**Calculations for D&RGW # 360/361 C21 class locomotive 2 ½
Scale 7 ½ gauge (preliminary)**

**Calculations based on the following**:

2750 lb train weight

1000 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/ton 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)

1000 lb locomotive x .25 = 200 lb TE

200 lb TE > 184 lb reqd.

**Locomotive specs:**

Drivers 8.1/8 in diameter

Pilot wheels 5.00 in diameter

Bore 3.00 in diameter

Stroke 4.1/8 in

Weight 1250 lb (750 locomotive 250 tender)

Length 131 in

Width 21 in

Height 31 in

Gauge 7.5 in

**Boiler specs**:

Shell diameter 11 ¾ in

Smoke box Dia. 12 in

Shell & firebox .375 ASTM A285 Grade C

Firebox length 10 ¾ in (inside)

Firebox width 7 5/8 in (inside)

Firebox Height 11 3/4 in (inside)

Tubes 3/4 od x 5/8 Id type K copper (rolled in)

Tube length 38 1/2 in

No of tubes 27

Staybolts ½ diameter on 3" centers

Pressure 125 psi (2 safeties 125 and 128)

Wheel speed

8 mph = 8448 in / min 8 1/8 in dia = 25 1/2 in / rev

8448 in / min / 25 1/2 in / rev = 330 rpm

Wheel torque

200 lb (TE) x 4 1/16 in (wheel rad) = 812 in lb torque

Wheel HP

(812 in lb x 330 rpm) / 63025 = 4 1/4 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 = 200 lbs Mep = 98 psi Stroke = .34 ft driver dia. = .677 ft

Using formulae bore = 2.1 in

3 inch (actual bore) > 2.1 (required bore)

Check piston speed

330 rpm x 8. 1/8 rod travel (4.06 in stroke x 2) = 2681 in / min = 223 ft / min

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

**Check boiler**

**Grate area**

Rule of thumb: grate area = TE /3.5

200 TE / 3.5 = 57 in sq. (required grate area)

actual grate area = 10 3/4 in x 7 5/8 in = 82 in sq.

57 in sq < 82 in sq

Tube area

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

Tube Area = 82 / 8 = 10.25 in sq

Actual tube area = .31 in sq x 27 tubes = 8.4 in sq (should add a few more tubes)

Stack diameter

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

82 in sq x .06 = 4.92 in sq = 2.5 in dia. (smallest diameter)

Stack length

Rule of thumb: stack length = 4.0 x diameter

2.5 in x 4 = 10.0 long (including peticote pipe)

Nozzle diameter

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

80 in sq x .005 = .30 in sq = .40 diameter