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Here's a helpful description of the rotor time constant from Edward Cheeseman:
Rotor time constant is L/R rotor resistance divided rotor inductance, in the simplest form. The units are seconds.
We used 0.04s, and did calculate this from a 11kW industrial motor I had the nameplate details from. (not the motor we used, but close)
Rotor Resistance
Basically, from the efficiency data at rated power, very approximately the rotor resistance is equivalent to 1/3 the total losses. (assume 1/3 stator, 1/3 core losses, bearing friction and windage etc)
Rated current was 19.8A, Full load efficiency 92.5% (a 400V50Hz motor)
11kW/.925 - 11 = 891W total.
Per phase (/3) =297W
In rotor (/3) = 99W.
Normalised current (current if rotor had same number of turns as stator) P=I*I*R
R=99/19.8/19.8=.25ohms
Rotor Inductance
Using above data plus Power factor (full load) .85
Find the complex motor impedance at rated load 230V(per phase)/19.8A(at .85pf)=Zmotor
Zmotor is Rmotor+2*pi()*f(50Hz)*Lmotor
Lmotor = 0.02H,
Basically assume motor inductance is 50/50 rotor/stator,
Lrotor = 0.01H
Rotor Time Constant
0.01/0.25=0.04
We have had success with values 0.04-0.048, depending (we think) on how warm the motor was. At any time/temperature, any number in that range would produce usable torque. Rotor Time Constant ideally needs to be dynamic - the rotor resistance changes with temperature, the inductance with current (saturation), and some IEEE papers also say with slip (although I haven't read up on that yet)
Resistance changes ~25%, Inductance a lot more. Both serve to reduce the constant.
So with a little data you can get a ball park figure!
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