Equivalent grade

[jsotto]

Mr. DSchmidt correctly describes a number of factors related to classic prototype curve resistance and superelevation, but keep in mind that the "0.04 percent per degree of curve" resistance translation is for a dry steel wheel on a dry steel rail.

Model railroad applications may involve plastic, nickel silver, steel, sintered iron, and brass combinations, giving slightly different coefficients of friction between wheel and rail, further affected by rail cleaning fluids or the lack thereof.

In recent years, the prototypes have utilized more extensive rail lubrication than in the past to reduce resistance. Locomotive radial truck designs also reduce resistance (and wear).

Superelevation actually slightly reduces the sharpness of a curve with a corresponding slight reduction of friction. The prototype calculation also does not apply precisely to curves of 2 degrees or less, since a new wheel profile will track around uniform curves of 2 degrees or less without flange contact, which is the source of most of the resistance on curves sharper than 2 degrees. Another source of resistance is the skidding effect of a rigid wheelset traveling a greater distance on the outer rail than the inner rail, so periodically one of the wheels has to slip to compensate. The axle absorbs some torsion until the axle stiffness forces a wheel to slip to relieve the torsional stress on the axle.

Most railroads no longer use superelevation greater than 6 or 6-1/2" due to the preponderance of slower freight traffic (vs. passenger) and the higher centers of gravity of covered hopper cars, for example. Heavy cars moving at less than the equillibrium speed of a superelevated curve place more weight on the low rail, causing premature failure of the rail.

Passenger equipment generally has a much lower center of gravity and was typically allowed to operate with 3" of superelevation unbalance to the outside of the curve. In the heyday of the 30s and 40's, most railroads did not use more than 7-1/2" of superelevation. Exceptions are always possible due to specific situations and limited varieties of equipment in a particular situation, but the values above are typical. Some freight equipment standing still on 9" superelevation will fall off the track, because as the weight shifts to the low side, truck springs are compressing, etc. so the center of gravity shifts, too.

As a practical matter, I simply use 5" where I want superelevation in my mainline curves because in HO scale it is enough to be noticed and not too much to cause problems with the equipment. Don't forget to provide a runoff of a least a foot (in HO scale and depending on how long and rigid your cars are) to transition from 0" to 5" suprerelevation and back down to 0". The runoff should be in the spiral easement and is one of the factors used in calculating a railroad spiral easement. That's a whole 'nother subject!

[Anonymous]

Thanks! I guess I didn't think the idea of super-elevation went that far back.

[Anonymous]

I grew up one block from the Missouri Pacific mainline and it began to curve just west of our location and the track was superelevated on the curve! That was in the 1950s. Can you imagine the track speeds of the "glory days" streamliners without superelevated track? We would have seen either a lot of passenger equipment on the ground, or REALLY SLOW passenger trains. No, I can't "imagine" it was much before the 1970s, but I can REMEMBER that it was. Enjoy the hobby.

[DSchmitt]

QUOTE: Originally posted by jsalemi

When did railroads start super-elevating curves? I can't imagine it was much before the 70's, but I'm probably wrong.

The book I got the information from Railway Track and Maintenance was originally published in 1897 as Railway Track and Trackwork.

[Anonymous]

When did railroads start super-elevating curves? I can't imagine it was much before the 70's, but I'm probably wrong.

[DSchmitt]

On the protype (as on the model) a moving train tends to move in a straight line even wnen the rails curve. On a curve force against the outer rail could be high enough to knock the rail out of alignment. Superelevation (raising the outer rail) uses gravity to to cause the train to travel in a curved path. The amount of superelevation used is a compromise since the "ideal' amount depends on the weight and speed of the train and degree of curve.

Charts with guidelines have been issued by various railroads, but ther is no uniformity.

For example: An American Railway Engineering Association Chart lists the following superelevations for a 3 degree (HO 236" radius curve)

20 mph 3/4 in, 30 mph 1-3/4 in, 40 mph 3-1/8 in, 50 mph 4-7/8 in, 60 mph 7-7/8 in and 70 mph 9-1/4 in

The Union Pacific chart for a 3 degree curve: 20 mph 3/4 in, 30 mph 1-3/4 in, 40 mph 3-1/4 in, 50 mph 5 in, 60 mph 7 in

Pensylvania Railroad: 1/2 in, 1 in, 2 in, 3-1/2 in, 5 in, 6-1/2 in

The sharper the curve the higher the super for a given speed, but sharper curves also had lower maximum speeds

On the AREA chart the superelevation for a 20 degree (HO 40" radius) curve is 5-1/4 in at 20 mph

Articles I have read about superelevation on model railroads generally consider it a scenic feature, not a method of improving operation. On both the prototype and the model care must be taken to not make the superelevation too great.

[jwar]

Being the only dumb question is, the one that hasent been asked...so here I go...
Would or could a bit of super elavation reduce the flange to the ball of the rail resistence?

[Anonymous]

Whew that means my friends 3% Grade approaching a 24" Radius curve probably puts a load on that engine closer to 5%. Luckily it flattens out some just prior to the summit that is just past the 90 degree 24"er.

[DSchmitt]

From the book Railway Track and Maintenance by EE Russell Tratman published in 1926:

"Compensating Grades for Curvature. - In order to equalize train resistance, it is usual to reduce the normal grade on curves, so that the combined grade and curve resistance will not exceed the grade resistance on tangent. A general rate of reduction is 0.04 percent per degree of curve, a normal 2 percent bening thus reduced to 1.76 percent on a 6-deg. curve. Other rates are 0.03 to 0.05....." It furher states that "In this as in other matters affecting train resistance, modern practice is goverened by arbitrary rules based upon experience and upon old tests made with relatively light engines and trains...."

In HO scale the 6 degree curve used in the example is 132 inch radius.
A 23 inch radius HO scale curve is 35 degrees. Using the 0.04 figure it is equivilant to a 1.4 percent grade.

I don't know if the prototype guidelines are relevant on a model railroad.

Railway Track and Maintenance has been reprinted by and is available from the National Model Railroad Association. A table giving equivalent radii, in each scale, for various degree of curve is included in the NMRA data sheets.

www.nmra.org

[Anonymous]

Anyone know how to compute the effect of a curve an equivelant grade?