20(ish) Vowels.

Officially English has twenty vowel sounds but only five vowel letters. The other vowel sounds are represented by combinations of two or more letters. Unfortunately most of these vowel sounds can be represented by multiple different combinations with no apparent logic or consistency. For example, the words “boot” and “hook” have quite different pronunciations, both of them closer to “u” sounds than “o”.
If a more phonetic form of English is desired then the vowel sounds seem a very logical place to start.
The five “basic” vowels are:
Usually written
mat, pat, lap
met, pet, let
bin, pit, lip
rot, pot, lot
fun, sun, luck = fun, sun, luhk
These are relatively consistent, so we will move on to the other vowel sounds. In the second column I suggest standardized letter combinations to represent these. Further discussion of these is in the section below:
ay/ ey
wait, day, late = wayt, day, layt.
ar/ aa
far, car
er/ ayr
air, care, where =ayer, kayr, wayr
sheep, meat, fiend, elite = shiip, miit, fiind, ayliit/ eyliit.
steer, near, here = stir, nir, hir
stir, her, word, bird, hurt = stur, hur, wurd, burd, hurt
ai/ iy
I, sign, fight, dry, ice = ai, sain, fait, drai, ais/ iy, siyn, fiyt, driy, iys.
u/ uu
do, doom, through, boot = du/ duu, duum, thru/ thruu, buut
coin, toy = koyn, toy
boat, note, snow, know = boht, noht, snoh, noh
for, oar, worn, door, more, saw, paw, lore = for, or, worn, dor, mor, sor, por, lor.
sound, cow, how, now = sound, kou, hou, nou
look, hook = luk, huk
few, due, cube = fyu, dyu, kyub.
One of the surprises in constructing this table is the variability of how “u” is used. The dictionary insists words like “do” and “through” are a “long u” (/u:/) while I would be inclined to pronounce them “du” and “thru”. Indeed, this would be my inclination to pronounce any word ending in a “u”. “Look” is obviously a short “u” sound, “luk”. Spelling “luck” phonetically in the above system gives us “luk” too although pronunciation is obviously different, hence I used “luhk”. Further examination of the ways “u” is used as a phoneme may be needed.
The “i” in words like “high” or “wire” is represented by “ay” in SaypYu. To my mind this is too likely to be taken as “-ay” as in “may” by English speakers. As far as I know “ay” is always pronounced “/eɪ/” in English. SaypYu’s use of “ay” requires the unnecessary respelling of many perfectly reasonably spelt English words. In the past I have suggested that this should be “ai”, pronounced as in “thai”. A good case can be made for instead using the letter combination “iy”. Thus words such a “fire” become “fiyr”, which is fairly easy to comprehend.
Saypyu uses “ey” to represent the “a” sound in words such as “may” or “same”. If “iy” or “ai” is used to represent the gliding “i” “ay” can be used to represent the gliding “a” and is more easily comprehended by English speakers. There may be a case made for using both “ey” and “ay”. “Ey” would be used for “/eɪ/” sounds not traditionally spelt “ay”. One problem with phonetically spelling English is it increases the number of homographs, something that the language hardly needs!
“er/ ayr” is another case where two different spellings may be used. Words such as “air”, “care” and “where” are more easily comprehended using the “ayr” spelling : “ayr”, “kayr”, “wayr”. The spelling of other words may be clearer using what is effectively a rhotic form of schwa. The distinction between these two may be more pronounced in some accents and dialects.
The long “a” is another phoneme that might be represented two ways. In the above table examples are given of a rhotic form but this may not be applicable for some words. Alternately “ah” may be used instead. Is “father” better spelt “fardher”, “fahdher” or “faadher”?
/ɔː/ as in “saw” or “sore” would usually be represented by “or”. For some uses such as /ɔːl/ or /ɔl/” in “ball” the use of “au” to create “aul” might be clearer.

Careful readers will have realised that the above options give this system more than twenty vowel sounds. They may also have noted that the two tables only have nineteen rows! The missing vowel sound is schwa, which is not represented by a letter in English. Unlike Saypyu I have attempted to create a vowel system that for the most part uses existing English constructions. This system should be comprehendible to native English speakers as well as easy for non-native speakers to learn. Schwa will usually be represented by “e” although in some words it may be clearer if another vowel is used.
The above vowel system is relatively easy to remember. Firstly, you have the digraphs that end in “-r” : ar, er, ir, or, and ur, to which we might add “ayr”.
Then come the doubled letters : ii, uu, au and possibly aa.
Next come the digraphs with a “y” in : yu, ay, ey, iy, oy.
And last, the other “o”s : oh, ou.
This gives seventeen vowels, which with schwa and the single letter vowels is twenty-three in total. Some of these vowels represent the same or similar phonemes. ah, eh, ih and uh might also be considered to be digraph vowels.  This gives us a much more logical and intuitive system than traditional English.
An example:
“Aul hyumen biingz ar born frii and iikwel in digniti and riytz. Dhey ar endoud widh riizen and konshens and shud akt tewordz wun enodher in ey spirit ov brodherhud.”