It has always puzzled me that some people are unable to understand that a raked fork has trail in the same way that a furniture castor does.
With a raked fork, the tire contact patch trails the projected steering axis in precisely the same way that as a furniture caster.
I’m personally not sure I’ve ever seen a chair caster or shopping cart, etc. with a raked fork - all the ones I’ve seen have a vertical fork with a trailing axis, like the Magni, TAG, and AR-1 configuration.
I’m not an engineer, physicist, High School science teacher, or gyro manufacturer, but one thing that struck me about the sketches in post 26 of the ongoing crosswind takeoff discussion is that the amount of trail shown is correct - for when the axle is pointed straight ahead. But as the fork starts turning, depending on factors such as the width of the tire, the amount of rake, and the displacement of the axle, the amount of trail diminishes - and I think there even comes a point where part of the tire starts to go
behind the steering axis (negative trail?) - and that proportion of the tire behind the turning axle progressively increases. My guess is that's well before 90 degrees of fork turn, especially for heavily-raked forks. For a vertical fork, that doesn't happen till more than 90 degrees of turn. I suspect that's why chairs and shopping carts are built as they are.
Something not said in all of this discussion (here and in the crosswind discussion) is the significance of the touchdown speed. At faster landing speed, more air is going across the rudder (making it more effective), so less pedal input is needed - and therefore there's less angle in the nosewheel for connected systems. Not only that, but the inertia of a faster landing means the nosewheel will be straightened out faster/easier and in the direction of travel. I truly think the bent keel plus the desire to touch down like a helicopter adds tremendously to landing issues in particular because of this. If people touch down with more speed, I suspect there'd be a lot less rollovers.
But back to the OP and the flapping warning device. The proposed device is waiting for the fire to already be started and hoping to stop the explosion (if you're hitting the teeter stops, you've already reached a critical amount of dyssymmetry). Fire prevention is always the best route! Training, of course, is essential. But if a gadget is wanted, wouldn't it be simpler to have one that sounds a buzzer if the wheels are turning AT ALL when the stick is not all the way back AND the rotor is below some safe-for-that-model number? That stops the pilot very early in the process and before the flap can develop.
I fly a Magni and these discussions are some of the biggest reasons I do so. Having pretty much only trained in a Magni, I was surprised to see people go on the runway (and tie it up) before even prerotating. I don't move from the runup area without at least 170RRPM and am using the stick back as a brake most of the time. WAAY more relaxed with regard to managing other traffic in the pattern, etc. I'm on the runway maybe 10 seconds and starting with 210-220RRPM, especially since I'm able to increase the RRPM as I'm taxiing. Flex cable prerotators are awesome, to me.
Another point on the departure issues: at Phil Harwood's class in AZ he talked about knowing where your gyro's throttle is set for cruise speed and using that setting for your first setting on takeoff. Then, once the nosewheel starts up, you can advance it to a climb power setting (but not necessarily full power) since the rotor has now proven it's generating enough lift. That seems very logical and even though I was informally doing something very similar before, his comments have me being more formal about what I'm doing. Incidentally, he speculated (and I think he's already being proven correct) that the 915s are going to result in more takeoff accidents because they're so powerful for the gyro and people will just push to full-throttle and exceed the rotor's ability to speed up. With my lowly 912, I really don't need to sweat that but it's definitely something to consider.