Tilt-up wind turbine/anemometer tower problem, redux

Today we calculated the actual vs. theoretical load on the tilt-up tower with the intention of checking the engineering safety margin, but ran into difficulties with the winch and made other errors. In particular, our load cell was reading incorrectly. Here is a partial fix:

What you know:

1. The tower is made of three 30-foot sections, each weighing 253 pounds
2. The gin pole when first manufactured weighed 369 pounds and was 18 feet long
3. Now it is 13 feet long
4. Payload (anemometry equipment) is less than 50 pounds
5. We will use pounds-feet, not Newton-meters, because the tower (a Bergey Excel 10kW model) was originally engineered using US "customary units"
6. This is normal. Much American engineering still uses these units

How to do the calculation:

1. Imagine the tower as a rigid lever with a 90 degree angle, like a crow-bar
2. Calculate the turning moment when the tower is horizontal:

• The center of gravity of a uniform shape tower 30 feet long is at 15 feet
• The weight of the tower is 3 x 253 pounds per section + 50 pounds payload = 809 pounds
• The turning moment is 809 pounds at 15 feet = 809 pounds x 15 feet = 12,135 pounds-feet

3. Calculate the gin pole turning moment:

• The weight of the gin pole is 13/18ths of 369 pounds = 266 pounds
• The center of gravity is 7.5 feet
• The turning moment = 266 pounds x 7.5 feet = 1,995 pounds-feet
• This bears only when the gin pole begins to angle away from the vertical
• This is why manual effort is required to tilt the tower in the first place, and to slow the final movement back to the vertical (so the rear anchor doesn't receive a shock load)

4. Calculate the winch force needed when the gin pole is vertical:

• The force that must be opposed by the winch when the tower is horizontal and the gin pole vertical is 12,135 pounds feet (minimum) 
• The gin pole lever arm is 13 feet
• 12,135 pounds feet divided by 13 feet is 934 pounds

5. Calculate the force based on the angled pull of the winch to the winch anchor:

• The winch doesn't pull perpendicularly to the gin pole. Instead it pulls at an angle down to the gin pole anchor
• The gin pole is 13 feet long. This length is represented in both the opposite and adjacent, so the starting angle of the pull is 45 degrees
• 934 pounds divided by cosine of 45 degrees = 934 pounds/0.70 = 1,334 pounds
• This means that all items in the system are within a safety margin of 100% or X2. The weakest links in the system are the smallest shackles at 4,000 pound rating. Since this was the main point of the exercise, we're good.

6. Compare to actual load as reported by the load cell.

• The actual reported by the load cell, once we solved the difficulty with the winch, was 1,100kg, which is 2,425 pounds, way too much, so something is either wrong with our theoretical load, or with our load cell
• The best explanation is load cell mis-calibration. We had experimented using humans of known weight (the only experimental "masses" large enough that we had), and discovered the load cell was over-reading significantly. Earlier too, I had weighed the spare tower section with the load cell at 340 kg, way too much
• The manufacturer's reported actual weight at 253 pounds is equivalent of 114 kg, so 114kg/340kg provides a possible correction factor of 0.34
• 2,425 pounds x 0.34 is 824 pounds, which is much closer to our actual result
• This isn't very satisfactory, but the best we can do until we get the load cell re-calibrated