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A short discussion of some basic physics may help explain other
discussions or just confuse them more. With a degree in Physics and
years of experience as an Electronic Engineer, sometimes I overlook the fact
that not everyone has a background to understand all the math and jargon.
An attempt to clear things a bit is presented.
Mass and weight are often incorrectly used interchangeably. Grams (mass) and ounces (force or weight) are not technically equivalent measures. Mass is the measure of the quantity of matter in an object, which is constant in space as well as on the earth. While weight is the force on it due to the gravitational effect between its and the earth's mass. Force and acceleration are vectors which have both a magnitude and a direction. While speed and mass are scalars having only magnitude. From Newton's law, force = mass * acceleration or Acceleration is a change per unit time in velocity; a vector made up of speed change and direction. Everything on the earth is accelerated due to its rotation causing a change in direction. Quasi constant over the earth's surface, the acceleration of gravity is about 32.17 feet / (second) s^2 or 9.807 meter / s^2 directed toward the earth's center of mass. In the PFS (pound-foot-second) system; a unit of mass called a slug, weighing 32.17 LB, was defined so In the KMS (kilogram-meter-second) metric system a unit of force, the newton = .2248 lb = 3.6 oz More common in smaller applications, in the CGS (centimeter-gram-second) system, force is measured using the dyne = 2.248 micro pounds = 36 micro oz = 10 micro newton. Under commercial pressure, a newer force, based on the earth weight of 1 gram mass, the gram force (gmf) or gram weight (gmw) was defined. This is now legal in supermarkets and has spread into engineering including small motor torque. You are probably familiar with the DEA use of its big brother, the kilo (kilogram force). 1 oz = 28.35 gmf Of interest, the only HO tractive effort test suggests 1 oz drawbar pull = 14.5, six inch = 43.55' cars, using Central Valley trucks. Kinetic energy is a measure of the work (W) done by a force moving a mass over a distance. You may push against a wall with all the force you can muster, until you are exhausted; but if the wall does not move, no work has been done. In the PFS and the OIS this is measured in foot-pounds or inch-ounces. While the common equivalent in the metric system is the joule. A far less common; a small, scientific, metric unit is the erg: The energy gained though velocity is responsible for momentum in both straight lines or curved as in a flywheel, where the angular velocity is used. A second type, potential energy is a stored amount that could produce work, if permitted to do so. Examples are dry and wet cells or a weight in a plane before it is dropped. In the first cases the energy is chemical; while in the second, the energy was gained by raising the weight to the altitude of the plane. Flywheels store energy upon spin-up. Loco motors produce work by moving a train. Some is stored and appears as momentum or coasting, when power is removed. Not normally used in MR, units of heat energy are the British thermal unit (BTU) and the calorie. It takes work to heat an object. In a steam locomotive, energy is temporarily stored in the steam and later produces mechanical work though the pistons to move the train, while losing some of this energy. Although a static, non-moving entity, torque (T) is measured in similar units of force * distance. Resembling a lever, this is a turning force applied at a distance from an axis, on wheels or gears. In the PFS system these quantities are usually stated in pound-feet or ounce-inches. See TORQUE DISCUSSION The work done during rotation is the torque times the angle (ø) in radians: Power is the measure of work done per unit time or the rate of doing work. In the PFS system the common unit is the horsepower (hp): To confuse the issue, the metric horsepower is: Apparently different standard horses were used. Which is used to rate your car? Since the metric system is used in all electrical and electronic work, the watt is more common: More commonly in electrical work, watts are computed from voltage and current: Your 200 hp car = 149 kilowatts. A house with 200 amp service under full load @ 125 volts = about 25 kilowatts. For model motors I prefer the mousepower (mp) to eliminate leading zeros: Note: ¶ = pi =3.141596 Power work and torque relationships are a bit more subtle, since the distance is around a circle. First, in physics, angles are usually measure in radians. A radian is the angle subtended by a length along the circumference (c) equal to the radius (r). Since the circumference is 2¶ * r and there are 360° around a circle: The important thing to note is that there are 2 ¶ radians around a circle and that 1 revolution = 2 ¶ radians. This is why 2 ¶ or multiples crop up in many equations involving circular and trigonometric functions. The angular velocity is 2 ¶ radians per minute = 1 RPM (revolutions per minute), so the distance (l) traveled in 1 minute at a radius (r) and some RPM is: The force is added to get power and T = f * r. Or power = work per unit time and since the angular velocity is 2 ¶ * RPM: The units for force, length and power will depend on the system used. Power factor (pf) introduces another headache. When a changing voltage is applied to a reactive circuit with inductance (L) or capacitance (C), the produced current waveform lags or leads the voltage waveform. (ELI the ICEman.) In sinusoidal power circuits, the phase angle (phi) is usually measured on an oscilloscope. The power-factor is the cosine of this angle. The apparent power is measured using an ammeter and voltmeter, yielding P (VA) = I * V. Since any straight or coiled conductor carrying current is an inductor, the power factor will almost always be less than 100%. Transformers , motors and switch machine solenoids are all fair sized inductors. Every device that converts one form of energy to another, loses some in the process. All of the energy consumed, eventually ends up as heat. The more efficient the process, the less heat is generated internally. Losses can be attributed to friction, vibration, resistance to electron flow, reluctance in magnetic fields and many others. More often the measurement of efficiency is taken as the ratio of the output power to the input power, expressed as a percentage. Particularly with output, measurements are difficult without specialized equipment and are usually calculated. One fact that is certain, the hotter the converter, the less its efficiency; excluding heaters of course. A classic example is the very hot incandescent bulb, compared to the cooler, more efficient fluorescent tube. Power factor also effects efficiency. We rarely think about the efficiency of our powerpacks , which may range from about 50% for rheostat versions to about 70% for solid state. Switching power supplies may exceed 90%. Transformers usually run from 70% to 90%. Model motors are discussed elsewhere. Electric energy usage bills are charged in kilowatt-hours = 3,600,000 joules: Cells and batteries are rated in ampere-hours since auto starter motors, bulbs and most devices used are rated in amps. Power in watts (p) = current (a) times voltage (v). A 12 v, 200 a-hr battery has an energy level of 2400 watt-hours. DC powerpack outputs were once rated by amperes at the rated voltage (usually 12 v), since most MR devices used the same ratings. AC transformers were usually rated in watts, often with no voltage reference. More recently powerpacks are rated in an apparent power term VA, without voltage or power factor reference. Since, in changing voltages and currents involving reactors (capacitors or inductors), the voltage and current are very rarely in phase, a power factor (pf) of less than one is introduced. Motors, switch machine coils and transformers are inductors. Even filtered DC has a pf of less than one. Since we are stuck with it, we must assume the voltage (12 v ?) and a pf = 1 for estimates. Can a 10 va pack handle a 1 amp motor? I = VA / V: Yields NO! Data supplied with motors do not often clearly state the units used to rate them. They must be determined and converted to common units for comparison. This must be taken into account when computing motor power since: 1 g (wt)-cm /s = .098 watt A motor torque of 1 oz-in = 70556 dyne-cm = .706 newton-cm. = 71.95 gmf-cm. Confusion reigns, but nobody got wet. BACK TO GEAR FUNCTIONS BACK TO GRADES BACK TO FLYWHEELS BACK TO MEASURING INDEX BACK TO MOTOR GRAPH BACK TO REMOTORING BACK TO WEIGHT |
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