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TVS Training Academy and Thiagarajar 
College of Engineering 
 
 
Assignment 1 & 2 
Date: July, 16, 2010 
 
 
Considered Car: BMW 740li 
By 
Dhaneesh.V.L (07G20) 
P.Mariraja (07G54) 
Assignment 1 
Vehicle Design Data 
 
 
 
 
 
 
BMW 740li – Petrol variant 
 
 
 
 
CAR SPECIFICATIONS 
ENGINE 
Displacement  2979cc
Stroke & bore  89.6 mm & 84.0 mm 
Compression ratio  10:2
Max. Power  240kw @5800rpm 
Max. Torque   450 Nm @1500‐4500 rpm
TRANSMISSION  Six speed automatic 
Gear ratios  I Gear 4.17 
II Gear 2.34 
III Gear 1.52 
IV Gear 1.4 
V Gear 0.87 
VI Gear 0.69 
Final drive ratio  3.73
CHASSIS 
Wheel base  3070 mm
Track front & rear  1611/1650 mm
Length  5072mm
Width  1902 mm
Height  1479mm
Ground clearance  144mm
Frontal area  2.41m2
Gross weight limit  2475 kg
Kerb weight  1860 kg
Wheels: Light weight alloy wheels, double spoke, 250/50R18        
tyres 
 
Formulas taken for calculation: 
Nmin= 800 to 1000 rpm 
Nmax= 1.1 Nrated 
B.P. = B.P.rated 
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−+
2
1
ratedratedrated N
N
N
N
N
N
 kW 
Te=
N
BP
π2
6000×
 Nm 
F=
r
GT Te η××
  
N 
V=
65.2×
×
G
rN
 
Air Resistance: 
Ra = KaAV2  
Rolling Resistance: 
Rr = (0.015+0.00016V)W 
Total Resistance: 
Rt = Ra+Rr  
We= (1.04 + 0.0025 G2
) W 
aP = 
e
T
W
RFg )( −
 
 
 
CALCULATION TABLE 
 
Air Resistance 
Ra 
N 
Rolling Resistance 
Rr 
N 
I  II  III  IV  V  VI  I  II  III  IV  V  VI 
5.47  17.44  41.375 49.19 126.82 201.39 71.62 97.63  130.32 138.74 200.3 242.78
21.85  69.82  165.5 196.77 507.26 805.58 104.99 158.2  223.51 240.35 363.43 448.33
49.38  157.06  372.38 442.72 1140.42 1812.55 138.94 218.7  314.7 341.96 526.4 653.93
87.79  279.27  661.96 787.07 2027.33 3222.32 172.87 279.24  409.88 443.58 689.46 859.54
137.18  436.31  1034.45 1229.8 3167.93 5034.87 206.81 339.75  503.09 545.2 852.57 1065.14
197.534  628.36  1489.53 1770.9 4562.67 7250.21 240.75 400.3  596.27 646.81 1015.64 1270.67
223.29  710.36  1684.11 2002.3 5157.79 8197.67 253.62 423.26  631.68 685.42 1077.61 1348.87
 
 
Engine 
speed 
N 
rpm 
Brake 
power 
BP 
kW 
Equivalent 
torque 
Te 
Nm 
Tractive force 
 
F 
N 
Velocity of the Vehicle 
V 
Km/hr 
I  II  III  IV  V  VI  I  II  III  IV  V  VI 
1000  47.28  451.59  16880.35  9476.88 6155.08 5644.87 3517.19 2789.89  8.56 15.28 23.533 25.66 41.2 51.92 
2000  101.45  484.4  18106.78  10165.41 6602.28 6055 3772.73 2992.57  17.1 30.57 47.07 51.32 82.4 103.84 
3000  155.13  493.8  18458.15  10362.68 6730.4 6172.5 3845.94 3050.64  25.71 45.85 70.6 76.98 123.55 155.76 
4000  200.94  479.7  17931.09  10066.78 6538.22 5996.2 3731.45 2963.53  34.28 61.14 94.13 102.64 164.73 207.68 
5000  231.5  442.1  16525.61  9277.72 6025.74 5526.2 3443.28 2731.2  42.85 76.42 117.67 128.3 205.92 259.6 
6000  239.42  381  14241.71  7995.5 5192.95 4762 2967.4 2353.77  51.42 91.17 141.2 153.96 247.1 311.52 
6380  234.92  351.7  13146.48  7380.63 4793.6 4392.2 2739.2 2172.76  54.67 97.51 150.14 163.71 262.75 331.25 
 
 
Total Resistance 
Rt 
N 
Acceleration of the vehicle 
ap 
m/s2 
I  II  III  IV  V  VI  I  II  III  IV  V  VI 
77.09  114.67  171.69  187.93 327.12 444.17 4.12844 3.074414  2.158002 1.990826 1.229358 0.897044
1126.84  228.02  389.01  437.12 870.7 1253.9 4.417941 3.261978  2.240571 2.04893 1.098879 0.664628
188.32  375.76  687.08  784.7 1666.8 2466.5 4.488277 3.279307  2.179409 1.965341 0.825688 0.256881
260.67  558.51  1071.84  1230.65 2716.79 4081.86 4.341488 3.122324  1.971458 1.738022 0.384302 ‐0.45872
343.98  776.06  1537.55  1775 4020.5 6100 3.975535 2.79103  1.617737 1.367992 ‐0.21916 ‐1.28848
438.28  1028.66  2085.77  2417.71 5577.3 8520.9 3.391437 2.287462  1.120285 0.856269 ‐0.98879 ‐2.35882
476.91  1133.62  2315.78  2681.72 6234.95 8829.35 3.11315 2.050968  0.893986 0.624873 ‐1.32518 ‐2.54536
 
 
 
 
 
 
 
 
 
 
Overall gear ratio G  15.55 8.73 5.67 5.2 3.24 2.57
Equivalent weight We 4070.15 3045.57 2772.62 2741.31 2638.95 2614.87
 
‐3
‐2.5
‐2
‐1.5
‐1
‐0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 50 100 150 200 250 300 350
ACCELERATION IN m/s^2
VEHICLE VELOCITY IN km/hr
ACCELERATION VS VELOCITY
I GEAR
II GEAR
III GEAR
IV GEAR
V GEAR
VI GEAR
 
 
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 50 100 150 200 250 300 350
FORCE IN NEWTON
VEHICLE VELOCITY IN km/hr
FORCE VS VELOCITY
I GEAR
II GEAR
III GEAR
IV GEAR
V GEAR
VI GEAR
TOTAL RESISTANCE
 
0
100
200
300
400
500
600
0
TORQUE IN Nm
1000 2000 3000
ENGINE S
T
4000
SPEED IN rpm
TORQUE
5000 6000 7000
 
TORQUE
 
0
50
100
150
200
250
300
0 1000 2000 3000 4000 5000 6000 7000
BRAKE POWER IN kW
ENGINE SPEED IN rpm
BRAKE POWER
BRAKE POWER
REPORT  
For  the  selected  car  BMW  740li  we  can  infer  from  the 
graphs  that  the  performance  of  the  car  will  be  good 
under  ideal  road  conditions.  The  optimum  amount  of 
ground  clearance  and  frontal  area  gives  the  car  its 
maximum  acceleration  with  low  air  resistance,  rolling 
resistance  is  reduced  by  equal  distribution  of  the  load. 
These  factors  help  the  car  to  reach  the  speed  of 
100km/hr  in  around  6‐8  seconds.  Under  actual  riding 
condition, the driving method and other external factors 
the cars performance may vary. 
 
 
 
 
 
 
 
Assignment 2 
Instantaneous Piston Velocity (Vp) : 
Vp= ⎟
⎠
⎞
⎜
⎝
⎛
+
2
2sin
sin
θλ
θωr  
Instantaneous Piston Acceleration (ap) : 
ap= )2cos(cos2
θλθω +r  
Volume of Cylinder at any Crank angle ‘θ’ (Vθ) : 
Vθ= )
2
sin
cos1(
41
2
2 θλ
θ
π
+−+
−
rB
R
V
c
s
 
SI Engine: 
Suction: 
θ → 0 to 180 
P= 1bar (assumed) 
Compression: 
θ → 180 to 360 
Governing equation PV
ncom
=constant 
ncom=1.36 to 1.4 
comn
V
V
P
P
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
210
180
180
210
 
Combustion: 
θ → 360 
== α
2
3
P
P
3.2 to 4.2 
Expansion: 
θ → 360 to 540 
exn
V
V
P
P
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
360
390
390
360
 
nex=1.23 to 1.3 
Exhaust: 
θ → 540 to 720 
P=1bar (assumed) 
Fg= 2
4
BPg
π
×  
Fi= 2
4
80 B
π
×  
Fr=Fg‐Fi 
Tangential force at crank pin: 
Ft=
φ
φθ
cos
)sin( +
rF  
Normal component of connecting rod force acting along crank arm: 
Fc=
φ
φθ
cos
)cos( +
RF  
Instantaneous Turning Moment: 
Fitm= rFt ×
 
  CALCULATION TABLE 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ANGULAR 
DISPLACEMENT
θ 
degrees 
INSTANTANOUS  
TURNING  
MOMENT 
Fitm 
Nm 
INSTANTANEOUS 
ACCELERATION OF 
PISTON 
ap 
m/s2
 
INSTANTANEOUS 
ACCELERATION OF 
PISTON 
vp 
ms
‐1
 
0  0  20,989  0 
30  ‐203  16543  16.78 
60  ‐118.16  6032  27.73 
90  88.683  ‐4462  27.19 
120  155.442  ‐10494  20.37 
150  91.662  ‐12081  10.42 
180  0  ‐12064  0 
210  ‐92.28  ‐12081  ‐10.41 
240  ‐161.218  ‐10494  ‐20.4 
270  ‐112.63  ‐4462  ‐27.2 
300  46.76  6032  ‐27.7 
330  49.625  16543  ‐16.778 
360  0  20989  0 
390  530.494  16543  16.78 
420  278.272  6032  27.73 
450  285.75  ‐4462  27.19 
480  249.69  ‐10494  20.37 
510  129.58  ‐12081  10.42 
540  0  ‐12064  0 
570  ‐91.662  ‐12081  ‐10.41 
600  ‐155.44  ‐10494  ‐20.4 
630  ‐88.623  ‐4462  ‐27.2 
660  118.16  6032  ‐27.7 
690  203.05  16543  ‐16.778 
720  0  20989  0 
ANGULAR 
DISPLACEMENT 
θ 
degrees 
INSTANTANEOUS
VOLUME OF 
CYLINDER 
Vθ 
mm3
 
INSTANTANEOUS 
PRESSURE OF 
CYLINDER 
Pθ 
bars 
0  53972  1 
30  95613  1 
60  203245  1 
90  335960  1 
120  451516  1 
150  525631  1 
180  550514  1 
210  525631  1.065 
240  451516  1.312 
270  335960  1.967 
300  203245  3.916 
330  95613  11 
360  53972  24.09 
360  53972  96.36 
390  95613  45.81 
420  203245  17.19 
450  335960  8.94 
480  451516  6.09 
510  525631  4.998 
540  550514  4.71 
540  550514  1 
570  525631  1 
600  451516  1 
630  335960  1 
660  203245  1 
690  95613  1 
720  53972  1 
 
 
 
 
 
 
θ  I  II  III  IV  V  VI 
0‐60  P  E  S  P  C  S 
60‐120  P  E  C  E  C  S 
120‐180  P  S  C  E  P  S 
180‐240  E  S  C  E  P  C 
240‐300  E  S  P  S  P  C 
300‐360  E  C  P  S  E  C 
360‐420  S  C  P  S  E  P 
420‐480  S  C  E  C  E  P 
480‐540  S  P  E  C  S  P 
540‐600  C  P  E  C  S  E 
600‐660  C  P  S  P  S  E 
660‐720  C  E  S  P  C  E 
 
Calculation for combined Turning Moment: 
Angular 
Displacement 
(θ) 
Instantaneous Turning Moment of each Cylinder 
Combined 
Turning Moment I  II  III  IV  V  VI 
0  0  ‐155.44  155.442  249.69  ‐161.218  0  88.474 
30  530.494  ‐88.623  91.662  129.58  ‐112.63  ‐203  347.483 
60  278.272  118.16  0  0  46.76  ‐118.16  325.032 
90  285.75  203.05  ‐92.28  ‐91.662  49.625  88.683  443.166 
120  249.69  0  ‐161.218  ‐155.44  0  155.442  88.474 
 
 
 
 
‐15,000
‐10,000
‐5,000
0
5,000
10,000
15,000
20,000
25,000
0 180 360 540 720
ACCELERATION IN mm/s^2
CRANK ANGLE
ACCELERATION VS CRANK ANGLE
instantaneous accelration of the piston
 
0
100000
200000
300000
400000
500000
600000
0 180 360 540 720
VOLUME IN mm^3
ANGULAR DISPLACEMENT IN DEG
VOLUME VS CRANK ANGLE
Series2
 
0
20
40
60
80
100
120
0 180 360 540 720
PRESSURE IN bars
ANGULAR DISPLACEMENT IN DEG
PRESSURE VS CRANK ANGLE
PRESSURE
PRESSURE IN bars
0
20
40
60
80
100
120
0 100000 200000
VO
300000
OLUME IN m
pv DIA
400000
mm^3
AGRAM
0 5000000 6000000
PRESSUR
 
RE
 
 
‐300
‐200
‐100
0
100
200
300
400
500
600
0 180 360 540 720
TURNING MOMENT IN Nm
ANGULAR DISPLACEMENT IN DEG
TURNING MOMENT
 
0
50
100
150
200
250
300
350
400
450
500
0
Turning Moment
20 40
C
60
Angular Disp
Combined
80
placement
 Turning M
100
Moment
120 1140
Turnin
 
ng Moment
 
REPORT 
The  obtained  graphs  for  angular  displacement  Vs 
instantaneous  velocity,  volume  of  cylinder, 
instantaneous  acceleration,  and  instantaneous  turning 
moment  and  also  the  p‐v  diagram  shows  the 
performance  of  a  petrol  engine  considered.  Also  the 
combined turning moment of the engine with six inline 
cylinders has been calculated. 
 

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BMW 740li report

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