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Flywheels are another area of unwarranted HYPE. Based on ignorance, claims are too often exaggerated. With the superiority of controllable momentum throttles, flywheels should not be considered for this use. Under the right conditions, they can contribute to much smoother mechanism performance. But they can be very dangerous in emergency braking, due to their uncontrollable momentum, possibly causing damage. The mathematics of momentum are fairly complicated but the proven conclusions in each section can serve as guide lines. Also the actual work to produce momentum effects on a given loco and train will vary drastically and is very difficult to compute or measure accurately. So for a basic understanding of the concepts, rationalized equations will be used to eliminate dimensional conversions. (In the metric system no rationalization is necessary , since 1 cc of water has a mass of 1 gram and cgs applies.) First we will use specific gravity (mass compared to equal volume water) instead of actual density. Steel = 7.8, brass = 9.8, lead = 11.34 and tungsten = 19.3. Tungsten flywheels were offered a few years ago. Since most loco flywheels are cylinders or slight variations, the discussion will be limited to these. The important factor is how much work can the flywheel do to keep a train moving. See PHYSICS for a discussion of the terms and relationships used. Mass (weight) m = d (density) x v (volume) The volume of a cylinder is: (¶ = pi =3.141596) Moment of inertia (J) Work (W) N = angular velocity = RPM W = 1/4 * ¶ * d * l * r^4 * N^2 NOTE: There is another term and value used to compute energy and momentum, the "radius of gyration". This is the radius of an equivalent zero thickness shell or tube, whose mass is that of the cylinder. Simply it is the RMS (root-mean-squared) = .707 times the radius for a plain right cylinder. Usage here is avoided to eliminate confusion. 1/4 and ¶ are constants. Only d, l, r and N can vary. This shows that tungsten could produce about twice as much work as brass. Doubling the length doubles the work. But doubling the radius provides 16 times the work. While doubling the RPM produces 4 times the work. It is obvious that the radius is the most effective factor. A .75" flywheel yields J = 5 times that of a .5" one. Increasing from 3/8" (Athearn 3/4" diameter) to 7/16" gives a work factor of 1.85. It can be shown that removing mass at the axis has far less effect. To compute losses from centered holes, treat the hole as a cylinder and subtract its moment from the whole. A 1/8" center hole in a 3/8" flywheel yields a reduction factor of only .9877. This accounts for the use of many large spoked flywheels to reduce the overall weight. To compute stepped or complex shapes, break down into separate cylinders, find J for each, add solids and subtract holes. For tapered truncated cones the equation is a complicated mess: J = 3/10 * d * v * (R^5 - r^5)/(R^3 - r^3) = 3/10 * d * [¶/3 * l * (R^2 + R*r + r^2)] * (R^5 - r^5)/(R^3 - r^3) J = ¶/10 * d * l * (R^2 + R * r + r^2) * (R^5 - r^5) / (R^3 - r^3) Next in effect is RPM with its square factor. Assume a constant flywheel. A typical road loco running at speed of 90 has a motor RPM of 14000. At yard speeds of 15, RPM is 2333 for a factor of 6. The work factor is 36. So the flywheel is only 1/36th as effective at the lower speed. How much larger must the radius be to provide the same work? Simply the fourth root of 36 (36^1/4) = 2.45 times the original. Not very practical, if you started with a 3/8", you would wind up with a .92" radius (1.84" diameter). Try to fit that one in your loco. Before discussing the energy stored by various arrangements, it should be pointed out that the resulting effects will vary with mechanism types mainly due to friction, gear ratios and rolling qualities. Particularly, friction eats up energy by requiring work to overcome it. For comparison, start with a common flywheel setup similar to Athearn's wide units. There are two 3/4" OD * 3/4" length brass flywheels at 10 k RPM @ 12V and ~ 100 SMPH (smiles per hour). The constants 1/4 * ¶ = .785. U = units or rationalized inch-ounces. Using: W = 1/4 * ¶ * d * l * r^4 * O^2 = units W = 2 * .785 * 9.8 * .75 * .375 ^4 * 10^2 = 2 * .785 * 9.8 * .0198 * 100 = 30.46 U. This may yield coasting from about 30 to 60 inches, which may prevent bunching derailments in long trains, if power is removed. But it could play hell in a cornfield meet. The over all effect is smoother operation and transitions at all speeds. At yard speeds of 15 SMPH the RPM is about 1.5 k. O^2 = 2.25. W = 2.25 / 100 * 30.46 = .689 U. The work ratio is 44.4:1 yielding coasting in the neighborhood of 5/8 to 1 1/4". This should be more than enough to clear frogs and most dirt, considering the long wheelbase and all wheel pickup. Segment cogging effects are reduced to almost imperceptible. Again a good throttle with correct adjustable pulse power is more effective. Next is NWSL brass flywheel 101-6 in a regeared, 108:1 MANTUA RDG A5 GOAT. r = .236, l = .276, RPM = 11 k @ 15 SMPH W = .785 * 9.8 * .276 * .236^4 * 13^2 = .785 * 9.8 * .276 * .0031 * 121 = .796 U. It should be noted that this is greater than the above case due to the much higher motor RPM at 15 SMPH. A direct comparison is not practical because the gear trains, ratios and mechanisms differ drastically. But with a work ratio of about 38:1, a ballpark estimate for coasting should be about an inch or so. Tests show it is enough to avoid stalling at frogs and dirt. Additionally it smoothes running by reducing cogging and, because of the high gear ratio, rod binding effects. Do you really want coasting while switching? The effects of RPM and gearing can be shown by comparing the same loco with the original 26:1 ratio and the same flywheel. RPM @ 15 SMPH = 2.62 k. This yields a work ratio of about 4.8. Compounding this with the slower RPM, cogging effects reduction would be much less. Crossable gaps would be reduced to about .2". But coupling speeds should be in the 2 to 5 SMPH area, if attainable, dropping energy to almost zero. This demonstrates that unless there is a large gear ratio to permit high motor RPM, flywheels are almost useless in switchers operating at slow speeds. This shows that a recently introduced flywheel-worm gear for this purpose, contributes almost nothing to slow speed operation . Even flywheels triple the mass of the heavier example above can not produce realistic acceleration and deceleration distances and rates to duplicate the prototype. This is better left to good momentum throttles. In an emergency too much uncontrollable flywheel momentum can prevent effective stopping and possibly cause a lot of damage. Here again good throttles have an emergency brake position. It appears that the major contribution of flywheels is to yield smoother mechanism performance . Even a relatively small one can help reduce segment cogging to yield non-skewed armature performance equal to skewed. With proper gearing they can improve operation over dirty track. They can even hide the effects of binding side rods and gears in poorer drives. Be aware that the heavy weight of large ones mounted on motor shafts will shorten bearing life, particularly with the sizes used in can motors. Imbalance will only aggravate the wear. It seems most of the larger flywheels are much larger than needed to provide smooth performance, especially when a good throttle is far superior to their over touted momentum effects. While some of the small ones are almost useless unless linked with proper gearing. Although skewed segment motors improve slow RPM performance by reducing cogging effects, by combining flywheels with proper gearing, a free-running mechanism and a good throttle with low end pulses, excellent results can be attained without resorting to a lower powered skewed can motor. QUESTIONS? BACK TO LOCO TESTING BACK TO METHODS INDEX BACK TO REPOWERING KNOW WHY BACK TO REPOWERING TOP BACK TO TESTING POWER PACKS AND TRANSFORMERS |
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