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)