However, something is still wrong here. This calculation does not match the experience, yet.
Let's start from the induction motor diagram.
The power transferred from stator to rotor it is:
Pi=m2*R2*I2^2/s where 2 it means "rotor" and m2=rotor number of phases.
s=(nsyn-n)/nsyn the slip where:
nsyn=synchronous rpm ; n=the actual rotor rpm.
I2=Vstator/SQRT(R1+R2/s)^2+X2^2) neglecting Io and X1[stator leakage reactance]. For simplification's sake I'll take the R1=0 as well- where 1 it means “stator".
The torque it is the power divided by velocity in rad/sec.
T=m2*R2*V^2/(R1+R2/s)^2+X2^2)/s/2/pi()/nsyn/(1-s)
If K=m2*R2/(2*pi()*nsyn) and R2^2=A X2^2=B Neglecting R1
T=K*V^2*s/(A+B*s^2-A*s-B*s^3)
Since s is very low we can say s^3=s^2=0
T=K*V^2*s/A(1-s)
For different V[Vi initial and Vf after change]:
Ti/Tf=(Vi/Vf)^2*si/sf/(1-si)*(1-sf)
We may consider (1-s1)/(1-s2)=1 and for a same required torque in different supply voltages Ti/Tf=1 then:
sf=(Vi/Vf)^2*si
s(415V)=(480/415)^2*3%=4%!!!
That means it is not 11.86% but only 4%. This result it is more possible.