I can reasonably assume that the longest string with no vowels is 26, minus the 5 vowels, - 1 (the letter "y" for words like "cry"), which is 19 characters.
0 vowels - 1b2c3d4f5g6h7j8k9l10m11n12p13q14r15s16t17w18x19q20z - 19 characters
1 vowel - ?
2 vowels - ?
3 vowels - ?
What do you guys think?
I think your math-fu needs work
All joking aside, with 1 vowel you already need to row just about the entire alphabet out.
Let's take U as only vowel. We'll need as many 1 syllable words as possible, with as many different consonants as possible..
run, buck, gull, null, full, (l would be good to get rid of) fun, buff, cup, cut, put, bud, mud, gun, gut, hull, hut, hug, jug, just,
My english vocabulary isn't strong enough to make all mutually exclusive letters... And I think this will boil down to good scriptwork.