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