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Annex A3: Air Resistance and resulting Energy Consumption of the MAGLEV-Cabins

a)
Source 1: Dr. Helmut Glück, Aerodynamik der Schienenfahrzeuge (Aerodynamics of Rail Vehicles), Cologne 1985 page 61; formula of Deutsche Versuchsanstalt for Luft- and Raumfahrt:

cw=cwFront+cwRear+0.02(Ak-Am)/S+nSA*cwSA+(cwa/cwa=max.)(cwR+cwTr+cwFT+cwWheel)

with:
cwR=O/S*(8.1+1.6log LZ)-2.5 and
cwa/cwa=max.=1.1
Ak, Am: Cross-section of head- resp. middle cars (m²)
S: normative area 10 m²
SA: pantographs
O: surface of the train
Tr: gap between cars
LZ:train length
FT: windows, doors
n: number
a: distance vehicle bottom - ground (track bed)
 

Term Value Unit Comment
cwFront
0.10
  yields cw = 0.28 for a single cabin
cwRear
0.16
   
Cross section Ak=Am (m2)
5.8
 
train length Lz=171m
38
cars at 4.6 m length per cabin
cwR
0.34
  according to formula
cwTr
0.00346
  *
cwFT
0.05
  *
cw,wheel
0.00
  constant cross section
cwtotal
0.69
   
speed
50
m/s  
power
325
kW  
efficiency
0.32
  primary energy->air gap
comparison value (air res)
1.67
l/100km/car primary petrol
comparison value (air res)
1.37
l/100km/car diesel oil at gas station**

*Values for cw -values for gaps between cars, windows and doors are estimated considering DB measurements of air resistance from 1975: A 26.4 m long modern express passenger car bears as compared to a C4 express passenger car a 23% lower cw-value per meter length.

**8 % losses for refinement, infrastructure and transport, diesel oil has 11% higher energy content per litre. Calculations according to E. Jänsch, eb 93 (1995) 1/2, 25

b)
Source 2: R. Fürst, Proceedings MAGLEV'95, S. 117 Fig. 6, similarity calculations for 10-sections TR 07:
 

Term Value Unit Comment
TR 07 10-S at 2% gradient
16.10
kW/to speed 180 km/h
TR 07 2-S at 2% gradient
18.30
kW/to speed 180 km/h
TR 07 10-S at 0% gradient
6.29
kW/to speed 180 km/h
TR 07 2-S at 0% gradient
8.47
kW/to speed 180 km/h
for air resistance
3.73
kW/to ***
for non-air resistance
4.74
kW/to specific power for non-air resistance
weight TR 07 2-S
90
t equals 45t per section
power at 0% gradient
762
kW  
of which for air resistance
335
kW  
for non-air resistance
427
kW for TR 07 2-sections

***see reference p. 421: TR 06 has 44% air resistance at 180 km/h, assume: TR 07 equally.

Source 3: Meeting of VDI: The Future of track guided traffic, Hamburg, 1998, Calculation of air resistance of a 10-sections-TR 08.
 

Term Value Unit Comment
weight TR 07 10-S
450
t equals 45t per section
power at 0% gradient
2831
kW according to source (see above)
for non-air resistance
2134
kW 5 times TR 07 2-S, proportional to number of sections
for air resistance TR 07
696
kW  
for air resistance TR 08
592
kW 15 % improved cw-value over TR 07 according to source

AUTOSHUTTLE Air Resistance by Aerodynamic Similarity Calculation with TR 08:
 

Term  Value Unit Comment
Car Convoy      
Cross-section=A
5.8
TR 07: 11m² cross-section
length
171
m similar body to TR 07 10-S
cars
38
  at 4.6 m per car
speed
180
km/h  
lump additional factor
1.05
  for steeper front and more gaps
power per car
8.62
kW in the air gap
total efficiency
0.32
   
compar. value (air resis only)
1.68
l/100km/car primary petrol
compar. value (air resis only)
1.38
l/100km/car diesel at gas station
       
Lorry Convoy      
cross section = A
17.58
TR 07: 11m² cross-section
length
298
m similar body to TR 07 10-S
number of 40 to-lorries
15
  at 20 m length per vehicle
speed
180
km/h  
power/lorry
67
kW in the air gap
total efficiency
0.32
  primary energy->air gap
comp. value (air resis only)
13.01
l/100km/40to primary petrol
comp. value (air resis only)
10.65
l/100km/40to diesel at gas station

The average value for both calculation methods a) and b) yields for a car convoy 1.37 l Diesel/100km/car and for a lorry convoy 10.61 l Diesel/100km/40to at a gas station each.