Weight question came up today while weighing my plane

[hubcap]

I will give the benefit of the doubt and assume these guys know what they are doing, since it is a "Repair Station" and they do this regularly.

We discussed several items that are on the "heavy" side of the longitudinal center-line, such as the intercooler, and the turbocharger. There were a couple of items mentioned that are in the wing of the heavy side that are not on the other side.

I hope to go fly Myrtle tomorrow for the first time in 6 months.

I doubt it will make much difference in the flying.
 

[wombat]

12 minutes ago, EricJ said:

The scale needs to be reasonably level as well so that the normal force on the scale is aligned with the measuring axis of the load cell.   That said, very small angle changes from level won't affect it much.   The amplitude of sin(theta) doesn't change much for very small values of theta.

This is what I was trying to say.    As a demonstration, I put one side of my bathroom scale on a 4X4 and compared my weight on that with my weight with the scale flat.

The weight difference was 7.4%

Sorry for the gross foot pictures, but my slippers and socks were too slick to stay on the scale when it was on an angle.

 

 

[PT20J]

27 minutes ago, 1980Mooney said:

I think you are exactly right.  

I agree that you need to level the plane to drain the fuel tanks to the same point between different weighings in time to insure the same amount of "unusable fuel" on board.  But if one does properly remove the usable fuel (leaving only "unusable"), at the moment the plane is weighed, the total weight of the plane will not change regardless if the plane is level or not.

If one measures the weight simultaneously from 3 points, using accurate load cells, the total weight will be the same regardless of the level, laterally or longitudinally.  A plane does not change in mass x the coefficient of gravity at that particular point on earth (i.e. "weight") regardless of if it is in a 15-degree climb, a 45-degree banked turn or completely nose down in a dive.  Physics are physics and they don't lie.

Perhaps the "level" talk is a vestige of the old days when they had to use a single massive mechanical scale which required jacking wheels up one at a time.  

I believe that the proper technique according to the maintenance manual is to completely drain the tanks (by removing the sump drains) and then add back the unusable fuel to each tank.

[1980Mooney]

58 minutes ago, wombat said:

This is what I was trying to say.    As a demonstration, I put one side of my bathroom scale on a 4X4 and compared my weight on that with my weight with the scale flat.

The weight difference was 7.4%

Sorry for the gross foot pictures, but my slippers and socks were too slick to stay on the scale when it was on an angle.

 

 

I think what you are demonstrating is the if the load cell is not perpendicular to the earths gravitational pull it will measure the cosine of the weight.  We are not talking about the load cell being unlevel - we are talking about the plane.  For example the plane could have a load cell under each wheel.  If the right main tire goes flat during 2 weighings it will still read the same total weight even though the right wing is now lower than the left side.

In fact looking at the cosine table, your 7.4% error would correspond to about 22 degrees of angle. - that looks about like what you have done.

Edited April 21, 2023 by 1980Mooney

[wombat]

4 hours ago, 1980Mooney said:

I think what you are demonstrating is the if the load cell is not perpendicular to the earths gravitational pull it will measure the cosine of the weight.  We are not talking about the load cell being unlevel - we are talking about the plane.  For example the plane could have a load cell under each wheel.  If the right main tire goes flat during 2 weighings it will still read the same total weight even though the right wing is now lower than the left side.

In fact looking at the cosine table, your 7.4% error would correspond to about 22 degrees of angle. - that looks about like what you have done.

Yup, that's what I was demonstrating.  Originally I phrased it something like "If the individual scales are not level, they might be measuring wrong" 

And the original situation I was envisioning is that the airplane is parked on a sloping smooth surface.   So not only is the airplane not level, any load cell (or scale) will also not be perpendicular to the earth's gravity.

[1980Mooney]

7 minutes ago, wombat said:

Yup, that's what I was demonstrating.  Originally I phrased it something like "If the individual scales are not level, they might be measuring wrong" 

And the original situation I was envisioning is that the airplane is parked on a sloping smooth surface.   So not only is the airplane not level, any load cell (or scale) will also not be perpendicular to the earth's gravity.

I disagree with your comment about the plane. It does not matter if the plane is tilted. At the point it contacts the load cell the plane pushes down directly in the direction of the earths gravitational pull. It could be balancing on the edge of the wing tip. It will have no bearing on measuring the total weight. Only if the loadcell mechanism is tilted, and not directly perpendicular to the gravitational pull of the earth will it read in error. The error will be calculated by basic trigonometry.  

[MikeOH]

6 minutes ago, 1980Mooney said:

I disagree with your comment about the plane. It does not matter if the plane is tilted. At the point it contacts the load cell the plane pushes down directly in the direction of the earths gravitational pull. It could be balancing on the edge of the wing tip. It will have no bearing on measuring the total weight. Only if the loadcell mechanism is tilted, and not directly perpendicular to the gravitational pull of the earth will it read in error. The error will be calculated by basic trigonometry.  

You miss his point (which he explicitly stated): "any load cell (or scale) will also not be perpendicular to the earth's gravity".  He was pointing out to be careful if the ground is not level.  I thought that was pretty clear.

[1980Mooney]

17 minutes ago, MikeOH said:

You miss his point (which he explicitly stated): "any load cell (or scale) will also not be perpendicular to the earth's gravity".  He was pointing out to be careful if the ground is not level.  I thought that was pretty clear.

No you are missing his point - “ So not-only is the airplane not level, ”. He is saying it is a function of both the tilt of the plane and the tilt of the load cell   It doesn’t matter if the plane is not level. It only matters if the load cell is tilted. You are missing my point which I thought was pretty clear. 

Edited April 22, 2023 by 1980Mooney

[T. Peterson]

1 hour ago, 1980Mooney said:

No you are missing his point - “ So not-only is the airplane not level, ”. He is saying it is a function of both the tilt of the plane and the tilt of the load cell   It doesn’t matter if the plane is not level. It only matters if the load cell is tilted. You are missing my point which I thought was pretty clear. 

I always enjoy reading you technical guys, probably out of envy as I wish I was that technically astute.

This little discussion has piqued my interest. This is my question: If your hangar floor had a six inch drop left to right or right to left, even though the whole airplane weighed the same as though level, would the low wheel weigh more than the high wheel?

[T. Peterson]

8 hours ago, wombat said:

This is what I was trying to say.    As a demonstration, I put one side of my bathroom scale on a 4X4 and compared my weight on that with my weight with the scale flat.

The weight difference was 7.4%

Sorry for the gross foot pictures, but my slippers and socks were too slick to stay on the scale when it was on an angle.

 

 

What if you did the same test with two scales, one under each foot. Do you think the total would add up accurately assuming the high scale would show less than the low scale? 

[EricJ]

54 minutes ago, T. Peterson said:

What if you did the same test with two scales, one under each foot. Do you think the total would add up accurately assuming the high scale would show less than the low scale? 

No, the tilted scale reads too low.    You can maybe see how if you imagine the extreme, with one scale on its side and one flat the way it is supposed to be.   The scale on its side may read zero, even if you have half of your weight on it, which would be supported in an axis other than what the load sensor can measure accurately.

This is why it is important to have scales on a level surface, especially if you are measuring something, like an airplane, with multiple scales and adding them up.   As mentioned previously, small deviations from level will not have much consequence, often within the error tolerance of the scales, but as any tilt increases it can become problematic if the angle starts to get significant.

[Hank]

9 hours ago, EricJ said:

The scale needs to be reasonably level as well so that the normal force on the scale is aligned with the measuring axis of the load cell.   That said, very small angle changes from level won't affect it much.   The amplitude of sin(theta) doesn't change much for very small values of theta.

cos(theta) doesn't change much for small angles around zero.    

If i remember right from back in the day, cos(theta) = theta if theta < 5°. This simplifies many calculations, and for weighing your plane, the floor can be up to 5° out of level with the effects showing up only in the third or fourth decimal place, i.e., they are negligible.

You will notice if the floor tilts more than 5° in any direction, that's about an inch per foot; water runs through pipes with 1/4" drop in three feet.

[MikeOH]

Just now, Hank said:

If i remember right from back in the day, cos(theta) = theta if theta < 5°. This simplifies many calculations, and for weighing your plane, the floor can be up to 5° out of level with the effects showing up only in the third or fourth decimal place, i.e., they are negligible.

You will notice if the floor tilts more than 5° in any direction, that's about an inch per foot; water runs through pipes with 1/4" drop in three feet.

It's actually the sine function; sin(theta)=theta (angles in radians, NOT degrees).  Pretty accurate up to about 30 degrees (PI/6 radians).  Cosine is similar but for angles close to 90 degrees, rather than 0.

[EricJ]

11 minutes ago, Hank said:

If i remember right from back in the day, cos(theta) = theta if theta < 5°. This simplifies many calculations, and for weighing your plane, the floor can be up to 5° out of level with the effects showing up only in the third or fourth decimal place, i.e., they are negligible.

You will notice if the floor tilts more than 5° in any direction, that's about an inch per foot; water runs through pipes with 1/4" drop in three feet.

cos( 5 degrees) = 0.9962, so less than a half percent off, which is usually within the error tolerance of the scale, anyway.   However, it's better to not use up the error budget on a tilt if it can be controlled.    cos( 3 degrees) = 0.9986, so less than two tenths of a percent off.   

So that kind of gives an idea.   You're right that 5 degrees is pretty noticeable, so if the scale itself is reasonably level, the error should be pretty small.

That's all not to be confused with error in CG calculation due to the airplane not being level, that can be be significant, even if the scales themselves are level.

[1980Mooney]

1 hour ago, T. Peterson said:

I always enjoy reading you technical guys, probably out of envy as I wish I was that technically astute.

This little discussion has piqued my interest. This is my question: If your hangar floor had a six inch drop left to right or right to left, even though the whole airplane weighed the same as though level, would the low wheel weigh more than the high wheel?

Yes the low wheel would weigh more compared tho the weight when weighed absolutely level. And the high wheel would weigh less by an equal amount. 

[Hank]

4 minutes ago, MikeOH said:

It's actually the sine function; sin(theta)=theta (angles in radians, NOT degrees).  Pretty accurate up to about 30 degrees (PI/6 radians).  Cosine is similar but for angles close to 90 degrees, rather than 0.

Huh. My calculator, in degrees because I HATE radians, shows this:

• Sin(1) = 0.01745
• Cos(1) = 0.9998

And for completeness, tan(1) = 0.01746

[1980Mooney]

46 minutes ago, EricJ said:

No, the tilted scale reads too low.    You can maybe see how if you imagine the extreme, with one scale on its side and one flat the way it is supposed to be.   The scale on its side may read zero, even if you have half of your weight on it, which would be supported in an axis other than what the load sensor can measure accurately.

This is why it is important to have scales on a level surface, especially if you are measuring something, like an airplane, with multiple scales and adding them up.   As mentioned previously, small deviations from level will not have much consequence, often within the error tolerance of the scales, but as any tilt increases it can become problematic if the angle starts to get significant.

He didn’t say “tilted scale”. He just said “lower”. 

[Hank]

2 minutes ago, 1980Mooney said:

He didn’t say “tilted scale”. He just said “lower”. 

If the floor isn't level but has a constant slant in one direction, both scales will read slightly low. Wish I could draw a simple picture!

If the plane is straddling a floor drain and both scales are tilted towards the middle? Dang, I need to sketch this out!!

If both scales are level but one sits higher than the other, you've got a weird floor.

[MikeOH]

3 hours ago, 1980Mooney said:

No you are missing his point - “ So not-only is the airplane not level, ”. He is saying it is a function of both the tilt of the plane and the tilt of the load cell   It doesn’t matter if the plane is not level. It only matters if the load cell is tilted. You are missing my point which I thought was pretty clear. 

Oh, I get your point: to criticize others whenever possible!

You really try so hard to read the most negative interpretation into posts, I've noticed. His entire quote, "So not only is the airplane not level, any load cell (or scale) will also not be perpendicular to the earth's gravity" I read that as pointing out that BOTH are not level...you choose to over reach and conclude he is saying the weights are a FUNCTION of both.  He claimed no such thing.

[EricJ]

1 minute ago, 1980Mooney said:

He didn’t say “tilted scale”. He just said “lower”. 

Derp...yeah.    If the same weight is on two reasonably level scales, they'll read the same regardless of relative height.     If you put the Eiffel tower on four scales and tilt the tower, even if the scales are locally level the CG of the tower moves with the tilt and puts more weight on the scales toward the tilt.   That's the basics of weight and balance.

[MikeOH]

6 minutes ago, Hank said:

Huh. My calculator, in degrees because I HATE radians, shows this:

• Sin(1) = 0.01745
• Cos(1) = 0.9998

And for completeness, tan(1) = 0.01746

Correct.  But, if you try Cos(2) you don't get close to 2!  That's why you have to use radians (unfortunately)...and Cos(theta) <> theta for angles near zero; only near 90 degrees.

[1980Mooney]

15 minutes ago, MikeOH said:

Oh, I get your point: to criticize others whenever possible!

You really try so hard to read the most negative interpretation into posts, I've noticed. His entire quote, "So not only is the airplane not level, any load cell (or scale) will also not be perpendicular to the earth's gravity" I read that as pointing out that BOTH are not level...you choose to over reach and conclude he is saying the weights are a FUNCTION of both.  He claimed no such thing.

No - I just read it how it is written. 

[MikeOH]

10 minutes ago, 1980Mooney said:

No - I just read it how it is written. 

No - You read it how you want it to read.

[wombat]

Beauty is in the eye of the beholder and interpretations are in the eye of the reader. If I wrote something that is being misinterpreted, the fault is at least partially mine.

What I was specifically trying to address was the error of each scale because the scale is not level which would be the case if the entire floor is not level..   As @Hank gave as an example (a better example than mine), a floor that slopes down toward the center,  the aircraft wheels are both at exactly the same elevation but the scales they are sitting on are sitting on a slope. Each scale will individually read less than the true weight that is on it. They would have the same relative error if the entire floor was sloped the same direction, which is the example I was using.

[EricJ]

10 hours ago, wombat said:

Beauty is in the eye of the beholder and interpretations are in the eye of the reader. If I wrote something that is being misinterpreted, the fault is at least partially mine.

What I was specifically trying to address was the error of each scale because the scale is not level which would be the case if the entire floor is not level..   As @Hank gave as an example (a better example than mine), a floor that slopes down toward the center,  the aircraft wheels are both at exactly the same elevation but the scales they are sitting on are sitting on a slope. Each scale will individually read less than the true weight that is on it. They would have the same relative error if the entire floor was sloped the same direction, which is the example I was using.

Yes, and as mentioned above the slope needs to be fairly significant, more than five degrees, to get an error greater than 1/2 of a percent (0.005).   The amount of slope needed to create a significant error in total weight is pretty noticeable.    The error in CG calculation may be significant, though, if the aircraft isn't level.