Do any of you use mechanical trail when designing a frame set?

I have never heard of mechanical trail before. It's off by less than 10 percent from the trail that everyone uses over a fairly normal range of head angles. I suppose you could have long arguments on the interwebs on which is more suitable.
But for comparison purposes, I think the usual definition is more appropriate.

Agree. Thank you. Question answered in a sufficient way.

I've never really understood the difference.

It shouldn't mater which dimension one uses as long as one is consistent within their own calculations and analysis. I use the horizontal version of trail. No pneumatic no mechanical. Andy

Trail as we usually talk about it is the distance along the ground between the steering axis and the contact point of the tire. Mechanical trail is the shortest distance from the steering axis to the contact point of the tire. So mechanical trail = trail * sin(head tube angle)

I'm using "contact point of the tire" as a shorthand for the intersection of the ground and a vertical line that goes through the front axle.

There is also pneumatic trail. When I see someone talking about that, I suspect they are counting on the fact that very few people actually understand it.