I think there are some practical problems with the idea you are presenting here.
Before addressing my main point, let me first get something out of the way that would confuse things.
In the video you linked to, showing that nifty self-balancing rod, the operating principle is not gyroscopic effect. The orienting mechanism of those wheels is called 'reaction wheels'. When the reaction wheel spins up around its axis the structure that it is attached to will rotate the other way, in proportion to the respective moments of inertia.
The reaction wheel mechanism is much simpler than gyroscopic effect mechanism. For one thing, for gyroscopic effect the wheels need to spin quite fast. As you can see: in the case of that self-balancing rod contraption the wheels rotate quite slowly. If the tilt sensors are very sensitive the reaction wheels can react very early to any deviation from plum, and then a slow rotation rate is sufficient to maintain an upright position of the rod.
About the survey-rod-with-physical-feedback that you describe:
If I understand you correctly, the usage would be:
- hold on to the top of the survey rod, allowing the bottom end to swing freely
- move close to the set point
- activate the physical feedback
- the feedback mechanism should swing out the bottom end of the survey rod towards the set point
It seems to me that while some form of physical feedback would be interesting, using reaction wheels would be a case of over-engineering.
Your hand is wrapped around the survey stick: how about the surface of the stick providing some sort of pulsation to the hand holding the stick. You can have 4 areas, at 0, 90, 180, 270 degrees, that can pulsate in some way. That can tell your hand in which direction it must move in order to be straight above the set point.
About the idea with reaction wheels: what should happen if the user does not respond right away to the nudge? Should the reaction wheel keep producing the same palpable push? The thing is, to do that the reaction wheel would have to keep increasing its spin rate. You feel the nudge as long as the spin rate keeps going up. But the reaction wheel cannot keep accelerating. At some point the angular velocity is maxed out and the acceleration has to level off. That is, after no more than a couple of seconds the nudging would drop off. I don't think that's a good user experience. Good feedback design is that the feedback is consistent and constant.
So yeah, I'm trying to talk you out of it.
If you need/want to do the reaction wheel idea anyway:
It seems to me that the constraint is how much weight increase for the survey rod is still acceptable. For a prototype use a motor-and-reaction-wheel-assembly that is just acceptable weightwise.
If that turns out to be underpowered, then the idea is non-viable, if it is overpowered you go down in size as you iterate through prototypes.