Calculate the change in ZTF camera focal plate saggita w.r.t. ΔT. Callahan 8/21/2014
Assume radius of curvature of the ZTF focal plane is from the f/2.5 beam. Calculate focal length then radius of curvature.
Initial conditions:
Expected
K
non-zero error due to polynomial fit to data
See calculation of thermal strain below.
f-ratio is 2.5.
Diameter of camera is roughly 500 mm
focal length
radius of curvature is 2f
This is the baseline radius of curvature (at 20C?)
Calculate the half length of the cord (l)
Initial length at T.ref
length after thermal expansion
See:http://en.wikipedia.org/wiki/Sagitta_(geometry)
Calculate radius for any T.
Calculate the saggita as a function of temperature
Calculate the difference between our baseline saggita for any ΔT from baseline.
Expected change in saggita at operating temperature (-100C)
Expected change in saggita for a change in temperature of 1C.
See:http://cryogenics.nist.gov/MPropsMAY/6061%20Aluminum/6061_T6Aluminum_rev.htm
Thermal coefficent of thermal expansion
instantaneous coefficient of expansion
Compares nicely to: http://cryogenics.nist.gov/MPropsMAY/6061%20Aluminum/AL-6061-T6_Plots/AL_6061-T6_Linear%20Expansion.JPG