**Calculations for Rio Grande Southern 4-6-0 # 20 2 ½
Scale 7 ½ gauge (preliminary)**

**Calculations based on the following**:

3000 lb train weight

750 lb engine weight

250 lb tender weight

20 lb/ton rolling resistance (sleeve bearings)

3 % maximum grade

45 foot minimum radius

8 mph maximum speed

**Total train resistance (worse case)**

Rolling resistance = 40 lb (20 lb/tom x 2 tons)

Grade resistance = 120 lb (40 lb/tom / % grade x 3)

Curve resistance = 24 lbs (12lb /ton @ 45 ft rad.)

Total = 184 lbs

Co-efficient of friction = .25 (cast iron on aluminum)

Maximum tractive effort (TE)

750 lb locomotive x .25 = 188 lb

188lb > 184 lb reqd.

**Locomotive specs:**

Drivers 8.75 in diameter

Pilot wheels 5.00 in diameter

Bore 2.75 in diameter

Stroke 4.00 in

Weight 1000 lb (750 locomotive 250 tender)

Length 123 in

Width 21 in

Height 31 in

Gauge 7.5 in

**Boiler specs**:

Shell diameter 11.0 in

Smoke box Dia. 11.5 in

Shell & firebox .312 ASTM A285 Grade C

Firebox length 18.75 in (inside)

Firebox width 4.00 in (inside)

Firebox Height 8.00 in (inside)

` tubes .875 od x .750 Id type K copper (rolled in)

Tube length 28 in

No of tubes 24

Staybolts ½ diameter on 3" centers

Pressure 125 psi (2 safeties 125 and 130)

Wheel speed

8 mph = 8448 in / min 8.75 in dia = 27.5 in / rev

8448 in / min / 27.5 in / rev = 307 rpm

Wheel torque

188 lb (TE) x 4.375 in (wheel rad) = 822.50 in lb torque

Wheel HP

(822.50 in lb x 307 rpm) / 63025 = 4.0 hp

**Cylinder/valve gear checks**

Stephenson valve gear 85% cutoff (full gear)

Calculate mean effective pressure (MEP)

At 85% cutoff mep = .98

Assume 20% pressure drop boiler to cylinders

125 psi x 80% = 100 psi

100psi x .98(mep) = 98 psi (average pressure at cylinders)

Check cylinder diameter

Te = 188 lbs Mep = 98 psi Stroke = .33 ft driver dia. = .708 ft

Using formulae bore = 2.01 in

2.75 (actual bore) > 2.01 (required bore)

Check piston speed

307 rpm x 8.0 rod travel (4.0 in stroke x 2) = 2456 in / min = 204.6 ft / min

204.6 ft / min < 300 ft / min (recommended max)

**Check boiler**

**Grate area**

Rule of thumb: grate area = TE /3.5

188 TE / 3.5 = 53.72 in sq. (required grate area)

actual grate area = 18.75 in x 4.0 in = 75 in sq.

53.72 in sq < 75 in sq

Tube area

Rule of thumb: tube area = 1/8 grate area

Tube Area = 75 / 8 = 9.38 in sq

Actual tube area = .442 in sq x 24 tubes = 10.608 in sq

10.608 in sq > 9.38 in sq

Stack diameter

Rule of thumb: stack area = .06 x grate area

75 in sq x .06 = 4.5 in sq = 2.4 in dia. (smallest diameter)

Stack length

Rule of thumb: stack length = 4.0 x diameter

2.4 in x 4 = 8.0 long (including peticote pipe)

Nozzle diameter

Rule of thumb: nozzle dia. = .004 x grate area

75 in sq x .005 = .30 in sq = .50 diameter

**Water consumption**

Cylinder volume

2.75 in (bore) = 5.93 sq in

5.93 sq in x 4 in (stroke) = 23.75 cu in

total volume = 23.75 cu in x 4 (strokes/rev) = 95.03 cu in / rev

from steam tables: 1cu in of water = 204 cu in of steam at 125 psi

95.03 cu in /rev / 204 cu in = .465 cu in /rev

.465 cu in /rev x 307 rpm = 142.75 cu in / min = .61gpm

(worse case approximation. From my experience designing to this
number works well)