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BMW 740li report
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- 3. 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
- 4. 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 Teη×× 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 )( −
- 5. 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
- 6. 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
- 7. ‐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 100150 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
- 8. 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 0 50 100150 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
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- 10. 0 50 100 150 200 250 300 0 1000 20003000 4000 5000 6000 7000 BRAKE POWER IN kW ENGINE SPEED IN rpm BRAKE POWER BRAKE POWER
- 11. 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.
- 12. 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
- 13. == 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 ×
- 14. 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
- 15. 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
- 16. 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
- 17. ‐15,000 ‐10,000 ‐5,000 0 5,000 10,000 15,000 20,000 25,000 0 180 360540 720 ACCELERATION IN mm/s^2 CRANK ANGLE ACCELERATION VS CRANK ANGLE instantaneous accelration of the piston
- 18. 0 100000 200000 300000 400000 500000 600000 0 180 360540 720 VOLUME IN mm^3 ANGULAR DISPLACEMENT IN DEG VOLUME VS CRANK ANGLE Series2
- 19. 0 20 40 60 80 100 120 0 180 360540 720 PRESSURE IN bars ANGULAR DISPLACEMENT IN DEG PRESSURE VS CRANK ANGLE PRESSURE
- 20. PRESSURE IN bars 0 20 40 60 80 100 120 0 100000 200000 VO 300000 OLUME IN m pv DIA 400000 mm^3 AGRAM 05000000 6000000 PRESSUR RE
- 21. ‐300 ‐200 ‐100 0 100 200 300 400 500 600 0 180 360540 720 TURNING MOMENT IN Nm ANGULAR DISPLACEMENT IN DEG TURNING MOMENT
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- 23. 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.