fiberstress,
I think you missed a bit. In your tonnage range, you should expect about 1.2 kW input for each ton output. That's an EER of 9.5 or a COP of 2.8. I'm working with the code minimums here, so yours might be less than 1.2 kW/ton.
In your 20-ton case, you'd have 24 kW (81,912 btu/h) input and 240,000 btu/h cooling. So input power is only about 34 percent of cooling capacity, not 75 percentl.
Your condenser has to reject the 240,000 btu/h plus the compressor heat (heat of compression plus inefficiency due to friction, etc...) that goes into the refrigerant stream. Ambient air takes care of the motor's waste heat, so about 7 to 8 percent of the 1.2 kW is lost in that manner. The rest of the work goes into the refrigerant and must be rejected by the condenser along with the heat gained in the space. In the 2.8 COP case, you'll have 1.2 kW x 0.92-ish or 1.1 kW to reject along with the space heat contribution. That gives 1.1 kW x 0.92 x 20T x 3413 btu/kW / 12000 btu/T or 5.76T. Your condenser has to reject 25.76T in this case. That's only 1.29 times the cooling capacity.
Large, efficient centrifugal refrigeration compressors get down into the 0.6 kW/T range, so a 1000T unit may need a cooling tower that can reject 1000T from the space plus 0.6 kW x 1000T x 3413 btu/kW / 12000 btu/T or 170.6T. (These machines have the motor in the refrigerant stream, so all heat goes there). End result is a cooling tower of 1170.6T or 1.17 times the cooling capacity.
I hope I haven't goofed that up. Wait for a few critics to reply before accepting my answer. I'm working on a Saturday with a body full of Red Bull and my mind is sometimes not right in these circumstances.
Best to you,
Goober Dave
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