So what would it take for a 1906 fast battleship?

I thought that I should try a British fast battleship for 1906, to be built instead of the Invincible class battlecruisers. I thought that the design could get by with 8-12in/45 BLR and 16-4in QF guns and a speed of 25 knots. Coal-fired boilers seemed to be a necessity, as that date. The armor basis would be 10in. With coal-fired boilers, the size really is too large. I wrestled with it for a while, even trying oil-fired boilers. The dimensions ended up as 590ft x 85ft x 27ft. The Washington Naval Treaty Standard Displacement ended up as 20,290 tons. The normal displacement is too great at 23,200 tons. That was what it took to achieve this with the technology level that was available, except accepting higer power output machinery (22.8 SHP/ton), which is a huge concession. This is the Springsharp report:

GB/BB/1906 Fast, Great Britain Battleship laid down 1906 (Engine 1912)

Displacement:
 19,449 t light; 20,290 t standard; 23,200 t normal; 25,528 t full load

Dimensions: Length overall / water x beam x draught
 590.00 ft / 590.00 ft x 85.00 ft x 27.00 ft (normal load)
 179.83 m / 179.83 m x 25.91 m  x 8.23 m

Armament:
      8 - 12.00" / 305 mm guns (4x2 guns), 864.00lbs / 391.90kg shells, 1906 Model
   Breech loading guns in turrets (on barbettes)
   on centreline ends, evenly spread, all raised mounts - superfiring
      16 - 4.00" / 102 mm guns in single mounts, 32.00lbs / 14.51kg shells, 1906 Model
   Quick firing guns in casemate mounts 
   on side, all amidships, all raised mounts - superfiring
 Weight of broadside 7,424 lbs / 3,367 kg
 Shells per gun, main battery: 90
 2 - 18.0" / 457.2 mm submerged torpedo tubes

Armour:
   - Belts:  Width (max) Length (avg)  Height (avg)
 Main: 10.0" / 254 mm 380.00 ft / 115.82 m 17.00 ft / 5.18 m
 Ends: 4.00" / 102 mm 190.00 ft / 57.91 m 17.00 ft / 5.18 m
   20.00 ft / 6.10 m Unarmoured ends
   Main Belt covers 99 % of normal length

   - Torpedo Bulkhead:
  1.00" / 25 mm 380.00 ft / 115.82 m 25.00 ft / 7.62 m

   - Gun armour: Face (max) Other gunhouse (avg) Barbette/hoist (max)
 Main: 10.0" / 254 mm 6.00" / 152 mm  10.0" / 254 mm
 2nd: 2.00" / 51 mm       -         -

   - Armour deck: 2.00" / 51 mm, Conning tower: 10.00" / 254 mm

Machinery:
 Coal fired boilers, steam turbines, 
 Direct drive, 4 shafts, 57,970 shp / 43,246 Kw = 25.00 kts
 Range 6,500nm at 15.00 kts
 Bunker at max displacement = 5,238 tons (100% coal)

Complement:
 939 - 1,221

Cost:
 £1.816 million / $7.265 million

Distribution of weights at normal displacement:
 Armament: 928 tons, 4.0 %
 Armour: 7,152 tons, 30.8 %
    - Belts: 3,285 tons, 14.2 %
    - Torpedo bulkhead: 352 tons, 1.5 %
    - Armament: 1,983 tons, 8.5 %
    - Armour Deck: 1,357 tons, 5.8 %
    - Conning Tower: 175 tons, 0.8 %
 Machinery: 2,543 tons, 11.0 %
 Hull, fittings & equipment: 8,826 tons, 38.0 %
 Fuel, ammunition & stores: 3,751 tons, 16.2 %
 Miscellaneous weights: 0 tons, 0.0 %

Overall survivability and seakeeping ability:
 Survivability (Non-critical penetrating hits needed to sink ship):
   35,613 lbs / 16,154 Kg = 41.2 x 12.0 " / 305 mm shells or 5.4 torpedoes
 Stability (Unstable if below 1.00): 1.03
 Metacentric height 4.1 ft / 1.3 m
 Roll period: 17.5 seconds
 Steadiness - As gun platform (Average = 50 %): 64 %
   - Recoil effect (Restricted arc if above 1.00): 0.83
 Seaboat quality  (Average = 1.00): 1.27

Hull form characteristics:
 Hull has rise forward of midbreak
 Block coefficient: 0.600
 Length to Beam Ratio: 6.94 : 1
 'Natural speed' for length: 24.29 kts
 Power going to wave formation at top speed: 52 %
 Trim (Max stability = 0, Max steadiness = 100): 50
 Bow angle (Positive = bow angles forward): -2.00 degrees
 Stern overhang: -2.00 ft / -0.61 m
 Freeboard (% = measuring location as a percentage of overall length):
    - Stem:  27.00 ft / 8.23 m
    - Forecastle (20 %): 25.00 ft / 7.62 m
    - Mid (67 %):  25.00 ft / 7.62 m (17.00 ft / 5.18 m aft of break)
    - Quarterdeck (15 %): 17.00 ft / 5.18 m
    - Stern:  17.00 ft / 5.18 m
    - Average freeboard: 22.52 ft / 6.86 m

Ship space, strength and comments:
 Space - Hull below water (magazines/engines, low = better): 87.7 %
  - Above water (accommodation/working, high = better): 169.5 %
 Waterplane Area: 36,668 Square feet or 3,407 Square metres
 Displacement factor (Displacement / loading): 118 %
 Structure weight / hull surface area: 164 lbs/sq ft or 802 Kg/sq metre
 Hull strength (Relative):
  - Cross-sectional: 0.95
  - Longitudinal: 1.63
  - Overall: 1.00
 Hull space for machinery, storage, compartmentation is adequate
 Room for accommodation and workspaces is excellent
 Good seaboat, rides out heavy weather easily