Further to MFJ-1786 loop antenna – measurements and NEC-4.2 model at 10.1MHz this article presents some other models of expected performance of the MFJ-1786 loop.
One of, if not the most popular loop calculator cited by hams is that by AA5TB. It is especially praised by ham loop enthusiasts.
Above is a screenshot of AA5TB's calculator with the real antenna dimensions and “Added Loss Resistance” to calibrate the model to the measured 8kHz half power bandwidth. It predicts an efficiency of 30.6%, 2.9 times that of the NEC model. Perhaps it is popular because it provides overly generous estimates, IMHO it lacks credibility for many reasons.
The uncalibrated model uses Rr calculated for a small loop in free space and Directivity of a small loop in free space.
This loop is a little large for the simple formula for Rr to be very accurate.
Calibrated using NEC derived factors for Rr and Directivity
Not only is the loop a little large for the simple formula for Rr to be accurate, but the proximity of ground modifies Rr, it also modifies the pattern so Directivity is different which flows into a different Gain figure.
Radiation efficiency of 10.188% reconciles well with the NEC-4.2 model's 10.61%, and estimated gain of -4,4dBi reconciles well the the NEC-4.2 model's -4.2dBi. The improved reconciliation demonstrates the need to factor in the effect of ground on radiation efficiency and gain.