If you are 400 pounds and all you have is a scale which weighs up to 250 pounds can you get two scales (250 pound limits) and stand up with one leg on each and add up the weights measured by each scale to get your actual weight?
Yes, but your accuracy rate suffers. If each scale is accurate to +/- 1 lb., together, two scales would only be accurate to +/- 2 lb.
True, though this is something of a “worst-case” scenario - it applies when the scales are inaccurate in the same direction.
Another problem is getting stable readings. As you look at one scale there is some tendency to move some of your weight that way, which of course changes what you read.
There another variable in here which doesn’t necessarily make the problem an additive one…
Some of the force exerted on the two scales is lateral since your center of gravity is between the two scales, but the scale was manufactured assuming your center of gravity is directly above the scale and all the force would be directed downward.
The difference might be slight, but the lateral force would slightly increase the friction between the supports between the movable top part of the scale that you’re standing on, and the bottom stationary base. Because some of the weight is being exerted laterally and gets transferred into extra friction your weight may be under-reported. A great deal depends on the design of the scale.
The usual method of “adding” errors is the root-sum-square. In this case I believe the most probable error is sqrt(2) = 1.4 lb.
In light of aaelghat’s perfectly sound observation, you’ll get the most accurate results if you put the scales as close together as possible, though don’t let them touch as this might affect the result.
You should always assume worst case when adding errors, unless there is a good reason not to. Knowing the most probable error (which BTW seems to assume independence between the two source which seems unreasonable) doesn’t help much in this context.
Sorry, but calculating “worst case error” is unrealistic (and unsound) for the vast majority of applications. As correctly stated by David Simmons, most metrologist use a statistical approach when calculating propagation errors. A very common and simple method is the root-sum-square (RSS) calculation.
I agree with you in general, Crafter_Man. For example, when calculating the tolerance stack-up of multiple parts, it’s unrealistic to assume a worst-case error, when that error is extremely unlikely.
However, muttrox has a good point in this particular case; namely, that the errors for each scale are quite likely not independant. Since the scales are presumably of identical (or at least similar) manufacture, and operating in the same environment, any errors introduced would likely affect both scales in the same way, and the error of each scale would most likely be in the same direction.
And I disagree (somewhat) with aaelghat’s observation. It’s true that there may be a lateral force between your feet and the scale (assuming that your feet are outboard of your hips). I should note in passing that this lateral force is not due to your center of gravity being offset from the scale, exactly. It’s more (or rather, also) due to the fact that your legs are jointed, giving a different force transmission through the body. For example, consider placing a chair on the same two scales and sitting on the chair. Your COG is still offset from the center of the scales, but the chair does not transmit a lateral force to the scale, because its legs are rigid.
Anyway, the lateral force you get from standing directly on the scale is in addition to the weight force; the weight is not being exerted laterally. That means your weight won’t be under-reported because it’s transferred into extra friction. However, there still is a friction force on the scale due to the lateral force. It isn’t clear to me what effect that force will have on the scale accuracy, if any. (For reference: how a bathroom scale works) It might cause the top and bottom of the scale to rub, thus under-reporting the weight. It might add an additional torque on the internal levers, thus over-reporting the weight.
I agree with the conclusion but not the reasoning.
The position of the center of mass doesn’t matter. What matters is the angle of force. If you stand on just one scale, the force on the scale is vertical because there’s nothing to push sideways against. But if you stand on two scales, you can push the two scales apart or together horizontally, which may cause an error.
It depends on how the error was determined. In this example, it would depend on what “±1 lb.” means.
If the error refers to non-linearity error, which is a systematic (and thus repeatable) bias in the reading as a function of weight, then I would agree. But if it refers to random error, you would assume the correlation coefficient is 0 and thus add the uncertainties in quadrature (using RSS).
Personally, I think if you already weigh 400lb+, it’s not like a half-pound margin of error is going to matter in any significant way.
“Woohoo, I lost half a pound today! Now I can fit into that tuxedo!”