The average daily max temp is 92.7 F in July in Houston. On a still sunny day,
a square foot of light-colored south shingles might absorb 0.2x250 = 50 Btu/h
and lose heat to outdoor air with a 2 Btu/h-F conductance, which makes the
equivalent shingle temp 92.7+50/2 = 118 F, so we might have something like
this, with attic air temp T (F), viewed in a fixed font:

T
0.5 | R1 | -----
-----www-------www------| -- |---|
| | RATT -----
| 118 | I
--- |
- outside|inside
| |
-

If 1250(118-T)/1.5 Btu/h that flows into the attic equals I that flows out
and I = 16.6Asqrt(H)(T-93)^1.5, with lesser vent area A ft^2 and height diff
H in feet, A = 190/144 = 1.3 ft^2 and H = 8' make T = 118-(T-93)^(2/3)/13.5
= 117.4 F, after 2 iterations. With A = 8 ft^2 (eg 2 2'x2' gable vents),
T = 114.5. Not a big difference, esp since the larger soffit area will add
about 40% to the flow in the first case, which isn't counted above.

A radiant barrier can help by increasing the R1 above.

Not much, altho larger vents help. A thermal chimney would also help
(how much?), by increasing H. It might have a transparent south side
or roof to collect sun and raise the "chimney" air temp and bouyancy
and flow in summertime and collect wintertime heat.

20 ASR=1250'south roof area (ft^2)
30 RSH=.2'shingle reflectivity
40 TA=92.7'outdoor temp (F)
50 GSA=2'shingle-outdoor conductance (Btu/h-F-ft^2)
60 TTS=TA+250*RSH/GSA'Thevenin equiv shingle temp (F)
70 FOR RATT=1 TO 4 STEP 3'R-value of roof (1-4 for radiant barrier)
80 KROOF=ASR/(1/GSA+RATT)'roof coefficient
90 H=8'vent height difference (feet)
100 FOR A=8 TO 32 STEP 8'vent area (ft^2)
110 C=16.6*A*SQR(H)/KROOF
120 T=TTS'initialize attic air temp (F)
130 TL=T'save previous value
140 IF TTA THEN T=2*TA-T'reflect up
150 T=TTS-C*(T-TA)^.666'find new value
160 IF ABS(T-TL).1 GOTO 130'iterate
170 PRINT RATT,A,T
180 NEXT:NEXT

RATT A (ft^2) Tattic (F)

1 8 114.2156
1 16 111.3843
1 24 109.0334
1 32 107.0474

4 8 109.0334
4 16 104.0215
4 24 101.0059
4 32 99.13989

Nick