The Leverage Scaling System:
How the leverage scaling system works and some associated problems.
The leverage scaling system, providing the means to scale a car using four bathroom scales, sounds at first like an accurate, inexpensive way to accomplish the task. In the real world, the proper design and implementation of the system is far more difficult and time consuming than it first appears. The theory of using the system is based on the principle of leverage. By having a fixed pivot point on one end, (b), the other end resting on a scale, (d), and a force between the two, (c), a leverage is created. To determine the weight of the corner of the car, it is necessary to find the leverage ratio of the system. This is done by finding the distance from the fixed pivot (b) to the center of force of the tire (c), (A in diagram), and finding the overall length between the two end pivots (B in diagram). To then find the corner weight of the car, take the scale reading, multiply by B, then divide by A. The ratio B/A is the leverage ratio of the system. For example, if the reading on the scale is 200 pounds, the distance from the fixed pivot to the center of force is 1 foot, and the distance between the two end pivots is 4 feet, the corner weight of the car is 200 x 4/1 = 800 lbs.
The primary problem with this system is that it is extremely sensitive to many criteria. First, the pads for the corners of the car must be level. In addition, after the car is on the pads, each individual lever system must be level, which may involve using shims. If using only one scale and lever device, to get an accurate reading it is critical that everything is checked and leveled before weighing each corner of the car. This can be very time consuming. Another critical aspect of the system is that the exact distances (a) must be very accurately determined. One way to do this is by using a pivot such as (c) in the diagram. By placing the pad where the tire sits on a pivot, it finds the center of force (e) of the tire. Due to things such as camber angle and tire construction, the center of force of the tire is not necessarily at the middle of the tread of the tire. To show how important the accurate measurement of the center of force of the tire is, suppose we miss the measurement of the center of force by 1 inch. Using the previous example of a 200 lbs. scale reading and a 4 foot (48 inch) overall length, the result could be either 200 x 48/11 =873 lbs. Or 200 x 48/13 = 738 lbs. This is a potential 135-pound difference in actual weights of the car from the same scale reading. Thus, there is a critical need for a device to accurately determine the center of force of the tire. Other accuracy problems can occur from improper materials. The accuracy of the scale is very important because the error of the scale is multiplied by the leverage ratio, B/A. With the previous example, if the scale being used has an accuracy of 1 pound, the accuracy of the final reading is 1 x 4/1 = 4 pounds. Using a scale with an accuracy of 5 pounds, the final reading has an accuracy of 5 x 4/1= 20 pounds. Additionally, it is necessary to make sure that the scale being used will be operating within its range. Most scales lose accuracy if the weight displayed is within 10% of the limit of the scale. This means that for a 300-pound electronic bathroom scale, a reading over 270 pounds introduces a significant inaccuracy. Also, the beam and the pivot bolts must be sufficiently rigid, as any bending will yield an inaccurate reading. The pivot at (d) is necessary to keep the interaction between the lever device and the scale accurate through the small deflection when the car is put on the lever system. These are a few of the potential problems with this scaling system, and there are more. Compared to a purpose built electronic scaling system, the amount of time that it takes to accurately scale the car is immense. If using only one of the lever devices, everything must be leveled and scaled four times, once for each corner of the car, for every change that is made to the car. If a single ride height adjustment is made, this means repeating the process eight times, moving the car on and off the setup each time. (The ideal approach, for accuracy, is to ROLL the car on and off the scales. Jacking adds further error into the system.) For multiple changes, the time necessary adds up rapidly. With four of the lever devices, the time required is significantly less, but still much longer than with a set of electronic scales. There is also a space problem, as the devices extend three to four feet beyond the edge of the car on each side. Finally, to have everything built properly, using four levers and scales, the total cost is not much less than a set of electronic scales. The net result is a system that although theoretically sound, is extremely difficult and time consuming to use properly at what very quickly becomes an insignificant price difference.
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