The profile will effect how the bike turns in. The rounded profile will turn in quicker than your flat tire.

It will also help traction as the rounder profile will have a larger contact patch.

As mentioned, I tried a Metzler flat profile stree tread pattern tire on the rear of my old BSA because the flat profile dirt knobby worked so well offroad. Unfortunately the street tread was miserable.  Made the head shake at speed and gave a "fall over" feeling at low speed. I replaced it with the old standby K-70 and all was well again.  I used the "runflat" Goodyears on my last Goldwing until they were no longer available.  They had a "semi" flat profile but not anywhere like the Metzlers of the '70's.  I am now using a 19" K-70 on the back and an 21" Avon Speedmaster on the front of my old Norton. It still handles as well as when it was raced in the early 50's---just not like new bikes.

Rod

PS---For those of you who are old enough to know, I use 19" and 21" wheels because the original 20" are impossible to find.

Interesting! Had the exact experience a couple of years ago with a Yam 660 "Aventure Tourer". Did an "Outback" {OZ} ride with four others on the same bikes of about 2500 miles in 7 days.Because the riding conditions would be varied and unknown, I decided to set my bike to the "possible" couple of miles of mud we might encounter,and fitted knobbies F&R and lifted my fr/mudguard.This strategy proved correct, however,on the highway at about 60 mph it had a very bad head shake which no one else was experiencing!{they all stayed with the standard 70% road and 30% dirt tyres} I partially overcame this with a very subtle weave.I put it down to the knobbies, but wasn't sure why! I now have  enduro style tyres and it handles beautifully on road and "off". The rear knobby I had on was slightly bigger than normal, would this have affected the steering head angle enough to cause any problems?

No.  It was the tires.

Financial issues overcame my principles, and I put a pair of MAxxis street tires on my old yamaha 850.  They have a tighter curvature than the Metzler laser/worn Kenda  that were on there. THe contact patch is MUCH narrower at both ends, and vaguely triangular at the front. I would not necessarily credit all the present attributes to the tighter curvature, but The steering is delightfully light and the cornering is very confidence inspiring.  My hardest cornering shows contact within about 1/8 inch of the full width at the rear, but is till miles away from full width on the front. They track over crummy road surface straight and true.  Over 80 mph there is a new tendency for a slight 1 Hz weave or slight headshake, but I am very pleased with the  handling and even the ride at all lower speeds, which is where do most all of mt riding anyway.

18 months later, 300-20 inch Avon Speedmasters are available, in Australia and New Zealand at least. In NZ from Britspares for around $120 and in Aus for anything between $121 and $260 depending on where you get 'em. Ryans is the best bet I've found.
I've been looking for a roadworthy 300-20 trials-universal pattern tyre.. still am.

evelrod, if you're about, I'd be interested to know if you detect any difference in handling on the road with a larger diameter front wheel, if not running a rear 400-19? Were your  Norton's original overall tyre diameters the same at both ends?
cheers

For good or bad, I'm still here.
My '48 Norton International/ES-2 is the bike that Australian World Trials Champion Bill Young rode in the early 50's.  It was restored in WA for $9000AU and shipped to the U.S. a few years back and it was already converted to the 19 and 21's.  Actually I rather like the 21 inch wheel as it rolls over the bumps that the rather primitive (by today's standards) front suspension does not handle.  The rear 19 is the same overall dia as the original 20 and bunches cheaper to purchase.  The bike cruises at 60/65 mph and handles well on smooth roads---at least as well as a 65 year old wants to push it! Actually, I recon, at 210 lbs. I am probably a bit too big for it but...!

As to the 20's being the same size, I would assume so as most all Nortons of that era were so equiped as I recall.

Rod

For good I should think.
20s were a popular size back then but the first I knew of them was as barely a teen-ager cutting my riding teeth in the late sixties on a BSA C11 which had 20s fore and aft. Still pretty keen on 'em.
The 20s, not the C11..

cheers, Geoffrey