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Issue #210 January 2008
INTELLIGENT ENERGY SOLUTIONS
Solar-Powering the Circuit Cellar
Part 2: From the Ground Up
by Steve Ciarcia
Start | Problem Solved | Pole Mounts | Under Construction | Success at Last | Sources & PDF
POLE MOUNTS
One of the things I asked about was the sturdiness of the pole mounts. This isn’t Florida, but it’s still hurricane country. The 16 solar panels had a surface area of 214 square feet, so Sunlight Solar Energy specified using the sturdiest pole mount on the market, a series 225-8/80 top-of-the-pole mount from POWER-FAB (see Figure 1). For the 10¢ × 20¢ array not to be touching the ground if set vertically, the top of the 0.5² thick 8/80 steel pole would have to be 11¢ out of the ground. According to the POWER-FAB installation documentation, it is suggested that the buried end of the pole be 7¢ into the ground and set in a hole (3¢ in diameter) filled with concrete (about 2.25 yards).
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| Figure 1a—This is a pictorial diagram of the POWER-FAB series 225-8/80 solar panel mounting rack used in the pole-mount arrays. b—The angle adjustment plate has six elevation angle set points: 15, 25, 35, 45, 55, and 65°. |
Perhaps because I am an engineer who can’t keep his fingers out of the frosting when it comes to technical things, I started thinking more about the pole mounts in general. After all, these were nothing but big sails in my book, and I wanted to know what would happen when the next hurricane comes blowing through Connecticut. The POWER-FAB spec says that their system is rated at 90 MPH. Of course, at 90 MPH, I have bigger problems elsewhere on the property, so it may be a moot point, but I was still curious.
I went looking for one of those wind load calculators on the Internet and found one at www.sailingusa.info/cal_wind_load.htm. Yes, I know it’s for vertically oriented fabric sails and not angled solar panels, but I just wanted some ballpark figures. Besides, the pole array can actually be tilted vertically (but not as a normally set position), so I suppose it constitutes a legitimate worst case. According to the calculator, the wind load formula (converted to MPH) is:
where SA is surface area in square feet. WS is wind speed in MPH. According to the calculator, 214 square feet produces the wind loads in Table 1.
Speed |
Vertical surface wind load |
Torque |
|---|---|---|
30 MPH |
626.80 lb. |
6,894.8 ft-lb. |
40 MPH |
1,114.4 lb. |
12,258.4 ft-lb. |
50 MPH |
1,741.2 lb. |
19,153.2 ft-lb. |
60 MPH |
2,507.3 lb. |
27,580.3 ft-lb. |
70 MPH |
3,412.7 lb. |
37,539.7 ft-lb. |
80 MPH |
4,457.5 lb. |
49,032.5 ft-lb. |
90 MPH |
5,641.5 lb. |
62,056.5 ft-lb. |
| Table 1—The wind loading on the 214 sq. ft pole-mounted panels is substantial and a lot of thought went into dealing with the torque produced at the base when this much force is applied to the top of an 11¢ moment arm. |
After you have the amount of force that the wind-loaded array is pushing against the top of the pole, you have to translate that into the fact that it becomes one long lever arm trying to bend the pole where it goes into the ground. Basically, it’s all converted to being one big 11¢ torque wrench, where torque = force × length (see Table 1).
This certainly seemed like a lot more force than I am used to dealing with, but the POWER-FAB features and specifications brochure clearly says, “Standard (225 sq ft) mounts are designed and warranted to withstand 30 lb/sq ft (approximately 90 MPH or 145 km/hr).” Do the math with 225 sq ft at 30 lb/sq ft and it is over 70,000 ft-lb of torque on an 11¢ pole. They must know what they are doing. Who am I to be a skeptic?
Still, I’ve always been a hardware guy and virtual claims are a hard sell, so I spent an entire day on the Internet re-experiencing why I chose electrical engineering instead of civil or mechanical way back when. I can’t say that I know enough to build a bridge or pipeline, but I’ve familiarized myself enough with cantilevered beams and moments of inertia to last me the rest of my life. All I can say is that after spending a day deciphering formulas and plugging numbers into online engineering calculators, that if the concrete base is secure, that pipe ain’t moving.
Even with 6,000 lb of force applied at the top of the 750-lb pole, any movement would be imperceptible compared to everything else going on at the same time (at 90 MPH). I also convinced myself that this long lever arm issue wasn’t a big deal either. The biggest single factor governing the strength of the pipe is the outside diameter—in this case 8.625². If a pipe is subjected to sufficient force, it will bend and the cross section will become oval at the interface location. This is pure elastic deformation, and the pipe cross section will return to normal when the force is removed. If the force is high enough to bend the pipe to the point it exceeds elasticity, then “strain hardening” occurs, which strengthens the pipe to resist more bending. When the force is removed in this case, however, the pipe will remain in the bent position. The final condition is when the force is great enough to exceed both previous conditions and the cross-section simply collapses and the pipe buckles.
The fact that this pole is set in concrete at the interface location where buckling might occur and the wall thickness is 0.5² immensely reduces any chances of buckling. The net result is that any failure-mode calculation regarding the pole pretty much gets down to looking at the tensile strength of steel as the limiting factor.
While it takes some pretty hairy math for exact numbers, a back-of-the-envelope calculation seems to illustrate that there is sufficient safety in the pole mount. Note that 62,000 ft-lb of torque translates to a tension of 93,000 lb on the tension side of the 8² pipe. With an 8.625² diameter and a wall thickness of 0.5², there are several square inches of steel resisting that tension—let’s just say it’s 5 square inches for approximately a 10² arc of the circumference to be conservative. Therefore, we’re exerting a pull of about 93,000/5, or 18,600 psi, on the side of the pipe that’s in tension.
Ordinary structural steel has a yield strength of 36,000 psi (high-strength steel is twice that or more), so I think we have plenty of margin even in a full hurricane. I’d certainly have bigger problems before the pole bends.
I loved the idea that Sunlight Solar Energy was going to be doing the pole mounts, but giving someone an impossible task wasn’t going to get me a completed PV system, even if it was their responsibility. Since I had concluded that the pipe was never going to bend and everything comes down to making sure that the concrete holding it doesn’t move either, I decided to dig a test hole where the pole mounts were going and see what 7 feet down looked like. I backed my trusty backhoe up to the designated area and started digging (see Photo 1).
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| Photo 1 —I suspected that they might have some problems installing standard concrete piers for the pole-mounted arrays. So, I decided to dig a test hole. Six feet down, I hit ledge. Time for Plan B. |
I suspected it before I even started the tractor. After all, I wouldn’t already own a backhoe if I didn’t encounter rock every time I picked up a shovel around this place. I hit ledge at about 5.5¢ to 6¢ deep. (The ledge was an irregular surface.) No simple 3¢ diameter, 7¢ deep, by-the-book pole mount installation here, guys. ;-)
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