Charles,

 

 If the engine develops 300 lbft of torque, then 300 lbft of torque is applied to the airframe.  In order for the aircraft to remain static, an opposing moment of 300 lbft must be applied somewhere on the airframe. Thus the combined change between the two scale values divided by two should be pretty close to 300 lbft divided by the distance between the gear. As long as the prop shaft is parallel to the ground surface, it shouldn't matter what height it is located. The only source of error that I can visualize is the effect of the propwash vorticity on the air frame. I don't have much of a feel for the likely magnitude of this impact so I am quite curios to see Paul's results. 

 

You stated that "the force vector at the scale due to the engine torque is normal to a line between the prop shaft and the scale". If this was correct with the aircraft in a static condition, then the gear would be exerting a lateral component of force as well as a vertical component. This would result in lateral movement of the aircraft. While I will agree that this is a valid issue as engine power is being changed, once the power stabilizes, the aircraft again becomes a static body and the lateral force at the gear returns to zero.  If it didn't, the aircraft would move laterally when ever it was on the ground and under power.

 

If Paul's formula gives a different value than mine, then one of us has obviously made an error somewhere. I don't have the time to review everything tonight, but I will try to sort out the difference in the next few days and report back.

 

Rob