allow some further clarification:

The taper in the treads is not for curves, it is for self centering down the straights.

The fillet (between the tread and the base of the flange) provides the larger diameter to allow travel without slippage.

This is one of the reasons we have slippage in our scale, as the fillet is not sufficient to allow a large enough diameter on the outer wheel on our over tight curves, way tighter than prototype.

That's also probably the reason that many wheels don't even have a fillet.

Also the gauge widening on curves is normally to accommodate the wheelbase of the trucks which again is woefully "long" compared to our curves (way tighter than prototype)

(I was schooled by a long time railroad track inspector, who has taught me many things about how stuff works)

Greg
Click to expand...

That's what I said, in a different form of English. I was trying to keep it in simple terms, so folks could understand it. Yes, your man has taught you well.
I started my career in railway track engineering 49 years, 4 months, 3 weeks, and 2 days ago........
 
Gavin Sowry said:
Allow me to expand on that comment. That is the reason that railway wheels are not flat, but rather, coned (usually 1 in 20). This is to allow the wheels, fixed on the same axle, to rotate and travel around curves with minimal slippage. The inside rail of a curved track, is a shorter distance than the outside rail. The cone shape of the wheels means that the further away from the flange you are, the smaller the diameter of the wheel. So then, the larger diameter follows the outside (longer) curved rail, and the smaller diameter, the shorter inside rail. This is why we also have gauge widening on curves.... to allow sideways movement of the wheels so that the wheels can adjust their line.
Click to expand...
Greg Elmassian said:
Allow some further clarification:

The taper in the treads is not for curves, it is for self centering down the straights.

The fillet (between the tread and the base of the flange) provides the larger diameter to allow travel without slippage.

This is one of the reasons we have slippage in our scale, as the fillet is not sufficient to allow a large enough diameter on the outer wheel on our over tight curves, way tighter than prototype.

That's also probably the reason that many wheels don't even have a fillet.

Also the gauge widening on curves is normally to accommodate the wheelbase of the trucks which again is woefully "long" compared to our curves (way tighter than prototype)

(I was schooled by a long time railroad track inspector, who has taught me many things about how stuff works)

Greg
Click to expand...
Which is why (slightly off-piste) you need to ensure that axles have a little side play, and we're back to making sure they're well lubricated.
 
Gavin Sowry said:
That's what I said, in a different form of English. I was trying to keep it in simple terms, so folks could understand it. Yes, your man has taught you well.
I started my career in railway track engineering 49 years, 4 months, 3 weeks, and 2 days ago........
Click to expand...

You have been taught well Obi Wan, the force is strong in you....

David
 
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Paradise said:
And the term 'sinusoidal oscillation' wasn't even uttered once. ;)
All I can say about that is...

Hunting_oscillation_section_ja_150px.gif
Hunting_oscillation_plan_ja_150px.gif
Click to expand...

Another term would be "hunting"!
 
Paradise said:
And the term 'sinusoidal oscillation' wasn't even uttered once. ;)
All I can say about that is...

Hunting_oscillation_section_ja_150px.gif
Hunting_oscillation_plan_ja_150px.gif
Click to expand...
Vic Mitchell (of Middleton Press and Ffestiniog Railway fame) built an axle with a large pair of truncated cones - no flanges - to demonstrate at the Midhurst Model Engineering Exhibition how train wheels stay on a track.

Not only, but also - the Docklands Light Railway (in London) has wheels that have a more pronounced slope (dunno the proper term) to enable trains to go around sharper curves, but the trade-off is that speed is limited to 50 mph (if my memory serves me well).
 
I think the treads on railway wheels are typically about 3% taper but that proved unstable for high speed trains so they made tolerances smaller and had far less angle to the tread taper to keep them on the track.

 
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They even used some G Scale Track for the cone tests. Wonder what skip that went into or perhaps Cpt. Slow purloined it for a G scale railway.
 
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