Computing the unbalance:

• domeWeight*domeRadius*sin(grCmZa)
• -chWeight*chRadius*sin(chEZa)
• -chCouterWeight*chCounterWeightDistance
• ResidualTorques: coming from asymmetries in the azimuth arm: vertex shelter, stairway topchord to bottom chord,etc.

• Wdome/Wch = 6.02
•  (from y08-y09 fit to tiedown tensions).
• the Dome center of mass za (grCmza) is 1.913 degrees downhill from the dome encoder za: grEZa.
• see y08-y09 fit to tiedown tensions.
  
• With the ch at 0, the dome balances the other side at zaEGr0=6.6  degrees or zaCmGr0=4.56 degrees.
• from td tension fits y08-y09
• When the zaEch = 8.83, the az arm is balanced with zaEGr = 7.968 degrees.
• See az swings to minimize the unbalanced moment.
• Dome weight: 215 kips.
• From jose Maldonado weighing the dome back in 2003.
• Ch counter weight radius (from the drawings) about 145 feet.
  

• ch counter weight: 45 kips
• ch weight: 35 kips
• ch za encoder to za center of mass. assumed to be 0.
• Radius for ch and dome center of mass: 430 feet.

• Residual azimuth arm torque (from vertex, stairway, etc.)
• compute using the grCmZa that balances when zaCh =0
• tqRes=Wgr*Rgr*sin(zaCmGr0) - Wcw*Rcw
• tqRes=215*430.*sin(4.56) - 145*45.
  
• tqRes=825 kip-Feet
• Compute using grEza=8 balances when zaECh=8.834
• tqRes=Wgr*Rgr*sin(grEZa-zaEOffset) - (Wcw*Rcw + Wch*Rch*sin(zaECh)
• tqRes=215*430.*sin(7.968-1.913) - (45*145 + 35*430.*sin(8.834)
• tqRes= 904 kip-feet
• Residual tq ch side: (904+825)/2=864 kip-feet.
• Equation to compute imbalance:
• unbal=(Wgr*Rgr*sin(zaEgr-zaEoff)) - (Wcw*Rcw + tqResCh + Wch*Rch*sin(zaECh))
• unbal=(215*430.*sin(zaEgr-1.913) - ( 45*145 + 864. + 35*430*sin(zaEch)
  

Plotting the unbalance:

• Top: dome moves 1.06 degrees to 19.69 degrees in za:
• ch at 8.83 degrees za (stow). This is the current setup we use.
• ch at 20 degrees za.
• ch  tracks  dome za when dome above za=10.
• Bottom: ch moves 0 to 20 degrees in za, dome remains fixed.
• dome at 8.83 degrees za (stow). This is the current setup we use.
• dome at 13.5 degrees za.
• dome at 15.0 degrees za.
• dome at 19.69 degrees za.

• The dashed horizontal lines show +/- 12000 kip-feet.
  

Notes:

• tracking with the ch when dome above 10 degrees za only saves 3000 kip feet when dome is at 19.69 deg. The resulting unbalance is still larger than the allowed 12000 kipfeet unbalance.