Net Lifting Force of a Meter Out Circuit

[tc7]

I have pneumatic cylinder application and have I have used a typical meter out control circuit with a constant vertical load, ~5000# dead weight (the lifting time is 10 seconds and the stroke is 7 inches). We have a 10-inch bore, 2-inch rod, single acting cylinder. I have set my operating pressure at 140 psig at the cap end for lifting. While lifting the 5000# weight, the system also must overcome a large, but unknown and unestimateable friction force. Both sides of the cylinder are free flow in/metered out. The system appears to be working fine.
BUT HERE IS MY PROBLEM......I cannot calculate or estimate the net lifting force applied by my air cylinder because I don't have pressure gauge readings at the exhaust side (rod side) (between cylinder outlet and meter valve) during lift, yet I am sure the force needed to exhaust the air through the metering valve must be substantial. I do not have an opportunity now to install additional gauges to acquire any data. What can I do to estimate the net lifting force? I can probably estimate the Cv of the meter valve to be ~.1 to 9, but I don't know that this helps in any calculation that I can make; I also assume the Cv of the meter out valve is much smaller than the Cv of the spool valve.

I hope you can help. Thanks in advance!!!!
Tom C